Math from Real Teaching Means Real Learning

I just read a blog entitled "Real Teaching Means Real Learning" where the author quotes Schoenfeld's "When Good Teaching Leads to Bad Results". There were many great blog posts about math instruction on this blog and I will visit it often. Schoenfeld concludes that students have four beliefs about math:

1. The processes of formal mathematics (eg. "proof") have little or nothing to do with discovery or invention. Corollary: Students fail to use information from formal mathematics when they are in problem solving mode.

2. Students who understand the subject matter can solve assigned mathematics problems in five minutes or less. Corollary: Students stop working on a problem after just a few minutes since, it they haven't solved it, they didn't understand the material (and therefore will not solve it).

3. Only geniuses are capable of discovering, creating or really understanding mathematics. Corollary: Mathematics is studied passively, with students accepting what is passed down "from above" without the expectation that they can make sense of it themselves.

4. One succeeds in school by performing the tasks, to the letter, as described by the teacher. Corollary: learning is an incidental by-product to "getting the work done".

Not a glowing review of what we do in school for mathematics! Certainly Paul Lockhart, Alfie Kohn, Conrad Wolfram and Dan Meyer have said similar things. Compare the above to Dan Meyer's description of his math students prior to changing the way kids learn in his class.

lack of initiative

lack of perserverance

lack of retention

aversion to word problems

eagerness for formula

See the similarities?

More evidence that we need to change the way our kids learn and view math.