טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentRaz Or
SubjectAdvancing Students in Calculus through Learning Workshops
DepartmentDepartment of Education in Science and Technology
Supervisor Professor Emeritus Abraham Berman
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


Abstract

The students at the Technion are required to study, as part of the basic mathematic studies, courses in calculus in their first academic year. The goal of these courses is to construct a good and solid foundation of mathematical knowledge that will enable the students to cope with the challenges in their academic studies at the Technion. The first course is calculus 1 and there are several similar courses designed for different faculties. The students’ achievements in these courses are very low, both in the midterm and final exams, clearly indicating the struggles of the students in coping with the syllabus. The main struggles are: inadequate ability to write mathematical proofs, partial or inadequate understanding of the limit definition and related concepts, difficulty understanding the visual appearance of function graphs, deficient realization of the need of algebraic manipulations for problem simplification and the attempt to use the familiar methods instead of thinking the problem through in order to find an original solution. In addition, the course was found to trigger a variety of negative emotions in the students participating in it.

In the current research, an attempt has been made to resolve the abovementioned difficulties as well as to change the students’ attitude towards the course. During the research, conducted on three successive semesters, the students participating in the research were enrolled into weakly 60 minutes long workshops in calculus. The workshops were designed so that the teaching was conducted in a unique manner including active learning accompanied with the use of heuristic strategies for calculus problem solving. The students participated in the workshops in addition to their regular attendance to the course lectures and tutorials. The workshops had two main goals: the first was to attempt to change the students’ attitude towards the course following their attendance in the workshops and the second goal was to find the teaching elements considered by the students as most contributing to their sense of ability to prove claims and solve unconventional calculus problem. Additionally, the reasons the students chose a specific element were also examined.

We found a significant improvement in the students’ attitude towards the course in the two semesters that the workshops were held. The improvement was mainly manifested by a positive change in self-confidence and sense of capability, accompanied by a decrease in anxiety. Additionally, five teaching elements were selected by the students as most contributing to their sense of achievement and capability: visualization, algebraic manipulations, limit definition, active learning and “thinking out loud”. These teaching elements can be incorporated into calculus teaching at the Technion, which could lead to improvement in the students' achievements and satisfaction from the course.