How to Write a Compare & Contrast Essay in Mathematics: All You Need to Know to Succeed

Writing a compare and contrast essay may seem like a task that does not require a lot of brainpower – after all, you simply have to draw a comparison between two (or more) things. What can be easier? Unfortunately, things are often far less straightforward. In middle and high school, essays of this type may have been easy to write because you primarily dealt with specific, real-world objects, concepts and categories of things. However, when it comes to mathematics, the situation gets much more complicated, as mathematics is a highly abstract discipline.

Your professors may ask you to analyze and compare extremely abstract and vague ideas, rules and principles. In order to do this without making all kinds of mistakes you should understand all the aspects of what you are doing – and you can find all the necessary information in this guide. Follow all its steps, and your next compare and contrast essay in mathematics will not present any difficulty to you.

How to Write a Compare & Contrast Essay in Mathematics: Pre-Writing

1. Choosing the Topic

Unless your professor has already assigned a topic to you or at least limited your choices, you will have to find, formulate and research a topic yourself. The good news is that when writing compare and contrast essays you do not have to be particularly inventive in this department – you simply have to pick the items you want to analyze and compare to each other. Optionally, you may limit the comparison to a particular area – for example, if you write about the development of mathematical thought in Europe and Asia, you may focus on a specific period of history and only cover the dominant schools that existed in both regions at the time, without talking about specific scholars.
When choosing a topic for a compare and contrast essay, it is a good idea to do some research before you commit yourself to anything. It is quite easy to settle on a topic only to find out that the items you chose for comparison are too inconvenient to analyze alongside one another. For example, you may discover that they do not have that many touch points and you simply cannot meaningfully compare them. In other essay types, it is usually possible to modify the topic a little bit to make your writing more manageable; in compare and contrast papers, however, you will have to choose another subject and start anew. So make sure to choose items that suit each other.
In the end, you should get something like this:

• Mathematical Thought in India and China across Modern Era;
• Pythagoras and Blaise Pascal: Their Contributions to and Influences on Mathematical Thought;
• Mathematical Tradition in Asia and in the West: Strong and Weak Points;
• Mathematics and Algebra: Differences and Similarities.

2. Making Sure the Comparison Is Meaningful

Writing a compare and contrast essay incorporates more than just setting two concepts against each other and discussing all their similarities and differences one by one. If you do this, your essay will look disjointed and amateurish. What turns it from a collection of unconnected points into a coherent and cohesive whole is an underlying idea. What does your comparison prove? Is it possible to come to a particular conclusion based on your analysis? Make sure comparing the items in question makes sense; otherwise, you may have to tweak your topic.

3. Brainstorming

Before you set about to further research the items you are going to compare, you have to systematize what you already know about it. You may simply write down the list of all their important characteristics and how they compare based on them. If you have an aptitude for visual learning, try out Venn diagrams – they represent differences and similarities in an easy-to-grasp form and can lead you to some useful insights.
Try to think of as many points as possible and do not care about their relevance at this point – you will have an opportunity to drop the less important ones later on. Make a note of what you should research: e.g., additional criteria for comparison and examples to prove particular points.

4. Researching

Whatever you already know about the topic, you will have to gather additional information before you make any deeper comparisons.
There are many ways to find sources of this information: consult your professor and ask if he/she can recommend any relevant publications, talk to a librarian or run a search in your college’s library on your own. However, probably the most promising approach would be to use one of many online academic databases and search engines – they incorporate information about thousands of scholarly journals, books and other publications and allow you to look for them in one place. You may use generalized ones, like Google Scholar and EBSCO, or take a look at more specialized ones (e.g., arXiv.org or CiteSeerX).

First, select a few keywords directly relevant for your topic and see what you can find. Then select several works that provide you with most information, and go through their bibliography sections (pay attention to other publications by the same authors as well). What you find this way should be more than enough to complete your job.

5. Picking the Most Suitable Structure

This is another thing to think about beforehand. Otherwise, you may discover that a different structure better fits your topic halfway through, and changing things at this stage can be very time-consuming.

There are three typical structures for compare and contrast essays.
Point by Point
You single out the most important comparison criteria and analyze the items from this viewpoint. For example, if you compare mathematical traditions of different civilizations, you can first compare when they introduced the concept of zero, move on to the idea of negative numbers and mention a few other crucial mathematical discoveries, one by one.
As a result, you get a well-structured comparison that analyzes each aspect of the concepts in question in detail and makes all the comparisons right away. This approach is best used when you have many points to discuss and do not want the reader to get confused.
Block by Block
First, you describe one item with all its characteristics, then move on to the next one and do the same for it, drawing the reader’s attention to what is similar and different about them. This approach is best used when you only have a few important points to discuss or want to first describe one item to then use it as a backdrop against which to analyze another one.

