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How to Write a Classification Essay in Mathematics: Everything You Have to Know

A classification essay is a common type of academic assignments you are likely to deal with irrespectively of what discipline you study. Although one does not have to write essays often when studying mathematics, if you are given such a task, the essay in question is very likely to be a classification essay.

The purpose of classification is to divide a set of things (“things” understood in the broadest sense – they can be anything, from theories and rules to concepts and ideas) into categories or groups. Most commonly, this type of writing is used to analyze a body of topic-related material, single out characteristic features relevant to its individual representatives so that you can compare then and draw conclusions from your findings.

Writing essays in mathematics is often complicated and involves challenges you do not often meet when working on other disciplines – which is exactly why we compiled this guide.

Pre-writing Stage

Brainstorming a Topic for Your Essay

Choosing a topic for a classification essay is somewhat different from when you do it for other types of academic assignments. You do not so much choose a topic per se as a set of criteria according to which you compare the group of things you intend to classify, the organizing principle you are going to use to divide them into groups. This means that you have to carry out a significant portion of your thinking and research before you write a single line of your essay or even start gathering information for it. After all, if you select the criteria for comparison and later realize that they are invalid for some things under scrutiny, or that there are important criteria that you missed, it means rewriting huge portions of the essay if not the text in its entirety.

Your instructor may give you a set of things to classify, or you may have complete freedom of choice. Irrespectively of what the case is in your situation, the quality of your topic is based on the applicability of the criteria you choose. Some good examples include:

  • Ancient Mathematical Systems Classified Based on Their Use of Zero;
  • Classification of Unsolved Mathematical Problems Based on Their Area of Application;
  • Classifying Fundamental Mathematical Lemmata Based on Their Relationships with Theorems;
  • Classification of Mathematical Schools of Thought Based on Their Connections to Philosophy;
  • Classifying Mathematical Concepts for Further Understanding.

List and Define Classification Criteria

Before you proceed to gathering the information and writing the essay proper, you should have clear understanding of the criteria you intend to use in your work. Make sure that:

Tired of all the guides and never-ending instructions?
  • You define what leads to the inclusion of an item into a particular category (i.e., it should be easy to decide where an item falls based on each criteria);
  • Your criteria make for distinctive boundaries between categories. You should not wonder whether an item belongs to one category or another;
  • If any category can be further subdivided into smaller groups, make sure you do it at this stage to prepare enough examples for each subcategory.

Classification essays can be roughly divided into two types: those that use a single classifying criterion for categorization and those that use two or more criteria. How your write and organize your essay heavily depends on which type it belongs to.

Prepare a Thesis Statement

A thesis statement expresses, in short, what the essay is about, what its main idea is. Just like in most other types of academic works, it should follow certain guidelines. It has to be:

  • Short – normally 20 to 35 words in a single sentence;
  • Unambiguous – express yourself clearly, without leaving any opportunities for misunderstanding;
  • Direct – only mention the most basic information absolutely necessary to express your point of view.

Depending on the type of classification essay, the contents of your thesis statement will be different. If you use a single criterion, mention and explain it here along with the categories that result from its application. If you use multiple criteria, doing it will bloat the thesis statement too much. This is why in this case you only mention the criteria you use and further develop the topic in the body paragraphs.

Prepare an Outline

An outline is a plan of your essay. Depending on your writing style and personal preferences, it may range from a very basic enumeration of criteria and categories you want to describe to careful and detailed plan of each paragraph including references to quotations, examples supporting each point and ways of connecting individual parts of the essay.

Writing Your Assignment

Writing Your Introduction

Start with a statement aimed at attracting the reader’s attention. You should express a thought behind your classification. Prove to the audience that your categorization is important and explain why you believe so. What do you expect to achieve by analyzing the items under scrutiny and dividing them into categories?

Start with broad opening statements covering the background information about the subject matter, then move to more specific matters involving the items you intend to categorize and the importance of your work. Complete it with the thesis statement you wrote earlier.

Writing Your Body Paragraphs

Depending on whether you use a single criterion or multiple criteria, your body paragraphs will look differently.
If you use a single criterion, you should mention all the categories that result from your classification in the thesis statement and dedicate each body paragraph to detailed investigation of each individual category:

  • Topic sentence names the category and explains how it results from the application of your criterion;
  • Supporting sentences elaborate on the category. Describe its main characteristics, provide examples, use references from authoritative academic sources;
  • Conclusion sums up what you said up to this point and connects the paragraph back to the thesis statement and to the rest of the essay.

