Looking back over five decades (more or less) of teaching high-school mathematics, I estimate that maybe 30–40 of the students I have taught over the years were truly accelerated in math. But let’s define our terms first:

• I am not talking about students who take courses labeled “honors,” who thereby end up taking an AP Calculus class in 12th grade; that’s just a normal route for a significant minority of kids these days.
• And I am not talking about students who switch school districts and thereby end up accidentally a year ahead of their peers (because of differences in curricula).
• And I am not talking about students who double up one year (most often Algebra II and Geometry) and thereby become a year advanced the following year.

So, you ask, who am I talking about? Mostly the kids who are so excited about math that they end up studying it outside of their regular school — either on their own or else in an enrichment course. I’ve taught many such enrichment courses (to upper elementary students and to high-school students (but not middle schoolers, thank you), so that gives me considerable personal experience even if I never collected hard data along the way. I also have limited personal experience from the student’s perspective, but more on that below.

I also have the perspective of two informative articles, recommended to me by my friend and colleague Leah Gordon:

• “The Greatest Educational Life Hack: Learning Math Ahead of Time,” by Justin Skycak.
• “Academic Acceleration in Gifted Youth and Fruitless Concerns Regarding Psychological Well-Being: A 35-Year Longitudinal Study,” by Brian O. Bernstein, David Lubinski, and Camilla P. Benbow.

I suggest reading both of them. The contrasting styles are well signaled by the titles. The former has a very opinionated point of view and is easily readable. The latter is much more academic, to put it mildly, with lots of data. I would have had no trouble reading it two years ago, before my brain injury, but now I found it rough going. For example, here is an excerpt picked more-or-less at random:

We show the relation of latent SES, latent psychological well-being, and the educational composite (Figure 3, top) and age of high school graduation (Figure 3, bottom). Fit indices for each of the two models were good. Model 1 (top) has a comparative fit index (CFI) = .959, square root mean residual (SRMR) = .030, and root mean square error of approximation (RMSEA) = .067 (90% CI [.060, .075]). Model 2 (bottom) has a CFI = .958, SRMR = .030, and RMSEA = .067 (90% CI [.060, .075]). In each model, using SES as a control, the path coefficient of interest, namely, from the indicator of academic acceleration to psychological well-being, was trivial: .06 (p = .03) in Model 1 and .02 (p = .491) in Model 2.

Both articles present evidence that learning math in an accelerated way is appropriate and helpful (for the right students) and does not cause the issues that many people bring up. The Skycak article, although easy to read, unfortunately contains altogether too many sentences that are somewhat offensive to teachers, like “[I]f you pre-learn the material, you’re not depending on the teacher to teach it to you, which means you’re immune to even the worst teaching.” Yes, but you’re also immune to the best teaching and will lose out on a good teacher’s perspective on what to emphasize and on how the good teacher will model answering questions.

I also have an issue with part of the point of view inherent in the very word “accelerated,” which suggests that you are moving quickly along a predetermined path. Too many of my students who have done just that ended up on the side of the road, with big holes in their knowledge. Nevertheless, it is reassuring (from the second article) to see that some of the predicted negative effects of acceleration in math do not turn out to be big problems. For example, “the reality is that educational acceleration does not lead to adverse psychological consequences in capable students.”

And that leads me to conclude with some remarks about my own experiences in various subjects. After I finished first grade, my family moved to a new state and therefore a new school district. By the end of first grade I had been reading fourth-grade books, but my new second-grade teacher proclaimed “if you are in second grade, you must read second-grade books,” and it turned out that that was the district’s policy. For that reason, even though my parents believed deeply in public schools, I ended up in private schools, starting in third grade. And math was similar, but in this case my dad started teaching me algebra when I was in third grade — just the sort of thing that the Skycak article recommends. The actual class proceeded slowly through the standard curricula of third, fourth, and fifth grades, while I happily solved quadratic equations and graphed functions. My parents turned down the offered opportunity for me to skip a grade at various points, feeling that I would be better off both socially and academically if I stayed with my peers and just learned more material on my own. We also set up a small out-of-school group as a science class taught by a scientist; that was maybe in fifth or sixth grade, I don’t exactly remember which. I am very glad that we went the enrichment route, not the grade-skipping route.

Categories: Math, Teaching & Learning