Proceedings of the Mathematics, Informatics, Science, and Education International Conference (MISEIC 2018)

Students’ Proof Schemes for Disproving Mathematical Proposition

Authors
Mochammad Amirudin, Yusuf Fuad, Pradnyo Wijayanti
Corresponding Author
Mochammad Amirudin
Available Online July 2018.
DOI
https://doi.org/10.2991/miseic-18.2018.25How to use a DOI?
Keywords
Proof, Proof Schemes, Disproving, Counterexample
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 11th 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-by-counterexample 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-by-counterexample 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, 5th level. Meanwhile, others were in the 4th 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.

Copyright
© 2018, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Volume Title
Proceedings of the Mathematics, Informatics, Science, and Education International Conference (MISEIC 2018)
Series
Advances in Intelligent Systems Research
Publication Date
July 2018
ISBN
978-94-6252-601-3
ISSN
1951-6851
DOI
https://doi.org/10.2991/miseic-18.2018.25How to use a DOI?
Copyright
© 2018, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - CONF
AU  - Mochammad Amirudin
AU  - Yusuf Fuad
AU  - Pradnyo Wijayanti
PY  - 2018/07
DA  - 2018/07
TI  - Students’ Proof Schemes for Disproving Mathematical Proposition
BT  - Proceedings of the Mathematics, Informatics, Science, and Education International Conference (MISEIC 2018)
PB  - Atlantis Press
SP  - 101
EP  - 105
SN  - 1951-6851
UR  - https://doi.org/10.2991/miseic-18.2018.25
DO  - https://doi.org/10.2991/miseic-18.2018.25
ID  - Amirudin2018/07
ER  -