Gifted Math Education: acceleration, enrichment, and the Calculus Trap
Quite often the question arises as to what is better for gifted kids — acceleration or enrichment. And it seems that many, many parents of gifted kids are adamant that only acceleration could possibly be appropriate for their children. That if they are are ready to take the next step, they should not be “held back” from taking it, and if they don’t learn something “new” they’re being denied the education they have a right to.I’d like to counter that enrichment is not only an appropriate means of meeting at least some of the needs of gifted math students, but in many cases may be a better choice than pure acceleration.
The problem is that, too often, schools say “enrichment” when they mean “do nothing, or at least very little”. And so parents have learned to be highly suspicious of the term.
When I advocate for enrichment for gifted math students, I mean two things:
- A student who is gifted in mathematics should IMO be given more and more difficult problems to solve with the “tricks” they already know. Because the problem solving skills are far more important than the particular bags of tricks.
- These students should be exposed to topics not usually covered (either at all, or at least not very deeply) in a standard curriculum, such as logic, number theory, combinatorics, set theory, recursion, etc…
In many cases, these activities are more beneficial to students, than acceleration. Rather than just completing the standard, rather-bare-bones math curriculum up through high school in record time, students instead get to explore interesting topics, stretch their minds with challenging puzzles, and learn more than the minimum curriculum (which was certainly not designed with the needs and abilities of the gifted learner in mind).
Most standard curricula spent little or not time on “non-routine” problem solving — working on the kinds of problems you might find in math competitions, problem of the week websites, etc. The argument is that there isn’t enough time. Well, I’d argue that it’s well worth making time, because, IMO, that kind of thinking and problem solving is a very important part of mathematics. But for gifted kids who have extra time because they zip through the standard curriculum so quickly, it’s even more of a no-brainer to give these kids this kind of experience that will deepen their mathematical thinking skills and better prepare them for higher-level mathematics, or indeed many other disciplines that require excellent thinking and problem-solving skills.
IMO, math is not a race. I say this as a parent, a mathematician, and a volunteer math educator. I’d encourage you to read this article: The Calculus Trap. It addresses the issue from the point of view of high school curriculum, but many of the same principles apply earlier on. It helped me think more clearly about the kinds of experiences that could be beneficial to gifted math students, and helped shape many of my views as articulated above.
Those who know me well probably won’t be surprised to hear that we’ve worked with our kids’ school to take a hybrid approach with our children. They work with kids a couple of years older than themselves, but also spend time on enrichment activities to deepen their mathematical learning and experiences. We’ve elected to have them join the “standard” honors stream here in high school, which starts with honors geometry in 9th grade. This means the have all of middle school to get through “Algebra I” which gives them lots of time to work on extra topics, problem solving, etc.
I have more to say on related topics, such as gifted kids being used as tutors and mentors for other students, possible topics for enrichment starting even in the primary grades, etc. But since this post is getting quite long already, I’ll save those for another day.