The Advantage of Abstract Examples in Learning Math
Jennifer A. Kaminski, Vladimir M. Sloutsky, and Andrew F. Heckler
April 25, 2008
We all remember our math teachers who tried, valiantly, to communicate the mysteries of fractions by using analogies to pizza slices, or to educate about systems of equations by referring to trains traveling in opposite directions. It was and is assumed that real-world comparisons make it easier for students to understand abstract math. But new research from Ohio State University suggests that concrete examples might actually "hinder the ability to recognize the same concept elsewhere." Real-world problems (even when coupled with the teaching of the same concept using abstract examples) can decrease a student's ability to transfer their knowledge to new problems and situations. This research gives scientific backing to earlier recommendations by the National Math Panel that schools ought to focus more on teaching fundamental facts, math algorithms and operating procedures and spend less time in the rain forest. Ultimately, say the Ohio State analysts, "if a goal of teaching mathematics is to produce knowledge that a student can apply... then presenting mathematical concepts through generic instantiations... may be more effective than a series of ‘good examples.'" The short paper can be found here. Those with a taste for methodology can download supporting material here.