Tuesday, May 09, 2006


I've always felt that manipulatives can have a place in the math curriculum, but only if they directly, and I do mean directly, relate to the math being done. In that vein I support Hands-On Equations for introductory pre-algebra and algebra, as the program is designed to transition students from manipulatives to symbolic manipulation on paper.

Now I read this:

In another series of studies (Amaya, Uttal, & DeLoache, under review) we investigated the effectiveness of concrete symbolic objects, known as manipulatives, in helping young elementary-school children learn the procedures associated with two-digit subtraction.... [T]hose children who learned with the manipulatives had trouble transferring knowledge to written versions of the math problems; they did not use what they had learned using the manipulatives to solve written versions of the same or similar problems. Moreover, learning with the manipulatives took almost three times as long as learning with the written method.
American Psychological Association Observer

Granted, that statement applies specifically to subtraction, but if it's applicable to more pervasive uses of manipulatives then I've been wise to caution against their use in most cases.


Anonymous said...

Manipulatives? Do I want to know?

Darren said...

Manipulatives are "toys" that students can use that supposedly will help teach or reinforce mathematical concepts.

Anonymous said...

I'm the author of the paper cited above.

It should not be interpreted as showing that manipulatives are either bad or good. It depends, of course, on how they are used. There are indeed situations in which manipulatives can be very helpful. Manipulatives seem to be more helpful for gaining knowledge about mathematical concepts than for learning mathematical procedures.

What we are challenging is a belief we sometimes run up against, the notion that concrete is always "good" and abstract is always "bad", or that concrete must always come before abstract.

Darren said...

I appreciate your comment. I want to make clear that I don't think, and didn't write, that manipulatives are either good or bad in and of themselves. Based on what you wrote above, I completely agree with your conclusions.