This study investigated middle school students' conceptual understanding of algebraic equations. Participants in the study--257 sixth- and seventh-grade students--were asked to solve one set of algebraic equations and to generate story problems corresponding with another set of equations. Structural aspects of the equations, including the number…

We compared the structure of discussions in a middle school mathematics classroom before (Year 1) and after (Year 2) teacher participation in professional development activities aimed at enhancing students' participation and the co-construction of mathematical ideas. Changes in the role of teacher and student were accompanied by identifiable…

Confidence intervals are beginning to play an increasing role in the reporting of research findings within the social and behavioral sciences and, consequently, are becoming more prevalent in beginning classes in statistics and research methods. Confidence intervals are an attractive means of conveying experimental results, as they contain a…

This study investigates middle school mathematics students' views and interpretations of graphical representations as they use graphs to answer algebraic questions--specifically, questions that require them to extrapolate information from graphs. From data gathered in videotaped interviews, students' verbal responses were analyzed as well as any…

The prominent role of Boolean classes in qualitative data analysis software is viewed by some as an encroachment of logical positivism on qualitative research methodology. The authors articulate an embodiment perspective, in which Boolean classes are viewed as conceptual metaphors for apprehending and manipulating data, concepts, and categories in…

Theories of learning in social settings, no matter their philosophical orientation, must address issues of intersubjectivity (IS). This paper starts with the premise that IS is a fundamental and unavoidable aspect of social interaction, and that understanding its nature is necessary for developing reliable theories of socially mediated learning…

In this paper, I explore two beliefs about learning and teaching that I argue are prevalent among educators. The first is the belief that subject matter expertise is sufficient for success in teaching. The second belief is that to learn a specific content area, one needs to begin with an understanding of the formal structure and abstract…

This paper explores the role of co-expressivity of drawing, speech, and gesture as sixth graders strive for intersubjectivity in their attempts to communicate solutions of a spatial reasoning task. Several obstacles to intersubjectivity are documented, particularly conflicts between a literal and geometric interpretation, limits of students'…