A Sense-making Approach to Proof: Initial Strategies of Students in Traditional and Problem-based Number Theory Courses

Abstract

This paper reports the results of an exploratory study

of the perceptions of and approaches to mathematical

proof of undergraduates enrolled in lecture-based and

problem-based "transition to proof' courses. While the

students in the lecture-based course demonstrated

conceptions of proof that reflect those reported in the

research literature as insufficient and typical of

undergraduates. the students in the problem-based course

were found to approach the construction of proofs in ways

that demonstrated efforts to make sense oj mathematical

ideas. This sense-making manifested itself in the ways in

which students employed initial strategies. notation. prior

knowledge and experiences, and concrete examples in the

prooJ construction process. These results suggest that such

a problem-based course may provide opportunities for

students to develop conceptions of proof that are more

meaningful and robust than does a traditional

lecture-based course.