# Spaced Math Repetition Repetition

I read an article a few weeks ago which reminded me to provide an update on my previous article on my spaced repetition experiment. The end of the quarter seems like a good time to review. The article which appeared in the New York Times described a recent study which showed that test-taking improved retention, which is exactly the hypothesis of the spaced repetition system. An article in Ars Technica reviewed a study which demonstrated that, to some extent, this effect can even occur during sleep!

Before this experiment, I was not really a fan of memorization. As a software developer, I often employed “concept mapping” by drawing diagrams and flow charts to aid my understanding of a system. I eventually memorized the details of most components of a project, but on an ad-hoc basis and with no real timeline. In my first semester of graduate school I realized how much mathematics I had forgotten (or never learned in the first place). Working on homework relies on many of the skills I used in my recent career: seeing the big picture, knowing when to dig in for more details; but to get up to speed I had to incorporate memorization into my routine.

For the months of January and February I was able to enter information into the Mnemosyne application at a rate of 15 “flash cards” per day. To date, I have just over 800 cards in the system. What do my cards look like? Mainly they consist of definitions, statements of theorems, examples and counterexamples. Additionally, I include important proofs and exercises. On a daily basis I usually review 30 cards per day. Lately I’ve skipped a few days and had a backlog of about 100.

How do I feel about the system? The first observation is simple: it works. The down side? Entering information is time consuming. Definitions and statements of theorems are easy enough; copying proofs is tedious but straightforward. The difficulty comes when writing solutions to exercises or developing questions which clear up your misunderstandings. I have a tendency to write these things down on scratch paper and forget them. A lot of times this information can make a great flash card, it’s just a matter of discipline to enter the information with enough detail to be useful later. I still don’t have a great system for fixing this issue. As far as reviewing, it’s very quick to spin through definitions and statements of theorems (though it’s important to write down your answer so you don’t fool yourself into thinking you know the material better than you do). Review of proofs and exercises can be a more time-consuming endeavour. I would only suggest entering those identified as essential, lest you become frustrated and skip them. Then you’ve wasted time both entering and reviewing the card. This brings me to my last point, a critique of Mnemosyne. The tagging system is a little underpowered for my liking. In retrospect I should have tagged my cards in a 2-dimensional fashion: by subject and “type”. Possible types would include definitions/theorem, examples, proofs, exercises.

After only 10 or 12 weeks of utilizing this application, I’m just beginning to form opinions of how to best take advantage of it for studying mathematics. For self-study I have found it a great way to formalize the memorization routine. It seems like it would also be useful in a classroom setting, with the instructor dishing out cards for the upcoming week. Over the break I hope to reflect on some of these ideas and tweak the process I have been using. I intend to continue with Mnemosyne until summer, at which point I may spend some time with another application. I will continue to record details of this experiment here.