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.

Several points disturb me in this article. It seems to imply that all students have difficulty with real-world problems and do better with abstract. The normal method is to primarily use manipulatives at the elementary stage when Piaget’s concrete stage is the main way of thinking for these students.
It doesn’t necessarily mean that manipulatives are bad because college level students have trouble using them and prefer to develop a solution via the abstract route. Again, Piaget indicates that abstraction is a higher level thinking skill that is more appropriate for that age level. It could be that concrete examples are a handicap for that level of thinking rather than an asset.
There should be serious questions about the direction and methodology of this expriment since it appears to ignore the very fundamental principles of learning stages as outlined by Piaget. Those who leap on the bandwagon against manipulatives should be cautioned that this study is flawed, incomplete, and overly presumptious.

[…] 19-11-2008 Math Manipulatives: It’s Only Money! Saved by carloscabanillas on Tue 18-11-2008 Manipulatives Make Math Mushy Saved by fernandezfs on Tue 18-11-2008 Musical blocks: physical manipulatives for musical […]

When manipulation and computation are integrated, students make a better transition to application. When the manipulatives are put away and students are sent home to do their homework, an important step is missing in what can be a very productive pedagogy.

Several points disturb me in this article. It seems to imply that all students have difficulty with real-world problems and do better with abstract. The normal method is to primarily use manipulatives at the elementary stage when Piaget’s concrete stage is the main way of thinking for these students.

It doesn’t necessarily mean that manipulatives are bad because college level students have trouble using them and prefer to develop a solution via the abstract route. Again, Piaget indicates that abstraction is a higher level thinking skill that is more appropriate for that age level. It could be that concrete examples are a handicap for that level of thinking rather than an asset.

There should be serious questions about the direction and methodology of this expriment since it appears to ignore the very fundamental principles of learning stages as outlined by Piaget. Those who leap on the bandwagon against manipulatives should be cautioned that this study is flawed, incomplete, and overly presumptious.

I agree that we shouldn’t put too much stock in any one study.

[…] 19-11-2008 Math Manipulatives: It’s Only Money! Saved by carloscabanillas on Tue 18-11-2008 Manipulatives Make Math Mushy Saved by fernandezfs on Tue 18-11-2008 Musical blocks: physical manipulatives for musical […]

When manipulation and computation are integrated, students make a better transition to application. When the manipulatives are put away and students are sent home to do their homework, an important step is missing in what can be a very productive pedagogy.