If you have more than two items to compare or there are many different criteria you want to cover, better avoid this method – otherwise your text will be too obviously divided into unrelated parts.
Similarities/Differences
First, you describe what the items under scrutiny have in common, then move on to their differences (or vice versa). This approach is effective when you want to draw attention to the fact that the items you compare are very different despite numerous similarities (or vice versa, very similar despite being dramatically different in some respects).

How to Write a Compare & Contrast Essay in Mathematics: Writing Tips

1. Writing an Outline

Begin your work with writing an outline. It is a good rule of a thumb when dealing with any writing assignment, but it is doubly useful when you write a compare and contrast essay, as it protects you from extensive rewrites and corrections that you may need if you just start writing.
An outline is more than a plan – it is more like a miniature of your entire essay. You write down all its parts and sections, make short notes on what you intend to say, what examples to use, how to connect individual parts with each other to ensure smooth flow of logic. You can be as basic or as detailed as you want – the important thing here is that it meets your requirements and works for your writing style. Some students write an outline in such detail that it only needs a little filling up to turn into a full-fledged essay.

2. Using the Right Transitional Words

Transitional words and phrases are used to connect individual parts of your essay, ensure that your writing reads naturally, without sudden leaps from one topic to another. Some of the most widespread ones include ‘while’, ‘however’, ‘unlike’, ‘however’, ‘similarly’, ‘likewise’, ‘differently’ and so on. Make sure you always use them in the beginning or the end of paragraphs to lead the reader up to the next thought.

3. Do not Forget about Supporting Evidence

When you talk about similarities or differences between the items you discuss, you should not simply state them as facts, however obvious they may be. When you say something, always back it up by examples, evidence from reliable publications, statistics and so on. Try to pay relatively equal amount of attention to each item and each comparison criterion. To that end, guesstimate how many paragraphs you will have to write and how many words you can use in each of them.

4. Cover Only the Most Important Points

You do not have to discuss absolutely everything about the items you compare. An essay is very limited in size, and if you try to say at least a couple of words about every little thing, your analysis will turn out to be comprehensive but extremely shallow. A better solution is to select a few important points and provide an in-depth comparison using them. Think about which of them will prove your vision even without the rest of the evidence, and which you can safely drop.

How to Write a Compare & Contrast Essay in Mathematics: Finishing Touches

1. Check Grammar and Spelling Using Online Spellcheckers

Of course, Microsoft Word has its own built-in spellchecking tool, and many students believe that it alone is more than enough to cover all their correction needs. Unfortunately, it is woefully inadequate for its task and only detects the most basic mistakes while missing quite obvious blunders and returning numerous false positives.
Some online spell- and grammar-checking tools (Grammarly, GrammarCheck, Scribens to name just a few) offer much better functionality, so try selecting a few and seeing if they suit you. Do not rely on them too much, however – none of them can replace a human proofreader.

2. Proofread Your Text Multiple Times

Human brain is simply not wired in a way that allows it to pay attention to multiple things simultaneously. If you try to proofread your essay with an idea of looking for mistakes in general, you will notice some, but they will probably be the most obvious ones. If you want to dig deeper, go over the text multiple times, each time focusing on its particular aspect: grammar, spelling, sentence structure, logical connections between sentences and so on. If you know yourself to be particularly prone to a particular type of mistakes, pay special attention to detecting it.

3. Alter the Way You Perceive the Text

As you read the text you yourself wrote, you anticipate too much. Make changes to break this anticipation: read the text aloud – it will allow you to slow down enough to start perceiving individual words rather than sentences. Read it backwards, sentence by sentence – thus you will focus more on sentence structure rather than the general flow. Print it out after fiddling a bit with font types and sizes – it will help you get a fresher perspective on your writing.

4. Double-Check the Numbers

When writing an essay on mathematics, you almost certainly will have to include some numbers, figures and formulas in your text. If so, then make sure to double check every number before handing the paper in. In mathematics, a small mistake in numbers can dramatically change the entire meaning, so be doubly careful about them.
Writing an essay in mathematics can, of course, be a lot of hassle, especially if you do not have experience. However, even if it is the first time you write something of this kind, you can achieve the desired results if you carefully follow this guide and meticulously perform every step.