math research topics for elementary students

251+ Math Research Topics [2024 Updated]

$Math research topics$

Mathematics, often dubbed as the language of the universe, holds immense significance in shaping our understanding of the world around us. It’s not just about crunching numbers or solving equations; it’s about unraveling mysteries, making predictions, and creating innovative solutions to complex problems. In this blog, we embark on a journey into the realm of math research topics, exploring various branches of mathematics and their real-world applications.

How Do You Write A Math Research Topic?

Writing a math research topic involves several steps to ensure clarity, relevance, and feasibility. Here’s a guide to help you craft a compelling math research topic:

Identify Your Interests: Start by exploring areas of mathematics that interest you. Whether it’s pure mathematics, applied mathematics, or interdisciplinary topics, choose a field that aligns with your passion and expertise.
Narrow Down Your Focus: Mathematics is a broad field, so it’s essential to narrow down your focus to a specific area or problem. Consider the scope of your research and choose a topic that is manageable within your resources and time frame.
Review Existing Literature: Conduct a thorough literature review to understand the current state of research in your chosen area. Identify gaps, controversies, or unanswered questions that could form the basis of your research topic.
Formulate a Research Question: Based on your exploration and literature review, formulate a clear and concise research question. Your research question should be specific, measurable, achievable, relevant, and time-bound (SMART).
Consider Feasibility: Assess the feasibility of your research topic in terms of available resources, data availability, and research methodologies. Ensure that your topic is realistic and achievable within the constraints of your project.
Consult with Experts: Seek feedback from mentors, advisors, or experts in the field to validate your research topic and refine your ideas. Their insights can help you identify potential challenges and opportunities for improvement.
Refine and Iterate: Refine your research topic based on feedback and further reflection. Iterate on your ideas to ensure clarity, coherence, and relevance to the broader context of mathematics research.
Craft a Title: Once you have finalized your research topic, craft a compelling title that succinctly summarizes the essence of your research. Your title should be descriptive, engaging, and reflective of the key themes of your study.
Write a Research Proposal: Develop a comprehensive research proposal outlining the background, objectives, methodology, and expected outcomes of your research. Your research proposal should provide a clear roadmap for your study and justify the significance of your research topic.

By following these steps, you can effectively write a math research topic that is well-defined, relevant, and poised to make a meaningful contribution to the field of mathematics.

251+ Math Research Topics: Beginners To Advanced

Prime Number Distribution in Arithmetic Progressions
Diophantine Equations and their Solutions
Applications of Modular Arithmetic in Cryptography
The Riemann Hypothesis and its Implications
Graph Theory: Exploring Connectivity and Coloring Problems
Knot Theory: Unraveling the Mathematics of Knots and Links
Fractal Geometry: Understanding Self-Similarity and Dimensionality
Differential Equations: Modeling Physical Phenomena and Dynamical Systems
Chaos Theory: Investigating Deterministic Chaos and Strange Attractors
Combinatorial Optimization: Algorithms for Solving Optimization Problems
Computational Complexity: Analyzing the Complexity of Algorithms
Game Theory: Mathematical Models of Strategic Interactions
Number Theory: Exploring Properties of Integers and Primes
Algebraic Topology: Studying Topological Invariants and Homotopy Theory
Analytic Number Theory: Investigating Properties of Prime Numbers
Algebraic Geometry: Geometry Arising from Algebraic Equations
Galois Theory: Understanding Field Extensions and Solvability of Equations
Representation Theory: Studying Symmetry in Linear Spaces
Harmonic Analysis: Analyzing Functions on Groups and Manifolds
Mathematical Logic: Foundations of Mathematics and Formal Systems
Set Theory: Exploring Infinite Sets and Cardinal Numbers
Real Analysis: Rigorous Study of Real Numbers and Functions
Complex Analysis: Analytic Functions and Complex Integration
Measure Theory: Foundations of Lebesgue Integration and Probability
Topological Groups: Investigating Topological Structures on Groups
Lie Groups and Lie Algebras: Geometry of Continuous Symmetry
Differential Geometry: Curvature and Topology of Smooth Manifolds
Algebraic Combinatorics: Enumerative and Algebraic Aspects of Combinatorics
Ramsey Theory: Investigating Structure in Large Discrete Structures
Analytic Geometry: Studying Geometry Using Analytic Methods
Hyperbolic Geometry: Non-Euclidean Geometry of Curved Spaces
Nonlinear Dynamics: Chaos, Bifurcations, and Strange Attractors
Homological Algebra: Studying Homology and Cohomology of Algebraic Structures
Topological Vector Spaces: Vector Spaces with Topological Structure
Representation Theory of Finite Groups: Decomposition of Group Representations
Category Theory: Abstract Structures and Universal Properties
Operator Theory: Spectral Theory and Functional Analysis of Operators
Algebraic Number Theory: Study of Algebraic Structures in Number Fields
Cryptanalysis: Breaking Cryptographic Systems Using Mathematical Methods
Discrete Mathematics: Combinatorics, Graph Theory, and Number Theory
Mathematical Biology: Modeling Biological Systems Using Mathematical Tools
Population Dynamics: Mathematical Models of Population Growth and Interaction
Epidemiology: Mathematical Modeling of Disease Spread and Control
Mathematical Ecology: Dynamics of Ecological Systems and Food Webs
Evolutionary Game Theory: Evolutionary Dynamics and Strategic Behavior
Mathematical Neuroscience: Modeling Brain Dynamics and Neural Networks
Mathematical Physics: Mathematical Models in Physical Sciences
Quantum Mechanics: Foundations and Applications of Quantum Theory
Statistical Mechanics: Statistical Methods in Physics and Thermodynamics
Fluid Dynamics: Modeling Flow of Fluids Using Partial Differential Equations
Mathematical Finance: Stochastic Models in Finance and Risk Management
Option Pricing Models: Black-Scholes Model and Beyond
Portfolio Optimization: Maximizing Returns and Minimizing Risk
Stochastic Calculus: Calculus of Stochastic Processes and Itô Calculus
Financial Time Series Analysis: Modeling and Forecasting Financial Data
Operations Research: Optimization of Decision-Making Processes
Linear Programming: Optimization Problems with Linear Constraints
Integer Programming: Optimization Problems with Integer Solutions
Network Flow Optimization: Modeling and Solving Flow Network Problems
Combinatorial Game Theory: Analysis of Games with Perfect Information
Algorithmic Game Theory: Computational Aspects of Game-Theoretic Problems
Fair Division: Methods for Fairly Allocating Resources Among Parties
Auction Theory: Modeling Auction Mechanisms and Bidding Strategies
Voting Theory: Mathematical Models of Voting Systems and Social Choice
Social Network Analysis: Mathematical Analysis of Social Networks
Algorithm Analysis: Complexity Analysis of Algorithms and Data Structures
Machine Learning: Statistical Learning Algorithms and Data Mining
Deep Learning: Neural Network Models with Multiple Layers
Reinforcement Learning: Learning by Interaction and Feedback
Natural Language Processing: Statistical and Computational Analysis of Language
Computer Vision: Mathematical Models for Image Analysis and Recognition
Computational Geometry: Algorithms for Geometric Problems
Symbolic Computation: Manipulation of Mathematical Expressions
Numerical Analysis: Algorithms for Solving Numerical Problems
Finite Element Method: Numerical Solution of Partial Differential Equations
Monte Carlo Methods: Statistical Simulation Techniques
High-Performance Computing: Parallel and Distributed Computing Techniques
Quantum Computing: Quantum Algorithms and Quantum Information Theory
Quantum Information Theory: Study of Quantum Communication and Computation
Quantum Error Correction: Methods for Protecting Quantum Information from Errors
Topological Quantum Computing: Using Topological Properties for Quantum Computation
Quantum Algorithms: Efficient Algorithms for Quantum Computers
Quantum Cryptography: Secure Communication Using Quantum Key Distribution
Topological Data Analysis: Analyzing Shape and Structure of Data Sets
Persistent Homology: Topological Invariants for Data Analysis
Mapper Algorithm: Method for Visualization and Analysis of High-Dimensional Data
Algebraic Statistics: Statistical Methods Based on Algebraic Geometry
Tropical Geometry: Geometric Methods for Studying Polynomial Equations
Model Theory: Study of Mathematical Structures and Their Interpretations
Descriptive Set Theory: Study of Borel and Analytic Sets
Ergodic Theory: Study of Measure-Preserving Transformations
Combinatorial Number Theory: Intersection of Combinatorics and Number Theory
Additive Combinatorics: Study of Additive Properties of Sets
Arithmetic Geometry: Interplay Between Number Theory and Algebraic Geometry
Proof Theory: Study of Formal Proofs and Logical Inference
Reverse Mathematics: Study of Logical Strength of Mathematical Theorems
Nonstandard Analysis: Alternative Approach to Analysis Using Infinitesimals
Computable Analysis: Study of Computable Functions and Real Numbers
Graph Theory: Study of Graphs and Networks
Random Graphs: Probabilistic Models of Graphs and Connectivity
Spectral Graph Theory: Analysis of Graphs Using Eigenvalues and Eigenvectors
Algebraic Graph Theory: Study of Algebraic Structures in Graphs
Metric Geometry: Study of Geometric Structures Using Metrics
Geometric Measure Theory: Study of Measures on Geometric Spaces
Discrete Differential Geometry: Study of Differential Geometry on Discrete Spaces
Algebraic Coding Theory: Study of Error-Correcting Codes
Information Theory: Study of Information and Communication
Coding Theory: Study of Error-Correcting Codes
Cryptography: Study of Secure Communication and Encryption
Finite Fields: Study of Fields with Finite Number of Elements
Elliptic Curves: Study of Curves Defined by Cubic Equations
Hyperelliptic Curves: Study of Curves Defined by Higher-Degree Equations
Modular Forms: Analytic Functions with Certain Transformation Properties
L-functions: Analytic Functions Associated with Number Theory
Zeta Functions: Analytic Functions with Special Properties
Analytic Number Theory: Study of Number Theoretic Functions Using Analysis
Dirichlet Series: Analytic Functions Represented by Infinite Series
Euler Products: Product Representations of Analytic Functions
Arithmetic Dynamics: Study of Iterative Processes on Algebraic Structures
Dynamics of Rational Maps: Study of Dynamical Systems Defined by Rational Functions
Julia Sets: Fractal Sets Associated with Dynamical Systems
Mandelbrot Set: Fractal Set Associated with Iterations of Complex Quadratic Polynomials
Arithmetic Geometry: Study of Algebraic Geometry Over Number Fields
Diophantine Geometry: Study of Solutions of Diophantine Equations Using Geometry
Arithmetic of Elliptic Curves: Study of Elliptic Curves Over Number Fields
Rational Points on Curves: Study of Rational Solutions of Algebraic Equations
Galois Representations: Study of Representations of Galois Groups
Automorphic Forms: Analytic Functions with Certain Transformation Properties
L-functions: Analytic Functions Associated with Automorphic Forms
Selberg Trace Formula: Tool for Studying Spectral Theory and Automorphic Forms
Langlands Program: Program to Unify Number Theory and Representation Theory
Hodge Theory: Study of Harmonic Forms on Complex Manifolds
Riemann Surfaces: One-dimensional Complex Manifolds
Shimura Varieties: Algebraic Varieties Associated with Automorphic Forms
Modular Curves: Algebraic Curves Associated with Modular Forms
Hyperbolic Manifolds: Manifolds with Constant Negative Curvature
Teichmüller Theory: Study of Moduli Spaces of Riemann Surfaces
Mirror Symmetry: Duality Between Calabi-Yau Manifolds
Kähler Geometry: Study of Hermitian Manifolds with Special Symmetries
Algebraic Groups: Linear Algebraic Groups and Their Representations
Lie Algebras: Study of Algebraic Structures Arising from Lie Groups
Representation Theory of Lie Algebras: Study of Representations of Lie Algebras
Quantum Groups: Deformation of Lie Groups and Lie Algebras
Algebraic Topology: Study of Topological Spaces Using Algebraic Methods
Homotopy Theory: Study of Continuous Deformations of Spaces
Homology Theory: Study of Algebraic Invariants of Topological Spaces
Cohomology Theory: Study of Dual Concepts to Homology Theory
Singular Homology: Homology Theory Defined Using Simplicial Complexes
Sheaf Theory: Study of Sheaves and Their Cohomology
Differential Forms: Study of Multilinear Differential Forms
De Rham Cohomology: Cohomology Theory Defined Using Differential Forms
Morse Theory: Study of Critical Points of Smooth Functions
Symplectic Geometry: Study of Symplectic Manifolds and Their Geometry
Floer Homology: Study of Symplectic Manifolds Using Pseudoholomorphic Curves
Gromov-Witten Invariants: Invariants of Symplectic Manifolds Associated with Pseudoholomorphic Curves
Mirror Symmetry: Duality Between Symplectic and Complex Geometry
Calabi-Yau Manifolds: Ricci-Flat Complex Manifolds
Moduli Spaces: Spaces Parameterizing Geometric Objects
Donaldson-Thomas Invariants: Invariants Counting Sheaves on Calabi-Yau Manifolds
Algebraic K-Theory: Study of Algebraic Invariants of Rings and Modules
Homological Algebra: Study of Homology and Cohomology of Algebraic Structures
Derived Categories: Categories Arising from Homological Algebra
Stable Homotopy Theory: Homotopy Theory with Stable Homotopy Groups
Model Categories: Categories with Certain Homotopical Properties
Higher Category Theory: Study of Higher Categories and Homotopy Theory
Higher Topos Theory: Study of Higher Categorical Structures
Higher Algebra: Study of Higher Categorical Structures in Algebra
Higher Algebraic Geometry: Study of Higher Categorical Structures in Algebraic Geometry
Higher Representation Theory: Study of Higher Categorical Structures in Representation Theory
Higher Category Theory: Study of Higher Categorical Structures
Homotopical Algebra: Study of Algebraic Structures in Homotopy Theory
Homotopical Groups: Study of Groups with Homotopical Structure
Homotopical Categories: Study of Categories with Homotopical Structure
Homotopy Groups: Algebraic Invariants of Topological Spaces
Homotopy Type Theory: Study of Foundations of Mathematics Using Homotopy Theory

In conclusion, the world of mathematics is vast and multifaceted, offering endless opportunities for exploration and discovery. Whether delving into the abstract realms of pure mathematics or applying mathematical principles to solve real-world problems, mathematicians play a vital role in advancing human knowledge and shaping the future of our world.

By embracing diverse math research topics and interdisciplinary collaborations, we can unlock new possibilities and harness the power of mathematics to address the challenges of today and tomorrow. So, let’s embark on this journey together as we unravel the mysteries of numbers and explore the boundless horizons of mathematical inquiry.

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181 Mathematics Research Topics From PhD Experts

$math research topics$

If you are reading this blog post, it means you are looking for some exceptional math research topics. You want them to be original, unique even. If you manage to find topics like this, you can be sure your professor will give you a top grade (if you write a decent paper, that is). The good news is that you have arrived at just the right place – at the right time. We have just finished updating our list of topics, so you will find plenty of original ideas right on this page. All our topics are 100 percent free to use as you see fit. You can reword them and you don’t need to give us any credit.

And remember: if you need assistance from a professional, don’t hesitate to reach out to us. We are not just the best place for math research topics for high school students; we are also the number one choice for students looking for top-notch research paper writing services.

Our Newest Research Topics in Math

We know you probably want the best and most recent research topics in math. You want your paper to stand out from all the rest. After all, this is the best way to get some bonus points from your professor. On top of this, finding some great topics for your next paper makes it easier for you to write the essay. As long as you know at least something about the topic, you’ll find that writing a great paper or buy phd thesis isn’t as difficult as you previously thought.

So, without further ado, here are the 181 brand new topics for your next math research paper:

Cool Math Topics to Research

Are you looking for some cool math topics to research? We have a list of original topics for your right here. Pick the one you like and start writing now:

Roll two dice and calculate a probability
Discuss ancient Greek mathematics
Is math really important in school?
Discuss the binomial theorem
The math behind encryption
Game theory and its real-life applications
Analyze the Bernoulli scheme
What are holomorphic functions and how do they work?
Describe big numbers
Solving the Tower of Hanoi problem

Undergraduate Math Research Topics

If you are an undergraduate looking for some research topics for your next math paper, you will surely appreciate our list of interesting undergraduate math research topics:

Methods to count discrete objects
The origins of Greek symbols in mathematics
Methods to solve simultaneous equations
Real-world applications of the theorem of Pythagoras
Discuss the limits of diffusion
Use math to analyze the abortion data in the UK over the last 100 years
Discuss the Knot theory
Analyze predictive models (take meteorology as an example)
In-depth analysis of the Monte Carlo methods for inverse problems
Squares vs. rectangles (compare and contrast)

Number Theory Topics to Research

Interested in writing about number theory? It is not an easy subject to discuss, we know. However, we are sure you will appreciate these number theory topics:

Discuss the greatest common divisor
Explain the extended Euclidean algorithm
What are RSA numbers?
Discuss Bézout’s lemma
In-depth analysis of the square-free polynomial
Discuss the Stern-Brocot tree
Analyze Fermat’s little theorem
What is a discrete logarithm?
Gauss’s lemma in number theory
Analyze the Pentagonal number theorem

Math Research Topics for High School

High school students shouldn’t be too worried about their math papers because we have some unique, and quite interesting, math research topics for high school right here:

Discuss Brun’s constant
An in-depth look at the Brahmagupta–Fibonacci identity
What is derivative algebra?
Describe the Symmetric Boolean function
Discuss orders of approximation in limits
Solving Regiomontanus’ angle maximization problem
What is a Quadratic integral?
Define and describe complementary angles
Analyze the incircle and excircles of a triangle
Analyze the Bolyai–Gerwien theorem in geometry
Math in our everyday life

Complex Math Topics

If you want to give some complex math topics a try, we have the best examples below. Remember, these topics should only be attempted by students who are proficient in mathematics:

Mathematics and its appliance in Artificial Intelligence
Try to solve an unsolved problem in math
Discuss Kolmogorov’s zero-one law
What is a discrete random variable?
Analyze the Hewitt–Savage zero-one law
What is a transferable belief model?
Discuss 3 major mathematical theorems
Describe and analyze the Dempster-Shafer theory
An in-depth analysis of a continuous stochastic process
Identify and analyze Gauss-Markov processes

Easy Math Research Paper Topics

Perhaps you don’t want to spend too much time working on your next research paper. Who can blame you? Check out these easy math research paper topics:

Define the hyperbola
Do we need to use a calculator during math class?
The binomial theorem and its real-world applications
What is a parabola in geometry?
How do you calculate the slope of a curve?
Define the Jacobian matrix
Solving matrix problems effectively
Why do we need differential equations?
Should math be mandatory in all schools?
What is a Hessian matrix?

Logic Topics to Research

We have some interesting logical topics for research papers. These are perfect for students interested in writing about math logic. Pick one right now:

Discuss the reductio ad absurdum approach
Discuss Boolean algebra
What is consistency proof?
Analyze Trakhtenbrot’s theorem (the finite model theory)
Discuss the Gödel completeness theorem
An in-depth analysis of Morley’s categoricity theorem
How does the Back-and-forth method work?
Discuss the Ehrenfeucht–Fraïssé game technique
Discuss Aleph numbers (Aleph-null and Aleph-one)
Solving the Suslin problem

Algebra Topics for a Research Paper

Would you like to write about an algebra topic? No problem, our seasoned writers have compiled a list of the best algebra topics for a research paper:

Discuss the differential equation
Analyze the Jacobson density theorem
The 4 properties of a binary operation in algebra
Analyze the unary operator in depth
Analyze the Abel–Ruffini theorem
Epimorphisms vs. monomorphisms: compare and contrast
Discuss the Morita duality in algebraic structures
Idempotent vs. nilpotent in Ring theory
Discuss the Artin-Wedderburn theorem
What is a commutative ring in algebra?
Analyze and describe the Noetherian ring

Math Education Research Topics

There is nothing wrong with writing about math education, especially if your professor did not give you writing prompts. Here are some very nice math education research topics:

What are the goals a mathematics professor should have?
What is math anxiety in the classroom?
Teaching math in UK schools: the difficulties
Computer programming or math in high school?
Is math education in Europe at a high enough level?
Common Core Standards and their effects on math education
Culture and math education in Africa
What is dyscalculia and how does it manifest itself?
When was algebra first thought in schools?
Math education in the United States versus the United Kingdom

Computability Theory Topics to Research

Writing about computability theory can be a very interesting adventure. Give it a try! Here are some of our most interesting computability theory topics to research:

What is a multiplication table?
Analyze the Scholz conjecture
Explain exponentiating by squaring
Analyze the Myhill-Nerode theorem
What is a tree automaton?
Compare and contrast the Pushdown automaton and the Büchi automaton
Discuss the Markov algorithm
What is a Turing machine?
Analyze the post correspondence problem
Discuss the linear speedup theorem
Discuss the Boolean satisfiability problem

Interesting Math Research Topics

We know you want topics that are interesting and relatively easy to write about. This is why we have a separate list of our most interesting math research topics:

What is two-element Boolean algebra?
The life of Gauss
The life of Isaac Newton
What is an orthodiagonal quadrilateral?
Tessellation in Euclidean plane geometry
Describe a hyperboloid in 3D geometry
What is a sphericon?
Discuss the peculiarities of Borel’s paradox
Analyze the De Finetti theorem in statistics
What are Martingales?
The basics of stochastic calculus

Applied Math Research Topics

Interested in writing about applied mathematics? Our team managed to create a list of awesome applied math research topics from scratch for you:

Discuss Newton’s laws of motion
Analyze the perpendicular axes rule
How is a Galilean transformation done?
The conservation of energy and its applications
Discuss Liouville’s theorem in Hamiltonian mechanics
Analyze the quantum field theory
Discuss the main components of the Lorentz symmetry
An in-depth look at the uncertainty principle

Geometry Topics for a Research Paper

Geometry can be a very captivating subject, especially when you know plenty about it. Check out our list of geometry topics for a research paper and pick the best one today:

Most useful trigonometry functions in math
The life of Archimedes and his achievements
Trigonometry in computer graphics
Using Vincenty’s formulae in geodesy
Define and describe the Heronian tetrahedron
The math behind the parabolic microphone
Discuss the Japanese theorem for concyclic polygons
Analyze Euler’s theorem in geometry

Math Research Topics for Middle School

Yes, even middle school children can write about mathematics. We have some original math research topics for middle school right here:

Finding critical points in a graph
The basics of calculus
What makes a graph ultrahomogeneous?
How do you calculate the area of different shapes?
What contributions did Euclid have to the field of mathematics?
What is Diophantine geometry?
What makes a graph regular?
Analyze a full binary tree

Math Research Topics for College Students

As you’ve probably already figured out, college students should pick topics that are a bit more complex. We have some of the best math research topics for college students right here:

What are extremal problems and how do you solve them?
Discuss an unsolvable math problem
How can supercomputers solve complex mathematical problems?
An in-depth analysis of fractals
Discuss the Boruvka’s algorithm (related to the minimum spanning tree)
Discuss the Lorentz–FitzGerald contraction hypothesis in relativity
An in-depth look at Einstein’s field equation
The math behind computer vision and object recognition

Calculus Topics for a Research Paper

Let’s face it: calculus is not a very difficult field. So, why don’t you pick one of our excellent calculus topics for a research paper and start writing your essay right away:

When do we need to apply the L’Hôpital rule?
Discuss the Leibniz integral rule
Calculus in ancient Egypt
Discuss and analyze linear approximations
The applications of calculus in real life
The many uses of Stokes’ theorem
Discuss the Borel regular measure
An in-depth analysis of Lebesgue’s monotone convergence theorem

Simple Math Research Paper Topics for High School

This is the place where you can find some pretty simple topics if you are a high school student. Check out our simple math research paper topics for high school:

The life and work of the famous Pierre de Fermat
What are limits and why are they useful in calculus?
Explain the concept of congruency
The life and work of the famous Jakob Bernoulli
Analyze the rhombicosidodecahedron and its applications
Calculus and the Egyptian pyramids
The life and work of the famous Jean d’Alembert
Discuss the hyperplane arrangement in combinatorial computational geometry
The smallest enclosing sphere method in combinatorics

Business Math Topics

If you want to surprise your professor, why don’t you write about business math? We have some exceptional topics that nobody has thought about right here:

Is paying a loan with another loan a good approach?
Discuss the major causes of a stock market crash
Best debt amortization methods in the US
How do bank loans work in the UK?
Calculating interest rates the easy way
Discuss the pros and cons of annuities
Basic business math skills everyone should possess
Business math in United States schools
Analyze the discount factor

Probability and Statistics Topics for Research

Probability and statistics are not easy fields. However, you can impress your professor with one of our unique probability and statistics topics for research:

What is the autoregressive conditional duration?
Applying the ANOVA method to ranks
Discuss the practical applications of the Bates distribution
Explain the principle of maximum entropy
Discuss Skorokhod’s representation theorem in random variables
What is the Factorial moment in the Theory of Probability?
Compare and contrast Cochran’s C test and his Q test
Analyze the De Moivre-Laplace theorem
What is a negative probability?

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Research Based Mathematics Interventions: 7 Strategies To Boost Learning

Christi Kulesza

Research based mathematics interventions can help all students with math, particularly struggling students . Whether students struggle with number sense and basic facts or more challenging topics, educators have a duty to plan and adapt teaching and learning strategies accordingly.

In this article, we dive into 8 of the most research based mathematics intervention strategies, exploring how, when, and why these need to be implemented.

What are research based mathematics interventions?

Research based mathematics interventions are instructional learning strategies or programs designed to improve students’ mathematical skills and understanding. They are based on evidence from educational research.

Evidence-based interventions provide additional instruction, support and resources to help students improve their understanding of math topics.

Research based math interventions can be carried out as group tutoring but are usually taught in a small group setting or one on one.

