טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentKoychu Boris
SubjectJunior High School Students' Heuristic Behaviours in
Mathematical Problem Solving
DepartmentDepartment of Education in Science and Technology
Supervisors Professor Emeritus Abraham Berman
Professor Michael Moore


Abstract

This work contributes to the growing body of research in mathematics education about teaching/learning heuristic strategies in problem solving. The study focuses on two main issues: the concept of heuristic behavior and the development of mathematical reasoning of junior high school students during heuristic training, where experts’ heuristic strategies were incorporated into a regular mathematical classroom.

The data about experts' heuristic strategies were collected from 20 in-service teachers and 4 mathematically gifted high-school students. About 90 8th graders and their four teachers took part in a 5-month classroom teaching experiment. Twelve students of the experimental group were chosen as key-subjects for identifying patterns of heuristic behaviors at the beginning, in the middle and after the intervention.

The study, which applied both quantitative and qualitative methodologies, involved multiple sources of data, including questionnaires, thinking-aloud and reflective interviews with the students and the teachers, field notes, students' and teachers' documents.

The main findings of the research are as follows:

·      Based on the experts' beliefs and their observed problem-solving performance, a set of universal heuristic strategies that cover the experts' heuristic repertoire was found. The heuristic strategies were classified by their usefulness for the experts. 

·      The intervention yields a positive effect on the mathematical reasoning ability of the 8th graders. Cause-effect relation between the 8th graders' heuristic development and the growth of their mathematical reasoning ability was found. The "weaker" students of the experimental group received the greatest benefits in heuristic development and in the development of their mathematical reasoning.

·      The concept of heuristic behavior was defined. Four patterns of heuristic behaviors in individual solving of (difficult) word and geometrical problems - 'naive', 'progressive', 'circular' and 'spiral' - were distinguished by means of the research tool, developed in accordance with the grounded theory.  A firm tendency of reducing the weight of the naive heuristic behavior was found, through the stages of heuristic training.