on math ed: the (possible) danger of breaking down problems ..

whoa -- from "u.s. math achievement: how bad is it" @psychologytoday

When the researchers broke problem-solving activities down into procedural activities and conceptual activities, they expected to find that the higher performing countries engaged in more conceptual problem solving. They found no such difference. But then they took a second step. They coded the data based on whether the teachers made the conceptual problems easier by converting them, for the students, in to procedural problems.

Looked at this way, it became clear that the US was an outlier (as was Australia, the only other low-performing nation in the study). Teachers in the US almost always converted challenging conceptual problems into procedural problems. In doing so, they did exactly the wrong thing. According to a seminal study by Hiebert and Grouws (2007) the two features of instruction that predict good math outcomes are

1. Being explicit about the conceptual structure, and interconnectedness, of mathematics
2. Allowing students to struggle to understand mathematical concepts.

By converting conceptual struggle into procedural learning, US math teaches were unintentionally depriving their students of two crucial elements of effective learning.

the unnerving thing is that, to me, "breaking down a problem" seems like a natural thing to do. it's how research goes, all the time.

the point, however, seems not for the teacher to do all of the reduction .. as (s)he would already know how .. but for the students to learn how to do it.