High impact tutoring guide for schools

How to choose, plan and fund the right tutoring approach for your students for maximum impact in your school

Math interventions are often performed during time set aside for RTI, or Response to Intervention. Response to Intervention , or RTI, is a multi-tiered system of support ( MTSS ) used by schools to assist all students learn and work at their grade level. The goal of RTI is to assist students in being successful and fill any educational gaps. There are 3 tiers within RTI:

Tier 1 : provides on-grade level math instruction.
Tier 2: provides targeted interventions to students not responding to Tier 1 interventions , and would benefit from additional instruction in a small group setting. These lessons can be on grade level or below grade level.
Tier 3 : provides intensive interventions for students not responding to Tier 1 or Tier 2 interventions .

The research based interventions discussed in this blog apply to various stages of the RTI process and work for students at all grade levels from elementary school to middle school and high school.

Why are research based mathematics interventions so important?

Research based mathematics interventions provide educators with tried and tested evidence-based strategies that effectively improve student achievement and address equity in education .

There are plenty of math intervention myths that can impact intervention decisions. As these teaching strategies have already been proven effective, there is no guessing whether the math intervention strategy “is a good one.” This saves time when planning for small group or one-on-one instruction.

Research based interventions are designed to address the diverse learning needs of all students in the general classroom. They target specific skills and topics students struggle with which helps close the achievement gap.

Early implementation of research based mathematics interventions can help eliminate long-term academic struggles and lead to students having a more positive attitude when it comes to math.

Some key characteristics of research based mathematics interventions have some key characteristics, include:

Evidence-based design
Targeted skills
Differentiated instruction
Assessment and progress monitoring
Scaffolded instruction
Duration and intensity

How to select which research based mathematics interventions to implement

To select the best interventions for individual students, follow a systematic approach that considers:

Student needs

Research evidence

Available resources, assess student needs.

Understand the specific needs of each students. Use student data previously collected to help identify students’ areas of strength and weakness, including:

Standardized test scores
Universal screening
Classroom assessments
Teacher observations

This data helps educators make the best decisions for each student.

Look for well-researched interventions and programs that show evidence of closing learning gaps.

The tried and tested nature of research based mathematics interventions is a huge advantage. It means educators can move forward with interventions already proven to work.

One on one math interventions with Third Space Learning’s math specialist tutors are proven to boost student achievement. Just one 45-minute session a week can boost progress by 7 months in just 14 sessions.

$7 months progress in 14 sessions using research based math interventions$

It is highly unlikely that the average classroom is equipped with top-of-the-line technology. Nor do they have access to enough trained personnel.

Before planning math interventions, evaluate what is readily available:

Teacher aids
Instructional materials

Assess the consistency of a math intervention program or summer tutoring program implementation with the resources available.

Math intervention resources , such as the math intervention packs are readily available to download for free in the Third Space Learning resource library to help save teachers time. Each pack is taken straight from Third Space Learning’s one on one math interventions. All math intervention packs contain teacher or tutor notes, lesson slides and questions and prompts to ask students if they are stuck.

Review of student needs, resources available and researched based interventions, helps schools select the best strategies for their students.

7 Research based mathematics interventions strategies

Here we look at what the different research based mathematics intervention strategies are, how to implement these math intervention strategies, when these strategies are the most effective and why you should consider trying these strategies in your classroom today.

1. Explicit instruction

What : Explicit instruction is a direct approach to teaching math. Concepts, strategies or skills are demonstrated with detailed explanations and modeling for students. This commonly takes place during the lesson plan phase for educators.

How : Create a detailed plan of how to teach a topic to ensure students are given the explanations and modeling needed to learn a new math concept.

When : Explicit instruction happens each time math learning is taking place. It can occur in whole group instruction, small group tutoring , and one-on-one instruction.

Why : Explicit instruction is effective for students who benefit from clear and structured learning environments. These students include students with learning disabilities, special education students, English language learners and struggling learners.

2. Visual representations

What : Visual representations are drawings or images of concepts. They can include:

Charts
Graphic organizers
Manipulatives

These representations can help students better understand more abstract concepts, such as fractions and multiplication. Visual representations can further help students make connections to other math concepts they have learned.

How : Visual representations can be used in many different ways. Using visual representations to introduce a new concept during whole group instruction allows all students access to the intervention.

Visuals can be displayed within the classroom, on anchor charts, in math journals, or posted in online classrooms.

When : Using visual representations can take place at any point in a students learning journey, including whole group instruction, small group instruction and one-to-one instruction.

Teaching students to draw visual representations when learning new concepts, reviewing older concepts or during tests can help to embed learning in students long-term memory.

Why : Using visual representations is effective for all students. Visual representations strengthen student understanding, engagement and retention of math concepts.

All Third Space Learning one-on-one tutoring sessions take place in an online, interactive classroom. Session slides use visual representations to help students understand abstract concepts such as proportional relationships. Tutors provide coherent explanations, alongside visuals, to match the pitch and pace of the student’s needs.

Visual representations to enhance understanding

3. Peer-assisted instruction

What : Peer-assisted instruction is an alternative to teacher-lead instruction. It involves students working in pairs or small groups to learn from each other.

To be successful, this strategy takes strategic planning and facilitating from the teacher or educator in the classroom.

Even though the learning sessions are student-led, the teacher should continue to provide direction, structure, and intervene as needed to ensure that the learning experience is positive and beneficial.

How : Peer-assisted instruction takes planning from the teacher. Select student tutors that demonstrate a strong understanding of the concept they will be ‘teaching’ to the other students.

You may decide to provide ‘training’ for these students, to help them better implement their tutoring.

Establish the tutoring pairs or groups for these students and continue to monitor sessions to ensure that the expectations are being met and followed.

Peers should never introduce new mathematical concepts to classmates. Their role is to provide targeted support to peers on “tough to learn” concepts.

When : Peer-assisted instruction usually happens in small group settings, typically during guided learning.

Why : Peer-assisted instruction has many benefits, including:

Improved mastery of math concepts
Increased self-confidence in math
Greater motivation
Engagement in learning

The power of peer interaction and instruction can open a gateway to learning for students who struggle most.

4. Problem-solving strategies

What : Problem solving strategies are techniques students can use to solve math problems. Some of these strategies use acronyms to help students remember the steps of the strategy.

For example:

Most strategies ensure students understand or read the problem carefully, identify key information, plan a solution and check their solution for accuracy. Some may require students to draw a picture or diagram as part of the problem-solving strategy.

How: To make an effective problem-solving strategy, determine which steps are the most important when tackling a word problem.

Posting these steps on an anchor chart for students to view or include in their math journals helps reinforce these steps.

When : When working on word problems with students, reinforce the learned problem-solving strategies. Model the steps to a whole group setting and then set expectations for students to use them anytime they are working in a small group or independently.

Why : When students are equipped with a plan to tackle math word problems, they become more confident and proficient math problem solvers. Keep student expectations here consistent.

5. Effective practice opportunities

What: Effective practice opportunities include activities and exercises that allow students to apply and practice their math knowledge and math skills meaningfully.

While worksheets are typically seen as the “easy” way to provide multiple practice opportunities for students, they are not the most effective.

How : Plan purposeful real-world problems for students to solve that include critical thinking and use of problem-solving skills.

Provide math games and brainteasers during guided math stations, allowing students to work as a team to solve problems. This is a great way to incorporate interactive technology tools. These tools can be effective in having students work on their fact fluency, as they get real-time feedback as they work through their math facts.

When : Allow students to practice their newly acquired math knowledge and skills in multiple ways. Traditionally, this would take place during guided or independent practice.

Why : When students practice their math skills in a safe and engaging way, they build confidence and have “fun” doing so! This gives students the ability to develop a deeper understanding and appreciation for the math they are learning.

6. Metacognitive strategy instruction

What: Metacognition is the awareness and understanding of one’s own thinking. Metacognitive strategies help students understand their own thinking, particularly when it comes to math.

Metacognitive strategies include:

Goal setting
Plan and organize solving a mathematical problem
Develop schema
Self-questioning
Reflect and evaluate grades

How : Teachers should model metacognition in the classroom through instruction. For example, while solving a word problem, model thinking through your plan to solve the question. Stop and ask questions aloud, so students can better grasp how to self-question. Talk students through setting goals before quizzes or exams and allow them time to reflect and evaluate their progress. This is all a part of metacognitive strategy instruction.

When : Model metacognitive strategies during all instruction so students do these things as well. As the facilitator of learning prompt students to verbalize their plan for a word problem or to say their questions aloud in small group settings.

Why : Metacognitive strategies in the classroom empower students to become more independent and prepare them to tackle complex math concepts and overcome obstacles that they will likely face during their K-12 mathematics instruction.

7. Formative assessment

What: Formative assessment is the continuous process of progress monitoring , assessing understanding and providing feedback to support student learning.

Formative instruction uses assessments as a tool to drive instruction and make data-driven decisions.

How : Often, the term assessment is associated with a formal sit down, with a pencil and paper to collect a grade. Formative assessment is more than a pen to paper exam.

Formative assessment such as warm-up questions check understanding from the previous lesson.

Alternatively, use exit tickets at the end of whole group teaching to gauge student understanding of the current lesson.

Formative assessment is a great strategy to collect data on concepts that students need prerequisite knowledge from a previous grade level. For example, display a 4th grade multiplication question for 5th graders to identify students who need a little more practice before tackling the standard algorithm.

All Third Space Learning one-on-one math tutoring sessions use a range of formative assessment strategies to assess students understanding of the taught math concepts. Students complete post-session questions to check student understanding and allow tutors to prepare concepts for the next session.

When : Formative instruction can be completed at different points of instruction. If students answer a quick question (think 1-3 minutes), then there should be time to collect formative data.

Why : Teachers who properly utilize formative instruction and assessment within their classrooms can properly intervene when they have a struggling student.

Through continuous progress monitoring, educators are constantly aware of which students are struggling.

Formative instruction allows teachers to use the data collected to drive instruction within the classroom. For example, if a handful of students struggling with adding decimals, create a small group to immediately support students.

8. One-on-one tutoring

What: One-on-one tutoring is personalized instruction from one tutor to one student. The tutor works closely with the student and teacher to address specific gaps and provide individualized support for the one student. One-on-one tutoring is a highly effective intervention strategy, particularly high-dosage tutoring .

How : Formative and summative data inform an individualized instruction plan for each student. Tutors then provide targeted support to the student according to their learning gaps. Personalized feedback in real-time accelerates math learning for each student.

When : One-on-one math tutoring should not take place when the rest of the class is learning a new concept. This can cause them to fall further behind. Ideally, it should take place before or after school, or during planned intervention periods. Sessions can be scheduled as needed, and as much as the student needs.

Why : For many reasons one-on-one tutoring is highly effective. Besides the personalized instruction each student receives, the tutor can build trust and rapport with the student they are tutoring.

One-on-one tutoring allows flexibility in scheduling as there is one student’s schedule to work around, not a small group of them.

Tutors can closely monitor student progress through one-on-one tutoring and make any changes in real-time.

Third Space Learning offers flexible math tutoring schedules. Sessions can take place before, during and after school to fit your schedule. Schools can pick the session length to suit students and change timeslots, students, dosage and frequency at any point in the school year.

flexible scheduling to adapt to school schedules

How to review the success of research based mathematics interventions

Once research based math interventions are implemented, educators and schools must assess their effectiveness.

Before any math intervention begins, establish the goals or objectives of the intervention and make them SMART – specific, measurable, achievable, relevant, and time-bound.

Collect data during interventions to progress monitor student learning towards the goal or objective set at the beginning. Once the implementation is complete, student achievement needs to be measured. This can be done through summative assessment , student surveys and observations.

A review of the data collected throughout the intervention period helps to determine the overall effectiveness of the interventions performed.

This helps educators make data-informed decisions and adjustments to all aspects of math instruction to ensure student success.

Research based math interventions provide educators with strategies to increase student learning within the math classroom and assist struggling students. Preparation, implementation, and assessment of the effectiveness of each classroom intervention is crucial.

Educators must empower themselves to continue to make data-driven decisions that are best suited for their students. Whether interventions take place during whole group instruction or in a one-on-one situation, feel confident that when delivered with fidelity, student learning will accelerate and reduce math anxiety .

Research based mathematics interventions FAQs

Research-based strategies are strategies that are evidence-supported for teaching and supporting learners within the math classroom.

While there are many different types of math interventions, some examples of math interventions include math fluency programs, small group instruction, peer tutoring and one-to-one tutoring.

There are many different types of evidence-based practices in math. Some examples of these practices include, but are not limited to, differentiated instruction, peer-assisted instruction, use of multiple problem-solving strategies, formative instruction and one-to-one tutoring.

Do you have students who need extra support in math? Give your students more opportunities to consolidate learning and practice skills through personalized math tutoring with their own dedicated online math tutor. Each student receives differentiated instruction designed to close their individual learning gaps, and scaffolded learning ensures every student learns at the right pace. Lessons are aligned with your state’s standards and assessments, plus you’ll receive regular reports every step of the way. Personalized one-on-one math tutoring programs are available for: – 2nd grade tutoring – 3rd grade tutoring – 4th grade tutoring – 5th grade tutoring – 6th grade tutoring – 7th grade tutoring – 8th grade tutoring Why not learn more about how it works ?

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Future themes of mathematics education research: an international survey before and during the pandemic

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Published: 06 April 2021
Volume 107 , pages 1–24, ( 2021 )

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math research topics for elementary students

Arthur Bakker ORCID: orcid.org/0000-0002-9604-3448 1 ,
Jinfa Cai ORCID: orcid.org/0000-0002-0501-3826 2 &
Linda Zenger 1

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Before the pandemic (2019), we asked: On what themes should research in mathematics education focus in the coming decade? The 229 responses from 44 countries led to eight themes plus considerations about mathematics education research itself. The themes can be summarized as teaching approaches, goals, relations to practices outside mathematics education, teacher professional development, technology, affect, equity, and assessment. During the pandemic (November 2020), we asked respondents: Has the pandemic changed your view on the themes of mathematics education research for the coming decade? If so, how? Many of the 108 respondents saw the importance of their original themes reinforced (45), specified their initial responses (43), and/or added themes (35) (these categories were not mutually exclusive). Overall, they seemed to agree that the pandemic functions as a magnifying glass on issues that were already known, and several respondents pointed to the need to think ahead on how to organize education when it does not need to be online anymore. We end with a list of research challenges that are informed by the themes and respondents’ reflections on mathematics education research.

Learning from Research, Advancing the Field

The Narcissism of Mathematics Education

Educational Research on Learning and Teaching Mathematics

Avoid common mistakes on your manuscript.

1 An international survey in two rounds

Around the time when Educational Studies in Mathematics (ESM) and the Journal for Research in Mathematics Education (JRME) were celebrating their 50th anniversaries, Arthur Bakker (editor of ESM) and Jinfa Cai (editor of JRME) saw a need to raise the following future-oriented question for the field of mathematics education research:

Q2019: On what themes should research in mathematics education focus in the coming decade?

To that end, we administered a survey with just this one question between June 17 and October 16, 2019.

When we were almost ready with the analysis, the COVID-19 pandemic broke out, and we were not able to present the results at the conferences we had planned to attend (NCTM and ICME in 2020). Moreover, with the world shaken up by the crisis, we wondered if colleagues in our field might think differently about the themes formulated for the future due to the pandemic. Hence, on November 26, 2020, we asked a follow-up question to those respondents who in 2019 had given us permission to approach them for elaboration by email:

Q2020: Has the pandemic changed your view on the themes of mathematics education research for the coming decade? If so, how?

In this paper, we summarize the responses to these two questions. Similar to Sfard’s ( 2005 ) approach, we start by synthesizing the voices of the respondents before formulating our own views. Some colleagues put forward the idea of formulating a list of key themes or questions, similar to the 23 unsolved mathematical problems that David Hilbert published around 1900 (cf. Schoenfeld, 1999 ). However, mathematics and mathematics education are very different disciplines, and very few people share Hilbert’s formalist view on mathematics; hence, we do not want to suggest that we could capture the key themes of mathematics education in a similar way. Rather, our overview of themes drawn from the survey responses is intended to summarize what is valued in our global community at the time of the surveys. Reasoning from these themes, we end with a list of research challenges that we see worth addressing in the future (cf. Stephan et al., 2015 ).

2 Methodological approach

2.1 themes for the coming decade (2019).

We administered the 1-question survey through email lists that we were aware of (e.g., Becker, ICME, PME) and asked mathematics education researchers to spread it in their national networks. By October 16, 2019, we had received 229 responses from 44 countries across 6 continents (Table 1 ). Although we were happy with the larger response than Sfard ( 2005 ) received (74, with 28 from Europe), we do not know how well we have reached particular regions, and if potential respondents might have faced language or other barriers. We did offer a few Chinese respondents the option to write in Chinese because the second author offered to translate their emails into English. We also received responses in Spanish, which were translated for us.

Ethical approval was given by the Ethical Review Board of the Faculties of Science and Geo-science of Utrecht University (Bèta L-19247). We asked respondents to indicate if they were willing to be quoted by name and if we were allowed to approach them for subsequent information. If they preferred to be named, we mention their name and country; otherwise, we write “anonymous.” In our selection of quotes, we have focused on content, not on where the response came from. On March 2, 2021, we approached all respondents who were quoted to double-check if they agreed to be quoted and named. One colleague preferred the quote and name to be deleted; three suggested small changes in wording; the others approved.

On September 20, 2019, the three authors met physically at Utrecht University to analyze the responses. After each individual proposal, we settled on a joint list of seven main themes (the first seven in Table 2 ), which were neither mutually exclusive nor exhaustive. The third author (Zenger, then still a student in educational science) next color coded all parts of responses belonging to a category. These formed the basis for the frequencies and percentages presented in the tables and text. The first author (Bakker) then read all responses categorized by a particular code to identify and synthesize the main topics addressed within each code. The second author (Cai) read all of the survey responses and the response categories, and commented. After the initial round of analysis, we realized it was useful to add an eighth theme: assessment (including evaluation).

Moreover, given that a large number of respondents made comments about mathematics education research itself, we decided to summarize these separately. For analyzing this category of research, we used the following four labels to distinguish types of comments on our discipline of mathematics education research: theory, methodology, self-reflection (including ethical considerations), interdisciplinarity, and transdisciplinarity. We then summarized the responses per type of comment.

It has been a daunting and humbling experience to study the huge coverage and diversity of topics that our colleagues care about. Any categorization felt like a reduction of the wealth of ideas, and we are aware of the risks of “sorting things out” (Bowker & Star, 2000 ), which come with foregrounding particular challenges rather than others (Stephan et al., 2015 ). Yet the best way to summarize the bigger picture seemed by means of clustering themes and pointing to their relationships. As we identified these eight themes of mathematics education research for the future, a recurring question during the analysis was how to represent them. A list such as Table 2 does not do justice to the interrelations between the themes. Some relationships are very clear, for example, educational approaches (theme 2) working toward educational or societal goals (theme 1). Some themes are pervasive; for example, equity and (positive) affect are both things that educators want to achieve but also phenomena that are at stake during every single moment of learning and teaching. Diagrams we considered to represent such interrelationships were either too specific (limiting the many relevant options, e.g., a star with eight vertices that only link pairs of themes) or not specific enough (e.g., a Venn diagram with eight leaves such as the iPhone symbol for photos). In the end, we decided to use an image and collaborated with Elisabeth Angerer (student assistant in an educational sciences program), who eventually made the drawing in Fig. 1 to capture themes in their relationships.

Artistic impression of the future themes

2.2 Has the pandemic changed your view? (2020)

On November 26, 2020, we sent an email to the colleagues who responded to the initial question and who gave permission to be approached by email. We cited their initial response and asked: “Has the pandemic changed your view on the themes of mathematics education research for the coming decade? If so, how?” We received 108 responses by January 12, 2021. The countries from which the responses came included China, Italy, and other places that were hit early by the COVID-19 virus. The length of responses varied from a single word response (“no”) to elaborate texts of up to 2215 words. Some people attached relevant publications. The median length of the responses was 87 words, with a mean length of 148 words and SD = 242. Zenger and Bakker classified them as “no changes” (9 responses) or “clearly different views” (8); the rest of the responses saw the importance of their initial themes reinforced (45), specified their initial responses (43), or added new questions or themes (35). These last categories were not mutually exclusive, because respondents could first state that they thought the initial themes were even more relevant than before and provide additional, more specified themes. We then used the same themes that had been identified in the first round and identified what was stressed or added in the 2020 responses.

3 The themes

The most frequently mentioned theme was what we labeled approaches to teaching (64% of the respondents, see Table 2 ). Next was the theme of goals of mathematics education on which research should shed more light in the coming decade (54%). These goals ranged from specific educational goals to very broad societal ones. Many colleagues referred to mathematics education’s relationships with other practices (communities, institutions…) such as home, continuing education, and work. Teacher professional development is a key area for research in which the other themes return (what should students learn, how, how to assess that, how to use technology and ensure that students are interested?). Technology constitutes its own theme but also plays a key role in many other themes, just like affect. Another theme permeating other ones is what can be summarized as equity, diversity, and inclusion (also social justice, anti-racism, democratic values, and several other values were mentioned). These values are not just societal and educational goals but also drivers for redesigning teaching approaches, using technology, working on more just assessment, and helping learners gain access, become confident, develop interest, or even love for mathematics. To evaluate if approaches are successful and if goals have been achieved, assessment (including evaluation) is also mentioned as a key topic of research.

In the 2020 responses, many wise and general remarks were made. The general gist is that the pandemic (like earlier crises such as the economic crisis around 2008–2010) functioned as a magnifying glass on themes that were already considered important. Due to the pandemic, however, systemic societal and educational problems were said to have become better visible to a wider community, and urge us to think about the potential of a “new normal.”

3.1 Approaches to teaching

We distinguish specific teaching strategies from broader curricular topics.

3.1.1 Teaching strategies

There is a widely recognized need to further design and evaluate various teaching approaches. Among the teaching strategies and types of learning to be promoted that were mentioned in the survey responses are collaborative learning, critical mathematics education, dialogic teaching, modeling, personalized learning, problem-based learning, cross-curricular themes addressing the bigger themes in the world, embodied design, visualization, and interleaved learning. Note, however, that students can also enhance their mathematical knowledge independently from teachers or parents through web tutorials and YouTube videos.

Many respondents emphasized that teaching approaches should do more than promote cognitive development. How can teaching be entertaining or engaging? How can it contribute to the broader educational goals of developing students’ identity, contribute to their empowerment, and help them see the value of mathematics in their everyday life and work? We return to affect in Section 3.7 .

In the 2020 responses, we saw more emphasis on approaches that address modeling, critical thinking, and mathematical or statistical literacy. Moreover, respondents stressed the importance of promoting interaction, collaboration, and higher order thinking, which are generally considered to be more challenging in distance education. One approach worth highlighting is challenge-based education (cf. Johnson et al. 2009 ), because it takes big societal challenges as mentioned in the previous section as its motivation and orientation.

3.1.2 Curriculum

Approaches by which mathematics education can contribute to the aforementioned goals can be distinguished at various levels. Several respondents mentioned challenges around developing a coherent mathematics curriculum, smoothing transitions to higher school levels, and balancing topics, and also the typical overload of topics, the influence of assessment on what is taught, and what teachers can teach. For example, it was mentioned that mathematics teachers are often not prepared to teach statistics. There seems to be little research that helps curriculum authors tackle some of these hard questions as well as how to monitor reform (cf. Shimizu & Vithal, 2019 ). Textbook analysis is mentioned as a necessary research endeavor. But even if curricula within one educational system are reasonably coherent, how can continuity between educational systems be ensured (cf. Jansen et al., 2012 )?

In the 2020 responses, some respondents called for free high-quality curriculum resources. In several countries where Internet access is a problem in rural areas, a shift can be observed from online resources to other types of media such as radio and TV.

3.2 Goals of mathematics education

The theme of approaches is closely linked to that of the theme of goals. For example, as Fulvia Furinghetti (Italy) wrote: “It is widely recognized that critical thinking is a fundamental goal in math teaching. Nevertheless it is still not clear how it is pursued in practice.” We distinguish broad societal and more specific educational goals. These are often related, as Jane Watson (Australia) wrote: “If Education is to solve the social, cultural, economic, and environmental problems of today’s data-driven world, attention must be given to preparing students to interpret the data that are presented to them in these fields.”

3.2.1 Societal goals

Respondents alluded to the need for students to learn to function in the economy and in society more broadly. Apart from instrumental goals of mathematics education, some emphasized goals related to developing as a human being, for instance learning to see the mathematics in the world and develop a relation with the world. Mathematics education in these views should empower students to combat anti-expertise and post-fact tendencies. Several respondents mentioned even larger societal goals such as avoiding extinction as a human species and toxic nationalism, resolving climate change, and building a sustainable future.

In the second round of responses (2020), we saw much more emphasis on these bigger societal issues. The urgency to orient mathematics education (and its research) toward resolving these seemed to be felt more than before. In short, it was stressed that our planet needs to be saved. The big question is what role mathematics education can play in meeting these challenges.

3.2.2 Educational goals

Several respondents expressed a concern that the current goals of mathematics education do not reflect humanity’s and societies’ needs and interests well. Educational goals to be stressed more were mathematical literacy, numeracy, critical, and creative thinking—often with reference to the changing world and the planet being at risk. In particular, the impact of technology was frequently stressed, as this may have an impact on what people need to learn (cf. Gravemeijer et al., 2017 ). If computers can do particular things much better than people, what is it that students need to learn?

Among the most frequently mentioned educational goals for mathematics education were statistical literacy, computational and algorithmic thinking, artificial intelligence, modeling, and data science. More generally, respondents expressed that mathematics education should help learners deploy evidence, reasoning, argumentation, and proof. For example, Michelle Stephan (USA) asked:

What mathematics content should be taught today to prepare students for jobs of the future, especially given growth of the digital world and its impact on a global economy? All of the mathematics content in K-12 can be accomplished by computers, so what mathematical procedures become less important and what domains need to be explored more fully (e.g., statistics and big data, spatial geometry, functional reasoning, etc.)?

One challenge for research is that there is no clear methodology to arrive at relevant and feasible learning goals. Yet there is a need to choose and formulate such goals on the basis of research (cf. Van den Heuvel-Panhuizen, 2005 ).

