what is a good conclusion an essay

Conclusions

What this handout is about.

This handout will explain the functions of conclusions, offer strategies for writing effective ones, help you evaluate conclusions you’ve drafted, and suggest approaches to avoid.

About conclusions

Introductions and conclusions can be difficult to write, but they’re worth investing time in. They can have a significant influence on a reader’s experience of your paper.

Just as your introduction acts as a bridge that transports your readers from their own lives into the “place” of your analysis, your conclusion can provide a bridge to help your readers make the transition back to their daily lives. Such a conclusion will help them see why all your analysis and information should matter to them after they put the paper down.

Your conclusion is your chance to have the last word on the subject. The conclusion allows you to have the final say on the issues you have raised in your paper, to synthesize your thoughts, to demonstrate the importance of your ideas, and to propel your reader to a new view of the subject. It is also your opportunity to make a good final impression and to end on a positive note.

Your conclusion can go beyond the confines of the assignment. The conclusion pushes beyond the boundaries of the prompt and allows you to consider broader issues, make new connections, and elaborate on the significance of your findings.

Your conclusion should make your readers glad they read your paper. Your conclusion gives your reader something to take away that will help them see things differently or appreciate your topic in personally relevant ways. It can suggest broader implications that will not only interest your reader, but also enrich your reader’s life in some way. It is your gift to the reader.

Strategies for writing an effective conclusion

One or more of the following strategies may help you write an effective conclusion:

• Play the “So What” Game. If you’re stuck and feel like your conclusion isn’t saying anything new or interesting, ask a friend to read it with you. Whenever you make a statement from your conclusion, ask the friend to say, “So what?” or “Why should anybody care?” Then ponder that question and answer it. Here’s how it might go: You: Basically, I’m just saying that education was important to Douglass. Friend: So what? You: Well, it was important because it was a key to him feeling like a free and equal citizen. Friend: Why should anybody care? You: That’s important because plantation owners tried to keep slaves from being educated so that they could maintain control. When Douglass obtained an education, he undermined that control personally. You can also use this strategy on your own, asking yourself “So What?” as you develop your ideas or your draft.
• Return to the theme or themes in the introduction. This strategy brings the reader full circle. For example, if you begin by describing a scenario, you can end with the same scenario as proof that your essay is helpful in creating a new understanding. You may also refer to the introductory paragraph by using key words or parallel concepts and images that you also used in the introduction.
• Synthesize, don’t summarize. Include a brief summary of the paper’s main points, but don’t simply repeat things that were in your paper. Instead, show your reader how the points you made and the support and examples you used fit together. Pull it all together.
• Include a provocative insight or quotation from the research or reading you did for your paper.
• Propose a course of action, a solution to an issue, or questions for further study. This can redirect your reader’s thought process and help them to apply your info and ideas to their own life or to see the broader implications.
• Point to broader implications. For example, if your paper examines the Greensboro sit-ins or another event in the Civil Rights Movement, you could point out its impact on the Civil Rights Movement as a whole. A paper about the style of writer Virginia Woolf could point to her influence on other writers or on later feminists.

Strategies to avoid

• Beginning with an unnecessary, overused phrase such as “in conclusion,” “in summary,” or “in closing.” Although these phrases can work in speeches, they come across as wooden and trite in writing.
• Stating the thesis for the very first time in the conclusion.
• Introducing a new idea or subtopic in your conclusion.
• Ending with a rephrased thesis statement without any substantive changes.
• Making sentimental, emotional appeals that are out of character with the rest of an analytical paper.
• Including evidence (quotations, statistics, etc.) that should be in the body of the paper.

Four kinds of ineffective conclusions

• The “That’s My Story and I’m Sticking to It” Conclusion. This conclusion just restates the thesis and is usually painfully short. It does not push the ideas forward. People write this kind of conclusion when they can’t think of anything else to say. Example: In conclusion, Frederick Douglass was, as we have seen, a pioneer in American education, proving that education was a major force for social change with regard to slavery.
• The “Sherlock Holmes” Conclusion. Sometimes writers will state the thesis for the very first time in the conclusion. You might be tempted to use this strategy if you don’t want to give everything away too early in your paper. You may think it would be more dramatic to keep the reader in the dark until the end and then “wow” them with your main idea, as in a Sherlock Holmes mystery. The reader, however, does not expect a mystery, but an analytical discussion of your topic in an academic style, with the main argument (thesis) stated up front. Example: (After a paper that lists numerous incidents from the book but never says what these incidents reveal about Douglass and his views on education): So, as the evidence above demonstrates, Douglass saw education as a way to undermine the slaveholders’ power and also an important step toward freedom.
• The “America the Beautiful”/”I Am Woman”/”We Shall Overcome” Conclusion. This kind of conclusion usually draws on emotion to make its appeal, but while this emotion and even sentimentality may be very heartfelt, it is usually out of character with the rest of an analytical paper. A more sophisticated commentary, rather than emotional praise, would be a more fitting tribute to the topic. Example: Because of the efforts of fine Americans like Frederick Douglass, countless others have seen the shining beacon of light that is education. His example was a torch that lit the way for others. Frederick Douglass was truly an American hero.
• The “Grab Bag” Conclusion. This kind of conclusion includes extra information that the writer found or thought of but couldn’t integrate into the main paper. You may find it hard to leave out details that you discovered after hours of research and thought, but adding random facts and bits of evidence at the end of an otherwise-well-organized essay can just create confusion. Example: In addition to being an educational pioneer, Frederick Douglass provides an interesting case study for masculinity in the American South. He also offers historians an interesting glimpse into slave resistance when he confronts Covey, the overseer. His relationships with female relatives reveal the importance of family in the slave community.

Works consulted

We consulted these works while writing this handout. This is not a comprehensive list of resources on the handout’s topic, and we encourage you to do your own research to find additional publications. Please do not use this list as a model for the format of your own reference list, as it may not match the citation style you are using. For guidance on formatting citations, please see the UNC Libraries citation tutorial . We revise these tips periodically and welcome feedback.

Douglass, Frederick. 1995. Narrative of the Life of Frederick Douglass, an American Slave, Written by Himself. New York: Dover.

Hamilton College. n.d. “Conclusions.” Writing Center. Accessed June 14, 2019. https://www.hamilton.edu//academics/centers/writing/writing-resources/conclusions .

Holewa, Randa. 2004. “Strategies for Writing a Conclusion.” LEO: Literacy Education Online. Last updated February 19, 2004. https://leo.stcloudstate.edu/acadwrite/conclude.html.

You may reproduce it for non-commercial use if you use the entire handout and attribute the source: The Writing Center, University of North Carolina at Chapel Hill

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How to Write a Conclusion for an Essay

By the time you get to the final paragraph of your paper, you have already done so much work on your essay, so all you want to do is to wrap it up as quickly as possible. You’ve already made a stunning introduction, proven your argument, and structured the whole piece as supposed – who cares about making a good conclusion paragraph?

The only thing you need to remember is that the conclusion of an essay is not just the last paragraph of an academic paper where you restate your thesis and key arguments. A concluding paragraph is also your opportunity to have a final impact on your audience. 

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How to write a conclusion paragraph that leaves a lasting impression – In this guide, the team at EssayPro is going to walk you through the process of writing a perfect conclusion step by step. Additionally, we will share valuable tips and tricks to help students of all ages impress their readers at the last moment.

Instead of Intro: What Is a Conclusion?

Before we can move on, let’s take a moment here to define the conclusion itself. According to the standard conclusion definition, it is pretty much the last part of something, its result, or end. However, this term is rather broad and superficial.

When it comes to writing academic papers, a concluding statement refers to an opinion, judgment, suggestion, or position arrived at by logical reasoning (through the arguments provided in the body of the text). Therefore, if you are wondering “what is a good closing sentence like?” – keep on reading.

What Does a Good Conclusion Mean?

Writing a good conclusion for a paper isn’t easy. However, we are going to walk you through this process step by step. Although there are generally no strict rules on how to formulate one, there are some basic principles that everyone should keep in mind. In this section, we will share some core ideas for writing a good conclusion, and, later in the article, we will also provide you with more practical advice and examples.

Here are the core goals a good conclusion should complete:

• “Wrap up” the entire paper;
• Demonstrate to readers that the author accomplished what he/she set out to do;
• Show how you the author has proved their thesis statement;
• Give a sense of completeness and closure on the topic;
• Leave something extra for your reader to think about;
• Leave a powerful final impact on a reader.

Another key thing to remember is that you should not introduce any new ideas or arguments to your paper's conclusion. It should only sum up what you have already written, revisit your thesis statement, and end with a powerful final impression.

When considering how to write a conclusion that works, here are the key points to keep in mind:

• A concluding sentence should only revisit the thesis statement, not restate it;
• It should summarize the main ideas from the body of the paper;
• It should demonstrate the significance and relevance of your work;
• An essay’s conclusion should include a call for action and leave space for further study or development of the topic (if necessary).

How Long Should a Conclusion Be? 

Although there are no strict universal rules regarding the length of an essay’s final clause, both teachers and experienced writers recommend keeping it clear, concise, and straight to the point. There is an unspoken rule that the introduction and conclusion of an academic paper should both be about 10% of the overall paper’s volume. For example, if you were assigned a 1500 word essay, both the introductory and final clauses should be approximately 150 words long (300 together).

Why You Need to Know How to End an Essay:

A conclusion is what drives a paper to its logical end. It also drives the main points of your piece one last time. It is your last opportunity to impact and impress your audience. And, most importantly, it is your chance to demonstrate to readers why your work matters. Simply put, the final paragraph of your essay should answer the last important question a reader will have – “So what?”

If you do a concluding paragraph right, it can give your readers a sense of logical completeness. On the other hand, if you do not make it powerful enough, it can leave them hanging, and diminish the effect of the entire piece.

