Teaching skills, not concepts

Posted on by

Dan sends along this article which reports a study saying that math is more effectively taught using drills instead of story problems. Speaking as a teacher (and without actually reading the report of the study), I’d say this is plausible. After 20 years of teaching, I’ve come to the conclusion that teaching skills works better than teaching concepts (or, should I say, trying to teach concepts).

I haven’t done such a good job of this in my own teaching, but it’s a goal. Dan writes, “People who learn the abstract rules don’t always figure out how to turn that into an ability to model reality. So for teaching applied math skills, you need to first teach abstract rules, and then give an opportunity to use them in models.” This is related to the fundamental insight that you can’t “cover” material in a course; students ultimately have to teach themselves how to do things No easy answers here, but I can certainly believe there are better and worse ways to proceed.

8 thoughts on “Teaching skills, not concepts”

  1. We need to be careful saying things like "teaching skills works better than teaching concepts" because it could be construed to support programs like NCLB, which focus on rote memorization over learning. That's not what this article and study are saying at all.

    Instead, what this is saying is that it's not as effective to start with an abstract example and teach the skills via extrapolation from the example. Instead, you should start by teaching the basic concept, such as single-factor algebra (example given), and then show how you would create such an equation given a "real world" example.

    The problem, which is not mentioned in the article, is this: for a long time, students thought math was boring because they didn't see how it applied to life. So, in came problems meant to show them examples of how they could use math in their lives. Unfortunately, the pendulum swung past that point about 15 years ago where the real life examples (the story problems, etc.) became the lesson, instead of the concept and associated skills. Now we'll see the pendulum swing back – just hopefully not so far that we lose the association with how to use math outside of the textbook. We don't want to lose the attention and interest of learners in mathematics.

    The last comments in the article about manipulatives should be taken cautiously and not construed as definitive until studies are completed. As mentioned in the article, overgeneralizing is a dangerous practice, and should not be applied to a diverse group of learners. If there's one thing that we have definitely learned in the past 15 years, it's that every student has a unique learning style, and thus our jobs as teachers become far more complex as we try to deliver concepts and skills in a manner that, at the very least, applies the 80/20 (or 70/30) rule for those different styles.

  2. Am I the only one who find the example in the article obfuscating? You have to click on the graphic to see it. When I look at the middle column (teaching concepts), I see 1+1 = 2, 2+2 = 1, 1+2 = 3, 2+3 = 2. What kind of math is this?

  3. It's modulo 3 (remainder after division by 3). BTW, if the examples as shown in the Times popup are the ones used in the actual study, I think it could have been possible that the shapes of the "abstract" symbols could be a confounding variable. Am I the only one seeing vague resemblance between the symbols and vase, bug, and the ring? What would have happened if they used symbols which are more abstract than those?

  6. I agree with Mikkel. It works if we replace 3 with 0. For something this abstract, I'm not surprised teaching with real examples don't work.

  7. The thing that really bothered me about the example there is that the training instances only talk about two people pointing to things, while the questions that are asked involve three or four people pointing. And I suspect that the reason the geometric example was much easier to generalize to the weird physical object example was that it just suggested an abstract pattern, rather than suggesting addition modulo 3. If the game with the children had somehow had a natural connection to addition, then I suspect the results would have gone the other way.

    it's not as effective to start with an abstract example and teach the skills via extrapolation from the example. Instead, you should start by teaching the basic concept, such as single-factor algebra (example given), and then show how you would create such an equation given a "real world" example.

    I think you must mean it's not as effective to start with a concrete example – I thought the study was saying that abstract examples work much better, so that students can learn the underlying concept and then separately learn to apply it, rather than trying to move analogously from one concrete application to another.

Comments are closed.