Several of the 2020 responses mentioned the sometimes problematic way in which numbers, data, and graphs are used in the public sphere (e.g., Ernest, 2020 ; Kwon et al., 2021 ; Yoon et al., 2021 ). Many respondents saw their emphasis on relevant educational goals reinforced, for example, statistical and data literacy, modeling, critical thinking, and public communication. A few pandemic-specific topics were mentioned, such as exponential growth.

3.3 Relation of mathematics education to other practices

Many responses can be characterized as highlighting boundary crossing (Akkerman & Bakker, 2011 ) with disciplines or communities outside mathematics education, such as in science, technology, engineering, art, and mathematics education (STEM or STEAM); parents or families; the workplace; and leisure (e.g., drama, music, sports). An interesting example was the educational potential of mathematical memes—“humorous digital objects created by web users copying an existing image and overlaying a personal caption” (Bini et al., 2020 , p. 2). These boundary crossing-related responses thus emphasize the movements and connections between mathematics education and other practices.

In the 2020 responses, we saw that during the pandemic, the relationship between school and home has become much more important, because most students were (and perhaps still are) learning at home. Earlier research on parental involvement and homework (Civil & Bernier, 2006 ; de Abreu et al., 2006 ; Jackson, 2011 ) proves relevant in the current situation where many countries are still or again in lockdown. Respondents pointed to the need to monitor students and their work and to promote self-regulation. They also put more stress on the political, economic, and financial contexts in which mathematics education functions (or malfunctions, in many respondents’ views).

3.4 Teacher professional development

Respondents explicitly mentioned teacher professional development as an important domain of mathematics education research (including teacher educators’ development). For example, Loide Kapenda (Namibia) wrote, “I am supporting UNESCO whose idea is to focus on how we prepare teachers for the future we want.” (e.g., UNESCO, 2015 ) And, Francisco Rojas (Chile) wrote:

Although the field of mathematics education is broad and each time faced with new challenges (socio-political demands, new intercultural contexts, digital environments, etc.), all of them will be handled at school by the mathematics teacher, both in primary as well as in secondary education. Therefore, from my point of view, pre-service teacher education is one of the most relevant fields of research for the next decade, especially in developing countries.

It is evident from the responses that teaching mathematics is done by a large variety of people, not only by people who are trained as primary school teachers, secondary school mathematics teachers, or mathematicians but also parents, out-of-field teachers, and scientists whose primary discipline is not mathematics but who do use mathematics or statistics. How teachers of mathematics are trained varies accordingly. Respondents frequently pointed to the importance of subject-matter knowledge and particularly noted that many teachers seem ill-prepared to teach statistics (e.g., Lonneke Boels, the Netherlands).

Key questions were raised by several colleagues: “How to train mathematics teachers with a solid foundation in mathematics, positive attitudes towards mathematics teaching and learning, and wide knowledge base linking to STEM?” (anonymous); “What professional development, particularly at the post-secondary level, motivates changes in teaching practices in order to provide students the opportunities to engage with mathematics and be successful?” (Laura Watkins, USA); “How can mathematics educators equip students for sustainable, equitable citizenship? And how can mathematics education equip teachers to support students in this?” (David Wagner, Canada)

In the 2020 responses, it was clear that teachers are incredibly important, especially in the pandemic era. The sudden change to online teaching means that

higher requirements are put forward for teachers’ educational and teaching ability, especially the ability to carry out education and teaching by using information technology should be strengthened. Secondly, teachers’ ability to communicate and cooperate has been injected with new connotation. (Guangming Wang, China)

It is broadly assumed that education will stay partly online, though more so in higher levels of education than in primary education. This has implications for teachers, for instance, they will have to think through how they intend to coordinate teaching on location and online. Hence, one important focus for professional development is the use of technology.

3.5 Technology

Technology deserves to be called a theme in itself, but we want to emphasize that it ran through most of the other themes. First of all, some respondents argued that, due to technological advances in society, the societal and educational goals of mathematics education need to be changed (e.g., computational thinking to ensure employability in a technological society). Second, responses indicated that the changed goals have implications for the approaches in mathematics education. Consider the required curriculum reform and the digital tools to be used in it. Students do not only need to learn to use technology; the technology can also be used to learn mathematics (e.g., visualization, embodied design, statistical thinking). New technologies such as 3D printing, photo math, and augmented and virtual reality offer new opportunities for learning. Society has changed very fast in this respect. Third, technology is suggested to assist in establishing connections with other practices , such as between school and home, or vocational education and work, even though there is a great disparity in how successful these connections are.

In the 2020 responses, there was great concern about the current digital divide (cf. Hodgen et al., 2020 ). The COVID-19 pandemic has thus given cause for mathematics education research to understand better how connections across educational and other practices can be improved with the help of technology. Given the unequal distribution of help by parents or guardians, it becomes all the more important to think through how teachers can use videos and quizzes, how they can monitor their students, how they can assess them (while respecting privacy), and how one can compensate for the lack of social, gestural, and embodied interaction that is possible when being together physically.

Where mobile technology was considered very innovative before 2010, smartphones have become central devices in mathematics education in the pandemic with its reliance on distance learning. Our direct experience showed that phone applications such as WhatsApp and WeChat have become key tools in teaching and learning mathematics in many rural areas in various continents where few people have computers (for a report on podcasts distributed through WhatsApp, community loudspeakers, and local radio stations in Colombia, see Saenz et al., 2020 ).

3.6 Equity, diversity, and inclusion

Another cross-cutting theme can be labeled “equity, diversity, and inclusion.” We use this triplet to cover any topic that highlights these and related human values such as equality, social and racial justice, social emancipation, and democracy that were also mentioned by respondents (cf. Dobie & Sherin, 2021 ). In terms of educational goals , many respondents stressed that mathematics education should be for all students, including those who have special needs, who live in poverty, who are learning the instruction language, who have a migration background, who consider themselves LGBTQ+, have a traumatic or violent history, or are in whatever way marginalized. There is broad consensus that everyone should have access to high-quality mathematics education. However, as Niral Shah (USA) notes, less attention has been paid to “how phenomena related to social markers (e.g., race, class, gender) interact with phenomena related to the teaching and learning of mathematical content.”

In terms of teaching approaches , mathematics education is characterized by some respondents from particular countries as predominantly a white space where some groups feel or are excluded (cf. Battey, 2013 ). There is a general concern that current practices of teaching mathematics may perpetuate inequality, in particular in the current pandemic. In terms of assessment , mathematics is too often used or experienced as a gatekeeper rather than as a powerful resource (cf. Martin et al., 2010 ). Steve Lerman (UK) “indicates that understanding how educational opportunities are distributed inequitably, and in particular how that manifests in each end every classroom, is a prerequisite to making changes that can make some impact on redistribution.” A key research aim therefore is to understand what excludes students from learning mathematics and what would make mathematics education more inclusive (cf. Roos, 2019 ). And, what does professional development of teachers that promotes equity look like?

In 2020, many respondents saw their emphasis on equity and related values reinforced in the current pandemic with its risks of a digital divide, unequal access to high-quality mathematics education, and unfair distribution of resources. A related future research theme is how the so-called widening achievement gaps can be remedied (cf. Bawa, 2020 ). However, warnings were also formulated that thinking in such deficit terms can perpetuate inequality (cf. Svensson et al., 2014 ). A question raised by Dor Abrahamson (USA) is, “What roles could digital technology play, and in what forms, in restoring justice and celebrating diversity?”

Though entangled with many other themes, affect is also worth highlighting as a theme in itself. We use the term affect in a very broad sense to point to psychological-social phenomena such as emotion, love, belief, attitudes, interest, curiosity, fun, engagement, joy, involvement, motivation, self-esteem, identity, anxiety, alienation, and feeling of safety (cf. Cobb et al., 2009 ; Darragh, 2016 ; Hannula, 2019 ; Schukajlow et al., 2017 ). Many respondents emphasized the importance of studying these constructs in relation to (and not separate from) what is characterized as cognition. Some respondents pointed out that affect is not just an individual but also a social phenomenon, just like learning (cf. Chronaki, 2019 ; de Freitas et al., 2019 ; Schindler & Bakker, 2020 ).

Among the educational goals of mathematics education, several participants mentioned the need to generate and foster interest in mathematics. In terms of approaches , much emphasis was put on the need to avoid anxiety and alienation and to engage students in mathematical activity.

In the 2020 responses, more emphasis was put on the concern about alienation, which seems to be of special concern when students are socially distanced from peers and teachers as to when teaching takes place only through technology . What was reiterated in the 2020 responses was the importance of students’ sense of belonging in a mathematics classroom (cf. Horn, 2017 )—a topic closely related to the theme of equity, diversity, and inclusion discussed before.

3.8 Assessment

Assessment and evaluation were not often mentioned explicitly, but they do not seem less important than the other related themes. A key challenge is to assess what we value rather than valuing what we assess. In previous research, the assessment of individual students has received much attention, but what seems to be neglected is the evaluation of curricula. As Chongyang Wang (China) wrote, “How to evaluate the curriculum reforms. When we pay much energy in reforming our education and curriculum, do we imagine how to ensure it will work and there will be pieces of evidence found after the new curricula are carried out? How to prove the reforms work and matter?” (cf. Shimizu & Vithal, 2019 )

In the 2020 responses, there was an emphasis on assessment at a distance. Distance education generally is faced with the challenge of evaluating student work, both formatively and summatively. We predict that so-called e-assessment, along with its privacy challenges, will generate much research interest in the near future (cf. Bickerton & Sangwin, 2020 ).

4 Mathematics education research itself

Although we only asked for future themes, many respondents made interesting comments about research in mathematics education and its connections with other disciplines and practices (such as educational practice, policy, home settings). We have grouped these considerations under the subheadings of theory, methodology, reflection on our discipline, and interdisciplinarity and transdisciplinarity. As with the previous categorization into themes, we stress that these four types are not mutually exclusive as theoretical and methodological considerations can be intricately intertwined (Radford, 2008 ).

Several respondents expressed their concern about the fragmentation and diversity of theories used in mathematics education research (cf. Bikner-Ahsbahs & Prediger, 2014 ). The question was raised how mathematics educators can “work together to obtain valid, reliable, replicable, and useful findings in our field” and “How, as a discipline, can we encourage sustained research on core questions using commensurable perspectives and methods?” (Keith Weber, USA). One wish was “comparing theoretical perspectives for explanatory power” (K. Subramaniam, India). At the same time, it was stressed that “we cannot continue to pretend that there is just one culture in the field of mathematics education, that all the theoretical framework may be applied in whichever culture and that results are universal” (Mariolina Bartolini Bussi, Italy). In addition, the wish was expressed to deepen theoretical notions such as numeracy, equity, and justice as they play out in mathematics education.

4.2 Methodology

Many methodological approaches were mentioned as potentially useful in mathematics education research: randomized studies, experimental studies, replication, case studies, and so forth. Particular attention was paid to “complementary methodologies that bridge the ‘gap’ between mathematics education research and research on mathematical cognition” (Christian Bokhove, UK), as, for example, done in Gilmore et al. ( 2018 ). Also, approaches were mentioned that intend to bridge the so-called gap between educational practice and research, such as lesson study and design research. For example, Kay Owens (Australia) pointed to the challenge of studying cultural context and identity: “Such research requires a multi-faceted research methodology that may need to be further teased out from our current qualitative (e.g., ethnographic) and quantitative approaches (‘paper and pencil’ (including computing) testing). Design research may provide further possibilities.”

Francisco Rojas (Chile) highlighted the need for more longitudinal and cross-sectional research, in particular in the context of teacher professional development:

It is not enough to investigate what happens in pre-service teacher education but understand what effects this training has in the first years of the professional career of the new teachers of mathematics, both in primary and secondary education. Therefore, increasingly more longitudinal and cross-sectional studies will be required to understand the complexity of the practice of mathematics teachers, how the professional knowledge that articulates the practice evolves, and what effects have the practice of teachers on the students’ learning of mathematics.

4.3 Reflection on our discipline

Calls were made for critical reflection on our discipline. One anonymous appeal was for more self-criticism and scientific modesty: Is research delivering, or is it drawing away good teachers from teaching? Do we do research primarily to help improve mathematics education or to better understand phenomena? (cf. Proulx & Maheux, 2019 ) The general gist of the responses was a sincere wish to be of value to the world and mathematics education more specifically and not only do “research for the sake of research” (Zahra Gooya, Iran). David Bowers (USA) expressed several reflection-inviting views about the nature of our discipline, for example:

We must normalize (and expect) the full taking up the philosophical and theoretical underpinnings of all of our work (even work that is not considered “philosophical”). Not doing so leads to uncritical analysis and implications.

We must develop norms wherein it is considered embarrassing to do “uncritical” research.

There is no such thing as “neutral.” Amongst other things, this means that we should be cultivating norms that recognize the inherent political nature of all work, and norms that acknowledge how superficially “neutral” work tends to empower the oppressor.

We must recognize the existence of but not cater to the fragility of privilege.

In terms of what is studied, some respondents felt that the mathematics education research “literature has been moving away from the original goals of mathematics education. We seem to have been investigating everything but the actual learning of important mathematics topics.” (Lyn English, Australia) In terms of the nature of our discipline, Taro Fujita (UK) argued that our discipline can be characterized as a design science, with designing mathematical learning environments as the core of research activities (cf. Wittmann, 1995 ).

A tension that we observe in different views is the following: On the one hand, mathematics education research has its origin in helping teachers teach particular content better. The need for such so-called didactical, topic-specific research is not less important today but perhaps less fashionable for funding schemes that promote innovative, ground-breaking research. On the other hand, over time it has become clear that mathematics education is a multi-faceted socio-cultural and political endeavor under the influence of many local and global powers. It is therefore not surprising that the field of mathematics education research has expanded so as to include an increasingly wide scope of themes that are at stake, such as the marginalization of particular groups. We therefore highlight Niral Shah’s (USA) response that “historically, these domains of research [content-specific vs socio-political] have been decoupled. The field would get closer to understanding the experiences of minoritized students if we could connect these lines of inquiry.”

Another interesting reflective theme was raised by Nouzha El Yacoubi (Morocco): To what extent can we transpose “research questions from developed to developing countries”? As members of the plenary panel at PME 2019 (e.g., Kazima, 2019 ; Kim, 2019 ; Li, 2019 ) conveyed well, adopting interventions that were successful in one place in another place is far from trivial (cf. Gorard, 2020 ).

Juan L. Piñeiro (Spain in 2019, Chile in 2020) highlighted that “mathematical concepts and processes have different natures. Therefore, can it be characterized using the same theoretical and methodological tools?” More generally, one may ask if our theories and methodologies—often borrowed from other disciplines—are well suited to the ontology of our own discipline. A discussion started by Niss ( 2019 ) on the nature of our discipline, responded to by Bakker ( 2019 ) and Cai and Hwang ( 2019 ), seems worth continuing.

An important question raised in several comments is how close research should be to existing curricula. One respondent (Benjamin Rott, Germany) noted that research on problem posing often does “not fit into school curricula.” This makes the application of research ideas and findings problematic. However, one could argue that research need not always be tied to existing (local) educational contexts. It can also be inspirational, seeking principles of what is possible (and how) with a longer-term view on how curricula may change in the future. One option is, as Simon Zell (Germany) suggests, to test designs that cover a longer timeframe than typically done. Another way to bridge these two extremes is “collaboration between teachers and researchers in designing and publishing research” (K. Subramaniam, India) as is promoted by facilitating teachers to do PhD research (Bakx et al., 2016 ).

One of the responding teacher-researchers (Lonneke Boels, the Netherlands) expressed the wish that research would become available “in a more accessible form.” This wish raises the more general questions of whose responsibility it is to do such translation work and how to communicate with non-researchers. Do we need a particular type of communication research within mathematics education to learn how to convey particular key ideas or solid findings? (cf. Bosch et al., 2017 )

4.4 Interdisciplinarity and transdisciplinarity

Many respondents mentioned disciplines which mathematics education research can learn from or should collaborate with (cf. Suazo-Flores et al., 2021 ). Examples are history, mathematics, philosophy, psychology, psychometry, pedagogy, educational science, value education (social, emotional), race theory, urban education, neuroscience/brain research, cognitive science, and computer science didactics. “A big challenge here is how to make diverse experts approach and talk to one another in a productive way.” (David Gómez, Chile)

One of the most frequently mentioned disciplines in relation to our field is history. It is a common complaint in, for instance, the history of medicine that historians accuse medical experts of not knowing historical research and that medical experts accuse historians of not understanding the medical discipline well enough (Beckers & Beckers, 2019 ). This tension raises the question who does and should do research into the history of mathematics or of mathematics education and to what broader purpose.

Some responses go beyond interdisciplinarity, because resolving the bigger issues such as climate change and a more equitable society require collaboration with non-researchers (transdisciplinarity). A typical example is the involvement of educational practice and policy when improving mathematics education (e.g., Potari et al., 2019 ).

Let us end this section with a word of hope, from an anonymous respondent: “I still believe (or hope?) that the pandemic, with this making-inequities-explicit, would help mathematics educators to look at persistent and systemic inequalities more consistently in the coming years.” Having learned so much in the past year could indeed provide an opportunity to establish a more equitable “new normal,” rather than a reversion to the old normal, which one reviewer worried about.

5 The themes in their coherence: an artistic impression

As described above, we identified eight themes of mathematics education research for the future, which we discussed one by one. The disadvantage of this list-wise discussion is that the entanglement of the themes is backgrounded. To compensate for that drawback, we here render a brief interpretation of the drawing of Fig. 1 . While doing so, we invite readers to use their own creative imagination and perhaps use the drawing for other purposes (e.g., ask researchers, students, or teachers: Where would you like to be in this landscape? What mathematical ideas do you spot?). The drawing mainly focuses on the themes that emerged from the first round of responses but also hints at experiences from the time of the pandemic, for instance distance education. In Appendix 1 , we specify more of the details in the drawing and we provide a link to an annotated image (available at https://www.fisme.science.uu.nl/toepassingen/28937/ ).

The boat on the river aims to represent teaching approaches. The hand drawing of the boat hints at the importance of educational design: A particular approach is being worked out. On the boat, a teacher and students work together toward educational and societal goals, further down the river. The graduation bridge is an intermediate educational goal to pass, after which there are many paths leading to other goals such as higher education, citizenship, and work in society. Relations to practices outside mathematics education are also shown. In the left bottom corner, the house and parents working and playing with children represent the link of education with the home situation and leisure activity.

The teacher, represented by the captain in the foreground of the ship, is engaged in professional development, consulting a book, but also learning by doing (cf. Bakkenes et al., 2010 , on experimenting, using resources, etc.). Apart from graduation, there are other types of goals for teachers and students alike, such as equity, positive affect, and fluent use of technology. During their journey (and partially at home, shown in the left bottom corner), students learn to orient themselves in the world mathematically (e.g., fractal tree, elliptical lake, a parabolic mountain, and various platonic solids). On their way toward various goals, both teacher and students use particular technology (e.g., compass, binoculars, tablet, laptop). The magnifying glass (representing research) zooms in on a laptop screen that portrays distance education, hinting at the consensus that the pandemic magnifies some issues that education was already facing (e.g., the digital divide).

Equity, diversity, and inclusion are represented with the rainbow, overarching everything. On the boat, students are treated equally and the sailing practice is inclusive in the sense that all perform at their own level—getting the support they need while contributing meaningfully to the shared activity. This is at least what we read into the image. Affect is visible in various ways. First of all, the weather represents moods in general (rainy and dark side on the left; sunny bright side on the right). Second, the individual students (e.g., in the crow’s nest) are interested in, anxious about, and attentive to the things coming up during their journey. They are motivated to engage in all kinds of tasks (handling the sails, playing a game of chance with a die, standing guard in the crow’s nest, etc.). On the bridge, the graduates’ pride and happiness hints at positive affect as an educational goal but also represents the exam part of the assessment. The assessment also happens in terms of checks and feedback on the boat. The two people next to the house (one with a camera, one measuring) can be seen as assessors or researchers observing and evaluating the progress on the ship or the ship’s progress.

More generally, the three types of boats in the drawing represent three different spaces, which Hannah Arendt ( 1958 ) would characterize as private (paper-folded boat near the boy and a small toy boat next to the girl with her father at home), public/political (ships at the horizon), and the in-between space of education (the boat with the teacher and students). The students and teacher on the boat illustrate school as a special pedagogic form. Masschelein and Simons ( 2019 ) argue that the ancient Greek idea behind school (σχολή, scholè , free time) is that students should all be treated as equal and should all get equal opportunities. At school, their descent does not matter. At school, there is time to study, to make mistakes, without having to work for a living. At school, they learn to collaborate with others from diverse backgrounds, in preparation for future life in the public space. One challenge of the lockdown situation as a consequence of the pandemic is how to organize this in-between space in a way that upholds its special pedagogic form.

6 Research challenges

Based on the eight themes and considerations about mathematics education research itself, we formulate a set of research challenges that strike us as deserving further discussion (cf. Stephan et al., 2015 ). We do not intend to suggest these are more important than others or that some other themes are less worthy of investigation, nor do we suggest that they entail a research agenda (cf. English, 2008 ).

6.1 Aligning new goals, curricula, and teaching approaches

There seems to be relatively little attention within mathematics education research for curricular issues, including topics such as learning goals, curriculum standards, syllabi, learning progressions, textbook analysis, curricular coherence, and alignment with other curricula. Yet we feel that we as mathematics education researchers should care about these topics as they may not necessarily be covered by other disciplines. For example, judging from Deng’s ( 2018 ) complaint about the trends in the discipline of curriculum studies, we cannot assume scholars in that field to address issues specific to the mathematics-focused curriculum (e.g., the Journal of Curriculum Studies and Curriculum Inquiry have published only a limited number of studies on mathematics curricula).

Learning goals form an important element of curricula or standards. It is relatively easy to formulate important goals in general terms (e.g., critical thinking or problem solving). As a specific example, consider mathematical problem posing (Cai & Leikin, 2020 ), which curriculum standards have specifically pointed out as an important educational goal—developing students’ problem-posing skills. Students should be provided opportunities to formulate their own problems based on situations. However, there are few problem-posing activities in current mathematics textbooks and classroom instruction (Cai & Jiang, 2017 ). A similar observation can be made about problem solving in Dutch primary textbooks (Kolovou et al., 2009 ). Hence, there is a need for researchers and educators to align problem posing in curriculum standards, textbooks, classroom instruction, and students’ learning.

The challenge we see for mathematics education researchers is to collaborate with scholars from other disciplines (interdisciplinarity) and with non-researchers (transdisciplinarity) in figuring out how the desired societal and educational goals can be shaped in mathematics education. Our discipline has developed several methodological approaches that may help in formulating learning goals and accompanying teaching approaches (cf. Van den Heuvel-Panhuizen, 2005 ), including epistemological analyses (Sierpinska, 1990 ), historical and didactical phenomenology (Bakker & Gravemeijer, 2006 ; Freudenthal, 1986 ), and workplace studies (Bessot & Ridgway, 2000 ; Hoyles et al., 2001 ). However, how should the outcomes of such research approaches be weighed against each other and combined to formulate learning goals for a balanced, coherent curriculum? What is the role of mathematics education researchers in relation to teachers, policymakers, and other stakeholders (Potari et al., 2019 )? In our discipline, we seem to lack a research-informed way of arriving at the formulation of suitable educational goals without overloading the curricula.

6.2 Researching mathematics education across contexts

Though methodologically and theoretically challenging, it is of great importance to study learning and teaching mathematics across contexts. After all, students do not just learn at school; they can also participate in informal settings (Nemirovsky et al., 2017 ), online forums, or affinity networks (Ito et al., 2018 ) where they may share for instance mathematical memes (Bini et al., 2020 ). Moreover, teachers are not the only ones teaching mathematics: Private tutors, friends, parents, siblings, or other relatives can also be involved in helping children with their mathematics. Mathematics learning could also be situated on streets or in museums, homes, and other informal settings. This was already acknowledged before 2020, but the pandemic has scattered learners and teachers away from the typical central school locations and thus shifted the distribution of labor.

In particular, physical and virtual spaces of learning have been reconfigured due to the pandemic. Issues of timing also work differently online, for example, if students can watch online lectures or videos whenever they like (asynchronously). Such reconfigurations of space and time also have an effect on the rhythm of education and hence on people’s energy levels (cf. Lefebvre, 2004 ). More specifically, the reconfiguration of the situation has affected many students’ levels of motivation and concentration (e.g., Meeter et al., 2020 ). As Engelbrecht et al. ( 2020 ) acknowledged, the pandemic has drastically changed the teaching and learning model as we knew it. It is quite possible that some existing theories about teaching and learning no longer apply in the same way. An interesting question is whether and how existing theoretical frameworks can be adjusted or whether new theoretical orientations need to be developed to better understand and promote productive ways of blended or online teaching, across contexts.

6.3 Focusing teacher professional development

Professional development of teachers and teacher educators stands out from the survey as being in need of serious investment. How can teachers be prepared for the unpredictable, both in terms of beliefs and actions? During the pandemic, teachers have been under enormous pressure to make quick decisions in redesigning their courses, to learn to use new technological tools, to invent creative ways of assessment, and to do what was within their capacity to provide opportunities to their students for learning mathematics—even if technological tools were limited (e.g., if students had little or no computer or internet access at home). The pressure required both emotional adaption and instructional adjustment. Teachers quickly needed to find useful information, which raises questions about the accessibility of research insights. Given the new situation, limited resources, and the uncertain unfolding of education after lockdowns, focusing teacher professional development on necessary and useful topics will need much attention. In particular, there is a need for longitudinal studies to investigate how teachers’ learning actually affects teachers’ classroom instruction and students’ learning.

