Cathy Kessel

The Theory of School Arithmetic: Whole Numbers

In 1999, Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States presented readers with a puzzle. Four of its six chapters concerned interviews of US and Chinese primary teachers. (Note that the two groups of teachers were not chosen to be representative or similar in status.) The teachers described how they would respond to four classroom situations: teaching subtraction with regrouping; addressing a mistake in multi-digit multiplication; creating a word problem for division by fractions; and addressing an incorrect student conjecture about area and perimeter. The puzzle: Why did the US teachers, all of whom had tertiary degrees and were enrolled in intensive post-graduate programs, show less knowledge of school mathematics than the Chinese teachers, who had so much less education?