ERIC Number: EJ1322061
Record Type: Journal
Publication Date: 2022
Pages: 17
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-1051-1970
EISSN: N/A
How Do Transition to Proof Textbooks Relate Logic, Proof Techniques, and Sets?
Dawkins, Paul Christian; Zazkis, Dov; Cook, John Paul
PRIMUS, v32 n1 p14-30 2022
Many mathematics departments have transition to proof (TTP) courses, which prepare undergraduate students for proof-oriented mathematics. Here we discuss how common TTP textbooks connect three topics ubiquitous to such courses: logic, proof techniques, and sets. In particular, we were motivated by recent research showing that focusing on sets is propitious to novice students' ability to reason about logic and construct valid arguments. Our objectives were to (1) analyze examples of how these connections were made in relation to what is known about student thinking and learning in TTP courses and also to (2) identify situations in these texts in which there are opportunities for such connections to be made that could benefit students' learning. We focus on how logic was used to explain ideas related to sets and proof techniques, and how sets were used to explain ideas in the other domains. In addition to providing examples from our textbook sample illustrating instances in which connections were (or potentially could be made), we suggest several key recommendations TTP instructors can leverage in their unit(s) on sets.
Descriptors: Mathematics Instruction, Mathematical Logic, Validity, Undergraduate Students, College Mathematics, Textbooks, Textbook Content
Taylor & Francis. Available from: Taylor & Francis, Ltd. 530 Walnut Street Suite 850, Philadelphia, PA 19106. Tel: 800-354-1420; Tel: 215-625-8900; Fax: 215-207-0050; Web site: http://www.tandf.co.uk/journals
Publication Type: Journal Articles; Reports - Evaluative
Education Level: Higher Education; Postsecondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A