In the surveys, respondents mainly referred to teachers as K-12 school mathematics teachers, but some also stressed the importance of mathematics teacher educators (MTEs). In addition to conducting research in mathematics education, MTEs are acting in both the role of teacher educators and of mathematics teachers. There has been increased research on MTEs as requiring professional development (Goos & Beswick, 2021 ). Within the field of mathematics education, there is an emerging need and interest in how mathematics teacher educators themselves learn and develop. In fact, the changing situation also provides an opportunity to scrutinize our habitual ways of thinking and become aware of what Jullien ( 2018 ) calls the “un-thought”: What is it that we as educators and researchers have not seen or thought about so much about that the sudden reconfiguration of education forces us to reflect upon?

6.4 Using low-tech resources

Particular strands of research focus on innovative tools and their applications in education, even if they are at the time too expensive (even too labor intensive) to use at large scale. Such future-oriented studies can be very interesting given the rapid advances in technology and attractive to funding bodies focusing on innovation. Digital technology has become ubiquitous, both in schools and in everyday life, and there is already a significant body of work capitalizing on aspects of technology for research and practice in mathematics education.

However, as Cai et al. ( 2020 ) indicated, technology advances so quickly that addressing research problems may not depend so much on developing a new technological capability as on helping researchers and practitioners learn about new technologies and imagine effective ways to use them. Moreover, given the millions of students in rural areas who during the pandemic have only had access to low-tech resources such as podcasts, radio, TV, and perhaps WhatsApp through their parents’ phones, we would like to see more research on what learning, teaching, and assessing mathematics through limited tools such as Whatsapp or WeChat look like and how they can be improved. In fact, in China, a series of WeChat-based mini-lessons has been developed and delivered through the WeChat video function during the pandemic. Even when the pandemic is under control, mini-lessons are still developed and circulated through WeChat. We therefore think it is important to study the use and influence of low-tech resources in mathematics education.

6.5 Staying in touch online

With the majority of students learning at home, a major ongoing challenge for everyone has been how to stay in touch with each other and with mathematics. With less social interaction, without joint attention in the same physical space and at the same time, and with the collective only mediated by technology, becoming and staying motivated to learn has been a widely felt challenge. It is generally expected that in the higher levels of education, more blended or distant learning elements will be built into education. Careful research on the affective, embodied, and collective aspects of learning and teaching mathematics is required to overcome eventually the distance and alienation so widely experienced in online education. That is, we not only need to rethink social interactions between students and/or teachers in different settings but must also rethink how to engage and motivate students in online settings.

6.6 Studying and improving equity without perpetuating inequality

Several colleagues have warned, for a long time, that one risk of studying achievement gaps, differences between majority and minority groups, and so forth can also perpetuate inequity. Admittedly, pinpointing injustice and the need to invest in particular less privileged parts of education is necessary to redirect policymakers’ and teachers’ attention and gain funding. However, how can one reorient resources without stigmatizing? For example, Svensson et al. ( 2014 ) pointed out that research findings can fuel political debates about groups of people (e.g., parents with a migration background), who then may feel insecure about their own capacities. A challenge that we see is to identify and understand problematic situations without legitimizing problematic stereotyping (Hilt, 2015 ).

Furthermore, the field of mathematics education research does not have a consistent conceptualization of equity. There also seem to be regional differences: It struck us that equity is the more common term in the responses from the Americas, whereas inclusion and diversity were more often mentioned in the European responses. Future research will need to focus on both the conceptualization of equity and on improving equity and related values such as inclusion.

6.7 Assessing online

A key challenge is how to assess online and to do so more effectively. This challenge is related to both privacy, ethics, and performance issues. It is clear that online assessment may have significant advantages to assess student mathematics learning, such as more flexibility in test-taking and fast scoring. However, many teachers have faced privacy concerns, and we also have the impression that in an online environment it is even more challenging to successfully assess what we value rather than merely assessing what is relatively easy to assess. In particular, we need to systematically investigate any possible effect of administering assessments online as researchers have found a differential effect of online assessment versus paper-and-pencil assessment (Backes & Cowan, 2019 ). What further deserves careful ethical attention is what happens to learning analytics data that can and are collected when students work online.

6.8 Doing and publishing interdisciplinary research

When analyzing the responses, we were struck by a discrepancy between what respondents care about and what is typically researched and published in our monodisciplinary journals. Most of the challenges mentioned in this section require interdisciplinary or even transdisciplinary approaches (see also Burkhardt, 2019 ).

An overarching key question is: What role does mathematics education research play in addressing the bigger and more general challenges mentioned by our respondents? The importance of interdisciplinarity also raises a question about the scope of journals that focus on mathematics education research. Do we need to broaden the scope of monodisciplinary journals so that they can publish important research that combines mathematics education research with another disciplinary perspective? As editors, we see a place for interdisciplinary studies as long as there is one strong anchor in mathematics education research. In fact, there are many researchers who do not identify themselves as mathematics education researchers but who are currently doing high-quality work related to mathematics education in fields such as educational psychology and the cognitive and learning sciences. Encouraging the reporting of high-quality mathematics education research from a broader spectrum of researchers would serve to increase the impact of the mathematics education research journals in the wider educational arena. This, in turn, would serve to encourage further collaboration around mathematics education issues from various disciplines. Ultimately, mathematics education research journals could act as a hub for interdisciplinary collaboration to address the pressing questions of how mathematics is learned and taught.

7 Concluding remarks

In this paper, based on a survey conducted before and during the pandemic, we have examined how scholars in the field of mathematics education view the future of mathematics education research. On the one hand, there are no major surprises about the areas we need to focus on in the future; the themes are not new. On the other hand, the responses also show that the areas we have highlighted still persist and need further investigation (cf. OECD, 2020 ). But, there are a few areas, based on both the responses of the scholars and our own discussions and views, that stand out as requiring more attention. For example, we hope that these survey results will serve as propelling conversation about mathematics education research regarding online assessment and pedagogical considerations for virtual teaching.

The survey results are limited in two ways. The set of respondents to the survey is probably not representative of all mathematics education researchers in the world. In that regard, perhaps scholars in each country could use the same survey questions to survey representative samples within each country to understand how the scholars in that country view future research with respect to regional needs. The second limitation is related to the fact that mathematics education is a very culturally dependent field. Cultural differences in the teaching and learning of mathematics are well documented. Given the small numbers of responses from some continents, we did not break down the analysis for regional comparison. Representative samples from each country would help us see how scholars from different countries view research in mathematics education; they will add another layer of insights about mathematics education research to complement the results of the survey presented here. Nevertheless, we sincerely hope that the findings from the surveys will serve as a discussion point for the field of mathematics education to pursue continuous improvement.

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Acknowledgments

We thank Anna Sfard for her advice on the survey, based on her own survey published in Sfard ( 2005 ). We are grateful for Stephen Hwang’s careful copyediting for an earlier version of the manuscript. Thanks also to Elisabeth Angerer, Elske de Waal, Paul Ernest, Vilma Mesa, Michelle Stephan, David Wagner, and anonymous reviewers for their feedback on earlier drafts.

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Appendix 1: Explanation of Fig. 1

We have divided Fig. 1 in 12 rectangles called A1 (bottom left) up to C4 (top right) to explain the details (for image annotation go to https://www.fisme.science.uu.nl/toepassingen/28937 )

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Bakker, A., Cai, J. & Zenger, L. Future themes of mathematics education research: an international survey before and during the pandemic. Educ Stud Math 107 , 1–24 (2021). https://doi.org/10.1007/s10649-021-10049-w

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How can mathematics research increase effective instruction and student success?

Elementary and middle school students in the US are underachieving in mathematics. Those without adequate understanding of basic mathematical concepts and skills after completing kindergarten go on to struggle throughout their maths education. So how can teaching maths be improved to enable children to learn best? Dr Jonathan Brendefur and colleagues at the Developing Mathematical Thinking Institute ( DMTI ) have developed the five dimensions of the Developing Mathematical Thinking framework, a professional development programme for teachers and other educators. They demonstrate how teachers implementing the DMT approach benefit through increased content knowledge and student success.

The US National Center for Education Statistics (NCES) has reported that elementary and middle school students in the US are underachieving in mathematics. Additionally, their overall performance is not improving over time. In comparison with national standards, recent studies have revealed that these students are neither mathematically literate nor proficient. Studies have shown that those students completing kindergarten with an inadequate understanding of basic mathematical concepts and skills go on to struggle throughout their maths education. This research indicates that teaching methodologies need to change, particularly for students at the elementary level.

A central question then arises: how can teaching maths be improved to enable children to learn? Rising to this challenge, Dr Jonathan Brendefur and his colleagues at the Developing Mathematical Thinking Institute (DMTI) have spent years in classrooms working with teachers and students to perfect the five dimensions of the Developing Mathematical Thinking (DMT) framework, a multi-year professional development programme for improving maths instruction. The framework ensures that every teacher, parent, student, and administrator engages in successful maths experiences.

Dr Brendefur explains how teachers must establish ‘equitable learning conditions that foster understanding’ to enable students to become better problem-solvers both inside and outside the classroom. DMTI offers maths professional development, helping teachers apply the DMT framework to develop students’ mathematical thinking. This involves building on students’ ideas, encouraging problem-solving, and strengthening mathematical vocabulary, ultimately solidifying concepts by communicating mathematically.

Improving instructional practice and student achievement

Over the last decade, the DMTI team has been developing, and rigorously evaluating, the DMT framework. The research team has carried out longitudinal evaluative studies that demonstrate how the DMT programme affords students a better understanding of mathematics, reinforced with ‘mathematising’ and ‘progressive formalisation’ philosophies. Mathematising involves employing mathematical thinking and vocabulary during routine activities such as play. Through the process of progressive formalisation, an initial intuitive understanding of a basic concept is acquired. Based on this, more exact, formal connotations and increasingly complex theories can then be cultivated. For example, moving from manipulative cubes, to bar models, to symbolic notations.

The DMT framework’s rubric comprises a five-dimensional approach to teaching mathematics. The researchers note, however, that these instructional practices are not mutually exclusive. The five dimensions are outlined below.

Taking students’ ideas seriously

Teachers initiate this first dimension by placing students in situations that engage their prior knowledge, enabling them to solve problems and expand their intuitive ideas. This is the onset of the development of mathematical understanding where educators should focus on processes of mathematising and progressive formalisation. Learning resources are required to provide teachers with options to differentiate groups of students and foster both their formal and informal knowledge.

Encouraging multiple strategies and models

The second aspect encourages students to try out multiple models and strategies. Modelling is crucial in the development of mathematical thinking. As such, students need to be able to examine their chosen problem-solving method and compare it with alternative approaches to progress their understanding. The DMT framework includes carefully selected tasks that teachers can use with their students as they advance from their initial informal ideas to more conventional mathematical models.

‘I saw great enthusiasm, great ownership of what they were learning. I saw huge growth in their ability to reason and problem-solve.’ Ann, 3rd-grade teacher.

‘DMTI felt like that missing piece of how do you get kids to think mathematically? It really had tangible ways of the how.’ Emily, 2nd-grade teacher.

Pressing students conceptually

This third component focuses on building connections between mathematical strategies and models, progressively formalising students’ problem-solving concepts. Teachers aim to create environments that enable students to move beyond surface-level understanding of procedures to conceptualise mathematics and establish connections between various methods and models.

Focusing on the structure of mathematics

In this fourth element, ‘structure’ refers to the rudiments of mathematics that are constant throughout the subject regardless of the level being studied, for example, concepts of units, relationships, and equivalence. Shifting the focus to structure helps students understand and establish connections between concepts and entrenches structural component language relating to tasks throughout each lesson. The framework’s formative assessment includes examples of students articulating and critiquing both their own and other students’ models.

Addressing misconceptions

In this fifth dimension, teachers use students’ misconceptions and mistakes as tools to construct deeper levels of mathematical understanding. When a teacher focuses their practices on the four dimensions above, their attention shifts toward the informal strategies their students use for problem-solving, the mathematical connections they’re making, the emerging conceptual understanding, and the structure of mathematics that brings about their misconceptions. By addressing these rather than ignoring them, teachers encourage their students to amend their thinking and make sense of maths. The framework embraces misconceptions and errors that can occur and encourages teachers to involve their students in justifying, evaluating, and inquiring into how they solve problems.

Teaching for understanding

Dr Brendefur and his team have carried out longitudinal evaluative studies that demonstrate the effectiveness of the DMT pedagogic framework’s five dimensions. They observed 268 lessons to find out how teachers’ knowledge relates to their teaching of mathematics in terms of their instructional practices. Analysis of the data collected over this six-year study revealed that providing teachers with professional development focused on increasing their students’ mathematical thinking also has a beneficial impact on the teachers’ knowledge. It was observed that those teachers who practised DMT in their classrooms increased their content knowledge as their instructional practices shifted towards teaching for understanding.

A review of the literature revealed a lack of rigorous quantitative research examining how teacher professional development correlates to students’ achievement. To measure the effectiveness of the DMT programme, the team employed a cluster-randomised design. DMTI provides multi-tiered levels of professional development for teachers, so the team analysed how the minimal, moderate, and prominent levels affected teachers’ instructional performance. They found that the achievement of those students whose teachers adopted all five dimensions increased the most. Furthermore, the programme positively impacted student achievement throughout the study.

Strategy versus drill

Students’ lack of multiplication fluency has been highlighted globally as a key factor that hinders mathematical performance. The researchers compared their DMT approach with traditional rehearsal and drilling practices in an experiment comparing the teaching of mathematics to grade 3, 4, and 5 students. Twelve teachers and 282 students from four schools with a history of below-average achievement took part in the study. Two schools formed the treatment group using the DMT strategy method, while the other two made up the comparison group employing the traditional drill technique.

The strategy group received fluency development instruction based on the DMT framework. The drill group received basic multiplication fluency instruction using methods favouring memorisation and repetition. At the beginning of the five-week unit students completed a pre-test made up of 30 multiplication questions. At the end of the unit, they completed the same questions in a post-test. The results demonstrated that while overall fact fluency is important, the performance of students in the strategy group increased much more than that of those in the drill group.

Building a strong foundation

Underpinned by their research into how we understand mathematics and structure mathematical ideas, the DMTI book, Math Facts: Kids Need Them. Here’s How to Teach Them details and demonstrates the key components required for children to develop robust foundations for learning mathematics. It includes demonstration lessons and resources for teachers and other educators to use with elementary and middle school students. Offering guidance that builds on the five dimensions, it opens with modelling number facts using blocks and dice to develop maths fluency and continues through to multiplying non-integer rational numbers.

How can mathematics research increase effective instruction and student success?

Key components of DMT

Exploration of mathematical concepts is promoted with the development of informal strategies while encouraging students to play with ideas. Students learn how and when to use more sophisticated models, having built a solid understanding of various models at their disposal. Students’ conceptualisation is strengthened together with their understanding of mathematical procedures when they contrast different models and recognise that particular methods are more efficient than others.

Concentrating on mathematical structure supports connections, allowing students to gain a deeper understanding of establishing connections between the fundamental concepts, thus increasing their knowledge. Dr Brendefur comments that ‘the more you know about the structure of something physically or theoretically the more you’re able to adapt in practice situations.’ Visual modelling enables students to understand why one strategy might work better than another. Misconceptions can be addressed and discussed during the modelling process, deepening students’ levels of understanding so they can avoid such mistakes in the future.

The DTMI team has demonstrated that teachers implementing the DMT approach benefit from increasing their content knowledge as they shift their focus to teaching for understanding and increase their students’ learning progressions and maths achievement.

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Research Topics & Ideas: Education

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The impact of teacher professional development on student learning
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The use of technology in the form of online tutoring

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Primary education.

Investigating the effects of peer tutoring on academic achievement in primary school
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The impact of character education programs on moral development in primary school students
Investigating the use of technology in enhancing primary school mathematics education
The impact of inclusive curriculum on promoting equity and diversity in primary schools
The impact of outdoor education programs on environmental awareness in primary school students
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Investigating the effects of early literacy interventions on reading comprehension in primary school students
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Exploring the benefits of inclusive education for students with special needs in primary schools
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Investigating the role of parental support in reducing academic stress in primary school children
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Examining the effects of early childhood education programs on primary school readiness
Examining the effects of homework on primary school students’ academic performance
The role of formative assessment in improving learning outcomes in primary school classrooms
The impact of teacher-student relationships on academic outcomes in primary school
Investigating the effects of classroom environment on student behavior and learning outcomes in primary schools
Investigating the role of creativity and imagination in primary school curriculum
The impact of nutrition and healthy eating programs on academic performance in primary schools
The impact of social-emotional learning programs on primary school students’ well-being and academic performance
The role of parental involvement in academic achievement of primary school children
Examining the effects of classroom management strategies on student behavior in primary school
The role of school leadership in creating a positive school climate Exploring the benefits of bilingual education in primary schools
The effectiveness of project-based learning in developing critical thinking skills in primary school students
The role of inquiry-based learning in fostering curiosity and critical thinking in primary school students
The effects of class size on student engagement and achievement in primary schools
Investigating the effects of recess and physical activity breaks on attention and learning in primary school
Exploring the benefits of outdoor play in developing gross motor skills in primary school children
The effects of educational field trips on knowledge retention in primary school students
Examining the effects of inclusive classroom practices on students’ attitudes towards diversity in primary schools
The impact of parental involvement in homework on primary school students’ academic achievement
Investigating the effectiveness of different assessment methods in primary school classrooms
The influence of physical activity and exercise on cognitive development in primary school children
Exploring the benefits of cooperative learning in promoting social skills in primary school students

Secondary Education

Investigating the effects of school discipline policies on student behavior and academic success in secondary education
The role of social media in enhancing communication and collaboration among secondary school students
The impact of school leadership on teacher effectiveness and student outcomes in secondary schools
Investigating the effects of technology integration on teaching and learning in secondary education
Exploring the benefits of interdisciplinary instruction in promoting critical thinking skills in secondary schools
The impact of arts education on creativity and self-expression in secondary school students
The effectiveness of flipped classrooms in promoting student learning in secondary education
The role of career guidance programs in preparing secondary school students for future employment
Investigating the effects of student-centered learning approaches on student autonomy and academic success in secondary schools
The impact of socio-economic factors on educational attainment in secondary education
Investigating the impact of project-based learning on student engagement and academic achievement in secondary schools
Investigating the effects of multicultural education on cultural understanding and tolerance in secondary schools
The influence of standardized testing on teaching practices and student learning in secondary education
Investigating the effects of classroom management strategies on student behavior and academic engagement in secondary education
The influence of teacher professional development on instructional practices and student outcomes in secondary schools
The role of extracurricular activities in promoting holistic development and well-roundedness in secondary school students
Investigating the effects of blended learning models on student engagement and achievement in secondary education
The role of physical education in promoting physical health and well-being among secondary school students
Investigating the effects of gender on academic achievement and career aspirations in secondary education
Exploring the benefits of multicultural literature in promoting cultural awareness and empathy among secondary school students
The impact of school counseling services on student mental health and well-being in secondary schools
Exploring the benefits of vocational education and training in preparing secondary school students for the workforce
The role of digital literacy in preparing secondary school students for the digital age
The influence of parental involvement on academic success and well-being of secondary school students
The impact of social-emotional learning programs on secondary school students’ well-being and academic success
The role of character education in fostering ethical and responsible behavior in secondary school students
Examining the effects of digital citizenship education on responsible and ethical technology use among secondary school students
The impact of parental involvement in school decision-making processes on student outcomes in secondary schools
The role of educational technology in promoting personalized learning experiences in secondary schools
The impact of inclusive education on the social and academic outcomes of students with disabilities in secondary schools
The influence of parental support on academic motivation and achievement in secondary education
The role of school climate in promoting positive behavior and well-being among secondary school students
Examining the effects of peer mentoring programs on academic achievement and social-emotional development in secondary schools
Examining the effects of teacher-student relationships on student motivation and achievement in secondary schools
Exploring the benefits of service-learning programs in promoting civic engagement among secondary school students
The impact of educational policies on educational equity and access in secondary education
Examining the effects of homework on academic achievement and student well-being in secondary education
Investigating the effects of different assessment methods on student performance in secondary schools
Examining the effects of single-sex education on academic performance and gender stereotypes in secondary schools
The role of mentoring programs in supporting the transition from secondary to post-secondary education

Tertiary Education

The role of student support services in promoting academic success and well-being in higher education
The impact of internationalization initiatives on students’ intercultural competence and global perspectives in tertiary education
Investigating the effects of active learning classrooms and learning spaces on student engagement and learning outcomes in tertiary education
Exploring the benefits of service-learning experiences in fostering civic engagement and social responsibility in higher education
The influence of learning communities and collaborative learning environments on student academic and social integration in higher education
Exploring the benefits of undergraduate research experiences in fostering critical thinking and scientific inquiry skills
Investigating the effects of academic advising and mentoring on student retention and degree completion in higher education
The role of student engagement and involvement in co-curricular activities on holistic student development in higher education
The impact of multicultural education on fostering cultural competence and diversity appreciation in higher education
The role of internships and work-integrated learning experiences in enhancing students’ employability and career outcomes
Examining the effects of assessment and feedback practices on student learning and academic achievement in tertiary education
The influence of faculty professional development on instructional practices and student outcomes in tertiary education
The influence of faculty-student relationships on student success and well-being in tertiary education
The impact of college transition programs on students’ academic and social adjustment to higher education
The impact of online learning platforms on student learning outcomes in higher education
The impact of financial aid and scholarships on access and persistence in higher education
The influence of student leadership and involvement in extracurricular activities on personal development and campus engagement
Exploring the benefits of competency-based education in developing job-specific skills in tertiary students
Examining the effects of flipped classroom models on student learning and retention in higher education
Exploring the benefits of online collaboration and virtual team projects in developing teamwork skills in tertiary students
Investigating the effects of diversity and inclusion initiatives on campus climate and student experiences in tertiary education
The influence of study abroad programs on intercultural competence and global perspectives of college students
Investigating the effects of peer mentoring and tutoring programs on student retention and academic performance in tertiary education
Investigating the effectiveness of active learning strategies in promoting student engagement and achievement in tertiary education
Investigating the effects of blended learning models and hybrid courses on student learning and satisfaction in higher education
The role of digital literacy and information literacy skills in supporting student success in the digital age
Investigating the effects of experiential learning opportunities on career readiness and employability of college students
The impact of e-portfolios on student reflection, self-assessment, and showcasing of learning in higher education
The role of technology in enhancing collaborative learning experiences in tertiary classrooms
The impact of research opportunities on undergraduate student engagement and pursuit of advanced degrees
Examining the effects of competency-based assessment on measuring student learning and achievement in tertiary education
Examining the effects of interdisciplinary programs and courses on critical thinking and problem-solving skills in college students
The role of inclusive education and accessibility in promoting equitable learning experiences for diverse student populations
The role of career counseling and guidance in supporting students’ career decision-making in tertiary education
The influence of faculty diversity and representation on student success and inclusive learning environments in higher education

Education-Related Dissertations & Theses

While the ideas we’ve presented above are a decent starting point for finding a research topic in education, they are fairly generic and non-specific. So, it helps to look at actual dissertations and theses in the education space to see how this all comes together in practice.

Below, we’ve included a selection of education-related research projects to help refine your thinking. These are actual dissertations and theses, written as part of Master’s and PhD-level programs, so they can provide some useful insight as to what a research topic looks like in practice.

From Rural to Urban: Education Conditions of Migrant Children in China (Wang, 2019)
Energy Renovation While Learning English: A Guidebook for Elementary ESL Teachers (Yang, 2019)
A Reanalyses of Intercorrelational Matrices of Visual and Verbal Learners’ Abilities, Cognitive Styles, and Learning Preferences (Fox, 2020)
A study of the elementary math program utilized by a mid-Missouri school district (Barabas, 2020)
Instructor formative assessment practices in virtual learning environments : a posthumanist sociomaterial perspective (Burcks, 2019)
Higher education students services: a qualitative study of two mid-size universities’ direct exchange programs (Kinde, 2020)
Exploring editorial leadership : a qualitative study of scholastic journalism advisers teaching leadership in Missouri secondary schools (Lewis, 2020)
Selling the virtual university: a multimodal discourse analysis of marketing for online learning (Ludwig, 2020)
Advocacy and accountability in school counselling: assessing the use of data as related to professional self-efficacy (Matthews, 2020)
The use of an application screening assessment as a predictor of teaching retention at a midwestern, K-12, public school district (Scarbrough, 2020)
Core values driving sustained elite performance cultures (Beiner, 2020)
Educative features of upper elementary Eureka math curriculum (Dwiggins, 2020)
How female principals nurture adult learning opportunities in successful high schools with challenging student demographics (Woodward, 2020)
The disproportionality of Black Males in Special Education: A Case Study Analysis of Educator Perceptions in a Southeastern Urban High School (McCrae, 2021)

As you can see, these research topics are a lot more focused than the generic topic ideas we presented earlier. So, in order for you to develop a high-quality research topic, you’ll need to get specific and laser-focused on a specific context with specific variables of interest. In the video below, we explore some other important things you’ll need to consider when crafting your research topic.

Get 1-On-1 Help

If you’re still unsure about how to find a quality research topic within education, check out our Research Topic Kickstarter service, which is the perfect starting point for developing a unique, well-justified research topic.

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Open access
Published: 11 March 2019

Enhancing achievement and interest in mathematics learning through Math-Island

Charles Y. C. Yeh ORCID: orcid.org/0000-0003-4581-6575 1 ,
Hercy N. H. Cheng 2 ,
Zhi-Hong Chen 3 ,
Calvin C. Y. Liao 4 &
Tak-Wai Chan 5

Research and Practice in Technology Enhanced Learning volume 14 , Article number: 5 ( 2019 ) Cite this article

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Conventional teacher-led instruction remains dominant in most elementary mathematics classrooms in Taiwan. Under such instruction, the teacher can rarely take care of all students. Many students may then continue to fall behind the standard of mathematics achievement and lose their interest in mathematics; they eventually give up on learning mathematics. In fact, students in Taiwan generally have lower interest in learning mathematics compared to many other regions/countries. Thus, how to enhance students’ mathematics achievement and interest are two major problems, especially for those low-achieving students. This paper describes how we designed a game-based learning environment, called Math-Island , by incorporating the mechanisms of a construction management game into the knowledge map of the elementary mathematics curriculum. We also report an experiment conducted with 215 elementary students for 2 years, from grade 2 to grade 3. In this experiment, in addition to teacher-led instruction in the classroom, students were directed to learn with Math-Island by using their own tablets at school and at home. As a result of this experiment, we found that there is an increase in students’ mathematics achievement, especially in the calculation and word problems. Moreover, the achievements of low-achieving students in the experimental school outperformed the low-achieving students in the control school (a control group in another school) in word problems. Moreover, both the low-achieving students and the high-achieving students in the experimental school maintained a rather high level of interest in mathematics and in the system.

