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The purpose of the study was to describe the instructional applications of a philosophically based model of a mathematical inquiry to the teaching of mathematics. The first phase of the study developed the model of inquiry based on the philosophical position known as Critical Fallibilism. In the second phase of the study, stratagems of teaching were derived from the Fallibilistic model of mathematical inquiry. This phase of the study also included an assessment of the Madison Project as a Fallibilistic approach to the teaching of mathematics. The philosophical portion of the study included a description of Critical Fallibilism as this position has been developed by Karl Popper. Since Popper’s description of Fallibilism is tied to a theory of the growth of scientific knowledge, it was necessary to undertake an application of Fallibilism to mathematics. This was done by analyzing the recent results obtained by Imre Lakatos. Moreover, the work of George Polya was considered and some of his ideas incorporated into the model of mathematical inquiry in so far as they applied to the description of the plausible reasoning aspects of mathematical inquiries. On the basis of this description, the growth of mathematics was characterized as being a conjecture and refutation process…In the next phase of the study, a model of instruction was derived from the paradigm of mathematical inquiry…The model of instruction was then utilized to assess the ways in which the Madison Project can be characterized as Fallibilistic in its approach to the teaching of mathematics. It was concluded that the Madison Project exhibits strong Fallibilistic tendencies. In general, approaching problems in the teaching of mathematics by means of a philosophically based model of inquiry seems to be a fruitful avenue of research.

Ph. D.

Includes bibliographical references.

doi:10.7282/T3Q23XCJ

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