An interesting item in this morning’s New York Times — Someone has finally done an experimental study on the math instructional technique that emphasizes the use of blocks, balls, and other concrete “manipulatives” to teach math. Researchers at Ohio State University created an experiment in which they randomly assigned subjects to be taught a new math concept either by focusing on the abstract math rule, focusing on the use of manipulatives, or combining both techniques. They then tested how well subjects had learned the math concept by having them apply it to a new situation. It turns out that students taught with manipulatives did the worst, the ones taught abstractly did the best, and the combined approach performed in the middle. It appears that those taught math with more concrete examples had a harder time transferring that math concept to a different concrete example. Kids taught math with tennis balls have a harder time applying the principle to railroad cars.