“As long as you do the classwork and the homework, you’ll do well on the test” is a maxim that almost all students know. However, too many students believe that as long as they do the work, and memorize the answers to the problems they solved, then they don’t have to worry about anything else. This is why it’s easy to forget what we have learned despite getting good grades on tests. When I was in Integrated III last semester, all of the test questions came directly from the homework and classwork problems, in fact, many math classes do this.

The problem is that this method promotes the idea of memorization being key to being able to understand math. However, there is a line between memorizing a concept to apply it on a test and memorizing an answer, and this line is often disregarded.

Math teacher Diana Loo said that the goal of this method of taking test questions from homework is to create a positive mentality toward the importance of doing the homework questions. 

“It’s really about shifting the students’ mindset and approach and understanding of homework to caring about how to solve the problem, as opposed to getting stuff down on paper, which may or may not be right,” Loo said.

This caused the teachers to make a joint effort to duplicate homework questions onto the test, to emphasize the importance of doing it. However, despite this effort, Loo also said that there has been no notable difference in students’ test scores from when they didn’t incorporate this practice. Homework is an important aspect of learning and understanding math concepts. It would be more effective if homework was promoted as a way to practice and perfect the understanding of math, while tests and quizzes should be used as ways to demonstrate this understanding.

Though memorization is essential when learning math–with all of the formulas and concepts–it’s not the most important aspect. Applying knowledge is a critical skill, as memory can be unreliable and won’t account for particular circumstances. 

According to the Mathematical Association of America, learning and understanding math can be split into three types: instrumental, relational, and formal. When students memorize formulas and get the right answers through repetition, this is instrumental understanding. Students are able to deduce the correct answer, but not the why of how the problem works. On the other hand, relational understanding is being able to understand the concepts behind the problem. More often than not, once that A is secured, students disregard the information they “learned.”

With the promotion of relational understanding by giving students diversified problems, students are able to better understand and learn new concepts easier. 

“Practice makes perfect” is another phrase that many are familiar with, but how are we able to perfect the understanding of a concept when everything is repetitive and focused on memorization? Memorization can only take you so far in math, and comprehension needs to be thoroughly developed to truly learn anything.