How Do You Study Math?

More than ever, our world is becoming more mathematical. The need to be proficient is not just about managing personal finances or solving puzzles anymore. In an increasingly mathematical world of computer logic and statistics necessary to shape important opinions regarding public policy, all should agree that studying math is important, but how do you study math? As a person who has worked in math-related fields, I get this question often. What follows outlines the basics of my answer.

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In English and many other humanities, students can learn about various topics simultaneously or vary the sequence. There is emphasis on progressing to “the big picture” without necessarily understanding the details. Unknown words or skipped passages often become clear from context or else can wait for review at a later time. However, in learning mathematics each step depends on the preceding one. A student has to learn counting before learning addition; mastering addition is essential before learning multiplication, which is essentially repeated addition. This critical dependence on each step is found in all mathematics—from arithmetic to algebra, calculus, and beyond.

The most important rule to remember when studying mathematics is not to miss any steps and to reinforce each piece of information as needed. Even math experts get lost, and when that happens, continuing without pause will lead to more frustration. When reviewing a problem in a textbook or even in the classroom, be aware that a single, confusing step may hide several steps. Recognizing when to back up, start over, take smaller, more bite-sized steps, refer to another example, or ask for help is the key to understanding mathematics for most people. It usually takes a minimum of three worked examples or other repetitions to remember a step superficially. Often, many more repetitions, followed by continued occasional use, are necessary for full mastery.

A misconception that hinders many people from achieving their best in mathematics is the myth of the “math genius.” Movies and popular culture foster the idea that mathematics is a magical power that is either present or missing at birth without any hard work required. Fictional prodigies spring up in highly unlikely families and circumstances. The reality is that most math or science prodigies come from living in a family environment that values and fosters acquiring knowledge, and even math prodigies, like all prodigies in general, do not achieve remarkable performance until they have studied extensively. Many are not even recognized as prodigies until later in life.

In the end, learning how to use mathematics is a goal that anyone can attain: You do not need to build a car from spare parts to become an expert at driving. Likewise, you do not need to be a “math genius” to become the best “math driver” around.

The advice for anyone learning math is to master each step in sequence and never to succumb to the “I am not a math person” mentality. In addition to patience and study, following these rules can help anyone become the person who is on the receiving end of the “How do you study math?” question.

Written on March 7, 2017