An Origin of Prescriptions for Our Mathematical Reasoning (Long version)

Uegatani Yusuke

Proceedings of 17th Annual Conference on Research in Undergraduate Mathematics Education

To build a supplementary theory from which we can derive a practical way of fostering inquiring minds in mathematics, this paper proposes a theoretical perspective that is compatible with existing ideas in mathematics education (radical constructivism, social constructivism, APOS theory, David Tall’s framework, the framework of embodied cognition, new materialist ontologies). We focus on the fact that descriptive and prescriptive statements can be treated simultaneously, and consider both descriptive and instantiated models in our minds. This indicates that descriptive statements in mathematics come from our descriptions of models, and prescriptive statements come from the instantiatedness of the instantiated models and non-existence of counterexample. As a practical suggestion from the proposed perspective, we point out that careful communication is needed so that students do not recognize the refutation of their arguments as a denial of their way of mathematical thinking.

Inquiring minds

Prescriptive perspective

Mathematical reasoning

Mathematics [ 410 ]

eng

The Special Interest Group of The Mathmatics Association of America (SIGMAA) for Research in Underguraduate Mathmatics Education

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