Prior knowledge and anchored instruction on students' complex mathematical problem-solving and transfer

Kathleen Carol Serafino, Fordham University

Abstract

Based upon research of anchored instruction, this study investigated the effects of students' prior knowledge and instructional models on students' achievement in complex mathematical problem solving and transfer. Examining 50 fifth-grade students in a suburban elementary school, the study hypothesized that students receiving the guided generation model of anchored instruction would demonstrate greater achievement than those in the structured problem solving model. The study also hypothesized that there would be significant interactive effects between instructional model and students' prior knowledge level.^ Two classes were randomly assigned a model of anchored instruction, guided generation or structured problem solving. Using a median split on the Iowa Tests of Basic Skills, students were categorized as high or low prior knowledge. For 15 lessons, both classes were taught a unit on statistics. The instructional model determined each teacher's role in the development of learning activities and the degree of structure and scaffolding provided. In the structured problem solving model, activities were highly organized by the teacher. In the guided generation model, problem generation by the students was emphasized.^ As hypothesized, significant differences existed between high and low prior knowledge level students with respect to academic achievement in complex mathematical problem solving and transfer. High prior knowledge subjects achieved significantly higher than low prior knowledge subjects. Also, significant differences occurred between the guided generation students and the structured problem-solving students on the authentic performance transfer task.^ Significant interactions occurred between domain specific prior knowledge levels and transfer. For high and low prior knowledge level students, the guided generation model of anchored instruction enhanced their achievement in transfer.^ The study expanded existing research on anchored instruction by examining the importance of differences in instructional design. It is suggested that the findings of this study demonstrate the need for all students, particularly at-risk students, to be taught using instructional strategies that promote generative problem-solving skills along with active collaboration within a community of learners. ^

Subject Area

Education, Mathematics|Education, Curriculum and Instruction

Recommended Citation

Kathleen Carol Serafino, "Prior knowledge and anchored instruction on students' complex mathematical problem-solving and transfer" (January 1, 1998). ETD Collection for Fordham University. Paper AAI9839519.
http://fordham.bepress.com/dissertations/AAI9839519

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