טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentKatzir Avivit
SubjectStudents Coping with Uncertainty Regarding the Truth of
Mathematical Claims
DepartmentDepartment of Education in Science and Technology
Supervisor Professor Orit Zaslavsky


Abstract

This study examines how undergraduate Linear Algebra students work on mathematical claims for which they encounter uncertainty regarding their truth value. Eleven tasks were developed, each based on a claim from Linear Algebra, which had the potential to create within the learner a sense of uncertainty regarding its truth, and which the student had to prove or disprove its validity. Nineteen students were assigned to 9 groups, each consisting 1-3 students. The students were given the tasks and were interviewed while working on the tasks. Written and oral responses to the tasks were analyzed in order to find common phenomena. The phenomena which were identified dealt with the following aspects: indicators for uncertainty regarding the truth value of the claims; types of use of examples; other tools for resolving the uncertainty and reaching a decision regarding the truth value of the claim. Episode analysis was conducted in order to identify the stages through which students went while engaged in the tasks and to identify patterns of episodes that occur repeatedly in the different groups and the different tasks.

Five uncertainty indicators were identified. The findings indicate that, for most tasks, a sense of uncertainty regarding their truth value was encountered. The main approaches to the solutions employed by the students were familiar methods that are common proving and disproving methods. Examples played a major role in dealing with the uncertainty. Two types of examples were observed: specific examples and general examples. The examples tipped the balance towards a decision regarding the truth value of the claim, and were instrumental in moving the group towards resolving the problem. The situation involving the engagement in the tasks seemed to create an inner need in the students to reflect on their solution