Relations Between Classroom Practices and Student Learning in the Domain of Fractions

In this article, we present an analysis of relations between (a) student achievement in the domain of fractions and (b) the extent to which classroom practices are aligned with principles recommended by current reform frameworks (e.g., National Council of Teachers of Mathematics, 1989). Hierarchical linear model analyses were performed on classroom observation and pre- and postinstruction achievement data collected in 19 upper elementary classrooms. These analyses revealed that alignment of classroom practices with reform principles was related to student achievement in problem solving but not in computation; furthermore, the relation differed for students who began instruction with different levels of prior knowledge as indexed by a pretest measure. For students who began with a rudimentary understanding of fractions, the relation between measures of classroom practice and problem solving was linear. In contrast, for students who began without a rudimentary understanding of fractions, the relation was nonlinear; in classrooms rated low on alignment with reform principles, performance on problem-solving items was near floor but increased at a certain threshold level of alignment. The findings demonstrate the value of reform principles as a guide for effective practice as well as the importance of a coordinated analysis of students' prior understandings and classroom practices in investigations of children's learning.