To Memorize or Not to Memorize? 

July 2023

Memorization seems to be a hot topic currently and, for that matter, for many years in the past. How often have you heard, “If only they had their basic facts memorized”? This perceived lack of knowledge of basic facts often gets used as an excuse when students struggle rather than looking at current instructional practices or examining the content taught to determine relevance. Too often, students get sorted by how quickly they can find the answers to basic facts—and after they are sorted, their experiences learning mathematics vary significantly. Those who don’t do the problems quickly enough get put into groups and tracks where students do activity sheets repeatedly while those who were faster are in groups and tracks where they reason and make sense of mathematics.

Do I want my students to have the basic facts memorized? Yes, and most teachers probably agree because it allows students’ working memories to be free to focus on new concepts. Do I want my students to learn those basic facts through memorization? No! So often mathematics educators complain about the lack of number sense; it is no wonder that this is the case because so many students memorize basic facts rather than using strategies to make sense of them. I would much rather have a student who learns that 8 + 9 = 17 by initially thinking of it as 8 + 10 –1 than one who has just memorized the fact through flash cards, timed tests, and other similar means. Having that strategy will help later with problems—like 28 + 39, 3.8 + 4.9, and

—ones for which students often want to use calculators because they aren’t facts typically memorized. Let’s allow our students the opportunities to think and reason.

But this debate about memorization should not just be about the basic facts. Do students really need to memorize the quadratic formula, or is it more important that they can use it appropriately? I would much rather have a student who looks online to find the quadratic formula and knows what the answers represent than a student who has the formula memorized and can calculate the answers but has little idea what those answers mean. I remember memorizing all the formulas for volume and surface area in geometry and doing well on the assessments. But it wasn’t until I started teaching that I recognized that the formulas for volumes of cylinders, triangular prisms, and rectangular prisms are all related. I want students who are able to make these connections rather than just substituting numbers into a formula and generating a correct answer.

When students attempt to learn their basic facts and much of mathematics strictly through memorization and don’t experience immediate success, it often leads to a negative mathematical identity. Consider how many adults say they hate mathematics and hated those timed tests of basic facts. I want my students’ mathematical experiences to be different. Having strategies and making connections will begin to build a positive identity in mathematics. As you continue to prepare for the upcoming school year, consider where you can deemphasize memorization and instead have students make sense of what they are learning.

Kevin Dykema
NCTM President
@kdykema