STUDI PEMAHAMAN BUKTI DAN PEMBUKTIAN DALAM GEOMETRI EUCLID MAHASISWA JURUSAN TADRIS MATEMATIKA IAIN TULUNGAGUNG
DOI:
https://doi.org/10.33474/jpm.v1i2.720Keywords:
Understanding, Proof, Proving, Euclid GeometryAbstract
One of the problems to be solved in mathematics is a proof. At the college level, proving to be more important than the previous levels. When someone has a hunch about something (theorem), one of the most appropriate way to ensure that something (theorem) is true is by proving mathematically valid (formally). That is, the truth of the theorem is based on logical statements. However, proof of this is a problem when introduced during the learning. Not only the beginning students, final year students, moreover those already graduated are still experiencing difficulties in proving. This study attempts to describe the understanding of the concept of proof in mathematics and describes the ability of students in validating and compiling of proof in mathematics, particularly in Euclidean geometry using qualitative research approach, the type of case studies.References
Alfeld, P. 2004. “Understanding Mathematics”, (http://www.math.utah.edu/~pa/math. html, diakses 03 Oktober 2014)
Arnawa, I Made. 2009. “Mengembangkan Kemampuan Mahasiswa dalam Memvalidasi Bukti pada Aljabar Abstrak melalui Pembelajaran Berdasarkan Teori APOS”, Jurnal Matematika dan Sains, Juni 2009, Vol. 14 No. 2
Barmby, P., et. all, 2007, “How Can We Assess Mathematical Understanding?”, dalam Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education, Vol. 2, pp. 41-48. Seoul: PME
Cockcroft, W. H. 1986. “Mathematics Counts”, (http://www.educationengland.org.uk/documents/ cockcroft/cockcroft00.html, diakses 27 Januari 2012)
Harel, Guershon & Larry Sowder. 1998. “Students’ proof schemes: results from exploratory studies.” In A.H. Schoenfeld, J. Kaput & E. Dubinsky (Eds.), Research in collegiate mathematics education, 1998, Volume 3, pp.234-283, Mathematical Association of America
........................ 2007. “Toward the comprehensive perspectives on the learning and teaching of proof.” In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning, 2007, pp. 805-842, Charlotte, NC: Information Age Publishing
Healy, Lulu & Celia Hoyles. 2000. “A study of proof conceptions in algebra”, Journal for Research in Mathematics Education, 2000, 31(4), 396-428.
Kassios, Y. 2009. “Formal Proof”, (http://www.cs.toronto.edu/~hehner/aPToP/formalproof-1.pdf, diakses tanggal 15 Oktober 2014)
Marsudi. 2010. Logika dan Himpunan. Malang: UB Press.
Michener, E. R. 1978. Understanding Understanding Mathematics. Cambridge, Massachusetts: Massachusetts Institute of Technology.
Polya, G. 1981. Mathematical Discovery: On Understanding, Learning and Teaching Problem Solving, Combined Edition. New York: John Willey & Sons, Inc.
Porteous, K. tt. “Understanding Mathematics”, (http://people.exeter.ac.uk/PErnest/pome23/ Porteous%20Understanding%20Mathematics.doc, diakses 03 Oktober 2014)
Rich, B. & Christopher Thomas. 2009. Geometry: includes plane, analytic, and transformational geometries Fourth Edition. New York: McGraw-Hill Companies, Inc.
Skemp, Richard R. 1976. “Relational Understanding and Instrumental Understanding”, (http://www.grahamtall.co.uk/skemp/pdfs/instrumental-relational.pdf, diakses 03 Oktober 2014)
Tall, D. 1989. “The Nature of Mathematical Proof”, dalam Mathematics Teaching, 127, hal. 23-32.
………...............1995. Cognitive Development, Representations, and Proof, Makalah dipresentasikan pada Conference on Justifying and Proving in School Mathematics, Institute of Education, Desember 1995, London.
…..................……..1998. The Cognitive Development of Proof: Is Mathematical Proof For All or Some? Conference of the University of Chicago School Mathematics Project.
Vanspronsen, H.D. 2008. Doctoral Dissertation: “Proof Processes Of Novice Mathematics Proof Writers.” Missoula: University of Montana.
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