טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentShir Karni
SubjectLearning a Meta-Mathematical Concept: The Case of a
Mathematical Definition
DepartmentDepartment of Education in Science and Technology
Supervisor Professor Orit Zaslavsky


Abstract

This study is an investigation of the processes involved in learning of a meta-mathematical concept: a definition. One part of the study deals with knowledge and understanding that are outcomes of long-term indirect learning processes that evolved prior to the study, while the second part closely examines the construction of new knowledge in the course of the study, within a definition-focused learning environment that was designed for the purpose of the study.

The population of the study consisted of four top-level (5-unit mathematics) 12th grade students; four average-level 9th grade students, and a convenience sample of 70 mixed-level (3, 4, and 5-units) 11th grade students. A qualitative methodology was employed in this study, in accordance to its goals - the identification and characterization of students ' conceptions and thought processes.

Students' conceptions of a definition were revealed mainly through individual and group activities in which they were asked to consider a number of possible definitions of four mathematical concepts: two geometric (a square and an isosceles triangle) and two analytic (an increasing function and a local maximum point of a function). Data consisted of written responses to questionnaires and transcriptions of recorded individual interviews and videotaped group discussions.

The findings point to students’ conceptions of a mathematical definition, and the development of their understanding of this notion. Their conceptions are described in terms of the features and roles they attribute to a mathematical definition. In addition, the contribution of the special learning environment to the refinement of students' understandings of the notion of a mathematical definition and of the defined concepts was identified and characterized.