Teachers frequently report that their most imaginative and thoughtful students bristle at the assumption that there is a single right answer and think about ways in which supposedly wrong answers might be true. These students must be reminded to be more simple-minded for the sake of the test. The test taking itself, of course, occurs only a few days a year. But the tests exert strong effects on the overall curriculum. But the developmental and educational theories of Jean Piaget, John Dewey, and others suggest that students can often learn basic concepts, and learn them most energetically and soundly, through such active endeavors.
Students can learn a good deal of math through carpentry projects.
And while they often find the math in textbooks abstract and tedious, they enthusiastically tackle the math that's required to build things, for it helps them fulfill their creative impulses. Many teachers feel that finding ways of introducing concepts and skills through creative activities is an exciting challenge. Unfortunately, projects take time and involve work that is unrelated to standardized tests. Textbooks and workbooks enable teachers to cover test-related material much more efficiently. So schools opt for the texts and workbooks, even though students rarely display any enthusiasm for them. .