Assumption and Definition Use in an Inquiry-Based Introduction to Proof Course

ABSTRACT

Students' proof abilities were explored in the context of an inquiry-based learning (IBL) approach to teaching an introductory proofs course. IBL is a teaching method that puts the responsibility for proof on students and focuses on student discussion and exploration. Data collected from each of the 70 participants included a portfolio consisting of their work on all proofs assigned during the course, as well as each student's final exam. Contrary to previous research conducted on introductory proof courses, this data analysis suggests that students developed an understanding of how to correctly use definitions and assumptions within the context of their proofs.

Keywords:

• Proof
• inquiry-based learning
• definitions
• assumptions
• structure

Additional information

Notes on contributors

T. A. Grundmeier

T. A. Grundmeier received his Ph.D. at the University of New Hampshire in Mathematics Education. His research focuses on undergraduate mathematics education. When teaching, he aims to engage his students in mathematics using mutliple forms of inquiry-based learning. When not at work, he tries to find time to play a little golf.

D. Retsek

D. Retsek is an operator theorist who received is Ph.D. at Washington University, Saint Louis. D. Retsek has 16 years experience teaching undergraduate and graduate mathematics. When not in the classroom, he can sometimes be found climbing tall walls.

A. Berg

A. Berg Prieto were all undergraduates at the time of this work. All three have since completed the teaching credential program at Cal Poly, San Luis Obispo and are teaching in high-need school districts in California.

S. Mann

S. Mann Prieto were all undergraduates at the time of this work. All three have since completed the teaching credential program at Cal Poly, San Luis Obispo and are teaching in high-need school districts in California.

A. Hamlin Prieto

A. Hamlin Prieto were all undergraduates at the time of this work. All three have since completed the teaching credential program at Cal Poly, San Luis Obispo and are teaching in high-need school districts in California.