Daniel Lemire's blog

, 3 min read

The mathematics we teach our kids…

Math education has made progress compared to my school days in specific areas. For example, I am really happy that statistics and probabilities are fully integrated with how we teach mathematics today. I cannot remember learning any notion of probabilities in class until I reached college. I do remember computing the probability that I would get a 7 if I were to throw the dice as a teenager, but this was never part of my schooling.

However, it is not clear that we are moving forward as fast as we need to.

  • As I have criticized before, we seem to stress too much the importance of rote memorization, in particular by pressuring student to memorize the addition and multiplication tables. I have never memorized these tables. To this day, to compute 6 times 9, I do… 6 times 10 minus 6. Not only do I feel no shame, I am convinced that rote memorization for its own sake can be detrimental. For one thing, it annoys students, making them hate the topic. For another, it encourages rote memorization as a way of doing mathematics.

If you think it is odd for someone trained in mathematics like myself not to know his multiplication tables, note that Benoit Mandelbrot, arguably one of the greatest mathematicians of the XXth century, never memorized his multiplication tables.- There is a strong emphasis on naming the concepts and memorizing the names. My oldest son was given the following test: if 5 times 10 is 50, what is 5? The correct answer was “a factor”. I am quite sure I would not have known what was demanded. The way geometry is taught is almost entirely about memorizing the names of various figures. Who cares about what a scalene triangle is? Math is not about learning definitions.

  • Generally, we stress trivial but complicated algorithms. As a professional scientist, I rarely have to add fractions, or to do long divisions. To be honest, I had to pause for a few seconds before I could explain how one goes about computing 12.53 times 13.21. Really, you never compute such a thing the long way in the real world. Though I read that it has been de-emphasized, and this makes me happy… I still do not know why you would drill anyone by asking them to divide 115.5 by 24.21 by hand. It is useless and boring.
  • Computational thinking is not encouraged. The students have to be able to divide 115.5 by 24.21 by hand, but they are not be made aware that they are using an algorithm. In fact, computational thinking appears to be almost entirely absent while rote memorization and mindless drilling rule.
  • The students are asked to do “real-world” problems, that are designed to be encouraging and relevant. So instead of an openly arbitrary 4-line word problem, we get a 3-page story about Any who is trying to organize a party and she has 12 friends who each need to drink 120mL of juice, but she can only buy juice in units of 1.2L. Except that she can go across town where she can buy cheaper juice in units of 1.5L, but then she has to pay for her cab. Except that she can ask her sister to drive her, but then she also needs to pick up blue curtains for her mother and they are across town anyhow. Or she could go to the local store and buy red drapes, but it is out of her way… You think I am joking, but I barely exaggerate… I guess that they are also trying to train kids in the art of filling out complicated tax forms or do some corporate job, so they need to read through long instructions with many details and plan ahead… Except that if I am turned off by these problems as a trained mathematician, I can only guess how people who proclaim to hate math must feel. No, I do not think that they are fooled into thinking that this is relevant because of how it is phrased.

How would I train kids in mathematics? Good old word problems combined with an introduction to programming.