How multiplication is usually taught in school and how it could be taught are discussed. Development of understanding is illustrated through children's words and work. (MNS)

The article reviews the development of mathematics error analysis as a means of diagnosing students' cognitive reasoning. Errors specific to addition, subtraction, multiplication, and division are described, and suggestions for remediation are provided. (CL)

Describes the characteristics of progressive schematization with regard to column multiplication and column division. Contrasts this with column arithmetic based on progressive complexity. Presents a summary of research data concerning column arithmetic. (TW)

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)

Discusses the two overgeneralizations "multiplications makes bigger" and "division makes smaller" in the context of solving word problems involving rational numbers less than one. Presents activities to help students make sense of multiplication and division in these situations. (MDH)

Presents five activities to help students construct meaning for multiplying fractions through real-world problem contexts, physical or pictorial models, the recognition of patterns, and the use of calculators. In the context of a garden plot, worksheets examine various aspects of parts of plots, patterns in plots, and a maximization problem.…

Recent research suggests that many middle school students approach mathematical story problems with strategies that are not based on possible meanings for the operations, yielding success for one-step problems, but providing a weak background for approaching algebra story problems. This document reports the findings and the materials developed by…