טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentKatz Efim
SubjectDevelopment of Aesthetic Sense in Solving Mathematical
Problems
DepartmentDepartment of Education in Science and Technology
Supervisors Professor Boris Koichu
Professor Emeritus Abraham Berman
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


Abstract

The goal of the present study was to identify cognitive, affective and situational factors involved in junior high school students’ perception of a mathematical problem as beautiful and to examine a way of incorporating aesthetic aspects of problem solving in mathematics instruction in the junior high school.

Three research questions were derived from the research goal.

  1. Which cognitive, affective and situational factors are involved in junior high school students’ perception of a mathematical problem as beautiful?
  2. What is the process of incorporating aesthetic aspects of problem solving in mathematics instruction in junior high school?
  3. How did the experimental teaching of aesthetic aspects of mathematical problem solving influence the development of the junior high school students’ attitude towards mathematics as a school subject and towards mathematical problem solving?

The main findings are:

a. Junior high school students’ judgment of a mathematical problem as beautiful is deeply individual and depends not only on the characteristics of the problem but also on a situation in which the problem is given and on the experience immediately preceding the engagement in the problem.

b. The study confirms that it is possible, under special conditions that can be created in a regular classroom, to promote aesthetic aspects of mathematical problem solving.

c. Most of the students of the experimental classes felt pressured when solving problems at the beginning of the experiment. As a result of the intervention, the experimental classes began to enjoy solving mathematical problems. The attitude towards problem solving in the contrast classes did not change.                         

This study has theoretical, methodological and practical contributions.

The theoretical contribution is two-fold. First, the study empirically confirmed, in controlled experimental settings, that “pleasant surprise” emerging in an emotionally secure problem-solving situation is an important factor of students’ aesthetical judgment. Second, the findings suggest that there is a long latent period in the process of development of the students’ aesthetic sense in mathematical problem solving. The methodological contribution consists of the attitude questionnaire that can be used in additional studies and the interview design involving ordered pairs of problems. Teaching materials related to the development of the aesthetic sense in the junior high school students and recommendations for teachers about how to develop an aesthetic sense in students constitute the practical contribution of the study.