טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentAtrash Eman
SubjectTeaching Linear Algebra: Pedagogical Practices of
Experienced Lecturers
DepartmentDepartment of Education in Science and Technology
Supervisor Professor Boris Koichu
Full Thesis textFull thesis text - English Version


Abstract

The introductory linear algebra course, which is usually taught in frontal large-group lectures, had been recognized in the literature as difficult for teaching and learning. While much research explored students' difficulties in this course, little is known about how the lecturers deal with students' difficulties. In the past two decades mathematics' education researchers have been raising the need for research that investigates the teaching of the linear algebra course. The present research aimed at addressing this need. The goal of the research was twofold: to characterize Pedagogical Practices of experienced linear algebra lecturers aimed at helping the students to Overcome their Difficulties (hereafter, PPOD) with the course material in two teaching environments: with and without Classroom Response Systems (hereafter, CRS), and to identify the pedagogical considerations underlying the lecturers' pedagogical practices. The research participants were two expert lecturers who taught the linear algebra course in a highly ranked research university. The data sources consisted of 168 hours of videotaped observations, a series of 10 stimulated- recall conversations with each lecturer and two semi- structured interviews conducted with each lecturer. The main findings of the study are as follows:

1.      Nine categories of PPOD that the lecturers employed were found: Giving Numerical Examples; Anchoring in Real Life; Using Visual Aids; Repeating Twice; Solving/Proving in Several Ways; Highlighting by Asking Questions; Making Intentional Mistakes; Encouraging to Keep Working; Advising to Do or Not Do Something.

2.      For each lecturer, the overall numbers of PPOD identified in lectures of different topics during the first semester were about the same, however, during the second semester differed across different topics.

3.      For each lecturer, the overall numbers of PPOD identified in the second semester were considerably larger than in the first semester.

4.      In the lectures, in which CRS were incorporated, the time of dealing with the students' anticipated mistakes was longer than in the lectures on the same topics, but without the CRS.

5.      The lecturers' considerations underlying their PPOD were related to time constraints inherited in the structure of the course, their comprehensions of the students' learning needs and pedagogical values that the lecturers believed to be important in teaching linear algebra.

The findings of this research contribute to the growing body of knowledge on the pedagogical practices of linear algebra lecturers. A practical implementation of the findings may be in the design of pedagogical development programs for university lecturers.