I agree. All students deserve practice to develop their working memory, as well as other thinking skills where gifted kids excel, and that implies different instructional criteria. I do hold tight to the notion that there is a core of "best" math ideas that all kids should learn, to develop both understanding and problem-solving, but they certainly don't need to learn them the same way.
ETA: I especially have misgivings about this part: Despite the widespread support for �problem-based� or �discovery-based� learning, studies indicate that current teaching approaches underestimate the amount of explicit guidance, �scaffolding� and practice children need to consolidate new concepts. Asking children to make their own discoveries before they solidify the basics is like asking them to compose songs on guitar before they can form a C chord.
Because some studies indicate that some kids are not ready to learn through problem-solving as well as through direct instruction (I disagree-- all kids should be encouraged to problem solve at an extremely young age, and it can be quite guided, plus they don't have to be mutually exclusive), this sounds like Jump Math may remove some vital learning opportunities from gifted kids, even if they're allowed to speed ahead through curriculum compacting.
I guess the technique of breaking something down into little steps can be useful for tutoring, or even for instruction to make sure someone understands a procedure. I'm not sure that all that focus on procedure will lead to deeper understanding in classrooms. This sort of score-boosting method is likely to spread because of its obvious attraction to administrators, especially in lower-performing schools. It reminds me of a news article from years ago of miraculous results of a teacher in an inner-city setting (I believe it was in Chicago) who was greatly boosting math achievement scores by teaching students mnemonic tricks, such as a sing-songy way to remember long division. I wonder how many students who learn that way ever become mathematicians.
Thanks for the post.
