research in cognitive science, anthropology, and other areas that has begun to provide real support for this notion in careful studies spanning a broad range of content (Gardner, 1991; Glaser, 1984; and Resnick, 1988). In addition, there are an extraordinary number of "existence proofs," of examples of teachers such as Jaime Escalante, who inspire "average" or ''below-average" students to intellectual heights others would not have thought possible. It was not just Jaime Escalante, it was the teacher next door to him, and the one next door to her, and the people and schools throughout the nation who emulated Escalante, who help to expand our understanding of the learning potential of all kinds of students. Nationally, we have the beginnings of strong evidence from surveys of advanced placement (AP) course taking. The number of AP courses taken and succeeded in by all types of kids has skyrocketed in the last eight or 10 years.4

We also have existence proofs from other sources such as studies of international achievement. Many Americans have been amazed and appalled that so many Japanese students score well on algebra tests in eighth grade while Americans fail miserably (Crosswhite et al., 1985; Stevenson and Baker, 1991; and UNESCO, 1983). It is not so amazing at all. In Japan most students take algebra in seventh grade, so they score pretty well in eighth grade. This makes a certain amount of sense. In most cities in the United States, however, we do not let our students take algebra in seventh grade. In fact, we greatly limit the percentage of students taking algebra in eighth grade because we—"we" being the general public and the people in the schools—do not believe that American students can learn it.

2. What you are taught matters. Again, we can look to the example of algebra, among other subject areas. If you are not taught a foreign language, you are probably not going to learn one. It is not just a matter of teaching a particular subject area, however; what is taught in a given subject area is equally important. If a student is taught only a tiny bit of mathematics or science in the first three or four years of elementary school, he or she is not going to score very well on a mathematics or science test. If a student is taught a great deal of math, in terms of both breadth and depth, he or she is likely to know more and to demonstrate that achievement on appropriate assessments. Despite the seeming simplicity of this logic, our schools have been slow to either deepen their courses or make other changes that would connect what is taught to what is tested (Madaus, 1991; UNESCO, 1983; and Resnick and Resnick, 1985).

4  

Since 1989, the number of AP tests taken in all subjects has increased by 150 percent, from approximately 456,000 to 684,000. The growth was even more pronounced for black, Hispanic, and Asian students, whose participation rates nearly doubled. The mean grade achieved also rose across all groups (College Entrance Examination Board, 1994). From 1984 to 1992, the percentage of students in the eleventh and twelfth grades who took the exams rose from 2.4 to 5.7 percent, almost a 240 percent increase. The participation rates of blacks and Hispanics in AP testing have increased by even greater margins to 3.5 and 3.7 times the 1984 levels, respectively.



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