Introduction

Mathematics has been regarded as a fundamental subject because arithmetic and logical reasoning are the basis of science and technology. For this reason, educational authorities emphasize students’ proficiency in computational skills and problem-solving. Recently, the results of the Program for International Student Assessment (PISA) and the Trends in Mathematics and Science Study (TIMSS) in 2015 (OECD 2016 ; Mullis et al. 2016 ) revealed a challenge for Taiwan. Although Taiwanese students had higher average performance in mathematics literacy compared to students in other countries, there was still a significant percentage of low-achieving students in Taiwan. Additionally, most Taiwanese students show low levels of interest and confidence in learning mathematics (Lee 2012 ).

The existence of a significant percentage of low-achieving students is probably due to teacher-led instruction, which still dominates mathematics classrooms in most Asian countries. It should be noted that students in every classroom possess different abilities and hence demonstrate different achievements. Unfortunately, in teacher-led instruction, all the students are required to learn from the teacher in the same way at the same pace (Hwang et al. 2012 ). Low-achieving students, without sufficient time, are forced to receive knowledge passively. Barr and Tagg ( 1995 ) pointed out that it is urgent for low-achieving students to have more opportunities to learn mathematics at their own pace. Researchers suggested one-to-one technology (Chan et al. 2006 ) through which every student is equipped with a device to learn in school or at home seamlessly. Furthermore, they can receive immediate feedback from Math-Island, which supports their individualized learning actively and productively. Thus, this may provide more opportunities for helping low-achieving students improve their achievement.

The low-interest problem for almost all students in Taiwan is usually accompanied by low motivation (Krapp 1999 ). Furthermore, students with continuously low performance in mathematics may eventually lose their interest and refuse to learn further (Schraw et al. 2001 ). This is a severe problem. To motivate students to learn, researchers design educational games to provide enjoyable and engaging learning experiences (Kiili and Ketamo 2007 ). Some of these researchers found that game-based learning may facilitate students’ learning in terms of motivation and learning effects (Liu and Chu 2010 ), spatial abilities and attention (Barlett et al. 2009 ), situated learning, and problem-solving (Li and Tsai 2013 ). Given these positive results, we hope that our educational game can enhance and sustain the student’s interest in learning mathematics.

In fact, many researchers who endeavored to develop educational games for learning mathematics have shown that their games could facilitate mathematics performance, enjoyment, and self-efficacy (Ku et al. 2014 ; McLaren et al. 2017 ). Although some of the studies were conducted for as many as 4 months (e.g., Hanus and Fox 2015 ), one may still criticize them for the possibility that the students’ interest could be a novelty effect—meaning their interest will decrease as the feeling of novelty diminishes over time (Koivisto and Hamari 2014 ). Due to the limitations of either experimental time or sample sizes, most studies could not effectively exclude the novelty effect of games, unless they were conducted in a natural setting for a long time.

In this study, we collaborated with an experimental elementary school for more than 2 years. The mathematics teachers in the school adopted our online educational game, Math-Island . The students used their own tablet PCs to learn mathematics from the game in class or at home at their own pace. In particular, low-achieving students might have a chance to catch up with the other students and start to feel interested in learning mathematics. Most importantly, because the online educational game was a part of the mathematics curriculum, the students could treat the game as their ordinary learning materials like textbooks. In this paper, we reported a 2-year study, in which 215 second graders in the school adopted the Math-Island game in their daily routine. More specifically, the purpose of this paper was to investigate the effect of the game on students’ mathematics achievement. Additionally, we were also concerned about how well the low-achieving students learned, whether they were interested in mathematics and the game, and how their interest in mathematics compared with that of high-achieving students. In such a long-term study with a large sample size, it was expected that the novelty effect would be considerably reduced, allowing us to evaluate the effect of the educational game on students’ achievement and interest.

The paper is organized as follows. In the “ Related works ” section, we review related studies on computer-supported mathematics learning and educational games. In the “ Design ” section, the game mechanism and the system design are presented. In the “ Method ” section, we describe the research method and the procedures of this study. In the “ Results ” section, the research results about students’ achievement and interest are presented. In the “ Discussion on some features of this study ” section, we discuss the long-term study, knowledge map design, and the two game mechanisms. Finally, the summary of the current situation and potential future work is described in the “ Conclusion and future work ” section.

Related works

Computer-supported mathematics learning.

The mathematics curriculum in elementary schools basically includes conceptual understanding, procedural fluency, and strategic competence in terms of mathematical proficiency (see Kilpatrick et al. 2001 ). First, conceptual understanding refers to students’ comprehension of mathematical concepts and the relationships between concepts. Researchers have designed various computer-based scaffolds and feedback to build students’ concepts and clarify potential misconceptions. For example, for guiding students’ discovery of the patterns of concepts, Yang et al. ( 2012 ) adopted an inductive discovery learning approach to design online learning materials in which students were provided with similar examples with a critical attribute of the concept varied. McLaren et al. ( 2017 ) provided students with prompts to correct their common misconceptions about decimals. They conducted a study with the game adopted as a replacement for seven lessons of regular mathematics classes. Their results showed that the educational game could facilitate better learning performance and enjoyment than a conventional instructional approach.

Second, procedural fluency refers to the skill in carrying out calculations correctly and efficiently. For improving procedural fluency, students need to have knowledge of calculation rules (e.g., place values) and practice the procedure without mistakes. Researchers developed various digital games to overcome the boredom of practice. For example, Chen et al. ( 2012a , 2012b ) designed a Cross Number Puzzle game for practicing arithmetic expressions. In the game, students could individually or collaboratively solve a puzzle, which involved extensive calculation. Their study showed that the low-ability students in the collaborative condition made the most improvement in calculation skills. Ku et al. ( 2014 ) developed mini-games to train students’ mental calculation ability. They showed that the mini-games could not only improve students’ calculation performance but also increase their confidence in mathematics.

Third, strategic competence refers to mathematical problem-solving ability, in particular, word problem-solving in elementary education. Some researchers developed multilevel computer-based scaffolds to help students translate word problems to equations step by step (e.g., González-Calero et al. 2014 ), while other researchers noticed the problem of over-scaffolding. Specifically, students could be too scaffolded and have little space to develop their abilities. To avoid this situation, many researchers proposed allowing students to seek help during word problem-solving (Chase and Abrahamson 2015 ; Roll et al. 2014 ). For example, Cheng et al. ( 2015 ) designed a Scaffolding Seeking system to encourage elementary students to solve word problems by themselves by expressing their thinking first, instead of receiving and potentially abusing scaffolds.

Digital educational games for mathematics learning

Because mathematics is an abstract subject, elementary students easily lose interest in it, especially low-achieving students. Some researchers tailored educational games for learning a specific set of mathematical knowledge (e.g., the Decimal Points game; McLaren et al. 2017 ), so that students could be motivated to learn mathematics. However, if our purpose was to support a complete mathematics curriculum for elementary schools, it seemed impractical to design various educational games for all kinds of knowledge. A feasible approach is to adopt a gamified content structure to reorganize all learning materials. For example, inspired by the design of most role-playing games, Chen et al. ( 2012a , 2012b ) proposed a three-tiered framework of game-based learning—a game world, quests, and learning materials—for supporting elementary students’ enjoyment and goal setting in mathematics learning. Furthermore, while a game world may facilitate students’ exploration and participation, quests are the containers of learning materials with specific goals and rewards. In the game world, students receive quests from nonplayer virtual characters, who may enhance social commitments. To complete the quests, students have to make efforts to undertake learning materials. Today, quests have been widely adopted in the design of educational games (e.g., Azevedo et al. 2012 ; Hwang et al. 2015 ).

However, in educational games with quests, students still play the role of receivers rather than active learners. To facilitate elementary students’ initiative, Lao et al. ( 2017 ) designed digital learning contracts, which required students to set weekly learning goals at the beginning of a week and checked whether they achieved the goals at the end of the week. More specifically, when setting weekly goals, students had to decide on the quantity of learning materials that they wanted to undertake in the coming week. Furthermore, they also had to decide the average correctness of the tests that followed the learning materials. To help them set reasonable and feasible goals, the system provided statistics from the past 4 weeks. As a result, the students may reflect on how well they learned and then make appropriate decisions. After setting goals, students are provided with a series of learning materials for attempting to accomplish those goals. At the end of the week, they may reflect on whether they achieved their learning goals in the contracts. In a sense, learning contracts may not only strengthen the sense of commitment but also empower students to take more control of their learning.

In textbooks or classrooms, learning is usually predefined as a specific sequence, which students must follow to learn. Nevertheless, the structure of knowledge is not linear, but a network. If we could reorganize these learning materials according to the structure of knowledge, students could explore knowledge and discover the relationships among different pieces of knowledge when learning (Davenport and Prusak 2000 ). Knowledge mapping has the advantage of providing students concrete content through explicit knowledge graphics (Ebener et al. 2006 ). Previous studies have shown that the incorporation of knowledge structures into educational games could effectively enhance students’ achievement without affecting their motivation and self-efficacy (Chu et al. 2015 ). For this reason, this study attempted to visualize the structure of knowledge in an educational game. In other words, a knowledge map was visualized and gamified so that students could make decisions to construct their own knowledge map in games.

To enhance students’ mathematics achievement and interests, we designed the Math-Island online game by incorporating a gamified knowledge map of the elementary mathematics curriculum. More specifically, we adopt the mechanisms of a construction management game , in which every student owns a virtual island (a city) and plays the role of the mayor. The goal of the game is to build their cities on the islands by learning mathematics.

System architecture

The Math-Island game is a Web application, supporting cross-device interactions among students, teachers, and the mathematics content structure. The system architecture of the Math-Island is shown in Fig. 1 . The pedagogical knowledge and learning materials are stored in the module of digital learning content, organized by a mathematical knowledge map. The students’ portfolios about interactions and works are stored in the portfolio database and the status database. When a student chooses a goal concept in the knowledge map, the corresponding digital learning content is arranged and delivered to his/her browser. Besides, when the student is learning in the Math-Island, the feedback module provides immediate feedback (e.g., hints or scaffolded solutions) for guidance and grants rewards for encouragement. The learning results can also be shared with other classmates by the interaction module. In addition to students, their teachers can also access the databases for the students’ learning information. Furthermore, the information consists of the students’ status (e.g., learning performance or virtual achievement in the game) and processes (e.g., their personal learning logs). In the Math-Island, it is expected that students can manage their learning and monitor the learning results by the construction management mechanism. In the meantime, teachers can also trace students’ learning logs, diagnose their weaknesses from portfolio analysis, and assign students with specific tasks to improve their mathematics learning.

The system architecture of Math-Island

Knowledge map

To increase students’ mathematics achievement, the Math-Island game targets the complete mathematics curriculum of elementary schools in Taiwan, which mainly contains the four domains: numerical operation , quantity and measure , geometry , and statistics and probability (Ministry of Education of R.O.C. 2003 ). Furthermore, every domain consists of several subdomains with corresponding concepts. For instance, the domain of numerical operation contains four subdomains: numbers, addition, and subtraction for the first and second graders. In the subdomain of subtraction, there are a series of concepts, including the meaning of subtraction, one-digit subtraction, and two-digit subtraction. These concepts should be learned consecutively. In the Math-Island system, the curriculum is restructured as a knowledge map, so that they may preview the whole structure of knowledge, recall what they have learned, and realize what they will learn.

More specifically, the Math-Island system uses the representational metaphor of an “island,” where a virtual city is located and represents the knowledge map. Furthermore, the island comprises areas, roads, and buildings, which are the embodiments of domains, subdomains, and concepts in the curriculum, respectively. As shown in Fig. 2 , for example, in an area of numeral operation in Math-Island, there are many roads, such as an addition road and a subtraction road. On the addition road, the first building should be the meaning of addition, followed by the buildings of one-digit addition and then two-digit addition. Students can choose these buildings to learn mathematical concepts. In each building, the system provides a series of learning tasks for learning the specific concept. Currently, Math-Island provides elementary students with more than 1300 learning tasks from the first grade to the sixth grade, with more than 25,000 questions in the tasks.

The knowledge map

In Math-Island, a learning task is an interactive page turner, including video clips and interactive exercises for conceptual understanding, calculation, and word problem-solving. In each task, the learning procedure mainly consists of three steps: watching demonstrations, practicing examples, and getting rewards. First, students learn a mathematical concept by watching videos, in which a human tutor demonstrates examples, explains the rationale, and provides instructions. Second, students follow the instructions to answer a series of questions related to the examples in the videos. When answering questions, students are provided with immediate feedback. Furthermore, if students input wrong answers, the system provides multilevel hints so that they could figure out solutions by themselves. Finally, after completing learning tasks, students receive virtual money according to their accuracy rates in the tasks. The virtual money is used to purchase unique buildings to develop their islands in the game.

Game mechanisms

In the Math-Island game, there are two game mechanisms: construction and sightseeing (as shown in Fig. 3 ). The former is designed to help students manage their learning process, whereas the latter is designed to facilitate social interaction, which may further motivate students to better develop their cities. By doing so, the Math-Island can be regarded as one’s learning portfolio, which is a complete record that purposely collects information about one’s learning processes and outcomes (Arter and Spandel 2005 ). Furthermore, learning portfolios are a valuable research tool for gaining an understanding about personal accomplishments (Birgin and Baki 2007 ), because learning portfolios can display one’s learning process, attitude, and growth after learning (Lin and Tsai 2001 ). The appearance of the island reflects what students have learned and have not learned from the knowledge map. When students observe their learning status in an interesting way, they may be concerned about their learning status with the enhanced awareness of their learning portfolios. By keeping all activity processes, students can reflect on their efforts, growth, and achievements. In a sense, with the game mechanisms, the knowledge map can be regarded as a manipulatable open learner model, which not only represents students’ learning status but also invites students to improve it (Vélez et al. 2009 ).

Two game mechanisms for Math-Island

First, the construction mechanism allows students to plan and manage their cities by constructing and upgrading buildings. To do so, they have to decide which buildings they want to construct or upgrade. Then, they are required to complete corresponding learning tasks in the building to determine which levels of buildings they can construct. As shown in Fig. 4 , the levels of buildings depend on the completeness of a certain concept, compared with the thresholds. For example, when students complete one third of the learning tasks, the first level of a building is constructed. Later, when they complete two thirds of the tasks, the building is upgraded to the second level. After completing all the tasks in a building, they also complete the final level and are allowed to construct the next building on the road. Conversely, if students failed the lowest level of the threshold, they might need to watch the video and/or do the learning tasks again. By doing so, students can make their plans to construct the buildings at their own pace. When students manage their cities, they actually attempt to improve their learning status. In other words, the construction mechanism offers an alternative way to guide students to regulate their learning efforts.

Screenshots of construction and sightseeing mechanisms in Math-Island

Second, the sightseeing mechanism provides students with a social stage to show other students how well their Math-Islands have been built. This mechanism is implemented as a public space, where other students play the role of tourists who visit Math-Island. In other words, this sightseeing mechanism harnesses social interaction to improve individual learning. As shown in Fig. 4 , because students can construct different areas or roads, their islands may have different appearances. When students visit a well-developed Math-Island, they might have a positive impression, which may facilitate their self-reflection. Accordingly, they may be willing to expend more effort to improve their island. On the other hand, the student who owns the island may also be encouraged to develop their island better. Furthermore, when students see that they have a completely constructed building on a road, they may perceive that they are good at these concepts. Conversely, if their buildings are small, the students may realize their weaknesses or difficulties in these concepts. Accordingly, they may be willing to make more effort for improvement. On the other hand, the student who owns the island may also be encouraged to develop their island better. In a word, the visualization may play the role of stimulators, so that students may be motivated to improve their learning status.

This paper reported a 2-year study in which the Math-Island system was adopted in an elementary school. The study addressed the following two research questions: (1) Did the Math-Island system facilitate students’ mathematics achievement in terms of conceptual understanding, calculating, and word problem-solving? In particular, how was the mathematics achievement of the low-achieving students? (2) What was students’ levels of interest in mathematics and the system, particularly that of low-achieving students?

Participants

The study, conducted from June 2013 to June 2015, included 215 second graders (98 females and 117 males), whose average age was 8 years old, in an elementary school located in a suburban region of a northern city in Taiwan. The school had collaborated with our research team for more than 2 years and was thus chosen as an experimental school for this study. In this school, approximately one third of the students came from families with a low or middle level of socioeconomic status. It was expected that the lessons learned from this study could be applicable to other schools with similar student populations in the future. The parents were supportive of this program and willing to provide personal tablets for their children (Liao et al. 2017 ). By doing so, the students in the experimental school were able to use their tablets to access the Math-Island system as a learning tool at both school and home. To compare the students’ mathematics achievement with a baseline, this study also included 125 second graders (63 females and 62 males) from another school with similar socioeconomic backgrounds in the same region of the city as a control school. The students in the control school received only conventional mathematics instruction without using the Math-Island system during the 2-year period.

Before the first semester, a 3-week training workshop was conducted to familiarize the students with the basic operation of tablets and the Math-Island system. By doing so, it was ensured that all participants had similar prerequisite skills. The procedure of this study was illustrated in Table 1 . At the beginning of the first semester, a mathematics achievement assessment was conducted as a pretest in both the experimental and the control school to examine the students’ initial mathematics ability as second graders. From June 2013 to June 2015, while the students in the control school learned mathematics in a conventional way, the students in the experimental school learned mathematics not only in mathematics classes but also through the Math-Island system. Although the teachers in the experimental school mainly adopted lectures in mathematics classes, they used the Math-Island system as learning materials at school and for homework. At the same time, they allowed the students to explore the knowledge map at their own pace. During the 2 years, every student completed 286.78 learning tasks on average, and each task took them 8.86 min. Given that there were 344 tasks for the second and third graders, the students could finish 83.37% of tasks according to the standard progress. The data also showed that the average correctness rate of the students was 85.75%. At the end of the second year, another mathematics achievement assessment was administered as a posttest in both schools to evaluate students’ mathematics ability as third graders. Additionally, an interest questionnaire was employed in the experimental school to collect the students’ perceptions of mathematics and the Math-Island system. To understand the teachers’ opinions of how they feel about the students using the system, interviews with the teachers in the experimental school were also conducted.

Data collection

Mathematics achievement assessment.

To evaluate the students’ mathematics ability, this study adopted a standardized achievement assessment of mathematics ability (Lin et al. 2009 ), which was developed from a random sample of elementary students from different counties in Taiwan to serve as a norm with appropriate reliability (the internal consistency was 0.85, and the test-retest reliability was 0.86) and validity (the correlation by domain experts in content validity was 0.92, and the concurrent validity was 0.75). As a pretest, the assessment of the second graders consisted of 50 items, including conceptual understanding (23 items), calculating (18 items), and word problem-solving (9 items). As a posttest, the assessment of the third graders consisted of 60 items, including conceptual understanding (18 items), calculating (27 items), and word problem-solving (15 items). The scores of the test ranged from 0 to 50 points. Because some students were absent during the test, this study obtained 209 valid tests from the experimental school and 125 tests from the control school.

Interest questionnaire

The interest questionnaire comprised two parts: students’ interest in mathematics and the Math-Island system. Regarding the first part, this study adopted items from a mathematics questionnaire of PISA and TIMSS 2012 (OECD 2013 ; Mullis et al. 2012 ), the reliability of which was sound. This part included three dimensions: attitude (14 items, Cronbach’s alpha = .83), initiative (17 items, Cronbach’s alpha = .82), and confidence (14 items Cronbach’s alpha = .72). Furthermore, the dimension of attitude was used to assess the tendency of students’ view on mathematics. For example, a sample item of attitudes was “I am interested in learning mathematics.” The dimension of initiatives was used to assess how students were willing to learn mathematics actively. A sample item of initiatives was “I keep studying until I understand mathematics materials.” The dimension of confidences was used to assess students’ perceived mathematics abilities. A sample item was “I am confident about calculating whole numbers such as 3 + 5 × 4.” These items were translated to Chinese for this study. Regarding the second part, this study adopted self-made items to assess students’ motivations for using the Math-Island system. This part included two dimensions: attraction (8 items) and satisfaction (5 items). The dimension of attraction was used to assess how well the system could attract students’ attention. A sample item was “I feel Math-island is very appealing to me.” The dimension of satisfaction was used to assess how the students felt after using the system. A sample item was “I felt that upgrading the buildings in my Math-Island brought me much happiness.” These items were assessed according to a 4-point Likert scale, ranging from “strongly disagreed (1),” “disagreed (2),” “agreed (3),” and “strongly agreed (4)” in this questionnaire. Due to the absences of several students on the day the questionnaire was administered, there were only 207 valid questionnaires in this study.

Teacher interview

This study also included teachers’ perspectives on how the students used the Math-Island system to learn mathematics in the experimental school. This part of the study adopted semistructured interviews of eight teachers, which comprised the following three main questions: (a) Do you have any notable stories about students using the Math-Island system? (b) Regarding Math-Island, what are your teaching experiences that can be shared with other teachers? (c) Do you have any suggestions for the Math-Island system? The interview was recorded and transcribed verbatim. The transcripts were coded and categorized according to the five dimensions of the questionnaire (i.e., the attitude, initiative, and confidence about mathematics, as well as the attraction and satisfaction with the system) as additional evidence of the students’ interest in the experimental school.

Data analysis

For the first research question, this study conducted a multivariate analysis of variance (MANOVA) with the schools as a between-subject variable and the students’ scores (conceptual understanding, calculating, and word problem-solving) in the pre/posttests as dependent variables. Moreover, this study also conducted a MANOVA to compare the low-achieving students from both schools. In addition, the tests were also carried out to compare achievements with the norm (Lin et al. 2009 ). For the second research question, several z tests were used to examine how the interests of the low-achieving students were distributed compared with the whole sample. Teachers’ interviews were also adopted to support the results of the questionnaire.

Mathematics achievement

To examine the homogeneity of the students in both schools in the first year, the MANOVA of the pretest was conducted. The results, as shown in Table 2 , indicated that there were no significant differences in their initial mathematics achievements in terms of conceptual understanding, calculating, and word problem-solving (Wilks’ λ = 0.982, F (3330) = 2.034, p > 0.05). In other words, the students of both schools had similar mathematics abilities at the time of the first mathematics achievement assessment and could be fairly compared.

At the end of the fourth grade, the students of both schools received the posttest, the results of which were examined by a MANOVA. As shown in Table 3 , the effect of the posttest on students’ mathematics achievement was significant (Wilks’ λ = 0.946, p < 0.05). The results suggested that the students who used Math-Island for 2 years had better mathematics abilities than those who did not. The analysis further revealed that the univariate effects on calculating and word problem-solving were significant, but the effect on conceptual understanding was insignificant. The results indicated that the students in the experimental school outperformed their counterparts in terms of the procedure and application of arithmetic. The reason may be that the system provided students with more opportunities to do calculation exercises and word problems, and the students were more willing to do these exercises in a game-based environment. Furthermore, they were engaged in solving various exercises with the support of immediate feedback until they passed the requirements of every building in their Math-Island. However, the students learned mathematical concepts mainly by watching videos in the system, which provided only demonstrations like lectures in conventional classrooms. For this reason, the effect of the system on conceptual understanding was similar to that of teachers’ conventional instruction.

Furthermore, to examine the differences between the low-achieving students in both schools, another MANOVA was also conducted on the pretest and the posttest. The pretest results indicated that there were no significant differences in their initial mathematics achievement in terms of conceptual understanding, calculating, and word problem-solving (Wilks’ λ = 0.943, F (3110) = 2.210, p > 0.05).

The MANOVA analysis of the posttest is shown in Table 4 . The results showed that the effect of the system on the mathematics achievement of low-achieving students was significant (Wilks’ λ = 0.934, p < 0.05). The analysis further revealed that only the univariate effect on word problem-solving was significant. The results suggested that the low-achieving students who used Math-Island for 2 years had better word problem-solving ability than those students in the control school, but the effect on conceptual understanding and procedural fluency was insignificant. The results indicated that the Math-Island system could effectively enhance low-achieving students’ ability to solve word problems.

Because the mathematics achievement assessment was a standardized achievement assessment (Lin et al. 2009 ), the research team did a further analysis of the assessments by comparing the results with the norm. In the pretest, the average score of the control school was the percentile rank of a score (PR) 55, but their average score surprisingly decreased to PR 34 in the posttest. The results confirmed the fact that conventional mathematics teaching in Taiwan might result in an M-shape distribution, suggesting that low-achieving students required additional learning resources. Conversely, the average score of the experimental school was PR 48 in the pretest, and their score slightly decreased to PR 44 in the posttest. Overall, both PR values were decreasing, because the mathematics curriculum became more and more difficult from the second grade to the fourth grade. However, it should be noted that the experimental school has been less affected, resulting in a significant difference compared with the control school (see Table 5 ). Notably, the average score of word problem-solving in the posttest of the experimental school was PR 64, which was significantly higher than the nationwide norm ( z = 20.8, p < .05). The results were consistent with the univariate effect of the MANOVA on word problem-solving, suggesting that the Math-Island system could help students learn to complete word problems better. This may be because the learning tasks in Math-Island provided students with adequate explanations for various types of word problems and provided feedback for exercises.

To examine whether the low-achieving students had low levels of interest in mathematics and the Math-Island system, the study adopted z tests on the data of the interest questionnaire. Table 5 shows the descriptive statistics and the results of the z tests. Regarding the interest in mathematics, the analysis showed that the interest of the low-achieving students was similar to that of the whole sample in terms of attitude, initiative, and confidence. The results were different from previous studies asserting that low-achieving students tended to have lower levels of interest in mathematics (Al-Zoubi and Younes 2015 ). The reason was perhaps that the low-achieving students were comparably motivated to learn mathematics in the Math-Island system. As a result, a teacher ( #T-301 ) said, “some students would like to go to Math-Island after school, and a handful of students could even complete up to forty tasks (in a day),” implying that the students had a positive attitude and initiative related to learning mathematics.

