Methods of Mathematical Proof and Logic in Mathematics Courses at the Faculty of Education – Sana'a University

Abstract

This study aimed to identify the extent to which mathematical proof and logic methods are achieved in mathematics courses for student-teachers at the University of Sana'a. To achieve this objective, the descriptive and analytical method was used. Checklists for analyzing mathematical content according to methods of mathematical proof and logic were developed, and a questionnaire was used to verify the validity of the checklists. The tools were validated by a jury of experts, and the degree of agreement was (98.1%) (85.82%). The tools were applied to a sample of mathematics courses, including mathematical analysis, real analysis and abstract algebra (1), (2). The findings revealed that the most frequent proof methods found in mathematical courses were proof by deduction and transgression (65.86%) of the total methods, followed by proof by mathematical induction (11.75%), and the least frequent was proof by contradiction (9.61%). The courses did not include method of evaluative, critical and reversed proof. The direct method of proof was (82.93%), whereas the occurrence of the indirect proof method was (17.07%). The course content also did not include method of evaluative, critical and reversed proof, and there were statistically significant differences at (0.01), between the weights of the methods of mathematical proof and logic, which were included in the current courses, and the weights that should be included.