# KAJIAN KESULITAN BELAJAR MAHASISWA DALAM KEMAMPUAN PEMBUKTIAN MATEMATIS DITINJAU DARI ASPEK EPISTEMOLOGI PADA MATA KULIAH GEOMETRI TRANSFORMASI

### Abstract

This research specifically aims to analyze the ability of mathematical proof, to analyze learning difficulties in terms of student epistemology on the material of transformation geometry. The long-term benefit of this study is the study of learning difficulties in terms of student epistemology related to mathematical proofing in the course of transformation geometry, is expected to provide encouragement to other lecturers to further develop the learning process or teaching materials in an effort to develop mathematical proof of mathematics students. This research uses descriptive method, while the subject of research is 9 students of Unswagati mathematics teacher candidate who contracted the course of transformation geometry. Methods of data collection used include: (1) test of mathematical proof capability; (2) observation; (3) interviews; and (4) documentation. The research results obtained there are 5 kinds of student difficulties viewed from epistemology related to the geology of transformation geometry, namely a) difficulty learning related difficulties in applying the concept; b) learning difficulties related to visualizing geometric objects; c) learning difficulties with difficulty in determining principles; d) learning difficulties related to understanding problems and e) related difficulties in mathematical proofing. Especially in mathematical proofing, students have difficulties such as: not knowing how to start construction of evidence, unable to use known concepts and principles, and tend to start construction of evidence with what must be proven.

### Downloads

### References

Christou, C., Mousoulides, N., Pittalis, M., & Pitta-Pantazi, D. 2004. Proofs Through Exploration In Dynamic Geometry Environments. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, 2004 Vol 2 pp 215–222.

Hinze, A. dan Reiss, K. (2004). Aiso Heinze, Kristina Reiss Reasoning and Proof: Methodological Knowledge as a Component of Proof Competence. [Online] http://www.dm.unipi.it/~didattica/CERME3/proceedings/Groups/ TG4/TG4 _Heinze_cerme3.pdf diakses pada tanggal 18 Oktober 2015 pukul 23.00.

Jones, K. dan Rodd, M. (2001). Geometry and Proof. Proceedings of the British Society for Research into Learning Mathematics 21(1) March 2001.

Knuth, E.J. (2002). Theachers’ Conception of Proof in the Context of Secondary School Mathematics. Journal of Mathematics Teacher Education 5: 61–88, 2002. © 2002 Kluwer Academic Publishers. Printed in the Netherlands

Leikin, R. 2009. Multiple Proof Tasks Teacher Practice and Teacher Education. Proceedings of the ICMI Study 19 Conference: Proof and Prooving in Mathematics Education, 31-35. Conference held on May 10-15, 2009 in Taipe, Taiwan.

Maarif, S. 2015. Pembelajaran Geometri Berbantuan Cabri 2 Plus (Panduan Praktis Mengembangkan Kemampuan Matematis). Bogor: In Media.

Malcolm Swan dan Jim Ridgway. Convincing and Proving' Tasks. [online] https://www.google.co.id/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&uact=8&ved=0CCwQFjABahUKEwi40KTi3YnJAhXLkpQKHSDwBEU&url=http%3A%2F%2Fwww.flaguide.org%2Fextra%2Fdownload%2Fcat%2Fmath%2Fconvincing%2Fconvince.rtf&usg=AFQjCNEK5FIYBotly5_CEXJT8iaZJeqAVA&bvm=bv.107406026,d.dGo.

Malek, A & Hadar, N.M. 2009. The Art of Constucting A Transparent P-Proof. Proceedings of the ICMI Study 19 Conference: Proof and Prooving in Mathematics Education, 70-75. Conference held on May 10-15, 2009 in Taipe, Taiwan.

Mariotti, M.A. (2001). Introduction To Proof: The Mediation Of A Dynamic Softwareenvironment. Educational Studies in Mathematics 44: 25–53, 2000. © 2001 Kluwer Academic Publishers. Printed in the Netherlands.

Moore, R. C. 1994. Making the Transition to Formal Proof. Educational Studies in Mathematics, 27, (3), 249-266.

National Council of Teachers of Mathematics. 2000. Principles and Standards for School Mathematics. Reston, VA: Author.

Reiss, K dan Renkl, A. (2001). Learning to prove: The idea of heuristic examples. ZDM Journal 2002 Vol. 34 (1).

Sumarmo, U. 2014. Advanced Mathematical Thinking dan Habits of Mind Mahasiswa. Bahan Ajar Matakuliah Kajian dan Isu Pendidikan Matematika Pascasarjana UPI dan STKIP Siliwangi Bandung. Dapat diakses di: http://utari-sumarmo.dosen.stkipsiliwangi.ac.id/2015/09 /makalah-advanced-math-thinking-dan-habit-of-mind/

Suryadi, D. 2007. Model Bahan Ajar dan Kerangka-Kerja Pedagogis Matematika untuk Menumbuhkembangkan Kemampuan Berpikir Matematik Tingkat Tinggi. Laporan Penelitian: Tersedia di: http://didi-suryadi.staf.upi.edu/artikel/

Tall, D. 1999. The Cognitive Development of Proof: Is Mathematical Proof For All or For Some?

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.