University Undergraduate Science Students’ Validation and Comprehension of Written Proof in the Context of Infinite Series

Abstract

The reported study explored undergraduate science students’ validation and comprehension of written proofs, reasons given either to accept or reject mathematical procedures employed in the proofs, and the difficulties students encountered in reading the proofs. The proofs were constructed using both the Comparison and the Integral tests in the context of infinite series. One-hundred and thirty-one second year science students majoring in mathematics were the subjects of the study. Data were collected through a written assignment and interviews. An inductive approach was adopted in developing categories of proof validation by students. The categories were then compared with Weber’s classification on proof validation. Proof comprehension was analysed using the model by Meija-Ramos and colleagues differentiating between understanding proof locally and holistically. The findings of the study show that students validated the proofs according to what in their view constituted proof or what they viewed as the most important characteristic(s) of proof from both their lecture notes and instruction. The validation of the mathematical procedures was mainly based on whether or not the Comparison Test and the Integral Test theorems were considered to be applied appropriately. The difficulties students encountered with proof were attributed to the way the proofs were presented. The majority of students required that each step of the proofs be explained or justified. Implications for teaching are presented.