Abstract

The study's objective was to empirically investigate an instructional approach (Hiebert, 1984) theorized to foster students' abilities to link conceptual and procedural understandings during the learning of mathematics. Seventy-two fifth- and sixth-grade students were randomly assigned to the treatment ( n = 36) and a control condition ( n = 36) and were administered a validated paper and pencil test (Saxe, Gearhart, & Nasir, 2001) of fractions knowledge and a researcher-developed fractions knowledge interview before and after instruction. Doubly multivariate analyses of covariance revealed that, consistent with the research hypotheses, students in the treatment condition demonstrated greater improvements in conceptual understandings of fractions ( p < .01) and in ability to link their knowledge of fractions procedures to their knowledge of fractions concepts ( p < .05). Contrary to the research hypotheses, control group students demonstrated comparable gains to students in the treatment group in procedural knowledge of fractions. The findings point to important instructional considerations for the effective support of students' development of conceptual knowledge and procedural skill related to specific points in the problem-solving process, and, more broadly, to a specific time in the course of their mathematics education.