Strategies to Crafting a Proper Conclusion

Although there are no strict rules for what style to use to write your conclusion, there are several strategies that have been proven to be effective. In the list below, you can find some of the most effective strategies with some good conclusion paragraph examples to help you grasp the idea.

One effective way to emphasize the significance of your essay and give the audience some thought to ponder about is by taking a look into the future. The “When and If” technique is quite powerful when it comes to supporting your points in the essay’s conclusion.

Prediction essay conclusion example: “Taking care of a pet is quite hard, which is the reason why most parents refuse their children’s requests to get a pet. However, the refusal should be the last choice of parents. If we want to inculcate a deep sense of responsibility and organization in our kids, and, at the same time, sprout compassion in them, we must let our children take care of pets.”

Another effective strategy is to link your conclusion to your introductory paragraph. This will create a full-circle narration for your readers, create a better understanding of your topic, and emphasize your key point.

Echo conclusion paragraph example: Introduction: “I believe that all children should grow up with a pet. I still remember the exact day my parents brought my first puppy to our house. This was one of the happiest moments in my life and, at the same time, one of the most life-changing ones. Growing up with a pet taught me a lot, and most importantly, it taught me to be responsible.” Conclusion:. “I remember when I picked up my first puppy and how happy I was at that time. Growing up with a pet, I learned what it means to take care of someone, make sure that he always has water and food, teach him, and constantly keep an eye on my little companion. Having a child grow up with a pet teaches them responsibility and helps them acquire a variety of other life skills like leadership, love, compassion, and empathy. This is why I believe that every kid should grow up with a pet!”

Finally, one more trick that will help you create a flawless conclusion is to amplify your main idea or to present it in another perspective of a larger context. This technique will help your readers to look at the problem discussed from a different angle.

Step-up argumentative essay conclusion example: “Despite the obvious advantages of owning a pet in childhood, I feel that we cannot generalize whether all children should have a pet. Whereas some kids may benefit from such experiences, namely, by becoming more compassionate, organized, and responsible, it really depends on the situation, motivation, and enthusiasm of a particular child for owning a pet.”

What is a clincher in an essay? – The final part of an essay’s conclusion is often referred to as a clincher sentence. According to the clincher definition, it is a final sentence that reinforces the main idea or leaves the audience with an intriguing thought to ponder upon. In a nutshell, the clincher is very similar to the hook you would use in an introductory paragraph. Its core mission is to seize the audience’s attention until the end of the paper. At the same time, this statement is what creates a sense of completeness and helps the author leave a lasting impression on the reader.

Now, since you now know what a clincher is, you are probably wondering how to use one in your own paper. First of all, keep in mind that a good clincher should be intriguing, memorable, smooth, and straightforward.

Generally, there are several different tricks you can use for your clincher statement; it can be:

• A short, but memorable and attention-grabbing conclusion;
• A relevant and memorable quote (only if it brings actual value);
• A call to action;
• A rhetorical question;
• An illustrative story or provocative example;
• A warning against a possibility or suggestion about the consequences of a discussed problem;
• A joke (however, be careful with this as it may not always be deemed appropriate).

Regardless of the technique you choose, make sure that your clincher is memorable and aligns with your introduction and thesis.

Clincher examples: - While New York may not be the only place with the breathtaking views, it is definitely among my personal to 3… and that’s what definitely makes it worth visiting. - “Thence we came forth to rebehold the stars”, Divine Comedy - Don’t you think all these advantages sound like almost life-saving benefits of owning a pet? “So we beat on, boats against the current, borne back ceaselessly into the past.”, The Great Gatsby

Conclusion Writing Don'ts 

Now, when you know what tricks and techniques you should use to create a perfect conclusion, let’s look at some of the things you should not do with our online paper writing service :

• Starting with some cliché concluding sentence starters. Many students find common phrases like “In conclusion,” “Therefore,” “In summary,” or similar statements to be pretty good conclusion starters. However, though such conclusion sentence starters may work in certain cases – for example, in speeches – they are overused, so it is recommended not to use them in writing to introduce your conclusion.
• Putting the first mention of your thesis statement in the conclusion – it has to be presented in your introduction first.
• Providing new arguments, subtopics, or ideas in the conclusion paragraph.
• Including a slightly changed or unchanged thesis statement.
• Providing arguments and evidence that belong in the body of the work.
• Writing too long, hard to read, or confusing sentences.

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Conclusion Paragraph Outline

The total number of sentences in your final paragraph may vary depending on the number of points you discussed in your essay, as well as on the overall word count of your paper. However, the overall conclusion paragraph outline will remain the same and consists of the following elements:

• A conclusion starter:

The first part of your paragraph should drive readers back to your thesis statement. Thus, if you were wondering how to start a conclusion, the best way to do it is by rephrasing your thesis statement.

• Summary of the body paragraphs:

Right after revisiting your thesis, you should include several sentences that wrap up the key highlights and points from your body paragraphs. This part of your conclusion can consist of 2-3 sentences—depending on the number of arguments you’ve made. If necessary, you can also explain to the readers how your main points fit together.

• A concluding sentence:

Finally, you should end your paragraph with a last, powerful sentence that leaves a lasting impression, gives a sense of logical completeness, and connects readers back to the introduction of the paper.

These three key elements make up a perfect essay conclusion. Now, to give you an even better idea of how to create a perfect conclusion, let us give you a sample conclusion paragraph outline with examples from an argumentative essay on the topic of “Every Child Should Own a Pet:

• Sentence 1: Starter
• ~ Thesis: "Though taking care of a pet may be a bit challenging for small children. Parents should not restrict their kids from having a pet as it helps them grow into more responsible and compassionate people."
• ~ Restated thesis for a conclusion: "I can say that taking care of a pet is good for every child."
• Sentences 2-4: Summary
• ~ "Studies have shown that pet owners generally have fewer health problems."
• ~ "Owning a pet teaches a child to be more responsible."
• ~ "Spending time with a pet reduces stress, feelings of loneliness, and anxiety."
• Sentence 5: A concluding sentence
• ~ "Pets can really change a child life for the better, so don't hesitate to endorse your kid's desire to own a pet."

This is a clear example of how you can shape your conclusion paragraph.

How to Conclude Various Types of Essays

Depending on the type of academic essay you are working on, your concluding paragraph's style, tone, and length may vary. In this part of our guide, we will tell you how to end different types of essays and other works.

How to End an Argumentative Essay

Persuasive or argumentative essays always have the single goal of convincing readers of something (an idea, stance, or viewpoint) by appealing to arguments, facts, logic, and even emotions. The conclusion for such an essay has to be persuasive as well. A good trick you can use is to illustrate a real-life scenario that proves your stance or encourages readers to take action. More about persuasive essay outline you can read in our article.

Here are a few more tips for making a perfect conclusion for an argumentative essay:

• Carefully read the whole essay before you begin;
• Re-emphasize your ideas;
• Discuss possible implications;
• Don’t be afraid to appeal to the reader’s emotions.

How to End a Compare and Contrast Essay

The purpose of a compare and contrast essay is to emphasize the differences or similarities between two or more objects, people, phenomena, etc. Therefore, a logical conclusion should highlight how the reviewed objects are different or similar. Basically, in such a paper, your conclusion should recall all of the key common and distinctive features discussed in the body of your essay and also give readers some food for thought after they finish reading it.

How to Conclude a Descriptive Essay

The key idea of a descriptive essay is to showcase your creativity and writing skills by painting a vivid picture with the help of words. This is one of the most creative types of essays as it requires you to show a story, not tell it. This kind of essay implies using a lot of vivid details. Respectively, the conclusion of such a paper should also use descriptive imagery and, at the same time, sum up the main ideas. A good strategy for ending a descriptive essay would be to begin with a short explanation of why you wrote the essay. Then, you should reflect on how your topic affects you. In the middle of the conclusion, you should cover the most critical moments of the story to smoothly lead the reader into a logical closing statement. The “clincher”, in this case, should be a thought-provoking final sentence that leaves a good and lasting impression on the audience. Do not lead the reader into the essay and then leave them with dwindling memories of it.

How to Conclude an Essay About Yourself

If you find yourself writing an essay about yourself, you need to tell a personal story. As a rule, such essays talk about the author’s experiences, which is why a conclusion should create a feeling of narrative closure. A good strategy is to end your story with a logical finale and the lessons you have learned, while, at the same time, linking it to the introductory paragraph and recalling key moments from the story.

How to End an Informative Essay

Unlike other types of papers, informative or expository essays load readers with a lot of information and facts. In this case, “Synthesize, don’t summarize” is the best technique you can use to end your paper. Simply put, instead of recalling all of the major facts, you should approach your conclusion from the “So what?” position by highlighting the significance of the information provided.

How to Conclude a Narrative Essay

In a nutshell, a narrative essay is based on simple storytelling. The purpose of this paper is to share a particular story in detail. Therefore, the conclusion for such a paper should wrap up the story and avoid finishing on an abrupt cliffhanger. It is vital to include the key takeaways and the lessons learned from the story.

How to Write a Conclusion for a Lab Report

Unlike an essay, a lab report is based on an experiment. This type of paper describes the flow of a particular experiment conducted by a student and its conclusion should reflect on the outcomes of this experiment.

In thinking of how to write a conclusion for a lab, here are the key things you should do to get it right:

• Restate the goals of your experiment
• Describe the methods you used
• Include the results of the experiment and analyze the final data
• End your conclusion with a clear statement on whether or not the experiment was successful (Did you reach the expected results?)

How to Write a Conclusion for a Research Paper

Writing a paper is probably the hardest task of all, even for experienced dissertation writer . Unlike an essay or even a lab report, a research paper is a much longer piece of work that requires a deeper investigation of the problem. Therefore, a conclusion for such a paper should be even more sophisticated and powerful. If you're feeling difficulty writing an essay, you can buy essay on our service.

