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.
Proof and proving play an important role for students in justifying the validity of mathematical propositions. This qualitative research was concerned to assess students' proof schemes for disproving mathematics propositions. The sample was 11 th grade students of SMAN 1 Surabaya. All students had to answer two tests, namely the mathematics ability test and the proof-by-counterexample test. Three volunteer students (girls), with high mathematics ability and high score in proof-bycounterexample test, were selected as research subjects. For investigating the students' proof schemes, semi-structured interview was conducted to three subjects. The data quality of proof schemes was categorized in 6 levels of proof-bycounterexample criteria. The results revealed that all students were able to prove the mathematics proposition and there were still differences each other. One student was able to demonstrate the falseness of the mathematical proposition by giving a general counterexample with mathematics symbols, so the student was in highest level, 5 th level. Meanwhile, others were in the 4 th levels because they were able to state that the falseness of the mathematics proposition by a specific counterexample. They couldn't change the specific counterexample to become a general counterexample with mathematics symbols. This finding suggests, the need for further research regarding to gender.
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