Mathematical Representation Skills

Instructor: David Broy

Dave has taught college-level math, physics, computer, and electronics courses and has a Master's Degree in Electrical Engineering.

Have you ever had trouble coming up with the right words to express yourself? Like English, French, or Italian, math is a language. And in any language, one must take care in piecing together words and symbols to communicate an intended meaning.

View Math as a Language

Mathematics has been universally accepted for hundreds of years as the symbolic language used to represent scientific theory, technical concepts, and numerical information. Whether communicating through your own handwriting or using a mathematics editor available in your computer's software, it is extremely important to use appropriate symbols in the correct order, arranged meaningfully relative to each other, in order to express the accurate and unambiguous message you wish to convey. Because mathematical expressions and relationships tend to consist of only individual symbols as opposed to collections of characters, or words, it is all the more important to be meticulous in your representation.

Write Neatly and Clearly

This is good advice when communicating in any language, but especially in a symbolic language such as mathematics. It is always important to write neatly and clearly. If you make a mistake, don't sweat it! It happens to the best of us. Just make sure to erase your mistakes completely, or, better yet, line through your mistakes completely, and show your corrections off to the side. It is very difficult to extract the intended meaning when incorrect notation is directly overwritten with correct notation.

Tell a Story

Show the steps of your work in a complete, organized, logical progression. Whether you are a teacher attempting to show your students how to solve a specific problem, or a student trying to convince your teacher that you understand a specific topic, it is important to guide your readers through the information you wish to communicate, without leaving gaps that they must fill in for themselves.

Use Distinct Symbols

A math instructor often has to ask Algebra students to clarify the notation they are using in the work they submit. It is particularly disconcerting when students look at their own handwriting and are unable to decipher it for themselves. For example, is:


supposed to be 22, 2z, or maybe even zz? Does the symbol


represent the numeral 1, the capital letter I, or the lower-case letter l? You will find it useful to practice drawing the numeral 2


different from the letter z,


and the numeral 1


different from a capital I


or a lower-case l




for the variable x, and


for a times sign. In general, do your best to mimic the notation that you see being used in your textbooks.

Avoid Using Inline Mathematics Notation

It is all too common for someone to attempt to represent an expression such as:


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