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…

Master narratives frame students' historical knowledge, possibly hindering access to more historical representations. A detailed analysis of students' historical narratives about the origins of their own nation is presented in terms of four master narrative characteristics related to the historical subject, national identification, the…

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…

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'…

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…

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 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…

Using data collected in 125 seventh-grade and 56 eighth-grade Texas classrooms in the context of the "Scaling Up SimCalc" research project in 2005-07, we examined relationships between teachers' mathematics knowledge, teachers' classroom decision making, and student achievement outcomes on topics of rate, proportionality, and linear…

The examination of alternative hypotheses can initiate students into scientific practices and equip them with scientific literacy skills that will help them participate in ongoing debates involving complex socio-scientific problems. Hypothesis testing, in which the examination of alternative hypotheses is situated, has received much attention in…

Using the perspective of instructional conversation, we investigated how one teacher regulated student participation and conceptual reasoning in the middle-school mathematics classroom. We examined the elicitations--questions and provocative statements--made by the teacher over a four-day algebra lesson. Analyses showed how the teacher…

Learning science includes learning to argue with "inscriptions": images used to symbolize information persuasively. This study examined sixth-graders learning to invest inscriptions with representational status, in a geographic information system (GIS)-based science investigation. Learning to reason with inscriptions was studied in emergent…

The present study contrasts mathematical knowledge that two sixth-grade teachers apparently used when teaching fraction multiplication with the Connected Mathematics Project materials. The analysis concentrated on those tasks from the materials that use drawings to represent fractions as length or area quantities. Examining the two teachers'…

This paper reports the mathematical generalizations of two groups of algebra students, one which focused primarily on quantitative relationships, and one which focused primarily on number patterns disconnected from quantities. Results indicate that instruction encouraging a focus on number patterns supported generalizations about patterns,…

This study explores whether the development of students' understanding of matter as something that occupies space and has weight involves conceptual change and restructuring rather than only simple belief revision. Based on an analysis of how the concepts in students' initial matter theory (henceforth MT1) may differ from the concepts in the…