Memorization gets a pretty bad rap. It’s a favorite punching bag of most teachers, and the hatred has spilled into popular culture as the push against rote learning has become more mainstream. Albert Einstein was even quoted on memorization, saying “Never memorize something that you can look up.”
I want to push back on this idea a little bit. I think when we say memorization, we’re actually conflating two different issues in education. First, in defense of memorization.
I have my perfect squares memorized to 625. Ok, that’s not normal, but it comes in handy during all kinds of math — it allows me insights when estimating products, working with quadratics, or applying the Pythagorean Theorem. Sure, I could take the time to calculate any of those, but having that immediate association allows the opportunity for insights that would not be possible if I had to break my train of thought to calculate something.
I have the symptoms of altitude sickness memorized. I spend a fair amount of time hiking at altitude, and have spent time working with kids hiking at altitude as well. I could look up the symptoms of Acute Mountain Sickness, High Altitude Pulmonary Edema, and High Altitude Cerebral Edema every time someone I. or someone I was with, felt funny up high — but that sounds absurd on its face. I wouldn’t get hired to do this if I couldn’t quickly and reliably categorize a hiker’s symptoms as mild or serious, and recommend what to do next. And I can do all of that because I have the relevant symptoms, their mechanisms, and possible treatments securely in long-term memory.
I have the streets with safe bike lanes in most of Boston memorized. I could always use the interweb and all of the great tools there. But instead of blindly following GPS directions (and getting lost if a direction is confusing or comes too late) I can devise my own, taking a longer route if I know it is worth the extra few minutes to ride on a safer road, or improvise a new route if record winter snowfall has made a road virtually impassable for bikes.
What Does All Of This Have In Common?
I would call this memorization. I have all of this information stored in long-term memory for instant recall, despite my ability to look any of it up. This largely consists of facts, though with a significant amount of understanding supporting them. But, most importantly, I memorized all of this information slowly, over time, with natural repetition in context, with a wealth of examples and non-examples, and opportunities to rehearse and consolidate the knowledge.
My goal is for students to have a learn deeply. By that, I mean I want them to know things, and I want them to be able to apply the things they know to a variety of contexts, to be able to work flexibly, and to use what they know to make sense of new information and continue learning.
Cognitively, this means my students are building mental models of a topic, connecting different representations, and looking past surface features to the deeper structure that they have in common. This can’t happen quickly. Unless students are already experts in a topic, information takes weeks or months to make it into long-term memory.
There are two things to look out for here. One is class structures that lead to shallow learning. Plenty of digital ink has been spilled there. But what I would call the negative side of memorization is when I am pushing students to learn something, but I am pushing them to learn it too quickly to allow the possibility of deep learning. Looking at the axes above, it’s impossible to do anything in the bottom right. Students naturally start with shallow knowledge, and over time and a great deal of experience, they gain deep knowledge
So I have a goal. I want my students to gain deep, flexible, contextualized knowledge. Step one is to make sure that my instruction provides the opportunity for deep learning. I need to ask high cognitive demand questions, push students to make connections between examples, provide opportunities to contextualize and decontextualize, look for and make use of structure, and model with mathematics. None of that is easy. But in addition to all of that, I need to acknowledge that, no matter how perfect my instructional activities are, my students are not going to gain deep knowledge overnight. If I try to push them too quickly, they will just regurgitate the same material from short-term memory without the opportunity for chunking and consolidation, and rely on concrete examples before they have a chance to abstract the deeper ideas. This is pretty scary, especially as I will be teaching Precalculus for the first time this year, and that course is fiendishly difficult to come up with overarching ideas for. But I also think this is incredibly important if I want to take seriously the idea of my students leaving my class and going on to the next teacher knowing what I want them to know.
So what do I do with all of this?
I have no idea. Maybe this is a critique of the structure of US elementary mathematics. Maybe it’s an argument for spiraled, activity-based learning. Maybe it supports continual distributed practice. All I know is, if I want students to learn something, and that idea or unit or principle is supposed to happen in just a few days, I need to think seriously about what the deep structure is that students need to take away, and how to revisit and consolidate that understanding over a longer period of time if I want them to truly learn it.