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…

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…

This paper examines how middle school students developed understanding of transformational geometry through design activities in Escher's World, a computationally rich design experiment explicitly modeled on an architectural design studio. Escher's World was based on the theory of pedagogical praxis (Shaffer, 2004a), which suggests that preserving…

This paper draws on mathematics achievement data from Milwaukee middle school students to illustrate the value-added approach to estimating school performance. Value-added indicators differ from traditional attainment indicators such as average test scores in that they are designed to capture the contribution of schools to growth in student…