The Teacher as Mathematician: Problem Solving for Today's Social Context

摘要

A current trend in social justice oriented education research is the promotion of certain intellectual virtues that support epistemic responsibility, or differently put, the dispositions necessary to be a good knower. On the surface, the proposition of epistemically responsible teaching, or teaching students to be responsible knowers is innocuous, even banal. In the mathematics classroom, however, it is patently at odds with current practice and with the stated goals of mathematics education. This dissertation begins by detailing the extant paradigm in mathematics education, which characterizes mathematics as a body of skills to be mastered, and which rewards ways of thinking that are highly procedural and mechanistic. It then argues, relying on a wide range of educational thinkers including John Dewey, Maxine Greene, Miranda Fricker, and a collection of scholars of white privilege, that an important element in social justice education is the eradication of such process-oriented thinking, and the promotion of such intellectual virtues as courage and humility. Because the dominant paradigm is supported by an ideology and mythology of mathematics, however, changing that paradigm necessitates engaging with the underlying conceptions of mathematics that support it. The dissertation turns to naturalist philosophers of education make clear that the nature of mathematics practice and the growth of mathematical knowledge are not characterized by mechanistic and procedural thinking at all. In these accounts, we can see that good mathematical thinking relies on many of the same habits and dispositions that the social justice educators recommend. In articulating an isomorphism between good mathematical thinking and socially responsive thinking, the dissertation aims to offer a framework for thinking about mathematics education in and for a democratic society. It aims to cast the goals of mathematically rigorous education and socially responsible teaching not only as not in conflict, but also overlapping in meaningful ways.