Why you shouldn't memorize math formulas in elementary and middle school

I was a very good student in elementary school. I was a math enthusiast who enjoyed all subjects, but math was always my favorite. I loved how math was logical and had usually one correct answer. Although I had some difficulties remembering facts, such as the multiplication facts of 9, 8 and 7, it wasn’t too stressful. I was placed in the advanced math group and did very well.

Until we hit percents. This was the first time I felt the pain of learning by memorizing. The percent word problems we solved were problems such as the following.

A restaurant makes fruit juice from fruits, of which 42 are bananas. If 35% of the fruits are bananas, how many fruits are used to make the juice?

Mrs. Cohen, my math teacher, noticed my difficulties and tried her best to help me. She appreciated me as a strong student and didn’t want percents to lower my self esteem. She took me for a one on one session and promised, "Everything is going to be alright. All percent word problems boil down to three formulas. If you remember them you’ll be able to solve all percent word problems in the world.” Sounds promising, I thought.

She continued, “If the whole is missing, we would use this formula:

And if the part is missing, we should use this formula:

And lastly, to find the percent we use this formula:

She assigned me a handful of problems and asked me to match a formula to each problem. I looked at the 3 formulas she wrote in my notebook, and thought to myself, I can do that! I read each problem, identified the missing piece and used the appropriate formula to solve the problem. It worked! I continued with the rest of the problems and felt things finally work well with percents.

The following week we had a quiz. I was confident and energized. After solving tens of percents word problems on my own, I was certain I master percent word problems. So for the fruit juice problem, I knew that the whole is missing. I tried to dig from my memory the appropriate formula. Was it Part divided by Percent or multiplied by Percent? Should I multiply by 100 or divide by 100? I had a blockout. I needed these formulas to help me. But my teacher didn't allow us to use a formula sheet. My confusion got mixed with frustration and betrayal. Mrs. Cohen, how can you not allow us to use the tool we have been using all along? These three formulas are hard to memorize. I was lost. What is wrong with me? Does it mean I am not smart enough?

Fortunately, over time, I've come to understand that my struggles with percents and formulas were not a reflection of my intelligence or ability, but rather a result of the way math was being taught. Math shouldn't be mainly about memorizing formulas, but rather about understanding concepts and using them to solve problems. This is true especially in elementary and middle school, when students build their STEM identity.

Don't get me wrong, following math formulas is not necessarily bad, as formulas are an essential part of mathematics and can be used to solve complex problems. However, relying solely on memorizing and applying formulas without understanding the underlying concepts can be limiting and hinder mathematical proficiency.

As an educator, I want my students to feel empowered by their understanding of math. By making math meaningful and relatable to their everyday lives, I hope to instill in them a love of learning and a confidence in their own abilities. The Brain Workout Academy provides ample of opportunities for students to enjoy the process of sense making and reasoning. We play strategy games and use hands-on activities that spark students' curiosity and light up their eyes.