Article Sidebar

Published
Feb 1, 2015
Download
PDF (Bahasa Indonesia)
Statistic
Read Counter : 1571 Download : 1304

Main Article Content

Abstract

ABSTRAK Makalah ini membahas tentang  berpikir matematika tingkat lanjut atau Advanced Mathematical Thinking (AMT) dan bagaimana cara meningkatkannya. AMT merupakan kemampuan dalam merepresentasi, mengabstraksi, berpikir kreatif, dan pembuktian matematis. Pentingnya pengembangan kemampuan AMT sesuai dengan harapan pemerintah yang menyadari pentingnya penguasaan kompetensi matematika untuk kehidupan peserta didik, Manfaat dari mengembangkan AMT diantaranya: 1) mahasiswa mampu menyampaikan gagasan atau ide yang dimilikinya baik secara verbal, simbol, tabel, grafik dan diagram.  2) menemukan keterkaitan yang mendalam di antara cabang-cabang matematika, 3) mengetahui hasil-hasil di dalam satu cabang yang dapat memicu konjektur pada cabang yang berkaitan, 4) teknik dan metode dari satu cabang dapat diterapkan untuk membuktikan hasil pada cabang yang berkaitan, 5) mampu menemukan gagasan baru dalam pemecahan masalah, dan 5) mampu memahami dan mengkonstruk bukti. Salah satu teori yang tidak hanya meningkatkan hasil belajar mahasiswa tetapi juga dapat mengkonstruk pengetahuan melalui aktivitas mental mahasiswa, meningkatkan kreativitas, menciptakan suasana kelas yang menyenangkan dan menantang, dan dapat meningkatkan kemampuan AMT mahasiswa adalah pendekatan APOS. Kata Kunci    :   Advanced Mathematical Thinking, Representasi, Abstraksi, Berpikir Kreatif, Pembuktian matematis, APOS ABSTRACTThis journal discuss about Advanced Mathematical Thinking (AMT) and how to enhance it.  AMT is ability in representing, abstracting, creative thinking, and mathematical proving.  The importance of AMT ability development in accord with government expectation who realize about the importance of mathematical competency mastery for student’s life. The advantage in developing AMT among others are: 1) student capable to deliver idea which is possessed in verbal, symbol, table, graphic and diagram.  2) Find deep connection among mathematic branches, 3) know the outcome in one of branch which can trigger conjecture in branch which is related, 4) technique and method from one branch can be applied to prove the outcome in branch which is related, 5) capable to find new idea in problem solving, and 6) capable to understand and construct the proof.   One of theory which not only enhance student’s learning outcome but also can construct knowledge through student’s mental activity, enhance creativity, create class atmosphere which is enjoyable and challenging, and capable to enhance student’s AMT ability is APOS approach. Keywords:            Advanced Mathematical Thinking, Representation, Abstraction, Creative Thinking, Mathematical Proving, APOS