However, given that a research paper is the second most popular kind of academic paper (after an essay), it is important to know how to conclude a research paper. Even if you have not yet been assigned to do this task, be sure that you will face it soon. So, here are the steps you should follow to create a great conclusion for a research paper:

• Restate the Topic

Start your final paragraph with a quick reminder of what the topic of the piece is about. Keep it one sentence long.

• Revisit the Thesis

Next, you should remind your readers what your thesis statement was. However, do not just copy and paste it from the introductory clause: paraphrase your thesis so that you deliver the same idea but with different words. Keep your paraphrased thesis narrow, specific, and topic-oriented.

• Summarise Your Key Ideas

Just like the case of a regular essay’s conclusion, a research paper’s final paragraph should also include a short summary of all of the key points stated in the body sections. We recommend reading the entire body part a few times to define all of your main arguments and ideas.

• Showcase the Significance of Your Work

In the research paper conclusion, it is vital to highlight the significance of your research problem and state how your solution could be helpful.

• Make Suggestions for Future Studies

Finally, at the end of your conclusion, you should define how your findings will contribute to the development of its particular field of science. Outline the perspectives of further research and, if necessary, explain what is yet to be discovered on the topic.

Then, end your conclusion with a powerful concluding sentence – it can be a rhetorical question, call to action, or another hook that will help you have a strong impact on the audience.

• Answer the Right Questions

To create a top-notch research paper conclusion, be sure to answer the following questions:

• What is the goal of a research paper?
• What are the possible solutions to the research question(s)?
• How can your results be implemented in real life? (Is your research paper helpful to the community?)
• Why is this study important and relevant?

Additionally, here are a few more handy tips to follow:

• Provide clear examples from real life to help readers better understand the further implementation of the stated solutions;
• Keep your conclusion fresh, original, and creative.

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So, What Is a Good Closing Sentence? See The Difference

One of the best ways to learn how to write a good conclusion is to look at several professional essay conclusion examples. In this section of our guide, we are going to look at two different final paragraphs shaped on the basis of the same template, but even so, they are very different – where one is weak and the other is strong. Below, we are going to compare them to help you understand the difference between a good and a bad conclusion.

Here is the template we used: College degrees are in decline. The price of receiving an education does not correlate with the quality of the education received. As a result, graduated students face underemployment, and the worth of college degrees appears to be in serious doubt. However, the potential social and economic benefits of educated students balance out the equation.

Strong Conclusion ‍

People either see college as an opportunity or an inconvenience; therefore, a degree can only hold as much value as its owner’s skillset. The underemployment of graduate students puts the worth of college degrees in serious doubt. Yet, with the multitude of benefits that educated students bring to society and the economy, the equation remains in balance. Perhaps the ordinary person should consider college as a wise financial investment, but only if they stay determined to study and do the hard work.

Why is this example good? There are several key points that prove its effectiveness:

• There is a bold opening statement that encompasses the two contrasting types of students we can see today.
• There are two sentences that recall the thesis statement and cover the key arguments from the body of the essay.
• Finally, the last sentence sums up the key message of the essay and leaves readers with something to think about.

Weak Conclusion

In conclusion, with the poor preparation of students in college and the subsequent underemployment after graduation from college, the worth associated with the college degree appears to be in serious doubt. However, these issues alone may not reasonably conclude beyond a doubt that investing in a college degree is a rewarding venture. When the full benefits that come with education are carefully put into consideration and evaluated, college education for children in any country still has good advantages, and society should continue to advocate for a college education. The ordinary person should consider this a wise financial decision that holds rewards in the end. Apart from the monetary gains associated with a college education, society will greatly benefit from students when they finish college. Their minds are going to be expanded, and their reasoning and decision making will be enhanced.

What makes this example bad? Here are a few points to consider:

• Unlike the first example, this paragraph is long and not specific enough. The author provides plenty of generalized phrases that are not backed up by actual arguments.
• This piece is hard to read and understand and sentences have a confusing structure. Also, there are lots of repetitions and too many uses of the word “college”.
• There is no summary of the key benefits.
• The last two sentences that highlight the value of education contradict with the initial statement.
• Finally, the last sentence doesn’t offer a strong conclusion and gives no thought to ponder upon.
• In the body of your essay, you have hopefully already provided your reader(s) with plenty of information. Therefore, it is not wise to present new arguments or ideas in your conclusion.
• To end your final paragraph right, find a clear and straightforward message that will have the most powerful impact on your audience.
• Don’t use more than one quote in the final clause of your paper – the information from external sources (including quotes) belongs in the body of a paper.
• Be authoritative when writing a conclusion. You should sound confident and convincing to leave a good impression. Sentences like “I’m not an expert, but…” will most likely make you seem less knowledgeable and/or credible.

Good Conclusion Examples

Now that we've learned what a conclusion is and how to write one let's take a look at some essay conclusion examples to strengthen our knowledge.

The ending ironically reveals that all was for nothing. (A short explanation of the thematic effect of the book’s end) Tom says that Miss Watson freed Jim in her final will.Jim told Huck that the dead man on the Island was pap. The entire adventure seemingly evaporated into nothingness. (How this effect was manifested into the minds of thereaders).

All in all, international schools hold the key to building a full future that students can achieve. (Thesis statement simplified) They help students develop their own character by learning from their mistakes, without having to face a dreadful penalty for failure. (Thesis statement elaborated)Although some say that kids emerged “spoiled” with this mentality, the results prove the contrary. (Possible counter-arguments are noted)

In conclusion, public workers should be allowed to strike since it will give them a chance to air their grievances. (Thesis statement) Public workers should be allowed to strike when their rights, safety, and regulations are compromised. The workers will get motivated when they strike, and their demands are met.

In summary, studies reveal some similarities in the nutrient contents between the organic and non-organic food substances. (Starts with similarities) However, others have revealed many considerable differences in the amounts of antioxidants as well as other minerals present in organic and non-organic foods. Generally, organic foods have higher levels of antioxidants than non-organic foods and therefore are more important in the prevention of chronic illnesses.

As time went by, my obsession grew into something bigger than art; (‘As time went by’ signals maturation) it grew into a dream of developing myself for the world. (Showing student’s interest of developing himself for the community) It is a dream of not only seeing the world from a different perspective but also changing the perspective of people who see my work. (Showing student’s determination to create moving pieces of art)

In conclusion, it is evident that technology is an integral part of our lives and without it, we become “lost” since we have increasingly become dependent on its use. (Thesis with main point)

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How To Write A Conclusion For An Essay?

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How to Conclude an Essay (with Examples)

Last Updated: April 3, 2023 Fact Checked

Writing a Strong Conclusion

What to avoid, brainstorming tricks.

This article was co-authored by Jake Adams and by wikiHow staff writer, Aly Rusciano . Jake Adams is an academic tutor and the owner of Simplifi EDU, a Santa Monica, California based online tutoring business offering learning resources and online tutors for academic subjects K-College, SAT & ACT prep, and college admissions applications. With over 14 years of professional tutoring experience, Jake is dedicated to providing his clients the very best online tutoring experience and access to a network of excellent undergraduate and graduate-level tutors from top colleges all over the nation. Jake holds a BS in International Business and Marketing from Pepperdine University. There are 8 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 3,208,243 times.

So, you’ve written an outstanding essay and couldn’t be more proud. But now you have to write the final paragraph. The conclusion simply summarizes what you’ve already written, right? Well, not exactly. Your essay’s conclusion should be a bit more finessed than that. Luckily, you’ve come to the perfect place to learn how to write a conclusion. We’ve put together this guide to fill you in on everything you should and shouldn’t do when ending an essay. Follow our advice, and you’ll have a stellar conclusion worthy of an A+ in no time.

Things You Should Know

• Rephrase your thesis to include in your final paragraph to bring the essay full circle.
• End your essay with a call to action, warning, or image to make your argument meaningful.
• Keep your conclusion concise and to the point, so you don’t lose a reader’s attention.
• Do your best to avoid adding new information to your conclusion and only emphasize points you’ve already made in your essay.

• “All in all”
• “Ultimately”
• “Furthermore”
• “As a consequence”
• “As a result”

• Make sure to write your main points in a new and unique way to avoid repetition.

• Let’s say this is your original thesis statement: “Allowing students to visit the library during lunch improves campus life and supports academic achievement.”
• Restating your thesis for your conclusion could look like this: “Evidence shows students who have access to their school’s library during lunch check out more books and are more likely to complete their homework.”
• The restated thesis has the same sentiment as the original while also summarizing other points of the essay.

• “When you use plastic water bottles, you pollute the ocean. Switch to using a glass or metal water bottle instead. The planet and sea turtles will thank you.”
• “The average person spends roughly 7 hours on their phone a day, so there’s no wonder cybersickness is plaguing all generations.”
• “Imagine walking on the beach, except the soft sand is made up of cigarette butts. They burn your feet but keep washing in with the tide. If we don’t clean up the ocean, this will be our reality.”
• “ Lost is not only a show that changed the course of television, but it’s also a reflection of humanity as a whole.”
• “If action isn’t taken to end climate change today, the global temperature will dangerously rise from 4.5 to 8 °F (−15.3 to −13.3 °C) by 2100.”

• Focus on your essay's most prevalent or important parts. What key points do you want readers to take away or remember about your essay?

• For instance, instead of writing, “That’s why I think that Abraham Lincoln was the best American President,” write, “That’s why Abraham Lincoln was the best American President.”
• There’s no room for ifs, ands, or buts—your opinion matters and doesn’t need to be apologized for!

• For instance, words like “firstly,” “secondly,” and “thirdly” may be great transition statements for body paragraphs but are unnecessary in a conclusion.

• For instance, say you began your essay with the idea that humanity’s small sense of sense stems from space’s vast size. Try returning to this idea in the conclusion by emphasizing that as human knowledge grows, space becomes smaller.

• For example, you could extend an essay on the television show Orange is the New Black by bringing up the culture of imprisonment in America.