Another teacher ( T-312 ) also indicated “some students who were frustrated with math could regain confidence when receiving the feedback for correct answers in the basic tasks. Thanks to this, they would not feel high-pressure when moving on to current lessons.” In a sense, the immediate feedback provided the low-achieving students with sufficient support and may encourage them to persistently learn mathematics. Furthermore, by learning individually after class, they could effectively prepare themselves for future learning. The results suggested that the system could serve as a scaffolding on conventional instruction for low-achieving students. The students could benefit from such a blended learning environment and, thus, build confidence in mathematics by learning at their own paces.

The low-achieving students as a whole were also attracted to the system and felt satisfaction from it. Teacher ( #T-307 ) said that, “There was a hyperactive and mischievous student in my class. However, when he was alone, he would go on to Math-Island, concentrating on the tasks quietly. He gradually came to enjoy learning mathematics. It seemed that Math-Island was more attractive to them than a lecture by a teacher. I believed that students could be encouraged, thus improve their ability and learn happily.” Another teacher ( #T-304 ) further pointed out that, “For students, they did not only feel like they were learning mathematics because of the game-based user interface. Conversely, they enjoyed the contentment when completing a task, as if they were going aboard to join a competition.” In teachers’ opinions, such a game-based learning environment did not disturb their instruction. Instead, the system could help the teachers attract students’ attention and motivate them to learn mathematics actively because of its appealing game and joyful learning tasks. Furthermore, continuously overcoming the tasks might bring students a sense of achievement and satisfaction.

Discussion on some features of this study

In addition to the enhancement of achievement and interest, we noticed that there are some features in this study and our design worth some discussion.

The advantages of building a long-term study

Owing to the limitations of deployment time and sample sizes, it is hard for most researchers to conduct a longitudinal study. Fortunately, we had a chance to maintain a long-term collaboration with an experimental school for more than 2 years. From this experiment, we notice that there are two advantages to conducting a long-term study.

Obtaining substantial evidence from the game-based learning environment

The research environment was a natural setting, which could not be entirely controlled and manipulated like most experiments in laboratories. However, this study could provide long-term evidence to investigate how students learned in a game-based learning environment with their tablets. It should be noted that we did not aim to replace teachers in classrooms with the Math-Island game. Instead, we attempted to establish an ordinary learning scenario, in which the teachers and students regarded the game as one of the learning resources. For example, teachers may help low-achieving students to improve their understanding of a specific concept in the Math-Island system. When students are learning mathematics in the Math-Island game, teachers may take the game as a formative assessment and locate students’ difficulties in mathematics.

Supporting teachers’ instructions and facilitating students’ learning

The long-term study not only proved the effectiveness of Math-Island but also offered researchers an opportunity to determine teachers’ roles in such a computer-supported learning environment. For example, teachers may encounter difficulties in dealing with the progress of both high- and low-achieving students. How do they take care of all students with different abilities at the same time? Future teachers may require more teaching strategies in such a self-directed learning environment. Digital technology has an advantage in helping teachers manage students’ learning portfolios. For example, the system can keep track of all the learning activities. Furthermore, the system should provide teachers with monitoring functions so that they know the average status of their class’s and individuals’ learning progress. Even so, it is still a challenge for researchers to develop a well-designed visualization tool to support teachers’ understanding of students’ learning conditions and their choice of appropriate teaching strategies.

Incorporating a gamified knowledge map of the elementary mathematics curriculum

Providing choices of learning paths.

Math-Island uses a representational metaphor of an “island,” where a virtual city is located and represents the knowledge map. Furthermore, the island comprises areas, roads, and buildings, which are the embodiments of domains, subdomains, and concepts in the curriculum, respectively. Because the gamified knowledge map provides students with multiple virtual roads to learn in the system, every student may take different routes. For instance, some students may be more interested in geometry, while others may be confident in exploring the rules of arithmetic. In this study, we noticed that the low-achieving students needed more time to work on basic tasks, while high-achieving students easily passed those tasks and moved on to the next ones. As a result, some of the high-achieving students had already started to learn the materials for the next grade level. This was possibly because high-achieving students were able to respond well to challenging assignments (Singh 2011 ). Therefore, we should provide high-achieving students with more complex tasks to maintain their interest. For example, Math-Island should provide some authentic mathematical problems as advanced exercises.

Visualizing the learning portfolio

In this study, we demonstrated a long-term example of incorporating a gamified knowledge map in an elementary mathematical curriculum. In the Math-Island game, the curriculum is visualized as a knowledge map instead of a linear sequence, as in textbooks. By doing so, students are enabled to explore relationships in the mathematics curriculum represented by the knowledge map; that is, the structure of the different roads on Math-Island. Furthermore, before learning, students may preview what will be learned, and after learning, students may also reflect on how well they learned. Unlike traditional lectures or textbooks, in which students could only follow a predefined order to learn knowledge without thinking why they have to learn it, the knowledge map allows students to understand the structure of knowledge and plan how to achieve advanced knowledge. Although the order of knowledge still remains the same, students take primary control of their learning. In a sense, the knowledge map may liberate elementary students from passive learning.

Adopting the mechanisms of a construction management game

This 2-year study showed that the adaptation of two game mechanisms, construction and sightseeing, into the elementary mathematical curriculum could effectively improve students’ learning achievement. The reason may be that students likely developed interests in using Math-Island to learn mathematics actively, regardless of whether they are high- and low-achieving students.

Gaining a sense of achievement and ownership through the construction mechanism

Regardless of the construction mechanism, Math-Island allows students to plan and manage their cities by constructing and upgrading buildings. Math-Island took the advantages of construction management games to facilitate elementary students’ active participation in their mathematical learning. Furthermore, students may manage their knowledge by planning and constructing of buildings on their virtual islands. Like most construction management games, students set goals and make decisions so that they may accumulate their assets. These assets are not only external rewards but also visible achievements, which may bring a sense of ownership and confidence. In other words, the system gamified the process of self-directed learning.

Demonstrating learning result to peers through the sightseeing mechanism

As for the sightseeing mechanism, in conventional instruction, elementary students usually lack the self-control to learn knowledge actively (Duckworth et al. 2014 ) or require a social stage to show other students, resulting in low achievement and motivation. On the other hand, although previous researchers have already proposed various self-regulated learning strategies (such as Taub et al. 2014 ), it is still hard for children to keep adopting specific learning strategies for a long time. For these reasons, this study uses the sightseeing mechanism to engage elementary students in a social stage to show other students how well their Math-Islands have been built. For example, in Math-Island, although the students think that they construct buildings in their islands, they plan the development of their knowledge maps. After learning, they may also reflect on their progress by observing the appearance of the buildings.

In brief, owing to the construction mechanism, the students are allowed to choose a place and build their unique islands by learning concepts. During the process, students have to do the learning task, get feedback, and get rewards, which are the three major functions of the construction functions. In the sightseeing mechanism, students’ unique islands (learning result) can be shared and visited by other classmates. The student’s Math-Island thus serves as a stage for showing off their learning results. The two mechanisms offer an incentive model connected to the game mechanism’s forming a positive cycle: the more the students learn, the more unique islands they can build, with more visitors.

Conclusion and future work

This study reported the results of a 2-year experiment with the Math-Island system, in which a knowledge map with extensive mathematics content was provided to support the complete elementary mathematics curriculum. Each road in Math-Island represents a mathematical topic, such as addition. There are many buildings on each road, with each building representing a unit of the mathematics curriculum. Students may learn about the concept and practice it in each building while being provided with feedback by the system. In addition, the construction management online game mechanism is designed to enhance and sustain students’ interest in learning mathematics. The aim of this study was not only to examine whether the Math-Island system could improve students’ achievements but also to investigate how much the low-achieving students would be interested in learning mathematics after using the system for 2 years.

As for enhancing achievement, the result indicated that the Math-Island system could effectively improve the students’ ability to calculate expressions and solve word problems. In particular, the low-achieving students outperformed those of the norm in terms of word problem-solving. For enhancing interest, we found that both the low-achieving and the high-achieving students in the experimental school, when using the Math-Island system, maintained a rather high level of interest in learning mathematics and using the system. The results of this study indicated some possibility that elementary students could be able to learn mathematics in a self-directed learning fashion (Nilson 2014 ; Chen et al. 2012a , b ) under the Math-Island environment. This possibility is worthy of future exploration. For example, by analyzing student data, we can investigate how to support students in conducting self-directed learning. Additionally, because we have already collected a considerable amount of student data, we are currently employing machine learning techniques to improve feedback to the students. Finally, to provide students appropriate challenges, the diversity, quantity, and difficulty of content may need to be increased in the Math-Island system.

Abbreviations

Program for International Student Assessment

The percentile rank of a score

Trends in Mathematics and Science Study

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Vélez, J., Fabregat, R., Bull, S., & Hueva, D. (2009). The potential for open learner models in adaptive virtual learning environments. In S. D. Craig & D. Dicheva (Eds.), AIED 2009: 14th International Conference on Artificial Intelligence in Education Workshops Proceedings Volume 8 (pp. 11–20). Brighton: International AIED Society.

Yang, E. F. Y., Cheng, H. N. H., Ching, E., & Chan, T. W. (2012). Variation based discovery learning design in 1 to 1 mathematics classroom. In G. Biswas, L.-H. Wong, T. Hirashima, & W. Chen (Eds.), Proceedings of the 20th International Conference on Computers in Education (pp. 811–815). Singapore: Asia-Pacific Society for Computers in Education.

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Acknowledgements

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors would like to thank the Ministry of Science and Technology of the Republic of China, Taiwan, for financial support (MOST 106-2511-S-008-003-MY3), and Research Center for Science and Technology forLearning, National Central University, Taiwan.

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Charles Y. C. Yeh

Central China Normal University, Science Hall 419, No. 152, Luoyu Road, Wuhan, 430079, China

Hercy N. H. Cheng

National Taiwan Normal University, No.162, Sec. 1, Heping E. Rd., Taipei City, 10610, Taiwan, Republic of China

Zhi-Hong Chen

National Taipei University of Nursing and Health Sciences, No.365, Mingde Rd., Beitou Dist., Taipei City, 11219, Taiwan, Republic of China

Calvin C. Y. Liao

Tak-Wai Chan

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CYCY contributed to the study design, data acquisition and analysis, mainly drafted the manuscript and execution project. HNHC was involved in data acquisition, revision of the manuscript and data analysis.ZHC was contributed to the study idea and drafted the manuscript. CCYL of this research was involved in data acquisition and revision of the manuscript. TWC was project manager and revision of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Charles Y. C. Yeh .

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Authors’ information.

Charles Y.C. Yeh is currently an PhD student in Graduate Institute of Network Learning Technology at National Central University. The research interests include one-to-one learning environments and game-based learning.

Hercy N. H. Cheng is currently an associate professor and researcher in National Engineering Research Center for E-Learning at Central China Normal University, China. His research interests include one-to-one learning environments and game-based learning.

Zhi-Hong Chen is an associate professor in Graduate Institute of Information and Computer Education at National Taiwan Normal University. His research interests focus on learning technology and interactive stories, technology intensive language learning and game-based learning.

Calvin C. Y. Liao is currently an Assistant Professor and Dean’s Special Assistant in College of Nursing at National Taipei University of Nursing and Health Sciences in Taiwan. His research focuses on computer-based language learning for primary schools. His current research interests include a game-based learning environment and smart technology for caregiving & wellbeing.

Tak-Wai Chan is Chair Professor of the Graduate Institute of Network Learning Technology at National Central University in Taiwan. He has worked on various areas of digital technology supported learning, including artificial intelligence in education, computer supported collaborative learning, digital classrooms, online learning communities, mobile and ubiquitous learning, digital game based learning, and, most recently, technology supported mathematics and language arts learning.

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Yeh, C.Y.C., Cheng, H.N.H., Chen, ZH. et al. Enhancing achievement and interest in mathematics learning through Math-Island. RPTEL 14 , 5 (2019). https://doi.org/10.1186/s41039-019-0100-9

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Mathematics learning
Game-based learning
Construction management games

Young Students Gravitate to Math. How Teachers Can Build on That Curiosity

Zachary Champagne’s 3rd and 4th graders figure out early on that this math class will be different when their teacher tells them: “I don’t care about the answer.”

The goal is to shift his elementary students’ thinking from some numerical endgame toward the problem-solving process itself. In his more than two decades as a classroom teacher and math researcher, Champagne has found this strategy can be a balm for math anxiety, spur students’ creativity, and pique their curiosity about a subject many find boring and irrelevant.

Telling students the answer doesn’t matter—or throwing it out early on, then working backwards, another of Champagne’s go-to strategies—"can reframe the way we think about mathematics,” said Champagne, who teaches at The Discovery School, a private school in Jacksonville, Fla.

Photo illustration of chemistry teacher working with young student.

“If we’re thinking about math where the solving is actually the interesting, important part, it frees kids from the stigma of ‘I’m not good at this because I always get things wrong,’” said Champagne, who spent more than a decade working in Florida’s Duval County public schools and served as a math researcher at Florida State University.

This problem-solving or open-ended approach, which emphasizes flexible thinking and real-world situations, is a powerful strategy for engaging the youngest learners in math . Kindergarten through 5th grade is an important time for building students’ skills, confidence, and interest in math—the critical building blocks for middle- and high-school-level math and science, experts say.

Though the approach has been around for decades, districts are striving to incorporate more real-world problem-solving into math class in recent years. California, for instance, recently adopted a controversial framework that puts a heavy emphasis on the approach . And there’s new urgency to get students motivated in math as federal data show students’ math achievement plummeting.

The vast majority of educators—92 percent—say students are more motivated to learn math and science if teachers employ a problem-solving approach, according to a survey of 1,183 district and school leaders and teachers, conducted by the EdWeek Research Center in April. Despite the fact that this approach is highly popular among educators, many have not been trained in how to use it, the same survey found.

Does using real-world problems motivate students?

The Canadian province of Quebec has been using a problem-based approach for decades—and it helps students connect with math and understand how to use it in the real world, said Krista Muis, a professor at McGill University in Montreal, who has studied student perceptions of the teaching strategy.

“When you look at the motivational profiles of students who are just given traditional word problems, or more standard types of math problems, or math content, their motivation is really low when it comes to the value of what they’re learning,” Muis said. “The main question they ask is, ‘why should I care? How is this relevant to me? How am I ever going to use this?’”

But when students tackle common real problems—a favorite of Muis’ asks elementary schoolers to map out the trick-or-treating route that nets the most Halloween candy—they get excited.

“They see the value in it,” Muis said. “And they’re fun problems. They can do them in groups together collaboratively, they can do them individually.”

Quebec students’ higher motivation in math may explain why the province outperforms the rest of Canada—and the United States— on the Trends in International Mathematics and Science Study or TIMMS , Muis said.

In 2019, the most recent year the test was given, Quebec’s 4th graders didn’t perform statistically differently from their U.S. counterparts in math. But 8th graders from the province scored significantly better than their U.S. peers . One reason may be the increased motivation to learn math that Muis believes stems from exposing students to a problem-solving approach early on.

To be sure, a problem-based or open-ended approach to teaching math is often pitted against more traditional, procedural methods—think of the math worksheets full of equations without context.

But many experts and educators see value in exposing students to both strategies.

“I think, really, these things can mutually support one another. And both are necessary,” said Julia Aguirre, a professor and the faculty director of teacher certification programs at the University of Washington Tacoma. “I think we can all agree that a math class that’s only about worksheets would not be a very fulfilling or interesting math class.”

Promote young students’ natural curiosity and creativity

The approach is most effective when teachers apply it to students’ existing interests.

That’s especially important for elementary school students, who start school with a natural curiosity that often dissipates by the time they get to high school, said Molly Daley, a regional math coordinator for Education Service District 112, which serves about 30 districts near Vancouver, Wash.

Thinking about “math is a universal human behavior, and people of all ages engage in math for their own purposes,” Daley said.

Students are using math when they play games and make crafts, she said, or even just look at the landscape.

For instance, a preschool teacher might take a picture of the classroom shoe rack and ask students questions like: How many shoes are there? What patterns do you notice? What shapes do you see?

“If we can honor the math that kids are doing beyond the classroom, then we’re more likely to create a mathematical connection and really allow every person to see how math is not just useful but enjoyable,” Daley said.

In Champagne’s mixed age classroom of 3rd and 4th graders in Florida—which he co-teaches with another educator—students turn to math early in the day, the time when younger students tend to be most able to focus on the subject, in Champagne’s view.

Champagne typically kicks off with a 10- or 15-minute math routine as a warm-up. That might be a “number talk” in which Champagne will put an equation on the board, say 29 plus 15, and then students will solve the problem in their heads.

They’ll spend the next few minutes comparing strategies for finding a solution. One student might have added 30 plus 15 and subtracted one, while another might have added 9 and 5, then 30.

The exercise is aimed at promoting flexibility and the idea that there are multiple ways to solve a problem, Champagne said. It lets students know: “I don’t have to revert to just one strategy. I can think about it in different ways,” he said. The idea is to gives students a chance to use their creative thinking skills in math class.

Students still learn the basics, but lessons are structured so that students can see how seemingly simple problems play out in different, real-world contexts. For instance, if students are learning about dividing with remainders, they may consider how four people can share 31 balloons. In that case, each person gets seven balloons, with three left over.

But what if it were 31 dollars instead of balloons? How does that change the answer? Or what if 31 people needed to get somewhere in four cars? How could they divide up?

Problems can also get more complex—and interdisciplinary—as students advance in elementary school.

Teachers need more training in the problem-solving approach

Tackling big problems with no clear answer is another way to engage elementary school students in math.

Last school year, Aguirre worked with Janaki Nagarajan’s 3rd graders outside Seattle on a project involving a real-life problem with salmon the students had raised and planned to release.

Inexplicably, the fish began dying. So Nagarajan’s students used mathematical modeling to estimate how quickly they were losing salmon, answering questions like: Will we have enough salmon for each student on release day? What can we do if we don’t? Students worked on the problem in groups, and then presented their answers. The class voted on the solution they thought would work best.

The project was “really engaging,” said Nagarajan. She believes that students will be motivated to learn math if they “feel the skills have some purpose outside the classroom.”

But she thinks that many teachers don’t know how common procedures learned in math class could be applied in the real world, so they struggle to make those connections for their students.

Nagarajan began teaching in Renton, a different, Seattle-area school district this school year, largely because it provides more support for teachers to use the real-world problem-solving approach in elementary school math.

Though the approach was encouraged in her previous school, Nagarajan said her new district uses a curriculum that embraces problem-solving and provides coaches who can help her implement the strategy.

Professional development in the problem-solving approach remains uneven. About one in five educators said they “completely agree” that their districts have offered deep and sustained professional development into how to teach math and science from a problem-solving perspective, while just over 40 percent said they disagree—at least somewhat—that they’ve been offered that level of support.

That professional development can be particularly important for elementary school teachers who typically “aren’t math specialists, right? They are generalists,” said Muis of McGill University. “Often, teachers who are not comfortable with mathematics don’t necessarily understand it fully themselves. And so when you bring in complexity that scares them. And then you see teachers kind of stepping back going, ‘I can’t really teach this, I don’t really know what I’m doing.’”

And the approach requires teachers to respond to what students see or notice, which can be stressful for some, Daley said.

“We can get too hyper focused on ‘this is my goal’” in a particular lesson, she said. That can look like: “We’re learning about fractions, but the student made a comment about multiplication. I gotta ignore that.’”

Teachers need to learn not to be afraid if students go off script, Daley said. A problem-solving approach is about “creating more space for students’ ideas and students’ thinking versus just letting your own dominate.”

Making that shift isn’t easy. But if teachers are successful, they positively shape their students’ relationship with math, potentially for years, Daley said.

“Especially with younger learners, when we’re following their lead, that’s how we’re going to tap into their connection and their motivation to engage with math and build up their sense of themselves as a mathematician,” she said.

Coverage of problem solving and student motivation is supported in part by a grant from The Lemelson Foundation, at www.lemelson.org . Education Week retains sole editorial control over the content of this coverage.

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15 Best & Fun Math Projects for Students

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Super Easy and Super Fun Math Project Ideas for Grade 1 Students

Exploratory ideas for math projects for grade 2 students, project-based learning math ideas for grade 3 students, math project-based learning ideas for grade 4 students, advanced math projects for students in grade 5, frequently asked questions (faqs).

Math projects for students are a great way to get kids interested in math . They can be used to teach new concepts, review old ones, or just provide some fun and engaging math practice. There are tons of great math projects out there, but we’ve compiled a list of fifteen easy and engaging math projects for elementary school students—the best of the best!

$Abacus with beads of different colors$

1. Scoop and Cone Matching Game

What you need:

Cones and scoops made from felt or cardstock
Marker or sketch pens

Description:

Write a number on the cone. Write different combinations of addition and subtraction equations to represent the number on the scoop.

Students have to solve the equations and match the correct scoop to the cone.

Skills Learned:

Addition, subtraction, and the concept of equations

2. More or Less Dot Games

Ten frame cards
A set of dots (or colorful buttons or plastic corks to use as dots)
A deck of cards

Give a student a card and add some dots to it. Ask them, “How many dots are there on the card?” Once students master this, you may ask them, “What number is one more/one less?” You can also give them two cards and ask which one has more or less dots.

For two or more students, card games are a gold mine! Take a deck of cards. Snip off their corners with numerals written on them. Place the cards with their face downward. Ask each student to turn up a card. Ask them to tell whose card is “more” or “less.” Each correct answer wins them a point!

Visualizing numbers, understanding the concept of more or less, comparing numbers, addition, and subtraction

3. Shape Graphs

Different geometric shapes in different colors and sizes
Graph papers with large rows and columns (with rows mentioning shape names and columns mentioning numbers)
Some crayons

Distribute some graph paper among the children. Spread out some shapes in front of them. They have to find out how many shapes of each type there are and color that many boxes of relevant columns.

Recognition of geometric shapes by their names, and understanding and representing data in pictorial form

$Drawing line on a sheet of paper with a ruler$

4. Elementary Architects

Instructions and photos of room designing projects
2-page student project sheet to promote reading in math
Note-taking forms
Sample blueprints for reference
Brainstorming sheet
Grid paper templates

Ask the students to design their rooms, calculate areas, and estimate flooring needs by reading the instructions, looking at the photos, and taking notes.

Students love to play architects. Allow them sufficient room for being creative to promote their spatial awareness.

Reading comprehension, estimation, area, and perimeter calculation

5. M&M’s Math Game

A box of colorful m&m’s
Graph papers for kids

Let your students dig into the box of m&m’s and take a few each. They have to count how many m&m’s of each color they got. If they count m&m’s of each color correctly, they can eat them! Otherwise, they have to return the m&m’s to the box and try again!

As they master their skills, you can take this math game to the next level. They can make a graph using graph paper and crayons! You may have to help them label the graph and the graphing part itself.

Counting, addition, making graphs

6. Hit a Home Run for Math Fact Fluency

DIY baseball game board with math facts
Number cards
Counters to use as baseball players—9 for each team

Write the numbers 1 to 9 in one row and 0 in the next row to make a baseball diamond.

Help your students write math facts such as doubles (2 + 2, 3 + 3, etc.), near doubles (9 + 8), addition/subtraction of 10 (8 + 2, 5 + 5), and related subtraction facts (7 – 3, 9 – 6) on the number cards.

To play, have each student roll two dice. They get to move one of their baseball players the number of spaces corresponding to the first die and then answer the math fact that corresponds to the number they landed on. If they answer correctly, they get to roll again. The first player to get three of their baseball players “home” wins!

Math facts fluency, addition, subtraction

$A tamarin monkey on a tree branch$

7. Place Value in the Wild Math Project

Digital and printable version of a student guide with detailed instructions and visuals
Student printables or digital recording sheets guiding students on how to select a habitat, research animals of that habitat, note sizes and lifespans of these animals, etc.

As third graders research animals as expedition scouts for Wildlife Explorers International, they learn about place values through various activities, such as representing numbers in different ways, comparing numbers, and estimating lengths, heights, and lifespans of animals.

You can ask students to use standard numbers, expanded forms, and word forms of numbers. They may also be introduced to decimals through this project.

Place value, estimation, decimals

8. The Time of Your Life

A printable or digital student guide with detailed instructions, visuals, and student printables
Analog and digital clocks (one per student pair)

In this project, students learn to read the time on both analog and digital clocks. They also practice setting the time on these clocks.

As they work in pairs, they take turns being the “teacher” and the “student.” The teacher explains to the student how to read the time on a clock. Then, the student sets the time on the clock according to the teacher’s instructions.

Or they tell how many seconds, minutes, or hours have elapsed in doing an activity.

It’s a great activity for third graders, where students can win prizes for being the best timekeepers!

Telling time, elapsed time

9. What’s Your Angle, Pythagoras?

A scorecard
Child-safe compass (optional)

Pythagorean principles are put to the test in this game! Players use a protractor and ruler (or child-safe compass) to draw angles and then measure the length of the sides of right triangles. The goal is to have the longest hypotenuse at the end of the game.

You can call out “Right-Angled Triangle” randomly, and the students have to arrange themselves in the shape in a flash. Those who do it correctly win!

You may also call out “Right Angle”, “Acute Angle”, or “Obtuse Angle” where students have to pair up instantly. If some fail to do it, they are out.

Angles, Pythagorean theorem

$Wooden desk calendar$

10. Calendar Math in the Classroom

A printable or digital calendar template

A perfect math review technique for fifth graders, calendar math is a great way to engage them in the concepts of days, weeks, months, and years. You have to display a calendar in the classroom and point out various aspects of it to the students. For example, you can ask them how many days there are in February, or how many months have 31 days, etc.

You can also use the calendar to teach place value. For instance, you can ask students to name the day on which their birthdays fall this year and write it down. Then, they can find out the day on which their birthdays will fall next year and so on.