Article Details

References

  1. Arnawa, M. (2006). Meningkatkan kemampuan Pembuktian Mahasiswa dalam Aljabar Abstrak melalui Pembelajaran Berdasarkan Teori APOS. Disertasi Doktor pada SPs UPI. Bandung: Tidak Diterbitkan
  2. Asiala, M. et al. (1997). “The development of students’ graphical understanding of the derivative”. Journal of Mathematical Behavior. 16(4), 399-431.
  3. Asiala, M. dkk. (1998). “The development of students’ understanding of permutations and symmetrics”. International Journal of Computers for Mathematical Learning.
  4. Gutiérrez, P. Boero (eds.). (2006). Handbook of Research on the Psychology of Mathematics Education: Past, Present and Future, 147–172. Sense Publishers. All rights reserved.
  5. Borich, G. D. (1994). Observation Skill for Effective Teaching. Englewood Clif fs: Merril Publisher.
  6. Brown, dkk. (1997). “Learning binary operations, groups, and subgroups”. International Journal of Mathematical Behavior
  7. Dubinsky, E. et al. (1994). “On Learning Fundamental Concepts of Group Theory”. Educational Studies in Mathematics, 27(3), 267-305.
  8. Dubinsky,E. & McDonald, M. (2001). “APOS: A Constructivist Theory of Learning in Undergraduate Mathematics Education Research”. Dalam D. Holton (ed.). The Teaching and Learning of Mathematics at University Level. Dordrecht: Kluwer Academic Publishers.
  9. Dubinsky, E dan Tall, D. (2002). “Reflective abstraction in advanced mathematical thinking”. Boston: Kluwer.
  10. Evans, J.R. (1991). Creative Thinking in the Decision and Management Sciences. Cincinnati, Ohio: South-Western Publishing Co.
  11. Goldin, G. A. (2002). Representation in Mathematical Learning and Problem solving. In L.D English (Ed). International Research in Mathematical Education IRME, 197-218. New Jersey: Lawrence Erlbaum
  12. G. Carmona. (1996). “The concept of tangent and its relationship with the concept of derivative”. International Journal Of Mathematical Education In Science & Technology.
  13. Grinnel, Jr., R. M. (1998). Social work research and evaluation. Illionis: F.E. Peacock Pub. Inc.
  14. Hake, R.R. (1999). Analyzing Change/Gain Scores. Woodland Hills: Dept. of Physics, Indiana University. [Online]. Tersedia: http://www.physics. ndiana.du/~sdi/AnalyzingChange-Gain.pdf [2 Januari 2013]
  15. Hwang, et al. (2007). Multiple Representation Skills and Creativity Effect on Mathematical Problem Solving Using a Multimedia Whiteboard System. Educational Technology & society. Vol. 10 No. 2 pp. 191-212
  16. Janvier, C. (1987). Problems of representation in the teaching and Learning of Mathematics, Hillsdale, New Jersey. London:Lawrence Erlbaum
  17. Kalathil, R.R., & Sherin, M.G. (2000). Role of Students’ Representation in the Mathematics Classroom. In B Fishman & S. O’Connor-Divelbiss (Eds). Fourth international Conference of the learning sciences (pp. 27-28). Mahwah, NJ:Erlbaum
  18. Mann, E.L. (2005). Mathematical Creativity and School Mathematics: Indicators of Mathematical Creativity in Middle School Students. A Dissertation of Doctor of Philosophy at the University of Connecticut. Tersedia [2 Maret 2010].
  19. McGregor, D. (2007). Developing Thinking Developing Learning. Poland: Open University Press.
  20. National Council of Teachers of Mathematics. (2000). Principles and Standars for School Mathematics. Reston, V.A: NCTM, Inc.
  21. Nurlaelah, (2009). Pencapaian daya dan Kreativitas Matematik Mahasiswa Calon Guru melalui Pembelajaran berdasarkan Teori APOS. Disertasi Doktor pada SPs UPI. Bandung: Tidak Diterbitkan.
  22. Polla, G. (2000). Efforts to Increase Mathematics for All through Communication in Mathematics Learning. [online]. Tersedia: www.icme-organisers.dk [15 Mei 2012]
  23. Proclus. (2006). Hystory Geometri. [Online]. Tersedia. http://www-history.mcs.st andrews.ac.uk/Extra/Proclus_history_geometry.html
  24. Rosengrant, D. (2005). An Overview of Recent Research on Multiple Representations. [Online]. Tersedia:http//paer.rutgers.edu/scientificAbilities /downloads/papers/DavidRosperc2011.pdf
  25. Sumarmo. (2011). Advanced Mathematical Thinking and Habits of Mind Mahasiswa. Hand Out Perkuliahan.
  26. Suryadi, D (2012). Membangun Budaya Baru dalam Berpikir Matematis. Bandung: Rizqi Press.
  27. Tall, D. (2002). “Advanced Mathematical Thinking”.Boston: Kluwer Tutorial SPSS 17 [Statistical Software]. (2008). Chicago:SPSS Inc.
  28. White, P., & Mitchelmore, M. C. (2010). Teaching for Abstraction: A Model. Mathematical Thinking & Learning. Available from: Education Research Complete, Ipswich, MA. Accessed March 4, 2012.
  29. Yerizon, (2011). Peningkatan Kemampuan Pembuktian Matematis dengan Pendekatan Modifikasi APOS pada Mahasiswa. Disertasi Doktor pada SPs UPI. Bandung: Tidak Diterbitkan.
  30. Yoo, S. (2008). Effects of Traditional and Problem Based Instruction on Conceptions of Proof and Pedagogy in Undergraduates and Prospective Mathematics Teacher, Dissertasion of The University of Texas at Austin: Tidak Dipublikasikan