Community Q&A

• Always review your essay after writing it for proper grammar, spelling, and punctuation, and don’t be afraid to revise. Thanks Helpful 2 Not Helpful 1
• Ask a friend, family member, or teacher for help if you’re stuck. Sometimes a second opinion is all you need. Thanks Helpful 2 Not Helpful 1

You Might Also Like

• ↑ https://www.uts.edu.au/current-students/support/helps/self-help-resources/grammar/transition-signals
• ↑ https://owl.purdue.edu/owl/general_writing/common_writing_assignments/argument_papers/conclusions.html
• ↑ http://writing2.richmond.edu/writing/wweb/conclude.html
• ↑ https://writingcenter.fas.harvard.edu/pages/ending-essay-conclusions
• ↑ https://www.pittsfordschools.org/site/handlers/filedownload.ashx?moduleinstanceid=542&dataid=4677&FileName=conclusions1.pdf
• ↑ https://www.cuyamaca.edu/student-support/tutoring-center/files/student-resources/how-to-write-a-good-conclusion.pdf
• ↑ https://library.sacredheart.edu/c.php?g=29803&p=185935

About This Article

To end an essay, start your conclusion with a phrase that makes it clear your essay is coming to a close, like "In summary," or "All things considered." Then, use a few sentences to briefly summarize the main points of your essay by rephrasing the topic sentences of your body paragraphs. Finally, end your conclusion with a call to action that encourages your readers to do something or learn more about your topic. In general, try to keep your conclusion between 5 and 7 sentences long. For more tips from our English co-author, like how to avoid common pitfalls when writing an essay conclusion, scroll down! Did this summary help you? Yes No

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Essay Conclusions

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Learn about the elements of a successful essay conclusion.

The conclusion is a very important part of your essay. Although it is sometimes treated as a roundup of all of the bits that didn’t fit into the paper earlier, it deserves better treatment than that! It's the last thing the reader will see, so it tends to stick in the reader's memory. It's also a great place to remind the reader exactly why your topic is important. A conclusion is more than just "the last paragraph"—it's a working part of the paper. This is the place to push your reader to think about the consequences of your topic for the wider world or for the reader's own life!

A good conclusion should do a few things:

Restate your thesis

Synthesize or summarize your major points

Make the context of your argument clear

Restating Your Thesis

You've already spent time and energy crafting a solid thesis statement for your introduction, and if you've done your job right, your whole paper focuses on that thesis statement. That's why it's so important to address the thesis in your conclusion! Many writers choose to begin the conclusion by restating the thesis, but you can put your thesis into the conclusion anywhere—the first sentence of the paragraph, the last sentence, or in between. Here are a few tips for rephrasing your thesis:

Remind the reader that you've proven this thesis over the course of your paper. For example, if you're arguing that your readers should get their pets from animal shelters rather than pet stores, you might say, "If you were considering that puppy in the pet-shop window, remember that your purchase will support 'puppy mills' instead of rescuing a needy dog, and consider selecting your new friend at your local animal shelter." This example gives the reader not only the thesis of the paper, but a reminder of the most powerful point in the argument!

Revise the thesis statement so that it reflects the relationship you've developed with the reader during the paper. For example, if you've written a paper that targets parents of young children, you can find a way to phrase your thesis to capitalize on that—maybe by beginning your thesis statement with, "As a parent of a young child…"

Don’t repeat your thesis word for word—make sure that your new statement is an independent, fresh sentence!

Summary or Synthesis

This section of the conclusion might come before the thesis statement or after it. Your conclusion should remind the reader of what your paper actually says! The best conclusion will include a synthesis, not just a summary—instead of a mere list of your major points, the best conclusion will draw those points together and relate them to one another so that your reader can apply the information given in the essay. Here are a couple of ways to do that:

Give a list of the major arguments for your thesis (usually, these are the topic sentences of the parts of your essay).

Explain how these parts are connected. For example, in the animal-shelter essay, you might point out that adopting a shelter dog helps more animals because your adoption fee supports the shelter, which makes your choice more socially responsible.

One of the most important functions of the conclusion is to provide context for your argument. Your reader may finish your essay without a problem and understand your argument without understanding why that argument is important. Your introduction might point out the reason your topic matters, but your conclusion should also tackle this questions. Here are some strategies for making your reader see why the topic is important:

Tell the reader what you want him or her to do. Is your essay a call to action? If so, remind the reader of what he/she should do. If not, remember that asking the reader to think a certain way is an action in itself. (In the above examples, the essay asks the reader to adopt a shelter dog—a specific action.)

Explain why this topic is timely or important. For example, the animal-shelter essay might end with a statistic about the number of pets in shelters waiting for adoption.

Remind the readers of why the topic matters to them personally. For example, it doesn’t matter much if you believe in the mission of animal shelters, if you're not planning to get a dog; however, once you're looking for a dog, it is much more important. The conclusion of this essay might say, "Since you’re in the market for a dog, you have a major decision to make: where to get one." This will remind the reader that the argument is personally important!

Conclusion paragraphs

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17 Essay Conclusion Examples (Copy and Paste)

Essay conclusions are not just extra filler. They are important because they tie together your arguments, then give you the chance to forcefully drive your point home.

I created the 5 Cs conclusion method to help you write essay conclusions:

I’ve previously produced the video below on how to write a conclusion that goes over the above image.

The video follows the 5 C’s method ( you can read about it in this post ), which doesn’t perfectly match each of the below copy-and-paste conclusion examples, but the principles are similar, and can help you to write your own strong conclusion:

💡 New! Try this AI Prompt to Generate a Sample 5Cs Conclusion This is my essay: [INSERT ESSAY WITHOUT THE CONCLUSION]. I want you to write a conclusion for this essay. In the first sentence of the conclusion, return to a statement I made in the introduction. In the second sentence, reiterate the thesis statement I have used. In the third sentence, clarify how my final position is relevant to the Essay Question, which is [ESSAY QUESTION]. In the fourth sentence, explain who should be interested in my findings. In the fifth sentence, end by noting in one final, engaging sentence why this topic is of such importance.

Remember: The prompt can help you generate samples but you can’t submit AI text for assessment. Make sure you write your conclusion in your own words.

Essay Conclusion Examples

Below is a range of copy-and-paste essay conclusions with gaps for you to fill-in your topic and key arguments. Browse through for one you like (there are 17 for argumentative, expository, compare and contrast, and critical essays). Once you’ve found one you like, copy it and add-in the key points to make it your own.

1. Argumentative Essay Conclusions

The arguments presented in this essay demonstrate the significant importance of _____________. While there are some strong counterarguments, such as ____________, it remains clear that the benefits/merits of _____________ far outweigh the potential downsides. The evidence presented throughout the essay strongly support _____________. In the coming years, _____________ will be increasingly important. Therefore, continual advocacy for the position presented in this essay will be necessary, especially due to its significant implications for _____________.

Version 1 Filled-In

The arguments presented in this essay demonstrate the significant importance of fighting climate change. While there are some strong counterarguments, such as the claim that it is too late to stop catastrophic change, it remains clear that the merits of taking drastic action far outweigh the potential downsides. The evidence presented throughout the essay strongly support the claim that we can at least mitigate the worst effects. In the coming years, intergovernmental worldwide agreements will be increasingly important. Therefore, continual advocacy for the position presented in this essay will be necessary, especially due to its significant implications for humankind.

As this essay has shown, it is clear that the debate surrounding _____________ is multifaceted and highly complex. While there are strong arguments opposing the position that _____________, there remains overwhelming evidence to support the claim that _____________. A careful analysis of the empirical evidence suggests that _____________ not only leads to ____________, but it may also be a necessity for _____________. Moving forward, _____________ should be a priority for all stakeholders involved, as it promises a better future for _____________. The focus should now shift towards how best to integrate _____________ more effectively into society.

Version 2 Filled-In

As this essay has shown, it is clear that the debate surrounding climate change is multifaceted and highly complex. While there are strong arguments opposing the position that we should fight climate change, there remains overwhelming evidence to support the claim that action can mitigate the worst effects. A careful analysis of the empirical evidence suggests that strong action not only leads to better economic outcomes in the long term, but it may also be a necessity for preventing climate-related deaths. Moving forward, carbon emission mitigation should be a priority for all stakeholders involved, as it promises a better future for all. The focus should now shift towards how best to integrate smart climate policies more effectively into society.

Based upon the preponderance of evidence, it is evident that _____________ holds the potential to significantly alter/improve _____________. The counterarguments, while noteworthy, fail to diminish the compelling case for _____________. Following an examination of both sides of the argument, it has become clear that _____________ presents the most effective solution/approach to _____________. Consequently, it is imperative that society acknowledge the value of _____________ for developing a better  _____________. Failing to address this topic could lead to negative outcomes, including _____________.

Version 3 Filled-In

Based upon the preponderance of evidence, it is evident that addressing climate change holds the potential to significantly improve the future of society. The counterarguments, while noteworthy, fail to diminish the compelling case for immediate climate action. Following an examination of both sides of the argument, it has become clear that widespread and urgent social action presents the most effective solution to this pressing problem. Consequently, it is imperative that society acknowledge the value of taking immediate action for developing a better environment for future generations. Failing to address this topic could lead to negative outcomes, including more extreme climate events and greater economic externalities.

See Also: Examples of Counterarguments

On the balance of evidence, there is an overwhelming case for _____________. While the counterarguments offer valid points that are worth examining, they do not outweigh or overcome the argument that _____________. An evaluation of both perspectives on this topic concludes that _____________ is the most sufficient option for  _____________. The implications of embracing _____________ do not only have immediate benefits, but they also pave the way for a more _____________. Therefore, the solution of _____________ should be actively pursued by _____________.

