Tag Archives: teaching

Practice, Don’t Memorize, Understand Justifications, Not Stories

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Teaching is one of those things that’s always controversial.

There seems to be a constant tug of war between two approaches. In one, thought of as old-fashioned and practical, students are expected to work hard, study to memorize facts and formulas, and end up with an impressive ability to reproduce the knowledge of the past. In the other, presented as more modern or more permissive, students aren’t supposed to memorize, but to understand, to get intuition for how things work, and are expected to end up more creative and analytical, able to come up with new ideas and understand things in ways their predecessors could not. This whole thing then gets muddled further with discussions of which skills actually matter in the modern day, with the technology of the hour standing in. If adults can use calculators, why should students be able to do arithmetic? If adults can use AI, why should students be able to draw, or write, or reason?

I’ve taught a little in my day, though likely less than I should. More frequently, I’ve learned. And, with apologies to the teachers and education experts who read this blog, I’ve got my own opinion.

I don’t think anyone in the old-fashioned/new-fashioned tug of war is thinking about education right.

People talk about memorization, when they should be talking about practice.

We want kids to be able to multiply and divide numbers. That’s not because they won’t have calculators. It’s because we want to teach them things that build on top of multiplying and dividing numbers. We want some of them to learn how to multiply and divide polynomials, and if you don’t know how to multiply and divide numbers, then learning to multiply and divide polynomials is almost impossible. We want some of them to learn abstract generalizations, groups and rings and fields, and if you’re not comfortable with the basics, then learning these is almost impossible. And for everyone, we want them to get used to making a logical argument why something is true, in a context where we can easily judge whether the argument works.

This doesn’t mean that we need students to memorize their times tables, though. It helps, sure. But we don’t actually care whether students can recite 5 times 7 equals 35, that’s not our end goal. Instead, we want to make sure that students can do these operations, and that they find them easy to do. And ultimately, that doesn’t come from memorization, but from practice. It comes from using the ideas, again and again, until it’s obvious how to step ahead to the results. You can’t replicate that with pure understanding, like some more modern approaches try to. You need the “muscle memory”, and that takes real practice. But you also can’t get there by memorizing isolated facts for an exam. You need to use them.

Understanding is important too, though. We need students to know the limits of their knowledge, not just what they’ve been taught but why it’s true. It’s the only way to get adults who can generalize, who can accept that maybe there is a type of math with numbers that square to zero without dismissing it as a plot to corrupt the youth. It’s the only way to get students who can go to the next level, and the next, and then generate new knowledge on their own.

But that understanding often gets left by the wayside, when teachers forget what it’s for. If you try to teach the Pythagorean theorem by showing a few examples, or tell students stories where different types of energy are different “stuff”, you’re trying to convey an intuitive understanding, but not the useful kind. What you’re trying to give the students is stories about how things work. But the kind of understanding we need students to have isn’t of stories. It’s of justifications, and arguments. Students should understand why what they are taught is true, and understanding why doesn’t mean having a feeling in their hearts about it: it means they can convince a skeptic.

It’s easier, for a world full of overworked teachers from a variety of backgrounds, to teach the simpler versions of these. It’s easy for a traditionalist teacher to drill their students on memorization, and test them on memorization. It’s easier for a sympathetic teacher to tell students stories, based on stories the teacher thinks they understand.

But if you want the traditionalist approach to work, you have to actually do things, to practice using ideas rather than merely know them, to have that experience down as reflexively as those times tables. And if you want the modern approach to work, you have to actually understand why what you’re teaching is true, the way you would convince a skeptic that it is true, and then convey those justifications to the students.

And if you, instead, are a student:

Don’t worry about memorizing facts, you’ll drill too hard and stress yourself out. Don’t worry about finding a comfortable story, because no story is true. Use the ideas you’re learning. Use them to convince yourself, and to convince others. Use them again and again, until you reach for them as easily as breathing. When you can use what you’re learning, and know why it holds, then you’re ready to move forward.

Requests for an Ethnography of Cheating

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What is AI doing to higher education? And what, if anything, should be done about it?

