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THE INFLUENCE OF RISK TAKING ON STUDENT CREATION OF MATHEMATICAL MEANING: CONTEXTUAL RISK THEORY
Abstract
The primary concerns of mathematics educators are learning and teaching mathematics. It is, therefore, natural to ask “what implications and benefits might there be if learning were perceived as a risk-taking event?” (Atkinson, 1957, p. 266). The underlying motivation of this study is to analyze the risks students take in the mathematics classroom and how risk influences student creation of meaning and development of understanding. I define risk in the mathematics classroom to be any observable act that entails uncertain outcome. The research presented here focuses on a table of four students: Andrew, Carina, Kam, and Mark as they grapple with the mathematical uncertainties inherent in the Ticket Line Task. In analyzing student work and development of mathematical understanding, I identify risks that students take and the benefits they claim result from doing so. Contextualized Risk Theory (CRT) is introduced to improve our understanding of the risks students take in learning mathematics in a student-centered classroom where students exercise personal agency in mathematical problem solving. Findings include characterization of risks these students took, significant student mathematical activity, student enjoyment of their work, student development of personal understanding of purposes and meanings of specific mathematics, and students achieving mathematical success as defined by the researcher and the participants.
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