This activity can be done with a physical calendar or a digital one. Students can use real-world objects like coins or candy to help them understand the concepts of place value, addition, and subtraction.

Days, weeks, months, years, place value, addition, subtraction

11. Run a Pizza Place

Pizza boxes or paper plates
Colorful cardboard pizzas

Bring fraction to life with this fun activity! Students run their own pizza place, where they take orders, make pizzas, and serve them to customers.

They can use play money to buy pizza toppings and then charge customers for their pizzas. They can also use fraction strips or circle fractions to create pizzas of different sizes.

Such math projects for students teach them concepts like halves, thirds, fourths, eighths, and more. And children will have a blast doing it!

Fractions, equivalent fractions, comparing fractions, adding and subtracting fractions

12. Hot Cocoa Project!

Hot cocoa stall
Marshmallows
Whipped cream (optional)
Chocolate shavings (optional)
Recipe book
Play money or real money

An excellent activity for young entrepreneurs (under adult supervision), this hot cocoa project simulates a hot cocoa stand. Students can make and sell hot cocoa to their classmates, using real or play money.

They can follow a recipe to make the hot cocoa mix, and then use it to make individual cups of hot cocoa. They can also add marshmallows, whipped cream, and chocolate shavings to their hot cocoa, and charge extra for these toppings.

This activity is a great way to teach children about money, measurement, and fractions. And they’ll love getting creative with the hot cocoa mix!

Money, measurement, fractions, addition, subtraction

$Children working on math project in class$

13. Performance Math Art

Props or costumes (optional)
A video recording device (such as a smartphone)

Divide students into groups of 2 to 4 and ask them to prepare a performance art (dramatic poetry, song, or a skit) to explain the Order of Operations (or any other mathematical concepts, such as area and perimeter, exponents and roots, or geometry).

After they have practiced, film their final performance. Students can watch the videos to revise the concept later.

Students may also review each other’s performance in terms of delivery, clarity, and creativity to give constructive feedback.

Order of operations, area and perimeter, exponents and roots, geometry

14. Probably Probability

DIY probability tables

An inspirational idea for kinesthetic learners, this activity gets students up and about as they experiment with probability.

Provide each student with a die (or multiple dice) and a coin. Ask them to roll the die (or dice), flip the coin, and record their results in a table. They can create their probability tables.

Once they have collected enough data, they can look for patterns and predict the probability of certain events.

Probability, independent and dependent events, expected values

15. The Theme Park Project

Theme Park templates (for guidance)
Construction paper
Glue or tape
Markers or crayons
Small toys (optional)

This project is perfect for a math class that is learning about geometry and measurement. Students will use their knowledge of shapes, angles, and measurements to create a mini theme park.

They can start by choosing a template (or creating their own) and then cutting out the shapes from construction paper. Once they have all the pieces, they can assemble their theme park and add details with markers or crayons.

They can also add small toys to their theme park if they wish. Finally, they can measure the area and perimeter of their creation.

Children can dream up new rides, give them outlandish names, create menus for concession stands, and research healthy and junk foods!

A lot of math happens in everyday life if we just look for it.

Geometry, measurement, area, perimeter

By working on these fun projects, students can learn and practice various math skills, from basic counting and graphing to more advanced concepts such as fractions and decimals. These math projects for students can be used to supplement your regular math curriculum or as a standalone activity. Either way, your students are sure to enjoy them!

How can I make sure my students are engaged in the project?

Make sure to give your students a chance to be creative and have fun with the projects. For example, with the “Theme Park Project,” encourage them to develop their own designs and be as creative as possible with the details. With the “Probably Probability” project, let them experiment with different ways of collecting data and see what patterns they can find.

Do I need to prepare anything in advance?

It largely depends on the project you choose. For some projects, you may want to prepare templates in advance. For others, such as the “Probably Probability” project, you only need dice and coins.

How long should the projects take?

Again, it depends on the project. Some math projects for students require several days to complete. Others can be done in one class period or a few minutes.

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Elementary Education Research Paper Topics

This comprehensive guide to elementary education research paper topics is designed to assist students and researchers in the field of education. The guide provides a wide array of topics divided into ten categories, each with ten unique topics, offering a diverse range of areas to explore in the field of elementary education. Additionally, the guide offers expert advice on how to choose a research topic and how to write an elementary education research paper. The final sections of the guide introduce iResearchNet’s professional writing services and encourage students to take advantage of these services for their research needs.

100 Elementary Education Research Paper Topics

Elementary education is a broad field with numerous areas to explore. Whether you’re interested in teaching methods, curriculum development, educational technology, or the social aspects of elementary education, there’s a research topic for you. Here, we present a comprehensive list of elementary education research paper topics, divided into ten categories. Each category contains ten unique topics, offering a diverse range of areas to explore in your research.

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1. Teaching Methods and Strategies

The effectiveness of Montessori methods in elementary education.
The role of play in learning in the early years.
The impact of differentiated instruction on student achievement.
The benefits and challenges of cooperative learning in the elementary classroom.
The role of feedback in promoting student learning.
The impact of teaching strategies on students’ motivation.
The effectiveness of inquiry-based learning in science education.
The role of storytelling in teaching literacy skills.
The impact of technology on teaching and learning in the elementary classroom.
The role of creativity in teaching and learning.

2. Curriculum and Instruction

The impact of curriculum design on student learning.
The role of interdisciplinary teaching in elementary education.
The effectiveness of project-based learning in teaching science.
The role of cultural relevance in curriculum design.
The impact of standardized testing on curriculum and instruction.
The role of critical thinking in the elementary curriculum.
The effectiveness of integrating arts in the curriculum.
The impact of curriculum alignment on student achievement.
The role of experiential learning in the elementary curriculum.
The challenges of teaching social studies in the elementary classroom.

3. Educational Technology

The impact of digital technology on student learning.
The role of educational games in teaching math.
The effectiveness of using iPads in the classroom.
The role of virtual reality in teaching science.
The impact of technology on student engagement.
The challenges of integrating technology in the classroom.
The role of technology in promoting collaborative learning.
The effectiveness of using technology in teaching reading skills.
The impact of technology on teacher-student communication.
The role of technology in personalized learning.

4. Social Aspects of Elementary Education

The impact of classroom climate on student learning.
The role of social-emotional learning in elementary education.
The effectiveness of character education programs.
The role of peer relationships in student learning.
The impact of school culture on student achievement.
The challenges of teaching diversity and inclusion in the elementary classroom.
The role of student-teacher relationships in student learning.
The effectiveness of anti-bullying programs in elementary schools.
The impact of parental involvement on student achievement.
The role of community partnerships in promoting student learning.

5. Special Education

The effectiveness of inclusive education in the elementary classroom.
The role of individualized education programs in supporting students with special needs.
The impact of teacher training on the success of inclusive education.
The challenges of teaching students with learning disabilities.
The role of assistive technology in supporting students with special needs.
The effectiveness of earlyintervention programs for students with special needs.
The impact of classroom accommodations on the academic success of students with special needs.
The role of collaboration between general and special education teachers.
The effectiveness of behavior management strategies for students with emotional and behavioral disorders.
The impact of special education policies on student outcomes.

6. Early Childhood Education

The impact of early childhood education on academic success.
The role of play in early childhood education.
The effectiveness of early literacy programs.
The role of parental involvement in early childhood education.
The impact of early childhood education on social skills development.
The challenges of teaching math in early childhood education.
The role of creativity in early childhood education.
The effectiveness of early intervention programs.
The impact of early childhood education on cognitive development.
The role of teacher-child relationships in early childhood education.

7. Educational Policies and Reforms

The impact of No Child Left Behind on elementary education.
The role of Common Core State Standards in curriculum development.
The effectiveness of school choice policies.
The role of educational policies in promoting equity in education.
The impact of teacher evaluation policies on teaching and learning.
The challenges of implementing educational reforms in elementary schools.
The role of educational policies in promoting teacher quality.
The effectiveness of policies aimed at reducing the achievement gap.
The impact of educational funding policies on student achievement.
The role of educational policies in promoting parental involvement.

8. Teacher Education and Professional Development

The impact of teacher education programs on teacher effectiveness.
The role of ongoing professional development in promoting teacher quality.
The effectiveness of mentorship programs for novice teachers.
The role of reflective practice in teacher professional development.
The impact of teacher beliefs on teaching practices.
The challenges of teaching in high-needs schools.
The role of teacher collaboration in professional development.
The effectiveness of teacher induction programs.
The impact of teacher leadership on school improvement.
The role of teacher autonomy in promoting job satisfaction.

9. Classroom Management

The impact of classroom management strategies on student behavior.
The role of positive reinforcement in promoting appropriate behavior.
The effectiveness of classroom rules and procedures.
The role of teacher-student relationships in classroom management.
The impact of classroom environment on student learning.
The challenges of managing disruptive behavior.
The role of behavior management strategies in promoting a positive classroom climate.
The effectiveness of conflict resolution strategies in the classroom.
The impact of classroom management on student engagement.
The role of classroom routines in promoting student responsibility.

10. Assessment and Evaluation

The impact of formative assessment on student learning.
The role of feedback in student assessment.
The effectiveness of performance-based assessment.
The role of self-assessment in promoting student learning.
The impact of standardized testing on teaching and learning.
The challenges of assessing student learning in diverse classrooms.
The role of assessment in curriculum planning.
The effectiveness of portfolio assessment.
The impact of grading policies on student motivation.
The role of assessment in identifying students at risk of academic failure.

This comprehensive list of elementary education research paper topics provides a wide range of areas to explore. Whether you’re interested in teaching methods, curriculum development, educational technology, or the social aspects of elementary education, there’s a research topic for you. Remember, the best research topic is one that you’re genuinely interested in and passionate about.

Elementary Education Research Guide

Elementary education, also known as primary education, is a crucial stage in the educational journey of a child. It is during these formative years that children acquire foundational skills in areas such as reading, writing, mathematics, science, and social studies. Additionally, they develop critical thinking skills, creativity, and social competencies that are essential for their overall growth and development.

Elementary education serves as the building block for all future learning. The experiences and knowledge gained during these years can significantly influence a child’s attitude towards learning, their academic success, and their lifelong learning habits. Therefore, it is essential to ensure that children receive quality education during these years.

Research in elementary education is of paramount importance. It helps educators, policymakers, and stakeholders understand the best practices, methodologies, and strategies to enhance learning outcomes in primary education. It also provides insights into the challenges faced in elementary education and how to address them effectively.

Elementary education research paper topics can span a wide range of areas, including teaching methods, learning styles, the impact of technology on learning, educational policies, classroom management, and many more. Choosing a research topic in this field requires careful consideration of various factors, including your interests, the relevance of the topic, and the availability of resources.

In the following sections, we provide a comprehensive list of elementary education research paper topics, expert advice on choosing a topic and writing a research paper, and information about iResearchNet’s professional writing services. Whether you are a student embarking on your first research project or a seasoned researcher looking for new areas to explore, this guide is designed to assist you in your research journey.

Choosing Elementary Education Research Paper Topics

Choosing a research topic is a critical step in the research process. The topic you select will guide your study, influence the complexity and relevance of your work, and determine how engaged you are throughout the process. In the field of elementary education, there are numerous intriguing topics that can be explored. Here are some expert tips to assist you in this process:

Understanding Your Interests: The first step in choosing a research topic is to understand your interests. What areas of elementary education fascinate you the most? Are you interested in how teaching methods influence student learning, or are you more intrigued by the role of technology in the classroom? Reflecting on these questions can help you narrow down your options and choose a topic that truly engages you. Remember, research is a time-consuming process, and your interest in the topic will keep you motivated.
Evaluating the Scope of the Topic: Once you have identified your areas of interest, the next step is to evaluate the scope of potential elementary education research paper topics. A good research topic should be neither too broad nor too narrow. If it’s too broad, you may struggle to cover all aspects of the topic effectively. If it’s too narrow, you may have difficulty finding enough information to support your research. Try to choose a topic that is specific enough to be manageable but broad enough to have sufficient resources.
Assessing Available Resources and Data: Before finalizing a topic, it’s important to assess the available resources and data. Are there enough academic sources, such as books, journal articles, and reports, that you can use for your research? Is there accessible data that you can analyze if your research requires it? A preliminary review of literature and data can save you from choosing a topic with limited resources.
Considering the Relevance and Applicability of the Topic: Another important factor to consider is the relevance and applicability of the topic. Is the topic relevant to current issues in elementary education? Can the findings of your research be applied in real-world settings? Choosing a relevant and applicable topic can increase the impact of your research and make it more interesting for your audience.
Seeking Advice: Don’t hesitate to seek advice from your professors, peers, or other experts in the field. They can provide valuable insights, suggest resources, and help you refine your topic. Discussing your ideas with others can also help you see different perspectives and identify potential issues that you may not have considered.
Flexibility: Finally, be flexible. Research is a dynamic process, and it’s okay to modify your topic as you delve deeper into your study. You may discover new aspects of the topic that are more interesting or find that some aspects are too challenging to explore due to constraints. Being flexible allows you to adapt your research to these changes and ensure that your study is both feasible and engaging.

Remember, choosing a research topic is not a decision to be taken lightly. It requires careful consideration and planning. However, with these expert tips, you can navigate this process more effectively and choose an elementary education research paper topic that not only meets your academic requirements but also fuels your passion for learning.

How to Write an Elementary Education Research Paper

Writing a research paper is a significant academic task that requires careful planning, thorough research, and meticulous writing. In the field of elementary education, this process can be particularly challenging due to the complexity and diversity of the field. However, with the right approach and strategies, you can write a compelling and insightful research paper. Here are some expert tips to guide you through this process:

Understanding the Structure of a Research Paper: A typical research paper includes an introduction, literature review, methodology, results, discussion, and conclusion. The introduction presents your research question and its significance. The literature review provides an overview of existing research related to your topic. The methodology explains how you conducted your research. The results section presents your findings, and the discussion interprets these findings in the context of your research question. Finally, the conclusion summarizes your research and suggests areas for future research.
Developing a Strong Thesis Statement: Your thesis statement is the central argument of your research paper. It should be clear, concise, and debatable. A strong thesis statement guides your research and helps your readers understand the purpose of your paper.
Conducting Thorough Research: Before you start writing, conduct a thorough review of the literature related to your topic. This will help you understand the current state of research in your area, identify gaps in the literature, and position your research within this context. Use academic databases to find relevant books, journal articles, and other resources. Remember to evaluate the credibility of your sources and take detailed notes to help you when writing.
Writing and Revising Drafts: Start writing your research paper by creating an outline based on the structure of a research paper. This will help you organize your thoughts and ensure that you cover all necessary sections. Write a first draft without worrying too much about perfection. Focus on getting your ideas down first. Then, revise your draft to improve clarity, coherence, and argumentation. Make sure each paragraph has a clear topic sentence and supports your thesis statement.
Proper Citation and Avoiding Plagiarism: Always cite your sources properly to give credit to the authors whose work you are building upon and to avoid plagiarism. Familiarize yourself with the citation style required by your institution or discipline, such as APA, MLA, Chicago/Turabian, or Harvard. There are many citation tools available online that can help you with this.
Seeking Feedback: Don’t hesitate to seek feedback on your drafts from your professors, peers, or writing centers at your institution. They can provide valuable insights and help you improve your paper.
Proofreading: Finally, proofread your paper to check for any grammatical errors, typos, or inconsistencies in formatting. A well-written, error-free paper makes a good impression on your readers and enhances the credibility of your research.
Incorporating Elementary Education Concepts: When writing an elementary education research paper, it’s crucial to accurately incorporate elementary education concepts. Make sure you understand these concepts thoroughly and can explain them clearly in your paper. Use examples where appropriate to illustrate these concepts.
Analyzing and Interpreting Data: If your research involves data analysis, be sure to explain your analysis process and interpret the results in a way that is understandable to your readers. Discuss the implications of your findings for the broader field of elementary education.
Discussing Real-World Applications: Elementary education is a practical field with many real-world applications. Discuss how your research relates to these applications. This can make your research more interesting and relevant to your readers.

Remember, writing a research paper is a process that requires time, effort, and patience. Don’t rush through it.Take the time to plan your research, conduct thorough research, write carefully, and revise your work. With these expert tips, you can write an elementary education research paper that is insightful, well-structured, and contributes to the field of elementary education.

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Setting Up High-Impact Tasks in Elementary School Math Centers

Allowing students to select math centers based on interest instead of skill level provides opportunities for them all to grow.

Elementary students working with math manipulatives

In our work as math coaches and consultants, we are often asked to help teachers structure small group practice time. Teachers who are required to implement “what I need” (WIN) groups or small group math time have questions about how to put it into practice so that the wide range of students’ needs are being met. We invite you to consider how prioritizing equity-based principles and providing high-impact tasks can offer a path to differentiating instruction, deepening skills and concepts, and strengthening problem-solving.

differentiation in math centers

Elementary teachers are often encouraged to use math workshop (also called math center time or math rotations) to differentiate. In this model, teachers create structures for small groups of students to move from one task to another in timed rotations to complete activities that the teacher has assigned and prepared for them. In this model, there is almost always a “teacher table,” where the teacher works closely with small groups of students on “what they need.”

This model can send unintended messages to students about what it means to be a successful, competent learner of mathematics. It can result in a math classroom that is hierarchical and leveled rather than one that supports students with multi-abilities. Students may begin at early ages to feel the impact of being identified and tracked . So what is the alternative?

designing better Tasks for math centers

Math centers offer ideal opportunities to go deep with the mathematics . The choice of tasks and the ways that teachers interact with students during the workshop impact essential equity standards. We prioritize activities or games with a low floor and high ceiling and that have a high cognitive demand with multiple solution strategies. These games and activities encourage students to make conjectures, to reason through multiple solutions, and to practice important mathematical and problem-solving skills .

One example we often begin with is counting collections . The task focuses on significant mathematics, and yet the directions are uncomplicated. Students choose a collection of items and then figure out how many items are in the collection . The complexity and rigor come from students having to figure out how to count and then how to represent their count. Students develop essential skills such as counting, sorting, grouping, and problem-solving.

Role of the teacher: Instead of having a teacher be stationary at a table where they supervise and lead students through a task, they move around the classroom listening to the students as they engage in the activities. They press on ideas, nudge and notice how students respond and interact. They ask probing questions to help surface mathematical ideas, and they take notes on what they observe and how students respond. Then they use their observations to assess student understanding and inform planning.

Teachers can still gather a small group of students together to bring forward some aspect of their work. In the example of counting collections, we sometimes bring together students to practice ideas related to one-to-one correspondence or extend skills related to number sense.

Grouping Students for centers

We plan tasks for math centers that allow us to leverage multiple competencies among learners and challenge spaces of marginality. In small groups or partnerships, students with different strengths learn with and from each other as they collaborate on activities. We see the variation in student abilities within a group as benefiting all group members, as it allows for greater richness of ideas and knowledge mobility . Students with varying skills and solution strategies work side-by-side using each other as equal thought partners who are able to engage in the mathematics as sense-makers.

Many math games, like the classic “compare” games , offer the kind of richness that makes them well-suited as tasks that leverage the multiple competencies of our students during math workshop. For instance, when they play “multiplication compare,” the game directions are routine: Draw the number of cards needed, figure out the product, and compare it to the product of your partner’s hand. We use sentence starters to support partner talk for all learners and develop protocols for partner decision-making .

The success of multi-ability groups depends on how the teacher establishes an equitable math learning community and how that community is nurtured and maintained throughout the year. We pair students randomly in order to disrupt any narrative that only certain kinds of learners are capable of engaging in deep mathematics. Random groupings position all learners as competent and capable.

Role of the teacher: Following a class period of math rotations, we debrief with our students , not only about the mathematical content they have been engaged in, but also about aspects of their group work and interactions. We help students acknowledge and describe how a partner’s solution offered something new and productive to consider.

Affirming Learners’ Math Identities

Because we see math centers as opportunities to position all students as competent, we prioritize student agency and expand access for all . We select games and activities that support students’ independence, interdependence, and decision-making. Choice is an essential part of the math workshop we are advocating for. When we reposition our students as competent independent learners and give them opportunities to make mathematical decisions, students will rise to the challenge in ways that surprise and excite their teachers as they develop more positive identities as math learners.

Role of the teacher: As we interact with students during math workshop, we press on important mathematical ideas and help shape how students view mathematics and how they view their relationship to mathematics. For example, during “counting collections,” we might say, “You have shown one way to count this quantity. Is there another way you and your partner could count this collection and represent it so that other people would know easily how many items there are? Mathematicians often make several attempts at representing their ideas in order to communicate them clearly to others. See what you might come up with for a second attempt.”

Or, after observing students at a table playing “multiplication compare,” we might say, “I noticed that your group had a few ways of figuring out who had the greater product. When we meet at the end of workshop time, it would be helpful for your classmates to hear your ideas. Why don’t you talk together now about how you might present your ideas to the whole group?”

What’s Next?

We believe it’s time to reconsider some of the assumptions and expectations that educators typically bring to the design and implementation of math workshop time. We suggest prioritizing the development of positive math identities for all students by providing opportunities for access, agency, collaboration, and independence by giving them choice and voice.

We have found that when we rethink the role of the teacher, the kinds of mathematically rich tasks we offer, and the way in which we group students, math workshop can become integral to the creation of equitable math classrooms and be a place for students to develop strong habits of mind alongside math competencies.

DigitalCommons@University of Nebraska - Lincoln

Home > CSMCE > Math in the Middle > MATHMIDACTIONRESEARCH

Math in the Middle Institute Partnership

Action research projects.

Using Cooperative Learning In A Sixth Grade Math Classroom , Teena Andersen

Algebra in the Fifth Grade Mathematics Program , Kathy Bohac

Real Life Problem Solving in Eighth Grade Mathematics , Michael Bomar

Holding Students Accountable , Jeremy Fries

Writing In Math Class? Written Communication in the Mathematics Classroom , Stephanie Fuehrer

The Role of Manipulatives in the Eighth Grade Mathematics Classroom , Michaela Ann Goracke

Reasonable or Not? A Study of the Use of Teacher Questioning to Promote Reasonable Mathematical Answers from Sixth Grade Students , Marlene Grayer

Improving Achievement and Attitude Through Cooperative Learning in Math Class , Scott Johnsen

Oral Communication and Presentations in Mathematics , Brian Johnson

Meaningful Independent Practice in Mathematics , Michelle Looky

Making Better Problem Solvers through Oral and Written Communication , Sheila McCartney

Student Understanding and Achievement When Focusing on Peer-led Reviews , Ryon Nilson

Students Writing Original Word Problems , Marcia Ostmeyer

Cooperative Grouping Working on Mathematics Homework , Maggie Pickering

Making Sense of Word Problems , Edie Ronhovde

Oral and Written Communication in Classroom Mathematics , Lindsey Sample

Written Communication in a Sixth-Grade Mathematics Classroom , Mary Schneider

The Use of Vocabulary in an Eighth Grade Mathematics Classroom: Improving Usage of Mathematics Vocabulary in Oral and Written Communication , Amy Solomon

Enhancing Problem Solving Through Math Clubs , Jessica Haley Thompson

Communication: A Vital Skill of Mathematics , Lexi Wichelt

Mathematical Communication through Written and Oral Expression , Brandee Wilson

Oral Presentation: Exploring Oral Presentations of Homework Problems as a Means of Assessing Homework

Building Confidence in Low Achievers through Building Mathematics Vocabulary , Val Adams

An Uphill Battle: Incorporating cooperative learning using a largely individualized curriculum , Anna Anderson

Using Descriptive Feedback In a Sixth Grade Mathematics Classroom , Vicki J. Barry

Does Decoding Increase Word Problem Solving Skills? , JaLena J. Clement

Using Non-Traditional Activities to Enhance Mathematical Connections , Sandy Dean

Producing More Problem Solving by Emphasizing Vocabulary , Jill Edgren

Reading as a Learning Strategy for Mathematics , Monte Else

Perceptions of Math Homework: Exploring the Connections between Written Explanations and Oral Presentations and the Influence on Students’ Understanding of Math Homework , Kyla Hall

Homework Presentations: Are They Worth the Time? , Kacy Heiser

Reduce Late Assignments through Classroom Presentations , Cole Hilker

Mathematical Communication, Conceptual Understanding, and Students' Attitudes Toward Mathematics , Kimberly Hirschfeld-Cotton

Enhancing Thinking Skills: Will Daily Problem Solving Activities Help? , Julie Hoaglund

Can homework become more meaningful with the inclusion of oral presentations? , Emy Jones

Confidence in Communication: Can My Whole Class Achieve This? , Emily Lashley

Exploring the Influence of Vocabulary Instruction on Students’ Understanding of Mathematical Concepts , Micki McConnell

Using Relearning Groups to Help All Students Understand Learning Objectives Before Tests , Katie Pease

Cooperative Learning in Relation to Problem Solving in the Mathematics Classroom , Shelley Poore

How Student Self-Assessment Influences Mastery Of Objectives , Jeremy John Renfro

RAP (Reasoning and Proof) Journals: I Am Here , Bryce Schwanke

Homework: Is There More To It Than Answers? , Shelly Sehnert

Written Solutions of Mathematical Word Problems , Marcia J. Smith

Rubric Assessment of Mathematical Processes in Homework , Aubrey Weitzenkamp

Calculators in a Middle School Mathematics Classroom: Helpful or Harmful? , Leah Wilcox

Pre-Reading Mathematics Empowers Students , Stacey Aldag

The Importance of Teaching Students How to Read to Comprehend Mathematical Language , Tricia Buchanan

Cooperative Learning as an Effective Way to Interact , Gary Eisenhauer

Generating Interest in Mathematics Using Discussion in the Middle School Classroom , Jessica Fricke

“Let’s Review.” A Look at the Effects of Re-teaching Basic Mathematic Skills , Thomas J. Harrington

The Importance of Vocabulary Instruction in Everyday Mathematics , Chad Larson

Understanding the Mathematical Language , Carmen Melliger

Writing for Understanding in Math Class , Linda Moore

Improving Student Engagement and Verbal Behavior Through Cooperative Learning , Daniel Schaben

Improving Students’ Story Problem Solving Abilities , Josh Severin

Calculators in the Classroom: Help or Hindrance? , Christina L. Sheets

Do Students Progress if They Self-Assess? A Study in Small-Group Work , Cindy Steinkruger

Why Are We Writing? This is Math Class! , Shana Streeks

Effects of Self-Assessment on Math Homework , Diane Swartzlander

The Effects Improving Student Discourse Has on Learning Mathematics , Lindsey Thompson

Increasing Teacher Involvement with Other Teachers Through Reflective Interaction , Tina Thompson

Increasing Conceptual Learning through Student Participation , Janet Timoney

Improving the Effectiveness of Independent Practice with Corrective Feedback , Greg Vanderbeek

Using Math Vocabulary Building to Increase Problem Solving Abilities in a 5th Grade Classroom , Julane Amen

Departmentalization in the 5th Grade Classroom: Re-thinking the Elementary School Model , Delise Andrews

Cooperative Learning Groups in the Eighth Grade Math Classroom , Dean J. Davis

Daily Problem-Solving Warm-Ups: Harboring Mathematical Thinking In The Middle School Classroom , Diana French

Student Transition to College , Doug Glasshoff

The Effects of Teaching Problem Solving Strategies to Low Achieving Students , Kristin Johnson and Anne Schmidt

The Effects of Self-Assessment on Student Learning , Darla Rae Kelberlau-Berks

Writing in a Mathematics Classroom: A Form of Communication and Reflection , Stacie Lefler

Math in the George Middle School , Tiffany D. Lothrop

Bad Medicine: Homework or Headache? Responsibility and Accountability for Middle Level Mathematics Students , Shawn Mousel

Self-Directed Learning in the Middle School Classroom , Jim Pfeiffer

How to Better Prepare for Assessment and Create a More Technologically Advanced Classroom , Kyle Lannin Poore

Cooperative Learning Groups in the Middle School Mathematics Classroom , Sandra S. Snyder

Motivating Middle School Mathematics Students , Vicki Sorensen

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For everyone whose relationship with mathematics is distant or broken, Jo Boaler , a professor at Stanford Graduate School of Education (GSE), has ideas for repairing it. She particularly wants young people to feel comfortable with numbers from the start – to approach the subject with playfulness and curiosity, not anxiety or dread.

