Good Memorization, Bad Memorization

Memorization is important, but let's do it right

The words “memorize” and “memorization” are polarizing for teachers. I think part of the reason is that it’s often not clear what people want students to memorize. To me, memorization means knowing something without having to think about it. My goal as a teacher is to pick out all the little pieces of knowledge that my students need when they're solving complex problems. If they know all the little stuff without having to think about it, that frees up room in their minds for the bigger, tougher stuff. That's why I think memorization is important. I don’t think it’s helpful to memorize something to help solve a very specific type of problem. That’s not what I want to spend time on in math class. Memorization is powerful when that knowledge is useful in lots of different places; memorizing something that’s only useful in a narrow context isn’t a good use of time and probably isn’t going to stick anyway.

(To be clear, I'm using memorization to describe knowing something without having to think about it, not how the student gets that knowledge. Lots of people assume memorization means drilling something over and over again. A better strategy is retrieval practice spaced over time. Memorization doesn't require extended repetitive drills.)

We could debate whether specific knowledge needs to be memorized. For instance, I could imagine an interesting disagreement about whether students should memorize the circumference and area formulas for a circle. There are reasonable arguments for and against. But the real value of memorization is in some of the smaller pieces of knowledge that teachers forget about. Teachers forget about them because we have them memorized, so we don't have to think about them! Walk into a typical 7th grade class that's learning about circles. I bet if you ask a few students the difference between diameter and radius some kids in that room won't know. That's exactly the type of knowledge that students need memorized. When teachers get caught up debating whether kids should memorize the area formula for a circle we miss all the little pieces that are under the surface. If a kid doesn't know radius vs diameter and has to constantly look in their notes or on a poster or just mixes them up, they'll have a hard time understanding and applying the circumference and area formulas. My goal when I think about memorization is to identify all the little stuff like radius/diameter that students need to know, and give students a chance to practice and commit those things to memory before we get to the bigger stuff.

Some teachers require students to memorize stuff like the quadratic formula, and math class becomes a slog of trying to commit this messy, silly thing to memory:

The quadratic formula is the opposite of the type of thing that's helpful to memorize. Lots of people think of the quadratic formula, or the unit circle, or random integration formulas when they think of memorization. It makes sense those come to mind, they’re hard to memorize. But then the conversation gets short-circuited and we forget about all the smaller pieces of knowledge that are important to know. The goal of memorizing stuff in math class is to focus on knowledge that comes up in a wide variety of places in the future. That's what kids need to commit to long-term memory.

Another bad way of thinking about memorization is trying to memorize a set of steps that's specific to one type of problem. I searched "how to solve equations" on TeachersPayTeachers and found this:

I’m not trying to pick on anyone, this was literally the first thing that came up

"First, we will remove the number with no variable attached." In some classrooms, memorization means memorizing steps like these that are specific to one type of problem and don't transfer to anything else. This is a bad use of memorization. If my goal is to help students solve two-step equations, a good first step is to practice one-step equations until students can solve them without having to think about it. With that foundation, two-step equations will make a lot more sense and I won't waste time with stuff like the image above. Again, I don't mean that kids should spend a week doing nothing but drilling one-step equations before getting to two-step equations. The best way to commit that skill to memory is to space practice out over time. I give my students a few one-step equations every week for months before our equations unit.

Memorization in math class is important, but only if we are specific about what needs to be memorized. There are lots and lots of little pieces of knowledge that come in handy in a wide range of places in the future. Diameter/radius. The difference between factors and multiples. The meaning of the > and < symbols. Multiplication facts. Common percentage/fraction conversions. Lots more.

Again, when I say “memorization” some people hear “repetitive rote endless drill day after day.” That’s not what I mean. I give a quick five-question retrieval practice Do Now at the start of each class for students to practice stuff I want them to memorize. Each question comes up a bunch of times at increasing intervals. It takes <5 minutes each day. I throw in some extra mini-lessons when I see that something isn’t sticking. That’s it! And then, because I don’t get stuck on all those little details, we can spend more of math class thinking about big ideas and solving harder problems.

Math class is about more than memorization. That means being really specific about exactly what needs to be memorized, memorizing it, and moving on to the bigger stuff.