The following is a comment I left at the Math Forum @ Drexel
My comment has not yet been “moderated” but here is the thread:
Although I am a very new teacher, I’m not sure I understand the controversy here. I see two continuums here: one about process and one about content. Devlin talks about traditional versus progressive ways to teach. I think many math teachers would not argue with using a more traditional approach to introduce concepts and then move towards a progressive approach for the students to practice and learn the concept. (Dy/Dan might be the exception, but one could argue that his students do need some underlying concepts to figure out the volume of water being filled. Or, he is showing a teaser that then some concepts have to be taught in order to proceed).
The second continuum is around content. Again, I don’t think there would be many math teachers who would argue against real-life application of the content. And, as with most continuums, it can be somewhat problematic to be at either extreme. Let’s let the teacher make that call depending on the lesson. I would suggest that lower order tasks could be done with less real-life application whereas high level order of thinking would be better accomplished with real-life application.