Date of Award

Spring 2003

Project Type

Dissertation

Program or Major

Mathematics Education

Degree Name

Doctor of Philosophy

First Advisor

Karen J Graham

Abstract

This study incorporated problem posing into a mathematics content course for preservice elementary and middle school teachers by extending George Polya's (1957) problem solving heuristic to include problem re-formulation and by having participants pose problems from sets of given information. The course provided pre-service teachers with a new mathematical perspective and this research examined participants' problem posing, beliefs about mathematics, and beliefs about the teaching and learning of mathematics.

Study participants were enrolled in a mathematics content course for pre-service teachers at the University of New Hampshire. There were twenty students in the course and nineteen agreed to be participants in the study by allowing all of their course work to be collected. Participants consisted of 4 sophomores, 7 juniors, 6 seniors, and 2 graduate students. All participants were working towards their teaching certification and most were mathematics education majors. Four of the nineteen participants agreed to be interviewed three times each during the semester.

Characteristics of participants' posed problems, beliefs about mathematics, and beliefs about teaching and learning mathematics were explored using researcher developed questionnaires that were given before and after the semester. Also, all student work, journal entries, and the interviews of four participants, which were focused on topics related to beliefs about problem posing, characteristics of posed problems, beliefs about mathematics, and beliefs about teaching and learning mathematics, were collected during the instructional treatment.

Problems posed by participants were organized and coded using a quantitative scale, while journal entries and interview data were analyzed qualitatively. Results showed an increase in participants' problem posing efficiency and ability to pose multi-step problems. Also participants tended to utilize higher level problem re-formulation techniques as the instructional treatment progressed. Throughout the instructional treatment participants were reflecting on the role of problem posing in teaching and learning mathematics and considering both the pros and cons of including problem posing in their future classrooms and its possible effect on student learning. All participants suggested that they would incorporate student problem posing in their classrooms to help students develop ownership of mathematics and exhibit creativity.

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