There are two basic forms of “memorization”: (a) Rote, through the repetition of the specifically, often decontextualized, data and (b) Habituation, through the repetition of acts that involve the information to be “memorized”. When we think of school, we tend to think of the first kind, because that’s the more efficient in the short-term, but it’s far less effective in the long-term. Closed-book tests, in particular, encourage rote memorization, which is why so many students have the experience of forgetting everything the day after the test.
Fluent speakers of a language don’t memorize by rote; they learn through repetition, trial-and-error, and contextualized honing. Likewise, most mathematicians hold most of their internalized knowledge through habit, not through rote.
When we’re learning something by rote, we’re usually acknowledging that we’ve failed to find a suitably meaningful context, and so we’re holding it in our brains long enough to get past the test. As a mathematics teacher, there are two things we can do with information that we notice most students are learning entirely by rote:
1. Provide an appropriate context
2. Get it out of our curriculum
That’s not to say that there’s no place for rote at all. It’s a common scaffold for a subset of facts so that we can (temporarily) focus on related facts.
There is also always tangentially related information that is “beyond the scope of the current course”, and there’s a place for simply memorizing that information. But that should be only a small portion of the total content.
If we as teachers really want to claim our students have “mastered” the information, they need to be able to synthesize and apply beyond rote. For the most part, announced timed tests that must be completed on a specific date get in the way of that because such tests encourage cramming, which in turn encourages rote memorization.
Students who have truly mastered information don’t need to study the night before. Review, yes. Cram, no.
A tragedy is: A growing number, perhaps even the majority, of math teachers are aware of this. The question is: What option do we have? Rubric-based assessments require more delicate, more time-consuming grading. If we reduce the number of graded opportunities to compensate, we face admin who question our lack of grades. Some students will simply cheat on assignments, and it is admittedly more difficult to cheat on a timed in-class assessment. We have curricula we are expected to cover, and we often have “common” assessments. Indeed, many districts believe that common assessments are a necessary part of educational equity, so if I’m on a team of teachers for a subject, I need buy-in from my colleagues, or I need to go rogue at my own risk.
Inertia is safe, so we maintain inertia, even when most of us know it’s extremely flawed.