Version 4 Filled-In

On the balance of evidence, there is an overwhelming case for immediate tax-based action to mitigate the effects of climate change. While the counterarguments offer valid points that are worth examining, they do not outweigh or overcome the argument that action is urgently necessary. An evaluation of both perspectives on this topic concludes that taking societal-wide action is the most sufficient option for  achieving the best results. The implications of embracing a society-wide approach like a carbon tax do not only have immediate benefits, but they also pave the way for a more healthy future. Therefore, the solution of a carbon tax or equivalent policy should be actively pursued by governments.

2. Expository Essay Conclusions

Overall, it is evident that _____________ plays a crucial role in _____________. The analysis presented in this essay demonstrates the clear impact of _____________ on _____________. By understanding the key facts about _____________, practitioners/society are better equipped to navigate _____________. Moving forward, further exploration of _____________ will yield additional insights and information about _____________. As such, _____________ should remain a focal point for further discussions and studies on _____________.

Overall, it is evident that social media plays a crucial role in harming teenagers’ mental health. The analysis presented in this essay demonstrates the clear impact of social media on young people. By understanding the key facts about the ways social media cause young people to experience body dysmorphia, teachers and parents are better equipped to help young people navigate online spaces. Moving forward, further exploration of the ways social media cause harm will yield additional insights and information about how it can be more sufficiently regulated. As such, the effects of social media on youth should remain a focal point for further discussions and studies on youth mental health.

To conclude, this essay has explored the multi-faceted aspects of _____________. Through a careful examination of _____________, this essay has illuminated its significant influence on _____________. This understanding allows society to appreciate the idea that _____________. As research continues to emerge, the importance of _____________ will only continue to grow. Therefore, an understanding of _____________ is not merely desirable, but imperative for _____________.

To conclude, this essay has explored the multi-faceted aspects of globalization. Through a careful examination of globalization, this essay has illuminated its significant influence on the economy, cultures, and society. This understanding allows society to appreciate the idea that globalization has both positive and negative effects. As research continues to emerge, the importance of studying globalization will only continue to grow. Therefore, an understanding of globalization’s effects is not merely desirable, but imperative for judging whether it is good or bad.

Reflecting on the discussion, it is clear that _____________ serves a pivotal role in _____________. By delving into the intricacies of _____________, we have gained valuable insights into its impact and significance. This knowledge will undoubtedly serve as a guiding principle in _____________. Moving forward, it is paramount to remain open to further explorations and studies on _____________. In this way, our understanding and appreciation of _____________ can only deepen and expand.

Reflecting on the discussion, it is clear that mass media serves a pivotal role in shaping public opinion. By delving into the intricacies of mass media, we have gained valuable insights into its impact and significance. This knowledge will undoubtedly serve as a guiding principle in shaping the media landscape. Moving forward, it is paramount to remain open to further explorations and studies on how mass media impacts society. In this way, our understanding and appreciation of mass media’s impacts can only deepen and expand.

In conclusion, this essay has shed light on the importance of _____________ in the context of _____________. The evidence and analysis provided underscore the profound effect _____________ has on _____________. The knowledge gained from exploring _____________ will undoubtedly contribute to more informed and effective decisions in _____________. As we continue to progress, the significance of understanding _____________ will remain paramount. Hence, we should strive to deepen our knowledge of _____________ to better navigate and influence _____________.

In conclusion, this essay has shed light on the importance of bedside manner in the context of nursing. The evidence and analysis provided underscore the profound effect compassionate bedside manner has on patient outcome. The knowledge gained from exploring nurses’ bedside manner will undoubtedly contribute to more informed and effective decisions in nursing practice. As we continue to progress, the significance of understanding nurses’ bedside manner will remain paramount. Hence, we should strive to deepen our knowledge of this topic to better navigate and influence patient outcomes.

See More: How to Write an Expository Essay

3. Compare and Contrast Essay Conclusion

While both _____________ and _____________ have similarities such as _____________, they also have some very important differences in areas like _____________. Through this comparative analysis, a broader understanding of _____________ and _____________ has been attained. The choice between the two will largely depend on _____________. For example, as highlighted in the essay, ____________. Despite their differences, both _____________ and _____________ have value in different situations.

While both macrosociology and microsociology have similarities such as their foci on how society is structured, they also have some very important differences in areas like their differing approaches to research methodologies. Through this comparative analysis, a broader understanding of macrosociology and microsociology has been attained. The choice between the two will largely depend on the researcher’s perspective on how society works. For example, as highlighted in the essay, microsociology is much more concerned with individuals’ experiences while macrosociology is more concerned with social structures. Despite their differences, both macrosociology and microsociology have value in different situations.

It is clear that _____________ and _____________, while seeming to be different, have shared characteristics in _____________. On the other hand, their contrasts in _____________ shed light on their unique features. The analysis provides a more nuanced comprehension of these subjects. In choosing between the two, consideration should be given to _____________. Despite their disparities, it’s crucial to acknowledge the importance of both when it comes to _____________.

It is clear that behaviorism and consructivism, while seeming to be different, have shared characteristics in their foci on knowledge acquisition over time. On the other hand, their contrasts in ideas about the role of experience in learning shed light on their unique features. The analysis provides a more nuanced comprehension of these subjects. In choosing between the two, consideration should be given to which approach works best in which situation. Despite their disparities, it’s crucial to acknowledge the importance of both when it comes to student education.

Reflecting on the points discussed, it’s evident that _____________ and _____________ share similarities such as _____________, while also demonstrating unique differences, particularly in _____________. The preference for one over the other would typically depend on factors such as _____________. Yet, regardless of their distinctions, both _____________ and _____________ play integral roles in their respective areas, significantly contributing to _____________.

Reflecting on the points discussed, it’s evident that red and orange share similarities such as the fact they are both ‘hot colors’, while also demonstrating unique differences, particularly in their social meaning (red meaning danger and orange warmth). The preference for one over the other would typically depend on factors such as personal taste. Yet, regardless of their distinctions, both red and orange play integral roles in their respective areas, significantly contributing to color theory.

Ultimately, the comparison and contrast of _____________ and _____________ have revealed intriguing similarities and notable differences. Differences such as _____________ give deeper insights into their unique and shared qualities. When it comes to choosing between them, _____________ will likely be a deciding factor. Despite these differences, it is important to remember that both _____________ and _____________ hold significant value within the context of _____________, and each contributes to _____________ in its own unique way.

Ultimately, the comparison and contrast of driving and flying have revealed intriguing similarities and notable differences. Differences such as their differing speed to destination give deeper insights into their unique and shared qualities. When it comes to choosing between them, urgency to arrive at the destination will likely be a deciding factor. Despite these differences, it is important to remember that both driving and flying hold significant value within the context of air transit, and each contributes to facilitating movement in its own unique way.

See Here for More Compare and Contrast Essay Examples

4. Critical Essay Conclusion

In conclusion, the analysis of _____________ has unveiled critical aspects related to _____________. While there are strengths in _____________, its limitations are equally telling. This critique provides a more informed perspective on _____________, revealing that there is much more beneath the surface. Moving forward, the understanding of _____________ should evolve, considering both its merits and flaws.

In conclusion, the analysis of flow theory has unveiled critical aspects related to motivation and focus. While there are strengths in achieving a flow state, its limitations are equally telling. This critique provides a more informed perspective on how humans achieve motivation, revealing that there is much more beneath the surface. Moving forward, the understanding of flow theory of motivation should evolve, considering both its merits and flaws.

To conclude, this critical examination of _____________ sheds light on its multi-dimensional nature. While _____________ presents notable advantages, it is not without its drawbacks. This in-depth critique offers a comprehensive understanding of _____________. Therefore, future engagements with _____________ should involve a balanced consideration of its strengths and weaknesses.

To conclude, this critical examination of postmodern art sheds light on its multi-dimensional nature. While postmodernism presents notable advantages, it is not without its drawbacks. This in-depth critique offers a comprehensive understanding of how it has contributed to the arts over the past 50 years. Therefore, future engagements with postmodern art should involve a balanced consideration of its strengths and weaknesses.

Upon reflection, the critique of _____________ uncovers profound insights into its underlying intricacies. Despite its positive aspects such as ________, it’s impossible to overlook its shortcomings. This analysis provides a nuanced understanding of _____________, highlighting the necessity for a balanced approach in future interactions. Indeed, both the strengths and weaknesses of _____________ should be taken into account when considering ____________.

Upon reflection, the critique of marxism uncovers profound insights into its underlying intricacies. Despite its positive aspects such as its ability to critique exploitation of labor, it’s impossible to overlook its shortcomings. This analysis provides a nuanced understanding of marxism’s harmful effects when used as an economic theory, highlighting the necessity for a balanced approach in future interactions. Indeed, both the strengths and weaknesses of marxism should be taken into account when considering the use of its ideas in real life.

Ultimately, this critique of _____________ offers a detailed look into its advantages and disadvantages. The strengths of _____________ such as __________ are significant, yet its limitations such as _________ are not insignificant. This balanced analysis not only offers a deeper understanding of _____________ but also underscores the importance of critical evaluation. Hence, it’s crucial that future discussions around _____________ continue to embrace this balanced approach.

Ultimately, this critique of artificial intelligence offers a detailed look into its advantages and disadvantages. The strengths of artificial intelligence, such as its ability to improve productivity are significant, yet its limitations such as the possibility of mass job losses are not insignificant. This balanced analysis not only offers a deeper understanding of artificial intelligence but also underscores the importance of critical evaluation. Hence, it’s crucial that future discussions around the regulation of artificial intelligence continue to embrace this balanced approach.

This article promised 17 essay conclusions, and this one you are reading now is the twenty-first. This last conclusion demonstrates that the very best essay conclusions are written uniquely, from scratch, in order to perfectly cater the conclusion to the topic. A good conclusion will tie together all the key points you made in your essay and forcefully drive home the importance or relevance of your argument, thesis statement, or simply your topic so the reader is left with one strong final point to ponder.

