Studentsr Proof Schemes for Disproving Mathematical Proposition

Abstract

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.

Construction of Examples and Counterexamples in Primary School to Verify the Truth of Statements

“…Skolēnu deduktīvās domāšanas spējas, veidojot pretpiemērus matemātikā, tiek iedalītas piecos līmeņos. Pirmais līmenis atbilst situācijai, ka skolēns nevar sasaistīt apgalvojumu ar piemēru izmantošanas nepieciešamību, ceturtais līmenisskolēns secina, ka izteikums ir nepatiess, konstruējot vienu vai dažus pretpiemērus, bet augstākais piektais līmenis ir skolēniem, kuri izveido pretpiemēra eksistences aprakstu, izmantojot matemātiskos simbolus (Amirudin, Fuad, & Wijayanti, 2018). Sākumskolas skolēniem ir grūti spriest deduktīvi, izmantojot tikai vārdus un simbolus, šādi bērni spēj labāk veikt deduktīvo spriešanu ar manipulatīviem objektiem vai veidojot "darbības pierādījumus (Semadeni, 1984).…”