Relations between classroom practices and student learning in the domain of fractions

In this article, we present an analysis of relations between (a) student ac hievement in the domain of fractions and (b) the extent to which classroom practices are aligned with principles recommended by current reform framewo rks (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 classroo ms. These analyses revealed that alignment of classroom practices with refo rm 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 pretes t measure. For students who began with a rudimentary understanding of fract ions, the relation between measures of classroom practice and problem solvi ng was linear. In contrast, for students who began without a rudimentary un derstanding of fractions, the relation was nonlinear; in classrooms rated l ow on alignment with reform principles, performance on problem-solving item s was near floor but increased at a certain threshold level of alignment. T he findings demonstrate the value of reform principles as a guide for effec tive practice as well as the importance of a coordinated analysis of studen ts' prior understandings and classroom practices in investigations of child ren's learning.