Students' mathematical conviction in Mathematics proof

Abstract

Students are often not convinced with proofs that they have constructed in a valid manner. As a result, it may affect their mathematical understanding completely. A conviction is a broad definition of proof. Proof is not only a physical and mental activity individually, but it is also followed by an activity of convincing one self and others. This research will elaborate the components of the cause of the mathematical conviction based on the proof construction of a Plane Euclidean Geometry theorem and a convictional questionnaires about mathematical proof construction of the theorem. These components are described from five respondents found in this study. The mathematical components of conviction have been investigated in this study, it consists of: statements in the system of axioms (strength); inference flow and form of proof (logic); conformity of proof representation (formality); identification of proof statement (completeness); generalization and the extent of proof (consistency); and precision of symbols and writing (accuracy). These six components renew and fill components that are available previously. Considering to these components within the implementation of learning, it is implied to improve students' ability in understanding proof and can convince others.