Why the Students Who Memorize Math Score the Lowest

If you study math by memorizing steps, you are using the strategy most associated with the lowest scores. That is not an opinion. It comes from one of the largest education datasets in the world.

Researchers analyzing results from the OECD's PISA assessment, which tests 15-year-olds across dozens of countries, looked at how students said they study math. As Stanford's Jo Boaler reports, the data from 13 million students show that "the lowest achieving students are those who focus on memorization," while "the highest achievers in the world are those who focus on big ideas in mathematics, and connections between ideas." The students who treated math as a pile of steps to remember did worse than the students who treated it as a web of connected ideas.

The OECD's own analysis explains the mechanism. In its report Is memorisation a good strategy for learning mathematics?, the OECD notes that memorization can carry a student through easy problems but is unlikely to work when the problem gets complex. A memorized procedure is a single path. When a question is phrased in an unfamiliar way, or combines two ideas, or asks you to work backward, the single path does not apply and the student has nothing to fall back on.

A student who understands why a procedure works has more than a path. They have the reason behind it, which they can re-derive or bend to fit a new situation. That is exactly the kind of question that separates scores at the top of a hard test.

The same OECD report adds a striking detail at the national level. Many of the countries that score highest in PISA math are not the ones where memorization is most common. Fewer 15-year-olds in places like Japan, Korea, and Singapore-region high performers reported relying on memorization than in several English-speaking countries they are often compared against. The cultures that out-score everyone are not out-memorizing everyone. If anything, the reverse.

This is worth sitting with, because the popular story is that top math countries succeed through relentless drilling. The data the OECD collected does not support that story.

It would be a misreading to conclude that facts do not matter, or that you should never practice. You still need to know that 7 times 8 is 56 without stopping to think, and you still need many reps to make a method automatic. Fluency is real and it helps.

The finding is narrower and sharper than "memorizing is bad." It is that memorizing as your primary strategy, treating math as a set of disconnected recipes to be retained, is the approach the lowest scorers reach for. The students who win are the ones who memorize less and connect more. We unpack where the line actually sits in Can math be memorized?.

Three changes turn studying from memorizing into connecting.

• After you solve a problem, ask why the method worked, not just whether you got the answer. If you cannot explain why, you have memorized a path, not learned an idea.
• Look for the shared idea across problems that look different. Many SAT Math questions are the same concept wearing different clothes. Spotting that is the connected-ideas skill the high scorers have.
• When you get something wrong, find the idea you were missing, not the step you forgot. A forgotten step is a symptom. A missing idea is the disease.

This is why our lessons lead with the deepest reusable idea before the procedure, and why every question is generated fresh so you cannot pattern-match your way through. You are forced to use the concept, not a remembered sequence.

The SAT Math section rewards the connected approach directly. The hardest questions rarely test whether you remember a formula. They test whether you can recognize which idea applies when the surface looks unfamiliar. A student who has memorized procedures hits a wall there. A student who understands the ideas adapts.

If your goal is a top score, the research points one direction: spend less effort memorizing steps and more effort understanding why they work. For what those top scores actually look like at selective schools, see What SAT Math score do you need for the Ivy League?.