I have been following the treads in this discussion and one theme that seems to be popping up is that having students build their own mathematical understanding at their own pace takes a great deal more time than teaching mathematics through conventional algorithm. Given the ever increasing burdens on teachers of non-educational tasks and responsibilities, where are our teachers expected to gain this time needed. While I understand and support the need to present real life problems so student understand math in the context of their everyday world, in the interest of efficiency should we not balance conceptual investigations with the ÃÂdreadedÃÂ --drill & kill-- so that students can experience more permutation of a given math problem. (i.e. couple word problems with the tried and true page-of-20-math-problems) As I remember my learning of math the more examples I had to go by the better and quicker understanding I could gain.
I find it a false dichotomy to say that a relatively small number of word problems generates a better understanding of how to do addition or subtraction than a sheet of 20 different addition problems. Cannot these two methods coexist in a well structured math program? To put the burden on parents to use flash cards at home by its very nature dooms students with uninvolved parent to constantly playing catch-up.
If students are unprepared to move on to the next grade or test into the next school (and I understand these are not isolated incidences) does that not speak volumes about how shallow our expectations are and what might be missing in this new teaching philosophy?