This study illuminates claims that teachers' mathematical knowledge plays an important role in their teaching of this subject matter. In particular, we focus on teachers' mathematical knowledge for teaching (MKT), which includes both the mathematical knowledge that is common to individuals working in diverse professions and the mathematical…

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…

This study investigated the use of block-building interventions to develop spatial-reasoning skills in kindergartners. Two intervention conditions and a control condition were included to determine, first, whether the block building activities themselves benefited children's spatial skills, and secondly, whether a story context further improved…

Probability is an important idea with a remarkably wide range of applications. However, psychological and instructional studies conducted in the last two decades have consistently documented poor understanding of probability among different populations across different settings. The purpose of this study is to develop a theoretical framework for…

Recent mathematics education reform efforts call for the instantiation of mathematics classroom environments where students have opportunities to reason and construct their understandings as part of a community of learners. Despite some successes, traditional models of instruction still dominate the educational landscape. This limited success can…

In a 3-year longitudinal, mixed-method study, 67 children in two schools were observed during literacy activities in Grades 1-3. Children and their teachers were interviewed each year about the children's motivation to read and write. Taking a grounded theory approach, content analysis of the child interview protocols identified the motivations…

Clinical interviewing is viewed here as a social interactional pattern in order to examine the nature and limits of the technique as a means of scientific data acquisition. I defend the technique against criticisms that it is ecologically suspect and prone to systematic biases, mainly due to influence of the interviewer on the interviewee or to…

Promoting the ability to reason generatively about novel phenomena and problems students may encounter in their everyday lives is a major goal of science education. This goal proves to be a formidable challenge in domains, such as molecular genetics, for which the accumulated scientific understandings are daunting in both amount and complexity. To…

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 examines how passage availability and reading comprehension question format (open-ended vs. multiple-choice) influence question answering. In two experiments, college undergraduates read an expository passage and answered open-ended and multiple-choice versions of text-based, local, and global bridging inference questions. Half the…

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…

This study was designed to identify the types of understandings, skills, and beliefs that affect pre-service teachers' evaluations of students' mathematical arguments in classroom contexts. Thirty-four pre-service teachers read a transcript of a third grade lesson in which the students were expected to prove a generalization. To investigate…

This study provided 5 weeks of direct strategy instruction about narrative elements and relations in 4 first-grade classrooms (n = 83), all with materials that made minimal decoding demands on children's reading. Two comparison classrooms (n = 40) received comparable instruction on language development and poetry. A battery of assessments given at…

Emergent leadership was examined in 12 discussion groups in 4 fourth-grade classrooms. Children's leadership moves were coded from transcripts of 10 free-flowing, open-format discussions of each of the 12 groups. The transcripts encompassed 26,000 turns for speaking, including 22,000 child turns of which 1,700 were judged to serve one of five…

Previous research has shown that students construct equations for word problems in which many of the terms have no referents. Experiment 1 attempted to eliminate some of these errors by providing instruction on canceling units. The failure of this method was attributed to the cognitive overload (Sweller, 2003) imposed by adding units to the…