RUME 26
2024
Omaha, Nebraska
Obstacles of Learning Proof by Cases
Page: 1292
Epistemological Obstacles (EOs) are defined as challenges that students face when exposed to concepts that contradict their pre-existing mathematical intuition (Norton & Arnold, 2023). The objective of our poster is to address EOs that emerge during the lesson on proving by cases, rather than circumventing them. This approach, as pursued by Norton and Arnold (2023), elicited EOs such as the Principal of Universal Generalization (PUG) and understanding the difference between the role versus the value of a quantified variable (Qrv). PUG entails proving “for all” statements with an arbitrary value. It was mainly encountered during mathematical induction by Norton and Arnold (2022), but its relation to proofs by cases was not studied. When proving statements with PUG, it may not occur to students that they need specific (x=0), or arbitrary (x is even) cases. Qrv teaches students to prioritize maintaining generality; however, loss of generality is allowed with proof by cases as it is preserved in the aggregate. The obstacle comes from students struggling to understand that generality is maintained differently depending on the situation. The two EOs are closely related; Qrv can be thought of as a direct product of PUG. Our poster aims to elaborate on our proof by cases lesson and get feedback on how to revise the lesson in preparation for us submitting a journal manuscript on EOs in proof by cases