Date of Completion


Document Type

Open Access Capstone

Degree Name

Master of Arts (MA)

First Advisor

Patricia S. Davidson

Second Advisor

Arthur B. Millman

Third Advisor

John R. Murray


This thesis focuses on an investigation I undertook to enhance my effectiveness to teach mathematics, a subject to which I was assigned, but for which I had not been formally trained. It describes my attempt to construct knowledge through the clinical interview method as to how middle school students construct knowledge about integers and think about the knowledge they are constructing. On one level, I was attempting to learn how students come to understand the concept of integers; on a level, I was creating an understanding of how a teacher can construct knowledge about the construction of knowledge. This two-tiered model cast me in the roles of teacher, learner and researcher; and my students in the roles of learner and teacher. Six sixth-grade students, interviewed in groups of two each, for four or five sessions, used a model where yellow chips represent positive integers, and blue chips represent negative integers. The investigation was concerned with how children construct knowledge about adding and subtracting integers, what they grasp easily or find difficult, what prior knowledge or misconceptions they bring, what connections they make to real-world applications, how they think about their thinking, how they create problems to solve, and how well they teach fourth graders. The study allowed me to concentrate on aspects of teaching mathematics emphasized by the Standards (1989) of the National Council of Teachers of Mathematics: using manipulative models, problem solving, communicating, connecting and reasoning. Three non-traditional techniques were used for evaluating children's understanding: reverse processing, metacognition, and the child as teacher. As background, this thesis reviews relevant literature on Constructivisn, meaning of knowledge, critical and creative thinking, the teacher's role, clinical interviewing, and representational models. Analyses of videotaped teacher/student scripts and other components of the interviewing process provided glimpses into the minds of children who learn in different ways (including interesting misconceptions held). Implications of this two-tiered model reinforce my belief that knowledge is not something passive to be given, but active to be created and re-created by both teacher and student on a day-to-day basis in the classroom.