The Conceptual Validity Aspect of Pre-service Mathematics Teachers' Reasoning on Linear Algebra

Abstract

The study aimed to analyze the conceptual validity aspect of Indonesian pre-service mathematics teachers' reasoning on linear Algebra. This research is a case study and involves as many as 42 second-semester students at a public university in Jakarta. A five-item test was administered, and based on their claims and reasons, participants' responses were analyzed and classified into four categories: fully valid, partially valid, invalid, and unidentified. The findings of this study are that most of the participants' responses fall in the partially valid category and have various obstacles in delivering their reasons. Based on these findings, it could be concluded that the success or the failure of participants in providing claims and reasons was at least influenced by four supporting factors or causes, namely: (1) conceptual understanding, (2) mathematical connections, (3) mathematical proof, and (4) mathematical communication. There are implications from the results of this study.