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…

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…

In two experiments, we examined fourth and fifth graders' comprehension of the source of information in texts presenting controversial issues. In Experiment 1, participants read short texts in which two people presented different arguments regarding an issue. Participants identified who said what and evaluated each source's knowledge of the issue.…

This study explores changes in students' strategies as they solve different types of volume problems. Fifth graders were presented with pictures showing 3D objects and a unit cube; they determined how many cubes made up the object and explained their responses. We examined whether children transferred strategies across problem types, varying in…

Reasoning about mechanisms is one of the hallmarks of disciplined inquiry in science and engineering, but comparatively little is known about its precursors and development. Children at grades 2 and 5 predicted and explained the motion of simple mechanical systems composed entirely of visible linkages (levers). Students' explanations of device…

This article presents a theoretical model of the process by which students construct and elaborate explanations of scientific phenomena using visual representations. The model describes progress in the underlying conceptual processes in students' explanations as a reorganization of fine-grained knowledge elements based on the Knowledge in Pieces…

This article examines the pedagogical practices of two science inquiry teachers and their students using a Web-based system called Web of Inquiry (WOI). There is a need to build a collective repertoire of pedagogical practices that can assist elementary and middle school teachers as they support students to develop a complex model of inquiry based…

This study builds on two lines of research that have so far developed largely separately: the use of additive methods to solve proportional word problems and the use of proportional methods to solve additive word problems. We investigated the development with age of both kinds of erroneous solution methods. We gave a test containing missing-value…

This study examines presentations of the distributive property (DP) in two widely used U.S. elementary text series and one main Chinese text series along three dimensions: problem contexts, typical problem types within each problem context, and variability in using the DP. In general, the two U.S. texts were found to resemble each other but to…

This study tests the hypothesis that cultural differences in group orientation predict an interaction between the student variable--ethnicity--and a learning context variable--reward structure--on math performance after group learning. One hundred and thirty-two African-American and European-American female and male fourth and fifth grade students…

To identify the challenges that students must meet to engage in effective self-directed inquiry, a class was followed for three years, from the fourth through the sixth grades, as they engaged in a sequence of progressively more demanding inquiry activities. Students made substantial progress in understanding the objectives of inquiry, identifying…

Previous research (e.g., De Bock, 2002) has shown that--due to the extensive attention paid to proportional reasoning in elementary and secondary mathematics education--many students tend to overrely on proportional methods in diverse domains of mathematics (e.g., geometry, probability). We investigated the development of misapplication of…

In this article, we analyze the complexity of using instructional dialogues in the teaching of mathematics. We trace a 10-lesson unit on functions and their graphs taught by Magdalene Lampert to a 5th-grade classroom. We use this trace to help analyze and systematize the complexity of the classroom discourse. Analysis shows that Lampert's…

The study examined children's understanding of scientific inquiry, through the lens of their conceptualization of uncertainty in investigations they had designed and implemented with a partner. These largely student-regulated investigations followed a unit about animal behavior that emphasized the scaffolding of independent inquiry. Participants…