In secondary mathematics, students are allowed to prepare their own memory aid for an exam. It must be handwritten and can only cover one piece of paper. Usually, this memory aid is used to write formulas or challenging examples of different concepts so that one isn’t lost when writing an exam.
As a tutor, I have some experience advising others on their memory aids (as well as my own time being a secondary student, of course). I’ve seen some memory aids that were nearly blank and some that were filled to the brim. Both approaches can work, and it entirely depends on the person.
However, one thing I’ve seen time and time again is a tendency for one to write down the formula as provided by a formal definition. This is an important note, because a formal definition can be much more confusing to a student than the rigorous definition. And, as the students I’ve tutored tend to have difficulties in the subject of mathematics, these definitions can make little sense.
I remember an interaction I had with a specific student, who was having a trouble with a certain problem. I looked on his memory aid, and pointed out the exact concept to him. He looked at the writing as if written in a foreign language, and I could plainly tell he didn’t understand what was there.
Then it clicked for me.
“Do you understand the formula and definition you wrote down?” I asked, and he shook his head.
Now, I’m not trying to make fun of my student, but I’m trying to illustrate a broad point. Memory aids have turned into a piece of paper in which we write down formulas that we don’t even know what their functions are! My student simply wrote down the exact formulas from a generic copy of a textbook. Of course he wouldn’t be able to understand it when he needed to use the memory aid, he just copied a textbook.
With a memory aid, the goal should be to not forget any formulas. What I mean by this is that it’s nice to not lose points on a test because you’ve forgotten the exact composition of the quadratic formula. However, a memory aid should not be a used as a crash-course on a topic. It can be done, but the trouble is better spent trying to understand the topic before an exam. Once you’re in an exam, the memory aid should help remind you of the composition of formulas, not how to do a problem (though I have been in situations in which the example I wrote on my memory aid is indeed a test question). This comes down to the fact that mathematics and science is about solving problems, not memorizing formulas.
I’ve written a lot about memory aids, formulas, and memorization here already, but it’s a great topic to think about. As it stands, we send somewhat confusing signals to students: sometimes it is appropriate to have a memory aid, and sometimes it is not.
The truth, of course, is that the kind of knowledge we want to teach students shouldn’t be something we can place on a memory aid. For mathematics and most of the sciences, a memory aid can be completely appropriate, yet not give away the contents of an exam. To make sure this does not happen, there’s no problem to giving students pre-made memory aids to put them all on an even playing field.
What I want to avoid are situations in which students blindly copy formulas onto their memory aids without knowing what they actually mean. Whenever possible, write down formulas in ways that you understand, and it will save you from that terrible feeling in an exam where you do not understand what you wrote on your memory aid at all.