Students’ Proof Scheme for Mathematical Proving and Disproving of Divisibility Proposition

Abstract

This study aimed to investigate and describe students' proof schemes for disproving mathematical proposition. Previous studies examined students' proof scheme of Calculus, Elementary Numbers Theory, Quadratic, and Geometry's Propositions. This study examined student proof schemes of Divisibility's Proposition which has never been studied before. The study participants were 20eleventh grade students from a private senior high school in Sidoarjo. All participants had to answer two tests, namely the mathematics ability test and the proof test. Three volunteer students (1 male and 2 female), with high mathematics ability and high score in proof test, were selected as research subjects. Semi-structured interview was conducted to three subjects for investigating the students' proof schemes. The qualitative data of proof schemes was categorized in Lee's proof scheme descriptors. The results show that all of the participants divisibility propositions in the 4th level because they were able to state that the falsity of the mathematics proposition by a specific counterexample. They couldn't change the specific counterexample to become a general counterexample with mathematics symbols. Meanwhile, for the true mathematical proposition, one subjects concluded that the proposition is true with informal deductive proof, the other subjects proved the proposition inductively by using specific examples. Therefore, the first subject is categorized into 5th level and 2 subjects are categorized into 2nd level.