Group work has been a main activity recommended by mathematics education reform. We aim at describing the patterns of interaction between teachers and students during group work. We ask: How do teachers scaffold group work during a problem-based lesson? We use data from a problem-based lesson taught in six geometry class periods by two teachers…

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…

Ambitious teaching is a form of teaching that requires a high level of teacher responsiveness to what students do as they actively engage with the subject matter. Thus, a teacher enacting ambitious teaching is often confronted with uncertainties about how to advance students' learning while also building on students' contributions. In…

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…

Increasingly, multi-representational educational technologies are being deployed in science classrooms to support science learning and the development of representational competence. Several studies have indicated that students experience significant challenges working with these multi-representational displays and prefer to use only one…

In this article, the author wishes to emphasize two fundamental points related to theory that were significantly underplayed in Simon et al.'s "A Developing Approach to Studying Students' Learning through Their Mathematical Activity" (2010). The author believes these points are central to any study of children's mathematical learning. The first…

This study explored the extent to which parents were able to scaffold their children's Self-Regulated Learning (SRL) in the context of authentic academic tasks and attempted to identify specific dimensions within the parent-child interaction (socioemotional and instructional) that were related to children's SRL. Fifteen Chilean parents and their…

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…

In this research, we examined overall performance and gender differences in measurement skills in elementary-school students from low-income families. In Study 1, accuracy and error patterns were analyzed in a large sample of fourth-graders; in Study 2 error patterns and strategy usage were examined with a smaller sample of fourth-graders. Study 1…

This study demonstrates an existence proof for "productive failure": engaging students in solving complex, ill-structured problems without the provision of support structures can be a productive exercise in failure. In a computer-supported collaborative learning setting, eleventh-grade science students were randomly assigned to one of two…

The theoretical perspective outlined here offers an alternative to explanations of knowledge transfer that posit its source in the construction and application of abstract, context-independent knowledge structures. A case study analysis of an undergraduate student's attempt to solve a series of problems related to an elementary statistical…

The aim of the study was to analyze the development of children's adaptive expertise in computing sums and differences up to 100. We defined the adaptive nature of children's strategy choices on the basis of problem (addition, subtraction), achievement, and strategy performance (accuracy, speed). Sixty-nine 2nd graders of high, above-average, or…

We examined the relation between self-explaining and encoding among kindergartners. For 5 days, children (n = 27) took turns solving addition problems with an adult expert who always used an advanced addition strategy. During the game, children explained the expert's answers (Explain-Expert), explained their own answers (Explain-Novice), or did…

In this study, we investigated the fluency with which first graders of different mathematical achievement levels applied multiple, school-taught strategies for finding arithmetic sums over 10. We characterized children's strategies with the 4 parameters of Lemaire and Siegler's (1995) model of strategy change (strategy repertoire, distribution,…

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…