We examine a hypothesis implied by Steffe's constructivist model of children's numerical reasoning: a child's "spontaneous" additive strategy may relate to a foundational form of multiplicative reasoning, termed multiplicative double counting (mDC). To this end, we mix quantitative and qualitative analyses of 31 fourth graders' responses…

This study presents the results of a series of design experiments that aimed to engage twelve fourth-grade students in mathematical activity exploring the volume of right prisms and cylinders as a dynamic sweep of a surface through a height, an approach that is referred to as Dynamic Measurement for Volume (DYME-V). This article describes this…

Research on collaborative learning has focused on its potential to foster successful problem solving. Less attention, though, has been given to issues of equity. In this article, we investigate how inequity can become amplified and attenuated within collaborative learning through small interactional moves that accumulate to produce broader…

This article integrates an ecological approach and design-based research in computer science education research by following the simultaneous development of a computer programming environment and curriculum for elementary school age children over 2-1/2 years. We studied the alignment of the affordances provided by the programming environment and…

Social skills involved in leadership were examined in a problem-solving activity in which 252 Chinese 5th-graders worked in small groups on a spatial-reasoning puzzle. Results showed that students who engaged in peer-managed small-group discussions of stories prior to problem solving produced significantly better solutions and initiated…

This study developed an analytic framework consisting of four patterns of talk and writing that can support students' engagement in construction and critique: "Talk only," "writing only," "use of talk and writing in sequence," and "use of talk and writing simultaneously." This study aimed to examine how each…

This article reports on students' problem-solving approaches across three representations--number lines, coordinate planes, and function graphs--the axes of which conventional mathematics treats in terms of consistent geometric and numeric coordinations. I consider these representations to be a part of a "hierarchical representational…

Art-based reading instruction and interventions for elementary and middle school students are growing in popularity despite scant theoretical rationale and empirical research support. This study explored the degree to which painting comprehension processes map onto text comprehension processes in this population. In particular, we used think aloud…

How can children's natural perceptuo-motor skills be harnessed for teaching and learning mathematical structure? We address this question in the case of the integers. Existing research suggests that adult mental representations of integers recruit perceptuo-motor functionalities involving symmetry. Building on these findings, we designed a…

This study, based on observation of 90 fifth-grade mathematics classes in Chinese elementary schools, examined how the task features, high cognitive demand, multiple representations, and multiple solution methods may relate to classroom discourse. Results indicate that high cognitive demand tasks were associated with teachers' use higher order…