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…

While many studies have considered the association between teachers' and students' conceptions of teaching and learning and classroom practices, few studies have researched the influence of teachers' conceptions on students' conceptions. Our objective was to analyze the influence of music teachers' conceptions on student…

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…

This study investigates whether Virtual Manipulatives (VM) within a Physical Manipulatives (PM)-oriented curriculum affect conceptual understanding of electric circuits and related experimentation processes. A pre-post comparison study randomly assigned 194 undergraduates in an introductory physics course to one of five conditions: three…

Achieving fluency with basic subtraction and add-with-8 or -9 combinations is difficult for primary grade children. A 9-month training experiment entailed evaluating the efficacy of software designed to promote such fluency via guided learning of reasoning strategies. Seventy-five eligible first graders were randomly assigned to one of three…

This research investigated how teachers express links between ideas in speech, gestures, and other modalities in middle school mathematics instruction. We videotaped 18 lessons (3 from each of 6 teachers), and within each, we identified "linking episodes"--segments of discourse in which the teacher connected mathematical ideas. For each…

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 article describes the initial implementation of an innovative program for elementary-age children involving origami and pop-up paper engineering to promote visuospatial thinking. While spatial ability measures correlate with science, technology, engineering, and math (STEM) success, a focus on spatial thinking is all but missing in elementary…

We examine how extended engagement in argumentation with peers leads to enhanced metalevel understanding of argumentive discourse. Following such engagement, young adolescents demonstrated enhanced understanding of counterargument and use of evidence as objectives of skilled argumentation, relative to a nonparticipating comparison group. Among the…

Previous research has demonstrated the effectiveness of particular instructional practices that support students' constructions of the partitive unit fraction scheme and measurement concepts for fractions. Another body of research has demonstrated the power of a particular mental operation--the splitting operation--in supporting students'…

An important goal of history education is the development of a chronological frame of reference that can be used to interpret and date historical images and documents. Despite the importance of this contextualization goal, little is known about the knowledge and strategies that allow students to situate information historically. Two studies were…

In this article, we report two studies investigating what mathematicians value in a pedagogical proof. Study 1 is a qualitative study of how eight mathematicians revised two proofs that would be presented in a course for mathematics majors. These mathematicians thought that introductory and concluding sentences should be included in the proofs,…

We illustrate a method, which is modeled on "breaching experiments," for studying tacit norms that govern classroom interaction around particular mathematical content. Specifically, this study explores norms that govern teachers' expectations for the doing of word problems in school algebra. Teacher study groups discussed representations of…

This article aims to account for students' assessments of the plausibility and applicability of analogical explanations, and individual differences in these assessments, by analyzing properties of students' underlying knowledge systems. We developed a model of explanation and change in explanation focusing on knowledge elements that provide a…

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…