Similarity is a fundamental concept in the middle grades. In this study, we applied Vergnaud's theory of conceptual fields to answer the following questions: What concepts-in-action and theorems-in-action about similarity surfaced when students worked in a novel task that required them to enlarge a puzzle piece? How did students use geometric…

This study compared one lesson across four U.S. "traditional" textbook series, two U.S. reform-based textbook series, and one Chinese mathematics textbook series in teaching the connection between multiplication and division. The results showed the differences across U.S. and Chinese lessons in both the teaching and the practice parts of…

Students in grades four-six were asked to complete multiplication examples and write a story problem (reported earlier, SE 533 279). Their stories were categorized in terms of their logic and realism. Many errors were noted, leading to the conclusion that knowledge of multiplication does not necessarily lead to logical multiplication. (MNS)

Eighty-seven pupils in grades 4-6 completed five multiplication examples and wrote a problem for another example. They were reasonably proficient, with mean scores of 82 percent in grade 4, 75 percent in grade 5, and 97 percent in grade 6. They did less well on developing a problem. (MNS)

The purpose of this study was to compare the achievement for the operations of multiplication and division on whole numbers of elementary grade students who were taught functional diagnostic strategies with a randomly selected group who were not taught the informal diagnostic strategies. Included are the methodology, results, and discussion. (KR)

Current practices in teaching about distributivity of multiplication over addition and subtraction are reviewed. Then a study is described in which two inventories were administered to 83 eighth-grade students; scores were low. Suggestions for teaching distributivity are presented. (MNS)

Discussed is the meaning of the word "of" as is found in mathematical expressions that involve fractional numbers. The conceptual rather than numerical distinction is stressed. Teaching techniques regarding difficulties with this concept are suggested. (CW)