manipulatives

I have learned this lesson over and over again at my job and will continue to emphasize its importance if I end up teaching math: Students will remember math better and perform better at solving math problems if they understand how the problem works, not just memorize the steps to solving it. This will allow them to deal with curve balls in classroom problems and later on in real life problems, applying math strategies to figuring out the answers to problems that are not identical to example 3 on pg. 112. One really key way to help students understand the whole picture is literally to present it in visual form. These manipulatives I found playing around on delicious are a really effective way to do that. They come presorted by grade level and concept, but more importantly they can provide an anchor to almost any major math concept. I firmly believe, however, that these are not just for teachers to show on a projector. I would use them to introduce a new concept, say the often confusing idea of input and output and definitions of functions, by having the students play around with the manipulatives themselves before I gave them all of the information. Not only would this provide an additional visual element that would help many if not all learners, the individual investigative discovery of concepts that would result from it would provide a much stronger base of understanding about functions than me presenting the material directly to them.