### Abstract:

It has been held that heuristic training alone is not enough for developing
one's mathematical thinking. One missing component is a mathematical point of
view. Many educational researchers have proposed problem-based curricula to
improve students' views of mathematical thinking. The present study reports
findings regarding effects of a problem-based calculus course, using historical
problems, to foster Taiwanese college students' views of mathematical thinking.
The present study consisted of three stages. During the initial phase, 44
engineering majors' views on mathematical thinking were tabulated by a six-item,
open-ended questionnaire and nine randomly selected students were invited to
participate in follow-up interviews. Students then received an 18-week problem-based
calculus course in which mathematical concepts were problematized in order to
challenge their personally expressed empirical beliefs in doing mathematics.
Several tasks and instructional approaches served to reach the goal.
Near the end of the semester, all participants answered the same
questionnaire and the same students were interviewed to pinpoint their shift in
views on mathematical thinking. It was found that participants were more likely to
value logical sense, creativity, and imagination in doing mathematics. Further,
students leaned toward a conservative attitude in the certainty of mathematical
knowledge. Participants focus seemingly shifted from mathematics as a product to
mathematics as a process.