The latest issue of AFT’s American Educator is all about curriculum (and a national one at that), and it’s worth a read. Specifically this piece on math by three scholars of education and education psychology. It is excerpted from a math journal, Notices of the American Mathematical Society.
The scholars point out that educators tend to view mathematics as a skills-oriented discipline, with problem-solving strategies (or lack thereof) dividing the achievers and non-achievers. But cognitive science doesn’t support this claim. Take chess, for example:
“[I]t takes at least ten years to become a chess master. What occurs during this period? When studying previous games, chess masters learn to recognize tens of thousands of board configurations and the best moves associated with each configuration … . The superiority of chess masters comes not from having acquired clever, sophisticated, general problem-solving strategies but rather from having stored innumerable configurations and the best moves associated with each in long-term memory.”
So it is building up a massive base of knowledge about the game that allows you to become a master. You can’t learn to think strategically about chess without such knowledge.
What does this mean for math? Well, among other things, that you cannot just teach kids “problem-solving” strategies and expect them to be able to apply those techniques to varied mathematical (or other) problems. They will not be able to do it if they lack the necessary knowledge, which, in the case of mathematics, is gained through experience doing math problems.
In the words of the authors: “Minimal instructional guidance in mathematics leads to minimal learning.” And: “There are no separate, general problem-solving strategies that can be learned.”
So why are so many American schools wasting resources and precious class time using reform curricula like Everyday Math that is based on an instruction-lite, discovery-driven approach to learning math? These scholars wonder…
“Instead of continuing to waste time devising “reform” curricula based on faulty ideas, mathematicians and math educators should work together to develop a sound K-12 curriculum that builds students’ mathematical knowledge through carefully selected and sequenced worked examples.”
Lynne Munson and Stephanie Porowski