JEWLScholar@MTSU Repository

# CONNECTING LOGIC AND PROOF TECHNIQUES: IDENTIFYING LEARNING IN AN INTRODUCTION TO PROOFS COURSE

 dc.contributor.advisor Bleiler-Baxter, Sarak K dc.contributor.author Reed, Samuel Douglas dc.date.accessioned 2021-07-16T01:04:09Z dc.date.available 2021-07-16T01:04:09Z dc.date.issued 2021 dc.identifier.uri https://jewlscholar.mtsu.edu/handle/mtsu/6473 dc.description.abstract Proof and proving are a core component of the discipline of mathematics and proving is a required exercise in many upper-level courses in mathematics at the undergraduate level. Writing proofs remains difficult for many students (Moore, 1994; Stylianides et al., 2017). To address this difficulty many universities have began offering Introduction to Proof courses. These courses typically cover three main areas, logic, proof techniques, and sets and functions (David & Zazkis, 2020). With this course’s importance in students’ transition to upper-level mathematics, it is worthwhile to investigate the connections that students make between the subcomponents of such a course. As such, in this dissertation study I sought to understand the connections that students make between logic and the techniques of proof in and Introduction to proofs course. In the first chapter I state the broad issues related to students learning of logic and proof techniques, to set the stage for the remainder of the manuscript. In the second chapter I present a research study on the connections that students make between logic, direct, and indirect modes of proof. In the third chapter I present a research study on the struggles that students face as they learn to write proofs with mathematical induction. In the fourth chapter I present a practitioner-minded piece where I highlight the typical issues that students face throughout an Introduction to Proofs course. Finally, in the fifth chapter I share some broad conclusions across these three manuscripts and reflect on students’ learning throughout an Introduction to Proofs course. dc.publisher Middle Tennessee State University dc.source.uri http://dissertations.umi.com/mtsu:11473 dc.subject Introduction to Proof dc.subject Logic dc.subject Proof dc.subject Proof Techniques dc.subject Proving dc.subject Mathematics education dc.title CONNECTING LOGIC AND PROOF TECHNIQUES: IDENTIFYING LEARNING IN AN INTRODUCTION TO PROOFS COURSE dc.date.updated 2021-07-16T01:04:09Z dc.language.rfc3066 en dc.contributor.committeemember Lischka, Alyson dc.contributor.committeemember Hart, James dc.contributor.committeemember Langston, William dc.contributor.committeemember Dawkins, Paul dc.thesis.degreelevel doctoral dc.description.degree Ph.D.
﻿