Kevin Drum, thoughtful as usual, wonders if the memory of his quizzing of a four year old years ago is accurate, as a year or so later a kid who clearly had mastered basic math could hardly do it at all. It turns out there is some evidence that people learn on a "U" shaped curve, that we get a handle on a cognitive skill, demonstrate it well, start processing it deeply, and become confused before the skills become more deeply set.
There's evidence that this U-shaped pattern is common (this paper, for example, compares 7-year-olds and 9-year-olds on certain kinds of math problems and finds that 7-year-olds do better). So is this what happened with my four-year-old friend? Did she learn simple arithmetic, then get confused about it during kindergarten, and then learn it for good in first grade? Maybe. Maybe I didn't imagine the whole episode after all.
If this is true, it obviously has disturbing implications for the use of standardized tests in primary schools to evaluate teacher performance. If students routinely go through U-shaped learning curves, it means that a terrific third grade teacher might produce mediocre test scores if her kids tend to be in the trough of the U at year-end, while the fourth grade teacher who gets the kids the following year reaps the benefits. I think we all have "U" shaped learning experiences, and for me it is another example of how the exigencies of profiting off of schools both politically and fiscally drive very simple minded "solutions" to educational issues. It also highlights a self-knowledge problem for students: what sort of kid might interpret the middle phase of her own learning pattern as a an end-point and thus evidence of inability and failure?
Something to think about.