Chris Drew (PhD)

Dr. Chris Drew is the founder of the Helpful Professor. He holds a PhD in education and has published over 20 articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education. [Image Descriptor: Photo of Chris]

• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ Social-Emotional Learning (Definition, Examples, Pros & Cons)
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• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ What is IQ? (Intelligence Quotient)
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Essay writing: Conclusions

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• Analysing questions
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“Pay adequate attention to the conclusion.” Kathleen McMillan & Jonathan Weyers,  How to Write Essays & Assignments

Conclusions are often overlooked, cursory and written last minute. If this sounds familiar then it's time to change and give your conclusions some much needed attention. Your conclusion is the whole point of your essay. All the other parts of the essay should have been leading your reader on an inevitable journey towards your conclusion. So make it count and finish your essay in style.

Know where you are going

Too many students focus their essays on content rather than argument. This means they pay too much attention to the main body without considering where it is leading. It can be a good idea to write a draft conclusion before  you write your main body. It is a lot easier to plan a journey when you know your destination! 

It should only be a draft however, as quite often the writing process itself can help you develop your argument and you may feel your conclusion needs adapting accordingly.

What it should include

A great conclusion should include:

A clear link back to the question . This is usually the first thing you do in a conclusion and it shows that you have (hopefully) answered it.

A sentence or two that summarise(s) your main argument but in a bit more detail than you gave in your introduction.

A series of supporting sentences that basically reiterate the main point of each of your paragraphs but show how they relate to each other and lead you to the position you have taken. Constantly ask yourself "So what?" "Why should anyone care?" and answer these questions for each of the points you make in your conclusion.

A final sentence that states why your ideas are important to the wider subject area . Where the introduction goes from general to specific, the conclusion needs to go from specific back out to general.

What it should not  include

Try to avoid including the following in your conclusion. Remember your conclusion should be entirely predictable. The reader wants no surprises.

Any new ideas . If an idea is worth including, put it in the main body. You do not need to include citations in your conclusion if you have already used them earlier and are just reiterating your point.

A change of style i.e. being more emotional or sentimental than the rest of the essay. Keep it straightforward, explanatory and clear.

Overused phrases like: “in conclusion”; “in summary”; “as shown in this essay”. Consign these to the rubbish bin!

Here are some alternatives, there are many more:

• The x main points presented here emphasise the importance of...
• The [insert something relevant] outlined above indicate that ...
• By showing the connections between x, y and z, it has been argued here that ...

Maximise marks

Remember, your conclusion is the last thing your reader (marker!) will read. Spending a little care on it will leave her/him absolutely sure that you have answered the question and you will definitely receive a higher mark than if your conclusion was a quickly written afterthought.

Your conclusion should be around 10% of your word count. There is never a situation where sacrificing words in your conclusion will benefit your essay.

The 5Cs conclusion method: (spot the typo on this video)

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5 Examples of Concluding Words for Essays

4-minute read

• 19th September 2022

If you’re a student writing an essay or research paper, it’s important to make sure your points flow together well. You’ll want to use connecting words (known formally as transition signals) to do this. Transition signals like thus , also , and furthermore link different ideas, and when you get to the end of your work, you need to use these to mark your conclusion. Read on to learn more about transition signals and how to use them to conclude your essays.

Transition Signals

Transition signals link sentences together cohesively, enabling easy reading and comprehension. They are usually placed at the beginning of a sentence and separated from the remaining words with a comma. There are several types of transition signals, including those to:

●  show the order of a sequence of events (e.g., first, then, next)

●  introduce an example (e.g., specifically, for instance)

●  indicate a contrasting idea (e.g., but, however, although)

●  present an additional idea (e.g., also, in addition, plus)

●  indicate time (e.g., beforehand, meanwhile, later)

●  compare (e.g., likewise, similarly)

●  show cause and effect (e.g., thus, as a result)

●  mark the conclusion – which we’ll focus on in this guide.

When you reach the end of an essay, you should start the concluding paragraph with a transition signal that acts as a bridge to the summary of your key points. Check out some concluding transition signals below and learn how you can use them in your writing.

To Conclude…

This is a particularly versatile closing statement that can be used for almost any kind of essay, including both formal and informal academic writing. It signals to the reader that you will briefly restate the main idea. As an alternative, you can begin the summary with “to close” or “in conclusion.” In an argumentative piece, you can use this phrase to indicate a call to action or opinion:

To conclude, Abraham Lincoln was the best president because he abolished slavery.

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As Has Been Demonstrated…

To describe how the evidence presented in your essay supports your argument or main idea, begin the concluding paragraph with “as has been demonstrated.” This phrase is best used for research papers or articles with heavy empirical or statistical evidence.

As has been demonstrated by the study presented above, human activities are negatively altering the climate system.

The Above Points Illustrate…

As another transitional phrase for formal or academic work, “the above points illustrate” indicates that you are reiterating your argument and that the conclusion will include an assessment of the evidence you’ve presented.

The above points illustrate that children prefer chocolate over broccoli.

In a Nutshell…

A simple and informal metaphor to begin a conclusion, “in a nutshell” prepares the reader for a summary of your paper. It can work in narratives and speeches but should be avoided in formal situations.

In a nutshell, the Beatles had an impact on musicians for generations to come.

Overall, It Can Be Said…

To recap an idea at the end of a critical or descriptive essay, you can use this phrase at the beginning of the concluding paragraph. “Overall” means “taking everything into account,” and it sums up your essay in a formal way. You can use “overall” on its own as a transition signal, or you can use it as part of a phrase.

Overall, it can be said that art has had a positive impact on humanity.

Proofreading and Editing

Transition signals are crucial to crafting a well-written and cohesive essay. For your next writing assignment, make sure you include plenty of transition signals, and check out this post for more tips on how to improve your writing. And before you turn in your paper, don’t forget to have someone proofread your work. Our expert editors will make sure your essay includes all the transition signals necessary for your writing to flow seamlessly. Send in a free 500-word sample today!

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What Are Rabbits Really Like?

People who haven’t lived with rabbits often ask those who do if rabbits make “good pets,” and if so, if they are more like dogs or cats? Most rabbit people don’t quite know how to respond to these questions; Not just because we have transcended these matters in our relationships with rabbits but also because the nature of the questions makes us feel uncomfortable.

“A Good Pet”

It seems that for most people, an animal is perceived as a “good pet” if she shows affection in ways human beings can understand without much effort (e.g., lapsitting or coming when called), if she participates in games humans easily comprehend (“catch,” “fetch,” or “chase the string”), or if she makes an apparent effort to communicate vocally (barking to be let in or out, mewing for supper). People usually seem fairly sure these qualities cannot be expected of a rabbit, so rabbits would not make “good pets.” Alternatively, some expect such traits in all rabbits and may be disappointed in a bunny unwilling or unable to comply with their expectations.

“Are rabbits more like cats or dogs?”

The second question, “Are rabbits more like cats or dogs?” is a natural to follow the first. My usual response is, “Are people more like fish or cockatoos?” After all, rabbits are, first and foremost, like rabbits , and the only way to find out what they are like is to live with one or more. You’ll find that rabbits share a few characteristics with dogs, a few with cats, and a few with humans. They probably even share a few with fish and cockatoos. But mostly, they’re like rabbits, and learning what rabbits are like is part of the joy of living with them. The fact that this question, like the “good pets” one, is asked at all makes clear the human position that to be considered of value, other species must conform to our notions of what is “good.”

What Is Good?

The other day I sat on the bedroom floor returning phone calls. Megan, our overweight and very aggressive New Zealand (who, paradoxically, adores being petted), galumphed up, grabbed the notebook out of my hand, bit a hole out of the corner, and stomped on it. She lunged at my hand as I retrieved the notebook, grazing it with her teeth, then shoved my leg and settled down against me. I grinned at her and stroked her head (as I had just been commanded to do). The caller told me about her rabbit, who wouldn’t let her pick him up, lunged and bit when approached, and seemed to “hate” the family. On the other hand, the family dog loved the children and played with them all the time; they were disappointed in the rabbit and wanted me to find him a new home.

I looked at Megan, her head pressed to the floor, eyes closed, ears relaxed, fat body spread out behind her. No, she doesn’t act like a dog. If a dog lunged and bit, you’d be justified in getting worried because human-canine relations are entirely different from those between humans and rabbits. But Megan and the caller’s rabbit act like rabbits, each in their own ways. The difference, I realized, is that I accept Megan’s aggression (and even revel in it!), while the caller seemed to resent her rabbit because his behavior did not conform to her idea of “a good pet.”

“Better Pets”

The implication that some animals (usually dogs and cats) are “better pets” than others rests on the assumption that to fit into our lives, all animals should resemble those to whom we are already accustomed. Such an assumption removes the responsibility for the relationship from the human being and places it solely on the animal. Although the rabbit is expected to comply with human expectations, all too often, humans never even consider complying with the bunny. But in almost every case, a wonderful new relationship is forged when you begin complying with the expectations of a rabbit. Megan accosts me, and I react in a way she finds appropriate, even though it initially seems odd to me. After a few weeks, Megan trusts me, likes me, and has me pegged as savvy – ‘but she still nips my foot if I venture too near her parsley!

Do we expect too much or not enough?

I hesitate to tell people not to expect their rabbits to jump up on their legs, leap into their laps, or lick their hands, because some rabbits do these things. But too many people expect such behaviors and express disappointment when their rabbits do not comply. None of the rabbits I live with currently do any of these dog-like things, but over the years I have discovered a range of interesting activities they engage in that the dogs and cats in our family never even thought about. Megan may not jump into my lap, and she’s more likely to bite my hand than lick it, but she terrorizes the cats daily, manages to growl in annoyance while simultaneously cavorting with joy across the floor, and makes demands more effectively than any of our noisier critters.

