The researchers conducted a qualitative case study to describe the teaching and learning of a third grade student with a learning disability as he worked on multiplicative tasks with a tutor. The student's strategies, at participatory and anticipatory levels of understanding, were analyzed to inform instructional decisions we made to support the…

Visual representations and manipulatives are a highly advocated mathematical tool for the teaching and learning of multiplication and division. Although there is some prior research on elementary teachers' general use of manipulatives and visual representations, there is little to no specific focus on use of such representations on a specific…

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…

For many students, developing mathematical reasoning can prove to be challenging. Such difficulty may be explained by a deficit in the core understanding of many arithmetical concepts taught in early school years. Multiplicative reasoning is one such concept that produces an essential foundation upon which higher-level mathematical thinking skills…

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…

Four hundred and three 3rd- and 5th-grade Chinese students took the Multiplication Estimation Test or participated in the interview on it, designed to assess their computational estimation performance on whole-number multiplication. Students perform better when tasks are presented visually than orally. Third graders tend to use rounding based…

Modern sophisticated computers are shown to multiply the same way the ancient Egyptians did more than 4000 years ago--by doubling and adding. (MN)

This study compares a pencil-and-paper drill strategy with a calculator drill strategy in facilitating the learning of multiplication facts. The results suggest pencil-and-paper drill is more effective. (MK)

A procedure for recording the prime factors of a composite number is explained. (DT)

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)

This study compares the effectiveness of two methods of training preservice elementary teachers to diagnose and treat students' arithmetical errors. (SD)