In this article, we use a two-dimensional assessment to examine the experimental impacts of a mathematics learning trajectory-oriented formative assessment program on student strategies for problems involving multiplication and division. Working from the theory that the development of students' multiplicative reasoning involves improvements in…

This article proposes a taxonomy of strategies for single-digit multiplication, then uses it to elucidate the nature of the learning tasks involved in multiplication. In preceding work, it has generally been assumed that much of children's strategy development is driven by changes in their general conceptual capabilities relating to number. In…

The relative efficacy of two approaches to teaching basic multiplication facts to third graders is examined. Support was indicated for the thinking strategies approach. Results also indicated it was possible to train teachers in two days of inservice education. (MP)

The relative efficacy of two strategies for teaching skills was investigated. The results suggest that the sequence of skill and understanding makes little difference in influencing mathematics achievement of above average middle school students. (MP)