What Needs To Be Memorized?

I’ve written a few times recently about memory. One thing I want to emphasize again is that I’m not arguing math class should mostly be about memorization. There are some pieces of knowledge that it is helpful to commit to long-term memory. If we can do that efficiently, we can free up math class for doing lots of other things. If we don’t do that efficiently we set ourselves up for either unnecessary drudgery taking the long road to long-term memory, or frustrated students who don’t have the knowledge they need.

But one thing I didn’t address is what, exactly, needs to be memorized. I don’t have a clear rule for this, but I think an example is helpful:

I wrote in a previous post about how, for a long time, I couldn’t remember the difference between affect and effect. I spend a lot of time writing, and I use those words and often have to look them up. I didn’t have them committed to long-term memory, but that didn’t prevent me from writing at a high level or using those words effectively. However, one part of writing is getting into a “flow” state where I have a clear idea of what I’m trying to communicate and how to get it across. Having to stop to look up the difference between affect and effect can break the flow. I have to spend working memory resources on figuring out which word to use, and maybe push the idea I had out of mind and interrupt the flow of writing.

I have a decent vocabulary, so situations like that don’t happen too often. Occasional interruptions like mine with affect/effect are inevitable. It’s impossible to have everything I could ever need to know committed to long-term memory beforehand.

Here’s another example. For a long time I had trouble remembering that 8 x 7 = 56. That didn’t prevent me from solving complex math problems. I’ve heard lots of mathematicians and experienced math teachers mention how they never memorized a few items in their times tables. I still don’t know my 12s very well past 72. But here’s the thing. I have never met someone who doesn’t have a large part of their times tables in long-term memory who was also successful in a mathematical field. Not everything needs to be committed to memory. But the stuff we come across most often is important to remember to free up cognitive resources for other things.

Trying to memorize everything is a silly and unnecessary exercise. Endless retrieval practice can suck time away from all the other stuff that’s valuable about math class. But it’s important for me to take a hard look at the content of my course and identify the highest-leverage stuff, the knowledge that comes up most often down the road, or that is a small piece of larger problem-solving. And then it’s my job to get that knowledge into my students’ long-term memory as efficiently as possible. There’s more to math class than memorization — but getting the basics down sets students up for success with all the other problem solving and exploring I value, and getting the basics down efficiently frees up time for everything else.