AN INSTRUCTIONAL MODEL OF MATHEMATICAL PROBLEM SOLVING/METACOGNITION DERIVED FROM SIXTH GRADERS' SOLUTIONS TO NON-ROUTINE PROBLEMS

CECELIA MARIE WAMBACH-SCHMIDT, Fordham University

Abstract

The intent of this study was to investigate sixth graders' problem solving/metacognition processes for the purpose of formulating an instructional model from the data. An interview was developed from the frameworks of Schoenfeld (1984), Garofalo and Lester (1985) and Burton (1984) that consisted of two parts: a categorized coding scheme to analyze problem-solving verbalizations for metacognitive content, and a questionnaire to further explicate the process.^ The following research questions were explored: (1) What metacognitive behaviors are activated during non-routine problem solving? (2) Is there a difference if participants work individually or in teams? (3) Do children solve problems sequentially or opportunistically?^ This investigation showed that sixth-graders actively monitor their process. They analyze their reading of the problem, evaluate themselves, the task and their methods consistently. They verbalize their strengths and weaknesses, and know what to do when they need assistance. They express knowledge of their problem-solving style and discuss strategies that are useful to them.^ There was no evidence to show that individual or team work generated different metacognitive activity. Participants were highly opportunistic, but self-reported that they use both opportunistic and logical procedures depending on the problem.^ Data derived from the interview were used to construct Zero-SPACE, an instructional model of problem solving/metacognition to be used in the elementary school classroom. Behaviors included in the model were focusing attention, scanning, probing, activating (making a plan, choosing a strategy and doing the work), communicating and evaluating.^ Twelve sixth grade students participated in the study, consisting of four individuals and four teams. Detailed description and analysis is included in the study, as well as the complete coded transcription record of the problem-solving process. ^

Subject Area

Mathematics education

Recommended Citation

WAMBACH-SCHMIDT, CECELIA MARIE, "AN INSTRUCTIONAL MODEL OF MATHEMATICAL PROBLEM SOLVING/METACOGNITION DERIVED FROM SIXTH GRADERS' SOLUTIONS TO NON-ROUTINE PROBLEMS" (1987). ETD Collection for Fordham University. AAI8725690.
http://fordham.bepress.com/dissertations/AAI8725690

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