If you use multiple criteria, you dedicate each paragraph to a single criterion and describe categories that arise from applying it:

  • Topic sentence names the criterion and explains what it means;
  • Supporting sentences enumerate the categories this classification creates along with examples and evidence from sources;
  • Conclusion sums up what you said.

Writing Your Conclusion

The conclusion of a classification essay restates the main points mentioned prior to this moment and re-emphasizes their importance. However, it does not mean that you are supposed to rewrite your thesis statement and introduction word for word – you should take into account what you already told the audience since then. The purpose of conclusion is to refresh the information you started out with in the reader’s memory and allow him/her to better judge the conclusions you reached in the process of writing. In a way, it is the opposite of the introduction: you start with speaking about specific things (categories and their characteristic features) and end up reaching broader conclusions (what your classification signifies and what further research may be in order to study it). Make sure you do not mention any new information that was not present before.

Accompany Everything with Examples

Classification essays, especially the ones dealing with obscure mathematical topics, thrive on carefully selected and relevant examples. Whenever you introduce a new category or subcategory, make sure you accompany it with an example (or several examples) that illustrates the most characteristic features of this particular category. If you found useful evidence by an authoritative author, do not hesitate to use it. In other words, back your own words with proofs whenever possible as long as you do not overload your writing with them.

Editing and Proofreading

Take a Break

If you can afford it, set your work aside for a while – 24 hours at the very least, more if you have enough time. This will let you see your writing from a fresh perspective. If you start revising and editing immediately after finishing your essay, you will be too much tempted to skip over entire pieces of text because you already know what and how you wrote in them. Although you will never be able to see the text as if you read it for the first time, taking a break allows you to move closer to this ideal.

Create an Error Checklist

Everybody has ‘favorite’ mistakes that he/she makes time and again, even though he/she knows about it perfectly well. Before you start proofreading, compile a list of such mistakes for yourself. It should not be limited to spelling or grammar. If you mix up the spelling of two similar words, note it down. If you tend to leave dangling modifiers, write it down, and so on. When you proofread, reread your essay multiple times, each time focusing on a particular type of mistakes.

Use Spellcheckers… but Sparingly

Spell- and grammar-checking software and tools, starting with Microsoft Word in-built tool and ending with many online services like Reverso or JSpell, can be of significant help, especially if you are not on friendly terms with rules yourself. However, all the tips you receive from them should be taken with a grain of salt – they are not very good at analyzing complex structures, and even simpler things like spellchecking can fall through in case you are dealing with mixed-up words. If you doubt the suggestion of such a tool, better check with a textbook or a professional proofreader.

Change the Way You Perceive Your Writing

Professional proofreaders and editors often choose to work with texts on hard copy rather than on the computer’s screen. This is not an affectation – changing the way the text looks can help you see it in a different way. If it is accompanied with a different font and font size, the result is even better. Other ways to changing the perception are also helpful – for example, reading the text aloud or proofreading it backwards, one sentence at a time.

Simplify, Shorten, Cut

In academic environment, students are often tempted to use more words, longer words and more complicated sentence structures not because they need it to express themselves but because it helps them increase the word count, make the essay look longer and themselves sound more sophisticated. This does not make for high-quality writing. If you want to improve, you have to be critical of your own writing and dedicate at least one editing session to shortening, simplifying and cutting the fat. Eliminate unnecessarily long and complicated words and replace them with shorter and simpler alternatives. Cut away everything you do not need to move your point forward. Get rid of excessive words, sentences or entire paragraphs. Your instructor will thank you when he/she reads your essay. More is not always better.

Peer Reviewing

Another person is always in a better position to evaluate a work than the one who wrote it. As an author, you tend to overlook things simply because you wrote them and are too familiar with the way they look. Find somebody whom you trust to read and revise your essay for you. You can be sure that he/she will be able to find many more mistakes than you believed were left in the essay. The same goes for logical inconsistencies and other structural flaws.

Writing academic texts in mathematics is always a somewhat disconcerting task, because mathematics is not a discipline that is primarily associated with essay writing. However, as long as you remember that you should follow all the basic rules of academic writing while sticking to what you learned in your mathematics course, you should be alright – and our tips are certain to help you out as well!