Chad Orzel at Counting Atoms had a post on this recently, tying the question to a broader point. There is a fundamental tension in universities, between actual teaching and learning and credentials. A student who just wants the piece of paper at the end has no reason not to cheat if they can get away with it, so the easier it becomes to get away with cheating (say, by using AI), the less meaningful the credential gets. Meanwhile, professors who want students to actually learn something are reduced to trying to “trick” these goal-oriented students into accidentally doing something that makes them fall in love with a subject, while being required to police the credential side of things.

Social science, as Orzel admits and emphasizes, is hard. Any broad-strokes picture like this breaks down into details, and while Orzel talks through some of those details he and I are of course not social scientists.

Because of that, I’m not going to propose my own “theory” here. Instead, think of this post as a request.

I want to read an ethnography of cheating. Like other ethnographies, it should involve someone spending time in the culture in question (here, cheating students), talking to the people involved, and getting a feeling for what they believe and value. Ideally, it would be augmented with an attempt at quantitative data, like surveys, that estimate how representative the picture is.

I suspect that cheating students aren’t just trying to get a credential. Part of why is that I remember teaching pre-meds. In the US, students don’t directly study medicine as a Bachelor’s degree. Instead, they study other subjects as pre-medical students (“pre-meds”), and then apply to Medical School, which grants a degree on the same level as a PhD. As part of their application, they include a standardized test called the MCAT, which checks that they have the basic level of math and science that the medical schools expect.

A pre-med in a physics class, then, has good reason to want to learn: the better they know their physics, the better they will do on the MCAT. If cheating was mostly about just trying to get a credential, pre-meds wouldn’t cheat.

I’m pretty sure they do cheat, though. I didn’t catch any cheaters back when I taught, but there were a lot of students who tried to push the rules, pre-meds and not.

Instead, I think there are a few other motivations involved. And in an ethnography of cheating, I’d love to see some attempt to estimate how prevalent they are:

  1. Temptation: Maybe students know that they shouldn’t cheat, in the same way they know they should go to the gym. They want to understand the material and learn in the same way people who exercise have physical goals. But the mind, and flesh, are weak. You have a rough week, you feel like you can’t handle the work right now. So you compensate. Some of the motivation here is still due to credentials: a student who shrugs and accepts that their breakup will result in failing a course is a student who might have to pay for an extra year of ultra-expensive US university education to get that credential. But I suspect there is a more fundamental motivation here, related to ego and easy self-deception. If you do the assignment, even if you cheat for part of it, you get to feel like you did it, while if you just turn in a blank page you have to accept the failure.
  2. Skepticism: Education isn’t worth much if it doesn’t actually work. Students may be skeptical that the things that professors are asking them to do actually help them learn what they want to learn, or that the things the professors want them to learn are actually the course’s most valuable content. A student who uses ChatGPT to write an essay might believe that they will never have to write something without ChatGPT in life, so why not use it now? Sometimes professors simply aren’t explicit about what an exercise is actually meant to teach (there have been a huge number of blog posts explaining that writing is meant to teach you to think, not to write), and sometimes professors are genuinely pretty bad at teaching, since there is little done to retain the good ones in most places. A student in this situation still has to be optimistic about some aspect of the education, at some time. But they may be disillusioned, or just interested in something very different.
  3. Internalized Expectations: Do employers actually care if you get a bad grade? Does it matter? By the time a student is in college, they’ve been spending half their waking hours in a school environment for over a decade. Maybe the need to get good grades is so thoroughly drilled in that the actual incentives don’t matter. If you think of yourself as the kind of person who doesn’t fail courses, and you start failing, what do you do?
  4. External Non-Credential Expectations: Don’t worry about the employers, worry about the parents. Some college students have the kind of parents who keep checking in on how they’re doing, who want to see evidence and progress the same way they did when they were kids. Any feedback, no matter how much it’s intended to teach, not to judge, might get twisted into a judgement. Better to avoid that judgement, right?
  5. Credentials, but for the Government, not Employers: Of course, for some students, failing really does wreck their life. If you’re on the kind of student visa that requires you maintain grades a certain level, you’ve got a much stronger incentive to cheat, imposed for much less reason.

If you’re aware of a good ethnography of cheating, let me know! And if you’re a social scientist, consider studying this!