We had a great discussion in my math ed. class yesterday in which I suggested to the students that not all math needed to be problem centered as suggested in the book. I think mathematics has an aesthetic component that students should learn to appreciate. As a group, we're reading a great book, Making Sense, by James Hiebert and several other great luminaries on the world of mathematics education.
Every so often, however, I feel I need to disagree with their wise words. I do this partly to get the students to think more critically and partly because I really do disagree. Although the book was written 14 years ago it is still very current except in those one or two areas where I think we've moved on. One of those areas is in the authors' need for all math to be problem centered.
Problem-centered math education arose in response to the traditional idea that students were passive participants in their own education and that their heads were simply to be filled with information. We know now that students must be actively engaged in their learning and that problem centered math education is one of the best ways of doing that. However, there is more to math that solving problems. Math education must have a strong and well planned aesthetic component in just the same way as do language arts and the teaching of reading. When children learn language they learn all about alliteration and onomatopoeia and how to write poetry and construct creative writing stories. Students never seem to ask "when am I going to need this" as they do in math class when asked to learn the strategy for finding the volume of a cylinder.
We need to make sure that students develop the same appreciation for the pattern and art (click screen and turn the volume up) created by numerical and spatial relationships that they do when exploring word images and the creation of feelings and sentiment through writing.
There's a practical side to all this too as the recognition of a pattern really helps with memory and understanding. Learning one's multiplication facts as just adding another multiple as in one 3, two 3s, three 3s and so on dramatically increases the efficiency of the task.
Click on the picture above. Can you stop the circles moving? Are they really moving?