Knowing and Teaching Elementary Mathematics@@@Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States

Partly this noninterest in mathematical expertise reflects an attitude widespread among educators [Hi] that “facts”, and indeed all subject matter, are secondary in importance to a generalized, subject-independent teaching skill and the development of “higherorder thinking”. Concerning mathematics in particular, the study [Be] is often cited as evidence for the irrelevance of subject matter knowledge. For this study, college mathematics training, as measured by courses taken, was used as a proxy for a teacher’s mathematical knowledge. The correlation of this with student achievement was found to be slightly negative. A similar but less specific method was used in the recent huge Third International Mathematics and Science Study (TIMSS) of comparative mathematics achievement in fortyodd countries. For TIMSS, U.S. students demonstrated adequate (in fourth grade) to poor (in