The Search For Undervalued Knowledge Chunks

One of the more promising things happening in education research is the attempt to learn which chunks of knowledge are the most useful. I think this will ultimately help us figure out how to get the most value out of teaching humanities, but for now we’re still working on the basics. The latest research says fractions and division are good; other things are not as good.

Analyses of large, nationally representative, longitudinal data sets from the United States and the United Kingdom revealed that elementary school students’ knowledge of fractions and of division uniquely predicts those students’ knowledge of algebra and overall mathematics achievement in high school, 5 or 6 years later, even after statistically controlling for other types of mathematical knowledge, general intellectual ability, working memory, and family income and education.

Obviously the hope is that we’ll be able to dig much deeper than this. Perhaps one day we’ll have evidence that understanding metaphor is more predictive of college achievement than understanding protagonist motivation. Or maybe knowing how to find the derivative of trigonometric functions will prove to be particularly predictive of STEM achievement in graduate school.

The fact that we’re still learning the marginal differences in value between certain mathematical concepts means we could probably do a better job making final grades more predictive of future success. For example, there may be kids who seem on track, but whose grades are “inflated” by excellent performance in the least important areas. Similarly, there may be kids who got “bad” grades, but excelled at all the things that are more important (e.g fractions) and struggled at all the things that are less important (e.g. decimals.)

A related issue is that the American school system is probably still a little too biased toward the view that each chronological unit is of roughly equal significance. For example, if learning fractions takes a third of the year, it’s likely to count for a third of a student’s grade. But what about if a truckload of research shows that fractions are much more important, and that additional instructional time isn’t worthwhile? Would a school make fractions worth half a student’s grade if it was only taught for a third of the year? I would think not, but doing so might be the right move.
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Siegler, R.S., Duncan, G.J., Davis-Kean, P.E., Duckworth, K., Claessens, A., Engel, M., Susperreguy, M.I. & Chen, M. (2012). Early Predictors of High School Mathematics Achievement Psychological Science DOI: 10.1177/0956797612440101

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