M.Sc Thesis
M.Sc Student Shehadey-Mubariki Salwa Integrating Beautiful Mathematical Problems Related to the Curriculum in Teaching Mathematics Department of Education in Science and Technology Professor Emeritus Abraham Berman

Abstract

Mathematics is one of the main and most important subjects taught in school. Nevertheless, a review of articles shows that Mathematics is the most problematic and most hated subject to students, and they hardly see any beauty in it.

So what is "seeing beauty" in Mathematics? And what is a beautiful mathematical problem?

There is no unequivocal definition for a beautiful mathematical problem. Despite of this, there are criteria in the literature for characterizing such problems.

In this study, we incorporated beautiful mathematical problems which are related to the curriculum in the regular lessons. This was done for two goals:

1)      To follow the changes in students' attitudes towards Mathematics before and after they were exposed to beautiful mathematical problems.

2)      To examine the characterization of a beautiful mathematical problem suggested by students.

The research was an action research, with participation of 37 ninth-graders. It utilized the mixed-method, combining qualitative and quantitative tools. These tools included a questionnaire, interviews and researcher's diary.

An analysis of the findings shows that the integration of the beautiful mathematical problems in the regular lessons improved the students' attitude towards Mathematics. This integration increased the students' interest in the subject: they loved the beautiful problems, asked for more examples and suggested their own beautiful problems.

In addition we can summarize that a beautiful mathematical problem was seen by students as: "a challenging problem", "a non-trivial problem", "a problem that requires deep thinking", "a problem that can be solved in different ways", "paradoxes", "games", "a problem that requires activities", "a problem that summarizes the studied material", "a problem that calls for a generalization", "a problem that has the potential for investigation", "a problem that uses knowledge from different fields" and "a problem with creative and surprising solutions".

It is interesting to point out the difference between the definitions suggested by "strong" and "weak" students. Students with high academic achievement defined beautiful mathematical problem as a nontrivial problem, a problem that requires deep thinking, a problem that can be solved in different ways and a problem which uses knowledge from different fields. In contrast, the "weaker" students defined a beautiful mathematical problem as an unusual one that can be easily solved, a problem that they have fun to solve, like games or a problem that requires activities in class.

I hope that the study may encourage teachers to integrate aesthetic problems during their lessons.