The term “pet”

No small part of the problem lies in using the term “pet.” After all, a pet is “one who is petted,” implying passivity and ownership. We seldom call other human beings “pets,” and most people would consider it an insult if we did. By using the term to describe animals, we diminish their importance in our lives. We are denying their right to individuality and a lifestyle that may or may not include allowing us to fawn over them. On the other hand, a rabbit who is a companion is one who – ‘like our human friends – ‘is encouraged to develop the personality nature gave her and is appreciated for who she is.

So what should we say when people ask if rabbits are “good pets”? I don’t want to assure folks that they are, because I know the implications of the phrase. On the other hand, if I hesitate and explain, they’ll think I’m making excuses. They may be unable to see what is special about rabbits. Perhaps those of us who know , through experience, what rabbits are like should decline to answer these questions at all. Instead, explain that rabbits make wonderful, exciting, intelligent companions for excellent, exciting, intelligent people. After all, living up to the expectations of a rabbit like Megan ‘or Trixie or Phoebe or Bandit takes a lot of work! Their type of person is adventurous, charmed by evidence of spunk and vigor, and willing to learn a new language, a new lifestyle, and a new code of behavior. Those who live by stereotyping, pigeon-holing, or typecasting need not apply.

©Copyright Elizabeth TeSelle. All Rights Reserved. Republished with the permission of the author.

What Are Rabbits Really Like? first appeared in the House Rabbit Journal Volume III, Number 5.

Elizabeth TeSelle

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E. B. White is one of the most famous children’s book authors. But he should be better known for his essays.

I was well into adulthood before I realized the co-author of my battered copy of The Elements of Style was also the author of Stuart Little and Charlotte’s Web . That’s right, the White of the revered style manual that everyone knew as “Strunk and White” also wrote children’s books…as well as some of the best essays in the English language.

If you’re of a certain age, you might well remember E. B. White’s pointers in The Elements of Style :

Place yourself in the background; write in a way that comes naturally; work from a suitable design; write with nouns and verbs; do not overwrite; do not overstate; avoid the use of qualifiers; do not affect a breezy style; use orthodox spelling; do not explain too much; avoid fancy words; do not take shortcuts at the cost of clarity; prefer the standard to the offbeat; make sure the reader knows who is speaking; do not use dialect; revise and rewrite.

That’s some good advice, much better than the terrible counsel offered on Page 76: “Avoid the elaborate, the pretentious, the coy, and the cute.” Thanks, E. B., I do what I want. ☹️

Born in 1899 in Mount Vernon, N.Y., Elwyn Brooks White attended Cornell University, where he earned the nickname “Andy.” (Weird historical fact: If your last name was White, you were automatically an Andy at Cornell, in honor of the school’s co-founder, Andrew Dickson White. There is no connection to fellow Cornell alum Andy Bernard .) After graduation, White worked as a journalist and an advertising copywriter for several years. He published his first article in The New Yorker the year it was founded, 1925.

White became a staff writer at The New Yorker in 1927, but was an early enthusiast of the work-from-home movement, initially refusing to come to the office and eventually agreeing to come in only on Thursdays. In those days, he shared a small office (“a sort of elongated closet,” he called it) with James Thurber.

His famous officemate later recalled that White had an odd a brilliant habit: When visitors were announced, he would climb out the office window and scamper down the fire escape. “He has avoided the Man in the Reception Room as he has avoided the interviewer, the photographer, the microphone, the rostrum, the literary tea, and the Stork Club,” Thurber later remembered of the chronically shy author. “His life is his own.”

In 1929, White and Thurber co-authored their first book, Is Sex Necessary? Or, Why You Feel the Way You Do . (Don’t worry: It was comic essays.) That same year, White married Katharine Angell, The New Yorker’s fiction editor from its inaugural year until 1960. She was the mother of Roger Angell , the famed essayist and baseball writer who himself became a fiction editor at The New Yorker in the 1950s.

In 1938, White and Katharine moved permanently to a farm in Maine they had purchased five years before. If you’re wondering about the inspiration for 1952’s Charlotte’s Web , look no further than White’s 1948 essay for The Atlantic, “ Death of a Pig .” (He bought the pig with the intention of fattening it for slaughter; instead, he later nursed it through a fatal illness and buried it on the farm.)

Stuart Little had been published seven years before Charlotte’s Web . Along with 1970’s The Trumpet of the Swan , these books have made White one of the nation’s best-known children’s authors. I’m sure White didn’t mind, but by all rights, he should be better known for his essays. He authored over 20 collections of such classics as “Once More to the Lake,” “The Sea and The Wind That Blow,” “The Ring of Time,” “A Slight Sound at Evening” and “Farewell, My Lovely!” Endlessly anthologized, many are also taught in writing workshops to this day.

In 1949, White published Here Is New York , a short book developed from an essay about the pros and cons of living in New York City. In a 2012 essay for America , literary editor Raymond Schroth, S.J., noted White’s juxtaposition in Here Is New York of technological terrors like nuclear bombers (the Soviet Union detonated its first atomic bomb in 1949) with the simple beauties of nature:

Grand Central Terminal has become honky tonk, the great mansions are in decline, and there is generally more tension, irritability and great speed. The subtlest change is that the city is now destructible. A single flight of planes no bigger than a flock of geese could end this island fantasy, burn the towers and crumble the bridges. But the United Nations will make this the capital of the world. The perfect target may become the perfect “demonstration of nonviolence and racial brotherhood.” A block away in an interior garden was an old willow tree. This tree, symbol of the city, White said, must survive.

“It is a battered tree, long suffering and much climbed, held together by strands of wire but beloved of those who know it,” White wrote in Here Is New York . “In a way it symbolizes the city: life under difficulties, growth against odds, sap-rise in the midst of concrete, and the steady reaching for the sun. Whenever I look at it nowadays, and feel the cold shadow of the planes, I think: ‘This must be saved, this particular thing, this very tree.’”

The tree lasted for another six decades —two more than the Cold War, in fact—before finally being chopped down in 2009.

In a 1954 review of books by White and James Michener, America literary editor Harold C. Gardiner, S.J. , said White “has one of the most distinctive styles discernible on the American literary scene.” Since even the most cursory review of Father Gardiner’s many years of commentary shows he hated almost everything, it was quite a compliment. (Later in the review, he noted that “Mr. Michener, who has done better in his other books, comes a cropper here mainly because his style is wooden, sententious and dull.”)

In 1963, White received the Presidential Medal of Freedom for his writings. Fifteen years later, he was awarded a special Pulitzer Prize for “his letters, essays, and the full body of his work.” In 2005, the composer Nico Muhly debuted a song cycle based on The Elements of Style at the New York Public Library. Among its signature moments was a tenor offering more of White’s good advice, this time in song:

Do not use a hyphen between words that can be better written as one word .

White died in 1985 at his farm in Maine. His wife Katharine had died eight years earlier. His obituary in The New York Times quoted William Shawn, the legendary editor of The New Yorker:

His literary style was as pure as any in our language. It was singular, colloquial, clear, unforced, thoroughly American and utterly beautiful. Because of his quiet influence, several generations of this country's writers write better than they might have done. He never wrote a mean or careless sentence. He was impervious to literary, intellectual and political fashion. He was ageless, and his writing was timeless.

Our poetry selection for this week is “ Another Doubting Sonnet ,” by Renee Emerson. Readers can view all of America ’s published poems here .

Also, news from the Catholic Book Club: We are reading Norwegian novelist and 2023 Nobel Prize winner Jon Fosse’s multi-volume work Septology . Click here to buy the book, and click here to sign up for our Facebook discussion group .

In this space every week, America features reviews of and literary commentary on one particular writer or group of writers (both new and old; our archives span more than a century), as well as poetry and other offerings from America Media. We hope this will give us a chance to provide you with more in-depth coverage of our literary offerings. It also allows us to alert digital subscribers to some of our online content that doesn’t make it into our newsletters.

Other Catholic Book Club columns:

The spiritual depths of Toni Morrison

What’s all the fuss about Teilhard de Chardin?

Moira Walsh and the art of a brutal movie review

​​Who’s in hell? Hans Urs von Balthasar had thoughts.

Happy reading!

James T. Keane

James T. Keane is a senior editor at America.

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Teens come up with trigonometry proof for Pythagorean Theorem, a problem that stumped math world for centuries

By Bill Whitaker

May 5, 2024 / 7:00 PM EDT / CBS News

As the school year ends, many students will be only too happy to see math classes in their rearview mirrors. It may seem to some of us non-mathematicians that geometry and trigonometry were created by the Greeks as a form of torture, so imagine our amazement when we heard two high school seniors had proved a mathematical puzzle that was thought to be impossible for 2,000 years. 

We met Calcea Johnson and Ne'Kiya Jackson at their all-girls Catholic high school in New Orleans. We expected to find two mathematical prodigies.

Instead, we found at St. Mary's Academy , all students are told their possibilities are boundless.

Come Mardi Gras season, New Orleans is alive with colorful parades, replete with floats, and beads, and high school marching bands.

In a city where uniqueness is celebrated, St. Mary's stands out – with young African American women playing trombones and tubas, twirling batons and dancing - doing it all, which defines St. Mary's, students told us.

Junior Christina Blazio says the school instills in them they have the ability to accomplish anything. 

Christina Blazio: That is kinda a standard here. So we aim very high - like, our aim is excellence for all students. 

The private Catholic elementary and high school sits behind the Sisters of the Holy Family Convent in New Orleans East. The academy was started by an African American nun for young Black women just after the Civil War. The church still supports the school with the help of alumni.

In December 2022, seniors Ne'Kiya Jackson and Calcea Johnson were working on a school-wide math contest that came with a cash prize.

Ne'Kiya Jackson: I was motivated because there was a monetary incentive.

Calcea Johnson: 'Cause I was like, "$500 is a lot of money. So I-- I would like to at least try."

Both were staring down the thorny bonus question.

Bill Whitaker: So tell me, what was this bonus question?