“Most people have only ever experienced what I call narrow mathematics – a set of procedures they need to follow, at speed,” Boaler says. “Mathematics should be flexible, conceptual, a place where we play with ideas and make connections. If we open it up and invite more creativity, more diverse thinking, we can completely transform the experience.”

Boaler, the Nomellini and Olivier Professor of Education at the GSE, is the co-founder and faculty director of Youcubed , a Stanford research center that provides resources for math learning that has reached more than 230 million students in over 140 countries. In 2013 Boaler, a former high school math teacher, produced How to Learn Math , the first massive open online course (MOOC) on mathematics education. She leads workshops and leadership summits for teachers and administrators, and her online courses have been taken by over a million users.

In her new book, Math-ish: Finding Creativity, Diversity, and Meaning in Mathematics , Boaler argues for a broad, inclusive approach to math education, offering strategies and activities for learners at any age. We spoke with her about why creativity is an important part of mathematics, the impact of representing numbers visually and physically, and how what she calls “ishing” a math problem can help students make better sense of the answer.

What do you mean by “math-ish” thinking?

It’s a way of thinking about numbers in the real world, which are usually imprecise estimates. If someone asks how old you are, how warm it is outside, how long it takes to drive to the airport – these are generally answered with what I call “ish” numbers, and that’s very different from the way we use and learn numbers in school.

In the book I share an example of a multiple-choice question from a nationwide exam where students are asked to estimate the sum of two fractions: 12/13 + 7/8. They’re given four choices for the closest answer: 1, 2, 19, or 21. Each of the fractions in the question is very close to 1, so the answer would be 2 – but the most common answer 13-year-olds gave was 19. The second most common was 21.

I’m not surprised, because when students learn fractions, they often don’t learn to think conceptually or to consider the relationship between the numerator or denominator. They learn rules about creating common denominators and adding or subtracting the numerators, without making sense of the fraction as a whole. But stepping back and judging whether a calculation is reasonable might be the most valuable mathematical skill a person can develop.

But don’t you also risk sending the message that mathematical precision isn’t important?

I’m not saying precision isn’t important. What I’m suggesting is that we ask students to estimate before they calculate, so when they come up with a precise answer, they’ll have a real sense for whether it makes sense. This also helps students learn how to move between big-picture and focused thinking, which are two different but equally important modes of reasoning.

Some people ask me, “Isn’t ‘ishing’ just estimating?” It is, but when we ask students to estimate, they often groan, thinking it’s yet another mathematical method. But when we ask them to “ish” a number, they're more willing to offer their thinking.

Ishing helps students develop a sense for numbers and shapes. It can help soften the sharp edges in mathematics, making it easier for kids to jump in and engage. It can buffer students against the dangers of perfectionism, which we know can be a damaging mindset. I think we all need a little more ish in our lives.

You also argue that mathematics should be taught in more visual ways. What do you mean by that?

For most people, mathematics is an almost entirely symbolic, numerical experience. Any visuals are usually sterile images in a textbook, showing bisecting angles, or circles divided into slices. But the way we function in life is by developing models of things in our minds. Take a stapler: Knowing what it looks like, what it feels and sounds like, how to interact with it, how it changes things – all of that contributes to our understanding of how it works.

There’s an activity we do with middle-school students where we show them an image of a 4 x 4 x 4 cm cube made up of smaller 1 cm cubes, like a Rubik’s Cube. The larger cube is dipped into a can of blue paint, and we ask the students, if they could take apart the little cubes, how many sides would be painted blue? Sometimes we give the students sugar cubes and have them physically build a larger 4 x 4 x 4 cube. This is an activity that leads into algebraic thinking.

Some years back we were interviewing students a year after they’d done that activity in our summer camp and asked what had stayed with them. One student said, “I’m in geometry class now, and I still remember that sugar cube, what it looked like and felt like.” His class had been asked to estimate the volume of their shoes, and he said he’d imagined his shoes filled with 1 cm sugar cubes in order to solve that question. He had built a mental model of a cube.

When we learn about cubes, most of us don’t get to see and manipulate them. When we learn about square roots, we don’t take squares and look at their diagonals. We just manipulate numbers.

I wonder if people consider the physical representations more appropriate for younger kids.

That’s the thing – elementary school teachers are amazing at giving kids those experiences, but it dies out in middle school, and by high school it’s all symbolic. There’s a myth that there’s a hierarchy of sophistication where you start out with visual and physical representations and then build up to the symbolic. But so much of high-level mathematical work now is visual. Here in Silicon Valley, if you look at Tesla engineers, they're drawing, they're sketching, they're building models, and nobody says that's elementary mathematics.

There’s an example in the book where you’ve asked students how they would calculate 38 x 5 in their heads, and they come up with several different ways of arriving at the same answer. The creativity is fascinating, but wouldn’t it be easier to teach students one standard method?

A depiction of various ways to calculate 38 x 5, numerically and visually. | Courtesy Jo Boaler

That narrow, rigid version of mathematics where there’s only one right approach is what most students experience, and it’s a big part of why people have such math trauma. It keeps them from realizing the full range and power of mathematics. When you only have students blindly memorizing math facts, they’re not developing number sense. They don’t learn how to use numbers flexibly in different situations. It also makes students who think differently believe there’s something wrong with them.

When we open mathematics to acknowledge the different ways a concept or problem can be viewed, we also open the subject to many more students. Mathematical diversity, to me, is a concept that includes both the value of diversity in people and the diverse ways we can see and learn mathematics. When we bring those forms of diversity together, it’s powerful. If we want to value different ways of thinking and problem-solving in the world, we need to embrace mathematical diversity.

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The Algebra Problem: How Middle School Math Became a National Flashpoint

Top students can benefit greatly by being offered the subject early. But many districts offer few Black and Latino eighth graders a chance to study it.

The arms of a student are seen leaning on a desk. One hand holds a pencil and works on algebra equations.

By Troy Closson

From suburbs in the Northeast to major cities on the West Coast, a surprising subject is prompting ballot measures, lawsuits and bitter fights among parents: algebra.

Students have been required for decades to learn to solve for the variable x, and to find the slope of a line. Most complete the course in their first year of high school. But top-achievers are sometimes allowed to enroll earlier, typically in eighth grade.

The dual pathways inspire some of the most fiery debates over equity and academic opportunity in American education.

Do bias and inequality keep Black and Latino children off the fast track? Should middle schools eliminate algebra to level the playing field? What if standout pupils lose the chance to challenge themselves?

The questions are so fraught because algebra functions as a crucial crossroads in the education system. Students who fail it are far less likely to graduate. Those who take it early can take calculus by 12th grade, giving them a potential edge when applying to elite universities and lifting them toward society’s most high-status and lucrative professions.

But racial and economic gaps in math achievement are wide in the United States, and grew wider during the pandemic. In some states, nearly four in five poor children do not meet math standards.

To close those gaps, New York City’s previous mayor, Bill de Blasio, adopted a goal embraced by many districts elsewhere. Every middle school would offer algebra, and principals could opt to enroll all of their eighth graders in the class. San Francisco took an opposite approach: If some children could not reach algebra by middle school, no one would be allowed to take it.

The central mission in both cities was to help disadvantaged students. But solving the algebra dilemma can be more complex than solving the quadratic formula.

New York’s dream of “algebra for all” was never fully realized, and Mayor Eric Adams’s administration changed the goal to improving outcomes for ninth graders taking algebra. In San Francisco, dismantling middle-school algebra did little to end racial inequities among students in advanced math classes. After a huge public outcry, the district decided to reverse course.

“You wouldn’t think that there could be a more boring topic in the world,” said Thurston Domina, a professor at the University of North Carolina. “And yet, it’s this place of incredibly high passions.”

“Things run hot,” he said.

In some cities, disputes over algebra have been so intense that parents have sued school districts, protested outside mayors’ offices and campaigned for the ouster of school board members.

Teaching math in middle school is a challenge for educators in part because that is when the material becomes more complex, with students moving from multiplication tables to equations and abstract concepts. Students who have not mastered the basic skills can quickly become lost, and it can be difficult for them to catch up.

Many school districts have traditionally responded to divergent achievement levels by simply separating children into distinct pathways, placing some in general math classes while offering others algebra as an accelerated option. Such sorting, known as tracking, appeals to parents who want their children to reach advanced math as quickly as possible.

But tracking has cast an uncomfortable spotlight on inequality. Around a quarter of all students in the United States take algebra in middle school. But only about 12 percent of Black and Latino eighth graders do, compared with roughly 24 percent of white pupils, a federal report found .

“That’s why middle school math is this flashpoint,” said Joshua Goodman, an associate professor of education and economics at Boston University. “It’s the first moment where you potentially make it very obvious and explicit that there are knowledge gaps opening up.”

In the decades-long war over math, San Francisco has emerged as a prominent battleground.

California once required that all eighth graders take algebra. But lower-performing middle school students often struggle when forced to enroll in the class, research shows. San Francisco later stopped offering the class in eighth grade. But the ban did little to close achievement gaps in more advanced math classes, recent research has found.

As the pendulum swung, the only constant was anger. Leading Bay Area academics disparaged one another’s research . A group of parents even sued the district last spring. “Denying students the opportunity to skip ahead in math when their intellectual ability clearly allows for it greatly harms their potential for future achievement,” their lawsuit said.

The city is now back to where it began: Middle school algebra — for some, not necessarily for all — will return in August. The experience underscored how every approach carries risks.

“Schools really don’t know what to do,” said Jon R. Star, an educational psychologist at Harvard who has studied algebra education. “And it’s just leading to a lot of tension.”

In Cambridge, Mass., the school district phased out middle school algebra before the pandemic. But some argued that the move had backfired: Families who could afford to simply paid for their children to take accelerated math outside of school.

“It’s the worst of all possible worlds for equity,” Jacob Barandes, a Cambridge parent, said at a school board meeting.

Elsewhere, many students lack options to take the class early: One of Philadelphia’s most prestigious high schools requires students to pass algebra before enrolling, preventing many low-income children from applying because they attend middle schools that do not offer the class.

In New York, Mr. de Blasio sought to tackle the disparities when he announced a plan in 2015 to offer algebra — but not require it — in all of the city’s middle schools. More than 15,000 eighth graders did not have the class at their schools at the time.

Since then, the number of middle schools that offer algebra has risen to about 80 percent from 60 percent. But white and Asian American students still pass state algebra tests at higher rates than their peers.

The city’s current schools chancellor, David Banks, also shifted the system’s algebra focus to high schools, requiring the same ninth-grade curriculum at many schools in a move that has won both support and backlash from educators.

And some New York City families are still worried about middle school. A group of parent leaders in Manhattan recently asked the district to create more accelerated math options before high school, saying that many young students must seek out higher-level instruction outside the public school system.

In a vast district like New York — where some schools are filled with children from well-off families and others mainly educate homeless children — the challenge in math education can be that “incredible diversity,” said Pedro A. Noguera, the dean of the University of Southern California’s Rossier School of Education.

“You have some kids who are ready for algebra in fourth grade, and they should not be denied it,” Mr. Noguera said. “Others are still struggling with arithmetic in high school, and they need support.”

Many schools are unequipped to teach children with disparate math skills in a single classroom. Some educators lack the training they need to help students who have fallen behind, while also challenging those working at grade level or beyond.

Some schools have tried to find ways to tackle the issue on their own. KIPP charter schools in New York have added an additional half-hour of math time to many students’ schedules, to give children more time for practice and support so they can be ready for algebra by eighth grade.

At Middle School 50 in Brooklyn, where all eighth graders take algebra, teachers rewrote lesson plans for sixth- and seventh-grade students to lay the groundwork for the class.

The school’s principal, Ben Honoroff, said he expected that some students would have to retake the class in high school. But after starting a small algebra pilot program a few years ago, he came to believe that exposing children early could benefit everyone — as long as students came into it well prepared.

Looking around at the students who were not enrolling in the class, Mr. Honoroff said, “we asked, ‘Are there other kids that would excel in this?’”

“The answer was 100 percent, yes,” he added. “That was not something that I could live with.”

Troy Closson reports on K-12 schools in New York City for The Times. More about Troy Closson

MyU : For Students, Faculty, and Staff

Clone of CSE welcomes 25 new faculty in 2023-24

Birds-eye view of the UMN Twin Cities campus, with the Minneapolis skyline.

STEM experts from across the world join the University of Minnesota

The University of Minnesota College of Science and Engineering (CSE) welcomes 25 faculty members this 2023-24 academic year—on its way to achieving its goal to hire 60 faculty in three years.

The expertise of this new group of CSE researchers and educators is broad. They range in areas such as hybrid intelligence systems, the reconstruction of past environments and climates, electric machines and magnetic levitation, reinforced concrete structures, and mathematical models to predict the electronic properties of novel materials.

Meet our new science and engineering faculty:

Rene Boiteau is an assistant professor of chemistry. He joins Minnesota from Oregon State University, where he held a joint faculty appointment in the Pacific Northwest National Laboratory. Boiteau earned a bachelor’s in chemistry at Northwestern University, a master’s in earth sciences at University of Cambridge, and a Ph.D. in chemical oceanography at Massachusetts Institute of Technology and Woods Hole Oceanographic Institution. Much of his work is focused on developing analytical chemical approaches, especially mass spectrometry.

Zhu-Tian Chen is an assistant professor of computer science and engineering. He received his bachelor’s in software engineering from South China University of Technology and Ph.D. in computer science from Hong Kong University of Science and Technology. Prior to Minnesota, Chen served as a postdoctoral fellow at Harvard University and postdoctoral researcher at the University of California San Diego. His recent work focuses on enhancing human-data and human-AI interactions in both AR/VR environments—with applications in sports, data journalism, education, biomedical, and architecture.

Gregory “Greg” Handy is an assistant professor of mathematics . He comes to Minnesota from the University of Chicago, where he was a postdoctoral scholar in the Departments of Neurobiology and Statistics. As an applied mathematician and theoretical biologist, Handy’s research strives to use biological applications as inspiration to create new mathematical techniques, and to combine these techniques with classical approaches to examine the mechanisms driving biological processes. This fall, he is teaching Math 2142: Elementary Linear Algebra.

Jessica Hoover is a professor of chemistry. She joins the University of Minnesota from West Virginia University, where she has been a faculty member since 2012. Hoover’s interest in catalysis has been the focus of her work since her undergraduate studies. She graduated with a bachelor’s from Harvey Mudd College before arriving at the University of Washington to pursue her Ph.D. She was a postdoctoral researcher at the University of Wisconsin, Madison.

Harman Kaur is an assistant professor of computer science and engineering—and a University of Minnesota alumna (2016 bachelor’s in computer science). Her research areas are human-centered artificial intelligence, explainability and interpretability, and hybrid intelligence systems. She is affiliated with the GroupLens Research Lab, a group of faculty and students in her department that’s focused on human computing interaction. Prior to Minnesota, Kaur served as a graduate researcher in the interactive Systems Lab and comp.social Lab at the University of Michigan, where she received both her master’s and Ph.D.

Yulong Lu is an assistant professor of mathematics. He joins the faculty from University of Massachusetts, Amherst. Lu received his Ph.D. in mathematics and statistics at the University of Warwick. His research lies at the intersection of applied and computational mathematics, statistics, and data sciences. His recent work is focused on the mathematical aspects of deep learning. This fall, Lu is teaching Math 2573H: Honors Calculus III to undergraduates and Math 8600: Topics in Applied Mathematics, Theory of Deep Learning to graduate students.

Ben Margalit is an assistant professor of physics and astronomy. As a theoretical astrophysicist, he studies the fundamental physics of star explosions, collisions and other examples of intergalactic violence such as a black hole passing near a galaxy and “shredding it to spaghetti.” As part of his job, Margalit works closely with observational astronomers in selecting the kinds of places to look for transient events. He holds bachelor’s and master’s degrees from the Hebrew University of Jerusalem, and a Ph.D. from Columbia University.

Maru Sarazola is an assistant professor of mathematics. She joins Minnesota from Johns Hopkins University, where she was a J.J. Sylvester Assistant Professor. Sarazola received her Ph.D. from Cornell University. Her research is focused on algebraic topology—specifically, her interest lies in homotopy theory (a field that studies and classifies objects up to different notions of "sameness") and category theory (“the math of math,” which looks to abstract all structures to study their behavior). This fall, she is teaching Math 5285H: Honors Algebra I.

Eric Severson is an associate professor of mechanical engineering—and University of Minnesota alumnus (2008 bachelor’s and 2015 Ph.D. in electrical engineering). He returns to his alma mater after being on the University of Wisconsin-Madison faculty for six years. Severson leads research in electric machines and magnetic levitation, with a renewed focus in addressing grand challenges in energy and sustainability through multidisciplinary collaborations. His interests include extreme efficiency, bearingless machines, flywheel energy storage, and electric power grid technology.

Kelsey Stoerzinger is an associate professor of chemical engineering and materials science. She was on the faculty at Oregon State University, with a joint appointment in the Pacific Northwest National Laboratory. She studies the electrochemical transformation of molecules into fuels, chemical feedstocks, and recovered resources. Her research lab designs materials and processes for the storage of renewable electricity. Stoerzinger holds a bachelor’s from Northwestern University, master’s from University of Cambridge, and Ph.D. from MIT.

Lynn Walker is a professor—and the L.E. Scriven Chair in the Department of Chemical Engineering and Materials Science. Previously, she was on the faculty at Carnegie Mellon University. Her research focuses on developing the tools and fundamental understanding necessary to efficiently process soft materials and complex fluids. This expertise is being used to develop systematic approaches to incorporate sustainable feedstocks in consumer products. Walker holds a bachelor’s from the University of New Hampshire and Ph.D. from the University of Delaware. She was a postdoctoral researcher at Katholieke Universiteit Leuven in Belgium.

Alexander “Alex” Watson is an assistant professor of mathematics—and former University of Minnesota postdoctoral researcher in the School of Mathematics. Watson earned his Ph.D. at Columbia University. He works on mathematical models used to predict the electronic properties of materials, especially novel 2D materials such as graphene and twisted multilayer “moiré materials.” In summer 2022 and 2023, he presented at the U’s MathCEP Talented Youth Mathematics Program on topics related to materials research at the University of Minnesota.

Anna Weigandt is an assistant professor of mathematics. She comes to Minnesota from the Massachusetts Institute of Technology, where she was an instructor. Weigandt completed her Ph.D. at the University of Illinois, and she was a postdoctoral assistant professor in the Center for Inquiry Based Learning at University of Michigan. She works in algebraic combinatorics, specifically Schubert calculus. This fall 2023, she is teaching Math 5705: Enumerative Combinatorics.

Michael Wilking is a professor of physics—and University of Minnesota alumnus (2001 bachelor’s in chemical engineering). He holds a master’s and Ph.D. from the University of Colorado. Prior to his return to the Twin Cities campus, Wilking served on the faculty at Stony Brook University. He completed his post-doc at TRIUMF, Canada's national particle accelerator center. Wilking was part of the Stony Brook research team honored with the 2016 Breakthrough Prize in Fundamental Physics.

Benjamin "Ben" Worsfold is an assistant professor of civil engineering —and a licensed professional engineer in both California and Costa Rica. His research interest lies in large-scale structural testing, finite element analysis of reinforced concrete structures, and anchoring to concrete. Worsfold earned his master’s and Ph.D. from the University of California, Berkeley, and bachelor’s from the University of Costa Rica.

Yogatheesan Varatharajah is an assistant professor of computer science and engineering —and a visiting scientist in neurology at the Mayo Clinic. His research lies broadly in machine learning for health. Varatharajah earned his master’s and Ph.D. from the University of Illinois Urbana-Champaign. Prior to Minnesota, he was a research assistant professor of bioengineering at the University of Illinois and faculty affiliate for the Center for Artificial Intelligence Innovation with the National Center for Supercomputing Applications.

Starting in January 2024:

Emily Beverly is an incoming assistant professor of earth sciences. Prior to joining the University of Minnesota, she was on the faculty at University of Houston. She earned a bachelor’s from Trinity University, a master’s from Rutgers University, and a Ph.D. from Baylor University. Beverly was a postdoctoral researcher at Georgia State University and University of Michigan. Her research focuses on understanding environmental drivers of human and hominin evolution. Beverly uses stable isotopes and geochemistry to answer questions about past and future climates with a firm foundation in sedimentary geology and earth surface processes.

Alexander “Alex” Grenning is an assistant professor of chemistry. He comes to Minnesota from the University of Florida, where he was a tenured faculty. Grenning earned a bachelor’s in chemistry and music from Lake Forest College, and a Ph.D. in organic chemistry from the University of Kansas. He was a postdoctoral researcher at Boston University. His work is focused on chemical synthesis and drug discovery.

Yu Cao is an incoming professor of electrical and computer engineering. Prior to Minnesota, Cao was a professor at Arizona State University. He holds a bachelor’s in physics from Peking University and a master’s in biophysics plus a Ph.D. in electrical engineering and computer sciences from the University of California-Berkeley. His research includes neural-inspired computing, hardware design for on-chip learning, and reliable integration of nanoelectronics. Cao served as associate editor of the Institute of Electrical and Electronics Engineers’s monthly Transactions on CAD .

Edgar Peña is an incoming assistant professor of biomedical engineering—and a University of Minnesota alumnus (2017 Ph.D. in biomedical engineering). He is a neuromodulation scholar who is interested in vagus nerve stimulation. Peña earned his bachelor’s degrees in electrical engineering and biomedical engineering from the University of California, Irvine. During his doctoral studies at the University of Minnesota Twin Cities, he used computational models to optimize deep brain stimulation.

Seongjin Choi is an incoming assistant professor of civil engineering. He received his bachelor’s, master’s, and Ph.D. from the Korea Advanced Institute of Science and Technology. He was a postdoctoral researcher at McGill University. His work involves using data analytics to draw valuable insights from urban mobility data and applying cutting-edge AI technologies in the field of transportation.

Pedram Mortazavi is an incoming assistant professor of civil engineering— and a licensed structural engineer in Canada . His interests lie in structural resilience, steel structures, large-scale testing, development of damping and isolation systems, advanced simulation methods, and hybrid simulation. Mortazavi holds a bachelor’s from the University of Science and Culture in Iran, a master’s from Carleton University in Ottawa, and Ph.D. from the University of Toronto.

Gang Qiu is an incoming assistant professor of electrical and computer engineering. He received his bachelor’s degree from Peking University in microelectronics and his Ph.D. in electrical and computer engineering from Purdue University. (He is currently a postdoctoral researcher at the University of California, Los Angeles.) Qiu’s research focuses on novel low-dimensional materials for advanced electronics and quantum applications. His current interest includes employing topological materials for topological quantum computing.

Qianwen Wang is an incoming assistant professor of computer science and engineering. She received her bachelor’s from Xi’an Jiao Tong University and her Ph.D. from Hong Kong University of Science and Technology. Prior to Minnesota, Wang served as a post-doctoral researcher at Harvard University in the Department of Biomedical Informatics. As a visualization researcher, she created interactive visualization tools that enable humans to better interpret AI and generate insights from their data.

Katie (Yang) Zhao is an incoming assistant professor of electrical and computer engineering. Her research interest resides in the intersection between Domain-Specific Acceleration Chip and Computer Architecture. In particular, her work centers around enabling AI-powered intelligent functionalities on resource-constrained edge devices. Zhao received her bachelor’s and master’s from Fudan University, China, and Ph.D. from Rice University. (She is currently a postdoctoral researcher at Georgia Institute of Technology.)

Learn more about our goal to hire 60 new faculty in three years at the CSE recruiting website .

If you’d like to support faculty research in the University of Minnesota College of Science and Engineering, visit our CSE Giving website .

Join our winning team

Our unique combination of science and engineering within one college in a vibrant, metropolitan area means more opportunities for you. Learn about faculty openings.