The influence of mathematical classics reading on university students' mathematics beliefs
Résumé
We report the influences of an undergraduate-level liberal-arts course, in which students in a medical university were guided to read through important parts of Euclid's Elements and taught about related cultural issues including logic and some Greek philosophy. Class questionnaires and reflexions showed that parts of students' beliefs changed after the course. Concerning the values of mathematics, students were more prone to believe that mathematics had real-world applications and improved one's sensibilities to beauty; for the nature of mathematics, they were more prone to believe proof was the only way to justify mathematical knowledge. The last change was expected but also interesting, since in another course in the same university about mathematics culture, students were confused about the context of discovery and that of justification. The course reported here was more helpful since it also had cultural connections but did not similarly confuse students, which is meaningful in a society where problem-solving, not logic, is considered the most useful aspect of mathematics.