PROSES BERPIKIR MAHASISWA DALAM MEMBUKTIKAN PROPOSISI: KONSEPTUALISASI-GAMBAR

Lathiful Anwar; Syaiful Hamzah Nasution; Sudirman Sudirman; Susiswo Susiswo

doi:10.17977/um076v2i22018p46-56

PROSES BERPIKIR MAHASISWA DALAM MEMBUKTIKAN PROPOSISI: KONSEPTUALISASI-GAMBAR

Lathiful Anwar, Syaiful Hamzah Nasution, Sudirman Sudirman, Susiswo Susiswo

Abstract

Evidence is an absolute feature of mathematics and a key component in mathematics education. Although the evidence is very important, the fact is that the evidence is something that is difficult to teach or learn. One of the difficulty factors is the inadequacy of conceptual concepts and the inability to use definitions to structure evidentiary structures. This paper will describe the thinking process of students in proving a geometric proposition. Four concept of image conceptualization framework is used as a tool to explore students' thinking processes in proving a geometric proposition. One student's work and vignette, FMZ, was analyzed to provide a visualization of the image-conceptualization process used by FMZ in identifying a proposition. The results of the analysis confirm that the ability to construct evidence is related to the ability to conceptualize images, find local-local conceptualizations (traits / conclusions related to one part of the image) and global conceptualization and link relational relationships between local conceptualizations and global conceptualization into a series of statements supporting propositions / conclusion which will be proven to be a series of logical statements.

Full Text:

[Download PDF]

References

Dumas, B. A., & McCarthy, J. E. (2014). Transition to Higher Mathematics: Structure and Proof. Saint Louis, Missouri: Washington University in St. Louis. https://doi.org/10.7936/K7Z899HJ

Guven, B., & Baki, A. (2010). Characterizing student mathematics teachers’ levels of understanding in spherical geometry. International Journal of Mathematical Education in Science and Technology, 41(8), 991–1013. https://doi.org/10.1080/0020739X.2010.500692

Handscomb, K. (2005). IMAGE-BASED REASONING IN GEOMETRY. SIMON FRASER UNIVERSITY.

Handscomb, K. (2006). PRINCIPLES OF CONCEPTUALIZATION FOR IMAGE-BASED REASONING IN GEOMETRY. In Proceedings of the Twenty Eighth Annual Meeting of the North American Chapter of the International Group for the the Psychology of Mathematics Education (Vol. 2, pp. 418–420). Mérida, México: Universidad Pedagógica Nacional.

Jone, K. (2000). The student experience of mathematical proof at university level. Inter-Nat. J. Math. Ed. Sci. Tech. https://doi.org/10.1080/002073900287381

Kwoen, J. (2002). Philosophical perspective on proof in mathematics education. Philos-Ophy of Mathematics Education Journal, 16.

Miyazaki, M., Fujita, T., & Jones, K. (2017). Students’ understanding of the structure of deductive proof. Educational Studies in Mathematics, 94(2), 223–239.

Miyazaki, M., Fujita, T., Jones, K., & Iwanaga, Y. (2017). Designing a Web-based Learning Support System for Flow-chart Proving in School Geometry. Digital Experiences in Mathematics Education, 3(3), 233–256.

Moore, R. C. (1994). Making the transition to formal proof. Educational Studies in Mathematics, 27(3), 249–266. https://doi.org/10.1007/BF01273731

NCTM. (2000). Principles and Standards for School Mathematics. School Science and Mathematics, 47(8), 868–279. Retrieved from www.nctm.org

Oflaz, G., Bulut, N., & Akcakin, V. (2016). Pre- Service Classroom Teachers ’ Proof Schemes in Geometry : A Case Study of Three Pre-service Teachers. Eurasian Journal of Educational Research, (63), 133–152. https://doi.org/10.14689/ejer.2016.63.8

Ozmantar, M. F. (2017). A Historical Analysis of Primary Mathematics Curricula in Terms of Teaching Principles. International Journal of Research in Education and Science, 327–327. https://doi.org/10.21890/ijres.327890

Stylianides, A. J. (2007). Proof and Proving in Mathematics Education. Journal for Research in Mathematics Education, 38(3), 289–321. https://doi.org/10.1007/978-94-007-2129-6

Tall, D. (1995). Cognitive development , representations and proof. In Justifying and Proving in School Mathematics (pp. 27–38). London.

Tall, D. (1999). The Cognitive Development of Proof: Is Mathematical Proof For All or For Some? Conference of the University of Chicago School Mathematics Project, 1–18.

Ufer, S., Heinze, A., & Reiss, K. (2009). Mental models and the development of geometric proof competency. Pme 33: Proceedings of the 33Rd Conference of the International Group for the Psychology of Mathematics Education, Vol 5, 5, 257–264.

Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics : teaching developmentally. Boston: Pearson Education Inc.

DOI: http://dx.doi.org/10.17977/um076v2i22018p46-56