Matching Assessment with Curriculum
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By Larry Mann
"What most of us experienced in math classes was not problem solving," insists Joe Mills, a mathematics assessment consultant. "Our textbooks taught skills, which we practiced, but that's not the same as problem solving," Mills says.
According to Mills, problem solving is generally characterized by a sense of experimentation: Students figure out the strategies, discover a variety of solutions along multiple paths, and apply knowledge in new situations. Sometimes, problem solving means discovering what to do when the path is unclear. The great value of problem solving is that it extends and deepens knowledge. As an assessment strategy, it illuminates how well students understand. Yet the problem with problem solving, says Mills, is that it is one of the hardest things for teachers to teach.
Many standards emphasize problem solving, Mills notes, but often, curriculums work against problem solving in favor of coverage. "This is one of the differences between the way the Japanese approach math instruction and the way Americans generally do it," says Mills, who has studied the findings in the recent TIMSS reports. "The Japanese explore examples in multiple ways," he explains. "Their mathematical strength comes out of this. With us, the approach has been skills first--and has not been as successful." Meaningful tasks and problem solving, Mills recommends, should be "the focus of instruction, not an afterthought; the beginning of learning, not the end."
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