The purposes of this study were to assess the effects of schema-based instruction (SBI) in promoting mathematical problem solving and to investigate schema induction as a mechanism in the development of mathematical problem solving. Twenty-four 3rd-grade teachers, with 366 students, were assigned randomly to conditions that provided instruction on 4 types of word problems. The 3 16-week conditions were contrast, SBI, and SBI with practice in sorting word problems into schemas. Students were pre-and posttested on mathematical problem-solving tests and were posttested on schema development. Students receiving SBI, with and without sorting practice, improved more than the contrast group on problemsolving measures. Concurrently, the SBI groups' schema development exceeded that of the contrast group, and schema development explained a substantial portion of unique variance in students' posttreatment problem-solving performance. Results also suggested the need for additional research testing the contribution of practice in sorting word problems.

Mathematical problem solving is a transfer challenge requiring children to develop schemas for recognizing novel problems as belonging to familiar problem types for which they know solutions. Schema-based transfer instruction (SBTI) explicitly teaches transfer features that change problems in superficial ways to make them appear novel even though they still require known solution strategies. This study assessed the effects of an expanded version of SBTI incorporating more challenging transfer features for broadening schemas and helping children recognize real-life math problems as solvable. Teachers were assigned randomly to 16-week control, SBTI, or expanded SBTI conditions. Students completed pretests and posttests focusing on increasing transfer distances. On a measure approximating real-life problem solving, the expanded SBTI group outperformed the SBTI group, which in turn outperformed the control group.

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