Introduction

Abstract

I completed my dissertation studies with Les Steffe and Ernst von Glasersfeld at the University of Georgia in 1983 and then accepted a faculty position at Purdue University in Indiana. The first study that I conducted at Purdue University was built on my dissertation work and focused on the psychological contexts within which young children interpret and attempt to solve arithmetical tasks in school (see Chapter 2). In this study, I interviewed approximately 40 first-grade students from two classrooms at the beginning, middle, and end of the school year. In the initial interviews, most of the children attempted to solve all types of arithmetical tasks presented by reasoning about quantities. However, in the interviews at the end of the school year, most of the same children attempted to solve all interview tasks that were similar to those in their school textbook by either using very elementary counting methods or by focusing on patterns in numerals regardless of whether they made sense in terms of relations between quantities. In this respect, the children’s solutions were reminiscent of those that Erlwanger (1973) had documented in his influential case of study of a fifth-grade student’s conception of mathematics.