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Cognitive Theories, Prior Knowledge, and Anchored Instruction on Mathematical Problem Solving and Transfer

Using constructivist theories as a framework, this study tested the effects of prior knowledge and two models (structured problem solving, SPS, and guided generation, GG) of anchored instruction on student mathematical problem solving and transfer to an analogous task. Two groups (N = 50) of randomly assigned students to treatments were taught by 2 teachers for 15 days, using tasks in the Jasper Woodbury Problem Solving Series. ANOVA and t tests showed a significant main effect for prior knowledge, significant differences on transfer to analogous tasks, a significant difference between groups on transfer favoring the GG model, and a significant interaction between low priors and the GG treatment on transfer. In particular, findings showing learning success in mathematics problem solving with low prior achievers support the notion of encouraging and expanding this line of research with at-risk learners.