How do transition to proof textbooks relate logic, proof techniques, and sets?

PROCEEDINGS OF THE 22ND ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION

2019

Oklahoma City, Oklahoma

How do transition to proof textbooks relate logic, proof techniques, and sets?

Page: 146

• John Paul Cook
• Paul Dawkins
• Dov Zazkis

Many mathematics departments have transition to proof (TTP) courses, which prepare undergraduate students for proof-oriented mathematics. Here we discuss how common TTP textbooks treat three topics ubiquitous to such courses: logic, proof techniques and sets. We show that these texts tend to overlook the rich connections sets have to proof techniques and logic. Recent research has shown that student thinking about sets is propitious to novice students’ ability to reason about logic and construct valid arguments. We suggest several key connections TTP courses can leverage to better take advantage of their unit(s) on sets.