Philosophizing with Children in the Course of Solving Modeling Problems in a Sixth Grade Mathematics Classroom

Abstract

Introduction: While the concept of a community of inquiry based on dialogue is an integral part of philosophy for children (Lipman 1988, 2003; Morehouse 2010), this concept is less prevalent in mathematics and science classes. In these subjects emphasis is usually placed on transmitting factual information as accurately and completely as possible. Children expect the teacher (or some other authority) to tell them what the "right" answer to a question is, and teachers expect children to reproduce that answer. There is little opportunity for uncertainty, query and dialog (see Gallas 1995, pp. 7-16; Sprod 2011, p. xiv). Discussions are often conducted between individual students and the teacher, but not among the students themselves. This style of teaching generates a kind of pressure that many children find onerous (Hausberg 2007). In addition, it encourages a vision of mathematics and science as fields of study that are highly abstract, detached from reality, and unfathomable. Pupils leave the classroom thinking that there is a predetermined right and wrong answer for everything in these subjects and no room for discovery. Therefore proponents of constructivist science education (e.g. Driver 1994) and philosophizing in science classes (see Nevers 2009; Sprod 2011), and advocates of modeling activities in mathematics classes such as G. Kaiser (2006) and R. Borromeo Ferri (2006, 2010), have proposed ways to enrich traditional classroom teaching in order to promote the active construction of knowledge by children and better conceptual understanding in science and math. Our paper presents an attempt to further this goal by philosophizing with children in the course of mathematical modeling exercises in a sixth grade math class.