Deeper, Not Faster

This

Not that!

Curiously, there is no pressure on schools to teach Shakespeare or Faulkner to ever younger students. In English, common sense prevails: if the student is exposed to a particular bit of literature at an appropriate age before graduation, that's good enough. In math, however, it is widely believed that younger is better, and that strong students will get bored if they are not accelerated.

Alas, the latter is true if the curriculum is shallow, and emphasizes recall and regurgitation! A certain type of student can handle an enormous amount of this, and since all students reflect the surrounding culture, they can't get enough of it, and get addicted to speed. Combine this with the relatively powerful position of their parents, who are typically professionals who put a fair amount of energy promoting their point of view in the school, and you have a recipe for nearly unstoppable hyper-acceleration. (See my previous post on the problems with this.)

Actually, hyper-acceleration also benefits some teachers. In schools where the most experienced teachers get to teach the most advanced classes, those teachers benefit from being in charge of the most obedient and cooperative students, leaving the more challenging kids to their less experienced colleagues. (I know, it makes no sense to organize things this way, but alas, it is a fairly common setup...)

In actual fact, the better solution for the vast majority of students is for math departments to resist hyper-acceleration. Instead, we should find ways to go for depth of understanding, challenging problem-solving, and enrichment. Of course, this is difficult to do when there is a lot community and administrative pressure going the other way. The most effective approach to such resistance is to use this four-prong strategy:

- Work to shift the departmental and school culture towards depth rather than speed. Deeper, not faster! One way to do it is to teach core topics with rich activities. Of course, changing the culture is not going to happen overnight, but any motion in that direction is well worth it even in the short run.

- Keep offering problems that are "too difficult" for even your top students, as suggested by Gord Hamilton here. This will benefit these students far more than just feeding them more techniques to memorize. Learning to handle frustration, learning ways to tackle tough problems, learning to work collaboratively as well as independently — all those are more valuable in the long run than rushing through next year's techniques, which in any case will not challenge those students, and will come soon enough.

- This needs to happen in math class, but because of time and other limitations, it should also be pursued in math clubs and teams. However the latter tend to cater mostly to boys. I strongly encourage you to look at the approach pioneered by the Julia Robinson Math Festivals which works for a wide spectrum of students. These blog posts include some examples, but it's not difficult to find additional challenging problems on the Web, in professional journals, and in past mathematical competitions.

- Finally, and paradoxically, a key ingredient in resisting hyper-acceleration is to implement some intelligently-conceived, moderate acceleration which doesn't expand learning gaps and which takes into account students' mathematical maturity and developmental readiness. I will elaborate on this in my next post.

--Henri