Calcea Johnson: It was to create a new proof of the Pythagorean Theorem. And it kind of gave you a few guidelines on how would you start a proof.

The seniors were familiar with the Pythagorean Theorem, a fundamental principle of geometry. You may remember it from high school: a² + b² = c². In plain English, when you know the length of two sides of a right triangle, you can figure out the length of the third.

Both had studied geometry and some trigonometry, and both told us math was not easy. What no one told  them  was there had been more than 300 documented proofs of the Pythagorean Theorem using algebra and geometry, but for 2,000 years a proof using trigonometry was thought to be impossible, … and that was the bonus question facing them.

Bill Whitaker: When you looked at the question did you think, "Boy, this is hard"?

Ne'Kiya Jackson: Yeah. 

Bill Whitaker: What motivated you to say, "Well, I'm going to try this"?

Calcea Johnson: I think I was like, "I started something. I need to finish it." 

Bill Whitaker: So you just kept on going.

Calcea Johnson: Yeah.

For two months that winter, they spent almost all their free time working on the proof.

CeCe Johnson: She was like, "Mom, this is a little bit too much."

CeCe and Cal Johnson are Calcea's parents.

CeCe Johnson:   So then I started looking at what she really was doing. And it was pages and pages and pages of, like, over 20 or 30 pages for this one problem.

Cal Johnson: Yeah, the garbage can was full of papers, which she would, you know, work out the problems and-- if that didn't work she would ball it up, throw it in the trash. 

Bill Whitaker: Did you look at the problem? 

Neliska Jackson is Ne'Kiya's mother.

Neliska Jackson: Personally I did not. 'Cause most of the time I don't understand what she's doing (laughter).

Michelle Blouin Williams: What if we did this, what if I write this? Does this help? ax² plus ….

Their math teacher, Michelle Blouin Williams, initiated the math contest.

Bill Whitaker: And did you think anyone would solve it?

Michelle Blouin Williams: Well, I wasn't necessarily looking for a solve. So, no, I didn't—

Bill Whitaker: What were you looking for?

Michelle Blouin Williams: I was just looking for some ingenuity, you know—

Calcea and Ne'Kiya delivered on that! They tried to explain their groundbreaking work to 60 Minutes. Calcea's proof is appropriately titled the Waffle Cone.

Calcea Johnson: So to start the proof, we start with just a regular right triangle where the angle in the corner is 90°. And the two angles are alpha and beta.

Bill Whitaker: Uh-huh

Calcea Johnson: So then what we do next is we draw a second congruent, which means they're equal in size. But then we start creating similar but smaller right triangles going in a pattern like this. And then it continues for infinity. And eventually it creates this larger waffle cone shape.

Calcea Johnson: Am I going a little too—

Bill Whitaker: You've been beyond me since the beginning. (laughter) 

Bill Whitaker: So how did you figure out the proof?

Ne'Kiya Jackson: Okay. So you have a right triangle, 90° angle, alpha and beta.

Bill Whitaker: Then what did you do?

Ne'Kiya Jackson: Okay, I have a right triangle inside of the circle. And I have a perpendicular bisector at OP to divide the triangle to make that small right triangle. And that's basically what I used for the proof. That's the proof.

Bill Whitaker: That's what I call amazing.

Ne'Kiya Jackson: Well, thank you.

There had been one other documented proof of the theorem using trigonometry by mathematician Jason Zimba in 2009 – one in 2,000 years. Now it seems Ne'Kiya and Calcea have joined perhaps the most exclusive club in mathematics. 

Bill Whitaker: So you both independently came up with proof that only used trigonometry.

Ne'Kiya Jackson: Yes.

Bill Whitaker: So are you math geniuses?

Calcea Johnson: I think that's a stretch. 

Bill Whitaker: If not genius, you're really smart at math.

Ne'Kiya Jackson: Not at all. (laugh) 

To document Calcea and Ne'Kiya's work, math teachers at St. Mary's submitted their proofs to an American Mathematical Society conference in Atlanta in March 2023.

Ne'Kiya Jackson: Well, our teacher approached us and was like, "Hey, you might be able to actually present this," I was like, "Are you joking?" But she wasn't. So we went. I got up there. We presented and it went well, and it blew up.

Bill Whitaker: It blew up.

Calcea Johnson: Yeah. 

Ne'Kiya Jackson: It blew up.

Bill Whitaker: Yeah. What was the blowup like?

Calcea Johnson: Insane, unexpected, crazy, honestly.

It took millenia to prove, but just a minute for word of their accomplishment to go around the world. They got a write-up in South Korea and a shout-out from former first lady Michelle Obama, a commendation from the governor and keys to the city of New Orleans. 

Bill Whitaker: Why do you think so many people found what you did to be so impressive?

Ne'Kiya Jackson: Probably because we're African American, one. And we're also women. So I think-- oh, and our age. Of course our ages probably played a big part.

Bill Whitaker: So you think people were surprised that young African American women, could do such a thing?

Calcea Johnson: Yeah, definitely.

Ne'Kiya Jackson: I'd like to actually be celebrated for what it is. Like, it's a great mathematical achievement.

Achievement, that's a word you hear often around St. Mary's academy. Calcea and Ne'Kiya follow a long line of barrier-breaking graduates. 

The late queen of Creole cooking, Leah Chase , was an alum. so was the first African-American female New Orleans police chief, Michelle Woodfork …

And judge for the Fifth Circuit Court of Appeals, Dana Douglas. Math teacher Michelle Blouin Williams told us Calcea and Ne'Kiya are typical St. Mary's students.  

Bill Whitaker: They're not unicorns.

Michelle Blouin Williams: Oh, no no. If they are unicorns, then every single lady that has matriculated through this school is a beautiful, Black unicorn.

Pamela Rogers: You're good?

Pamela Rogers, St. Mary's president and interim principal, told us the students hear that message from the moment they walk in the door.

Pamela Rogers: We believe all students can succeed, all students can learn. It does not matter the environment that you live in. 

Bill Whitaker: So when word went out that two of your students had solved this almost impossible math problem, were they universally applauded?

Pamela Rogers: In this community, they were greatly applauded. Across the country, there were many naysayers.

Bill Whitaker: What were they saying?

Pamela Rogers: They were saying, "Oh, they could not have done it. African Americans don't have the brains to do it." Of course, we sheltered our girls from that. But we absolutely did not expect it to come in the volume that it came.  

Bill Whitaker: And after such a wonderful achievement.

Pamela Rogers: People-- have a vision of who can be successful. And-- to some people, it is not always an African American female. And to us, it's always an African American female.

Gloria Ladson-Billings: What we know is when teachers lay out some expectations that say, "You can do this," kids will work as hard as they can to do it.

Gloria Ladson-Billings, professor emeritus at the University of Wisconsin, has studied how best to teach African American students. She told us an encouraging teacher can change a life.

Bill Whitaker: And what's the difference, say, between having a teacher like that and a whole school dedicated to the excellence of these students?

Gloria Ladson-Billings: So a whole school is almost like being in Heaven. 

Bill Whitaker: What do you mean by that?

Gloria Ladson-Billings: Many of our young people have their ceilings lowered, that somewhere around fourth or fifth grade, their thoughts are, "I'm not going to be anything special." What I think is probably happening at St. Mary's is young women come in as, perhaps, ninth graders and are told, "Here's what we expect to happen. And here's how we're going to help you get there."

At St. Mary's, half the students get scholarships, subsidized by fundraising to defray the $8,000 a year tuition. Here, there's no test to get in, but expectations are high and rules are strict: no cellphones, modest skirts, hair must be its natural color.

Students Rayah Siddiq, Summer Forde, Carissa Washington, Tatum Williams and Christina Blazio told us they appreciate the rules and rigor.

Rayah Siddiq: Especially the standards that they set for us. They're very high. And I don't think that's ever going to change.

Bill Whitaker: So is there a heart, a philosophy, an essence to St. Mary's?

Summer Forde: The sisterhood—

Carissa Washington: Sisterhood.

Tatum Williams: Sisterhood.

Bill Whitaker: The sisterhood?

Voices: Yes.

Bill Whitaker: And you don't mean the nuns. You mean-- (laughter)

Christina Blazio: I mean, yeah. The community—

Bill Whitaker: So when you're here, there's just no question that you're going to go on to college.

Rayah Siddiq: College is all they talk about. (laughter) 

Pamela Rogers: … and Arizona State University (Cheering)

Principal Rogers announces to her 615 students the colleges where every senior has been accepted.

Bill Whitaker: So for 17 years, you've had a 100% graduation rate—

Pamela Rogers: Yes.

Bill Whitaker: --and a 100% college acceptance rate?

Pamela Rogers: That's correct.

Last year when Ne'Kiya and Calcea graduated, all their classmates went to college and got scholarships. Ne'Kiya got a full ride to the pharmacy school at Xavier University in New Orleans. Calcea, the class valedictorian, is studying environmental engineering at Louisiana State University.

Bill Whitaker: So wait a minute. Neither one of you is going to pursue a career in math?

Both: No. (laugh)

Calcea Johnson: I may take up a minor in math. But I don't want that to be my job job.

Ne'Kiya Jackson: Yeah. People might expect too much out of me if (laugh) I become a mathematician. (laugh)

But math is not completely in their rear-view mirrors. This spring they submitted their high school proofs for final peer review and publication … and are still working on further proofs of the Pythagorean Theorem. Since their first two …

Calcea Johnson: We found five. And then we found a general format that could potentially produce at least five additional proofs.

Bill Whitaker: And you're not math geniuses?

Bill Whitaker: I'm not buying it. (laughs)

Produced by Sara Kuzmarov. Associate producer, Mariah B. Campbell. Edited by Daniel J. Glucksman.

Bill Whitaker is an award-winning journalist and 60 Minutes correspondent who has covered major news stories, domestically and across the globe, for more than four decades with CBS News.

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