Discusses examples of children's invented equal-sharing strategies that lay a foundation for reasoning about equivalence by connecting ideas from multiplication, division, and fractions. (KHR)

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)

Describes the psychological analysis of the instruction of the concept of multiplication in the former Soviet Union. Presents a system of instructional situations in introducing multiplication and the main results of instruction for grade two. (MDH)

Applies the Lesh Translation Model to develop conceptual understanding by showing relationships between five modes of representation proposed by Lesh to learn multiplication of fractions. Presents five teaching activities based on the translation model. (MDH)

This paper proposes a theory that can account for differences between everyday and formal mathematics knowledge and a set of processes by which informal knowledge is transformed into formal mathematics. After an introduction, the paper is developed in five sections. The first section lays out the nature of informal, everyday mathematics knowledge.…

The author analyzes his 11-year-old daughter's investigation of patterns in multiplication. In an investigation initiated herself, Becca generates hypotheses, discovers patterns, asks questions, and discards procedures that do not produce desired results. Providing a classroom environment that values questioning is a key recommendation. (MLN)