Memorization Versus Understanding: Better Approaches to Teaching Mathematics
I loved math. I was intrigued by the numbers, by the equations, by the intricacy of formulas that helped me find the area of a space, determine the point at which to hit the cue ball, and figure out how many different combinations of yummy muffins I could make with three or four add-ins.
I loved the tools—calculators, rulers, protractors. Yes, I’m old enough to remember the compass and protractor sets that I used to keep in my three-ring binder.
I loved math (and science) so much that I applied for and attended a summer engineering program at the local state university. When I headed off to college, I thought my future was certain. I was going to major in mathematics and be an engineer so I could design and build big things. Big things for what, I wasn’t sure; but space, manufacturing, and nuclear energy were all possibilities. It was intoxicating; I could hardly wait.
At college, I tested well. I didn’t end up in the developmental education quagmire often associated with mathematics. I received a good mathematics background early, completing calculus by the end of my senior year in high school.
Now I recognize how lucky I was. So many students—in particular, students of color—are not afforded the same opportunities, and as we’ve learned, being middle-class does not shield students of color from structural inequities in our education system.
College is also when math got hard for me. But I recognize that for many in our education system, math becomes a barrier much earlier in their schooling.
I was fortunate in that I experienced mathematics as a beautiful and logical language; I relished working through endless problem sets and proofs. As I moved into the more advanced and abstract math courses in college—Abstract Algebra and Real Variables—I could no longer easily grasp the concepts. For me, math was becoming disconnected from anything real or tangible, and I kept thinking, “Why do I need to know this to build something big?”
Slowly, my love for math turned to anguish. Looking back, I can see that my experience could be attributed to old instructional models, teaching methods pervasive on college campuses when I was in school—and often, unfortunately, today.
Lecture was the norm, and memorization was the key to success. In fact, I remember one professor telling me as I approached her for help with my frustrations, “Just memorize it. That’s all you need to do.”
I remember thinking that I can’t memorize it if I don’t understand it.
Memorization may be beneficial for taking in information and repeating it later. But memorization does not, can not, foster deep understanding. When math became difficult for me, I needed context and applicability of the new concepts in order to understand the nuanced abstractions in the advanced mathematics topics.
When I was advised just memorize it rather than provided with the strategies and scaffolding I needed, I found myself for the first time expressing what I had heard so many other students say before: “Why do I need to know this, and when am I ever going to use this stuff?”
I completed my requirements to earn an undergraduate degree in mathematics using the suggested strategy—I joylessly memorized the proofs.
And then I quickly moved away from any career that required an extensive mathematical background. No more engineering. No more aerospace. No more big, complicated machines. I closed those doors because I no longer identified as a “math person.”
And yet today I see great promise in the transformation of math instruction across all levels of the education system. Instruction in K–12 now focuses on building conceptual understanding, giving students a deeper grasp of the subject matter to move beyond mere memorization of procedures and into comprehending the concepts themselves.
This focus on comprehension should better prepare students for the mathematics they will encounter in college. In higher education, mathematics instruction is moving toward more active learning, such that students learn mathematics situated within, and necessary for, real-life contexts.
I’m excited about this shift in mathematics instruction because of its potential for students, especially the ones near and dear to me.
My nieces and nephews are experiencing math instruction in a way I never could have imagined. As early as first grade, they are building number sense. In middle school, they are learning more than procedures; they are using procedures to solve problems in context and learning how to communicate their thinking. And what they’re experiencing is quite different from what their parents did in school.
I’m hopeful that the transition to active learning strategies and real-world applications of all mathematics will continue to develop as they and their peers matriculate into their colleges of choice.
I don’t want anyone else to see their hopes of becoming an engineer dashed by a figure of authority and scholarlship advising, “Just memorize it.” Our students deserve better. And so do we all.
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