Collegiate student's epistemologies and conceptual understanding of the role of models in precalculus mathematics : a focus on the exponential and logarithmic functions Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/cj82kb466

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  • Collegiate student's conceptual distinctions of what define a mathematical and a physical model seems to be affected by the epistemological beliefs they hold about this knowledge. These beliefs seem to influence student's thinking and reasoning as they embark on problem solving activities in collegiate mathematics. Student's epistemological beliefs of mathematical models and the descriptive role that such models hold with physical phenomena was established using a modified version of a preexisting instrument titled Student's Understanding of Models in Science (SUMS). The modified version contains additional items that were developed to capture student's mathematical epistemologies. These new items were interwoven into the SUMS existing subscales. Confirmatory factor analysis established that the scales are independent, thereby lending to the construct validity of the modified SUMS. The sample examined was college-level students enrolled in Precalculus Mathematics at two Pacific Northwest colleges during the 2007 summer term. The results of this research laid the foundation for a subsequent study aimed at establishing some of the common misconceptions that students share in their precalculus mathematics studies. In particular, efforts were made to more clearly identify student's epistemological beliefs and conceptual understanding of the exponential and logarithmic functions, logb x, abx, ln x, ex and the utilization of these function in the modeling of physical phenomena. Detailed questionnaires, along with comprehensive interview sessions generated evidence for student's deep-seated conceptions about the fundamental properties of these functions and their use in modeling physics-based phenomena. This phase of the research helped to establish transitional spans in the gap between a student's level of assisted and independent performance as problems containing these functions evolved in complexity. Subsequent changes in student's conceptions were established using the modified SUMS instrument as a post test instrument.
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