Philosophy and the Faces of Abstract Mathematics

Abstract

Introduction: Several years ago, while teaching middle and high school mathematics at a small progressive school in upstate New York, I was asked to evaluate and reconceptualize the school's approach to teaching mathematics. From its inception in the early 1960s, the school had prided itself on its progressive ideals. It was child-centered, committed to both project-based learning and to the social and emotional development of children, and a place where independent and critical thinking was highly valued. Yet, it was clear that our mathematics program was not delivering results in line with our expectations. Academically, our students were not low achievers. Yet, to our dismay, very few of our middle and high school students actually liked their mathematics studies.