Exploring students’ proof comprehension of the Cauchy Generalized Mean Value Theorem

Abstract

AbstractUndergraduate students majoring in mathematics often face difficulties in comprehending mathematical proofs. Inspired by a number of studies related to students’ proof comprehension, and Mejia-Ramos et al.’s study in particular, a test was designed in relation to the proof comprehension of the Cauchy Generalized Mean Value Theorem (CGMVT). The test mainly focused on (a.) investigating students’ understanding of relations between the statements within the CGMVT proof and (b.) the relations between the CGMVT and other theorems. Thirty-five first-year university students voluntarily participated in this study. In addition, 10 of these students were subsequently interviewed to seek their opinion about the test. Test results indicated that most of the students lacked an understanding of the relations between the mathematical statements within the CGMVT proof, and the relations between the CGMVT and other theorems. The results of interviews showed that this type of assessment was new to students and helped them to improve their insights into mathematical proofs. The findings suggested such a test design could be used more frequently in assessments to aid instructors’ understanding of students’ proof comprehension and to teach students how mathematical proofs should be learned.