Argumentasi Siswa Dalam Pembuktian Konjektur

Intan Carolina Savitri, Toto Nusantara, Swasono Rahardjo

Abstract


Penelitian ini bertujuan untuk mendeskripsikan Struktur argumentasi siswa dalam pembuktian konjektur. Penelitian ini menggunakan metode kualitatif dengan jenis penelitian deskriptif. Subjek pada penelitian adalah 8 orang siswa kelas XI SMAN 1 Rogojampi. Subjek diminta membuktikan konjektur kemudian dikelompokan berdasarkan hasil pembuktian yang diberikan. Kemudian setiap subjek akan diwawancara untuk mengetahui argumentasinya. Hasil wawancara akan dianalisis berdasarkan struktur argumentasi Toulmin. Hasil penelitian menunjukan bahwa struktur argumentasi siswa yang menghasilkan pembuktian dengan contoh generik hampir sama dengan siswa yang menghasilkan pembuktian dengan contoh empirik. Struktur argumentasi siswa yang membuktikan dengan contoh lebih rumit dan memuat lebih banyak jenis komponen argumentasi dibanding siswa yang membuktikan secara formal.

Keywords


Prove; Argumentation; Generic Example; Empiric Example

Full Text:

PDF

References


Aberdein, A. (2012). The parallel structure of mathematical reasoning. In The argument of mathematics (pp. 351–370). citeulike-article-id:12227960%5Cnhttp://www.worldcat.org/oclc/818963739

Alcock, L., & Weber, K. (2010). Referential and syntactic approaches to proving: Case studies from a transition-to-proof course. 1711553, 93–114. https://doi.org/10.1090/cbmath/016/04

Aricha-Metzer, I., & Zaslavsky, O. (2017). The nature of students’ productive and non-productive example-use for proving. Journal of Mathematical Behavior, 53, 304–322. https://doi.org/10.1016/j.jmathb.2017.09.002

Ayalon, M., & Even, R. (2008). Deductive reasoning: In the eye of the beholder. Educational Studies in Mathematics, 69(3), 235–247. https://doi.org/10.1007/s10649-008-9136-2

Chartrand, G., Polimeni, A. D., & Zhang, P. (2018). Mathematical proofs : a transition to advanced mathematics.

Chazan, D. (1993). High school geometry students’ justification for their views of empirical evidence and mathematical proof. Educational Studies in Mathematics, 24, 359–387.

Christou, C., & Papageorgiou, E. (2007). A framework of mathematics inductive reasoning. Learning and Instruction, 17(1), 55–66. https://doi.org/10.1016/j.learninstruc.2006.11.009

Clark, D. B., Sampson, V., Weinberger, A., & Erkens, G. (2007). Analytic frameworks for assessing dialogic argumentation in online learning environments. Educational Psychology Review, 19(3), 343–374. https://doi.org/10.1007/s10648-007-9050-7

Conner, A. M., Singletary, L. M., Smith, R. C., Wagner, P. A., &

Francisco, R. T. (2014). Teacher support for collective argumentation: A framework for examining how teachers support students’ engagement in mathematical activities. Educational Studies in Mathematics, 86(3), 401–429. https://doi.org/10.1007/s10649-014-9532-8

de Villiers, M. (1990). The role and function of proof in Mathematics. Pythagoras, 24(November 1990), 17–23.

Erduran, S., Simon, S., & Osborne, J. (2004). TAPping into argumentation: Developments in the application of Toulmin’s Argument Pattern for studying science discourse. Science Education, 88(6), 915–933. https://doi.org/10.1002/sce.20012

Hakyolu, H., & Ogan-Bekiroglu, F. (2016). Interplay between content knowledge and scientific argumentation. Eurasia Journal of Mathematics, Science and Technology Education, 12(12), 3005–3033. https://doi.org/10.12973/eurasia.2016.02319a

Hales, T. (2008). Formal proof. Notices of the AMS, 55(11), 1370–1380.

Healy, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31(4), 396–428. https://doi.org/10.2307/749651

Inglis, M., Mejia-Ramos, J. P., & Simpson, A. (2007). Modelling mathematical argumentation: The importance of qualification. Educational Studies in Mathematics, 66(1), 3–21. https://doi.org/10.1007/s10649-006-9059-8

Knipping, C. (2004). Argumentation structures in classroom proving situations. European Research in Mathematics Education III, 1–9.

Knipping, Christine, & Reid, D. A. (2016). Argumentation Analysis for Early Career Researchers. In G. Kaiser & N. Presmeg (Eds.), Compendium for Early Career Researchers in Mathematics Education (pp. 3–32).

Kosko, K. W., & Zimmerman, B. S. (2019). Emergence of argument in children’s mathematical writing. Journal of Early Childhood Literacy, 19(1), 82–106. https://doi.org/10.1177/1468798417712065

Laamena, C. M., Nusantara, T., Irawan, E. B., & Muksar, M. (2018). How do the Undergraduate Students Use an Example in Mathematical Proof Construction: A Study based on Argumentation and Proving Activity. International Electronic Journal of Mathematics Education, 13(3), 185–198. https://doi.org/10.12973/iejme/3836

Lakatos, I. (1976). Proofs and refutations. The logic of mathematical discovery. Cambridge University Press.

Leron, U., & Zaslavsky, O. (2013). Generic proving: Reflections on scope and method. For the Learning of Mathematics, 33(3), 24–30. https://doi.org/10.1515/9781400865307-017

Mason, J., & Pimm, D. (1984). Generic examples: Seeing The General in The Particular. Educational Studies in Mathematics, 2(231–250).

Mills, M. (2014). A framework for example usage in proof presentations. Journal of Mathematical Behavior, 33, 106–118. https://doi.org/10.1016/j.jmathb.2013.11.001

Pedemonte, B. (2001). Some Cognitive Aspects of the Relationship between Argumentation and Proof in Mathematics. In M. van den Heuvel-Panhuizen (Ed.), Proceeding of the 25th conference of the international group for the Psychology of Mathematics Education PME-25 (pp. 33–40).

Pedemonte, Bettina. (2007). How can the relationship between argumentation and proof be analysed? Educational Studies in Mathematics, 66(1), 23–41. https://doi.org/10.1007/s10649-006-9057-x

Rø, K., & Arnesen, K. K. (2020). The opaque nature of generic examples: The structure of student teachers’ arguments in multiplicative reasoning. Journal of Mathematical Behavior, 58(December 2019), 100755. https://doi.org/10.1016/j.jmathb.2019.100755

Siswono, T. Y. E., Hartono, S., & Kohar, A. W. (2020). Deductive or inductive? prospective teachers’ preference of proof method on an intermediate proof task. Journal on Mathematics Education, 11(3), 417–438. https://doi.org/10.22342/jme.11.3.11846.417-438

Tall, D., & Mejia-Ramos, J. P. (2010). The long-term cognitive development of reasoning and proof. Explanation and Proof in Mathematics: Philosophical and Educational Perspectives, due, 137–149. https://doi.org/10.1007/978-1-4419-0576-5_10

Uğurel, I., Morah, S., Koyunkaya, M. Y., & Karahan, O. (2016). Pre-service Secondary Mathematics Teachers’ Behavior in the Proving Process. Eurasia Journal of Mathematics, Science and Technology, 12(2), 203–231.

Watson, A., & Mason, J. (2005). Mathematics as a constructive activity: Learners generating examples. Erlbaum.

Yopp, D. A., & Ely, R. (2016). When does an argument use a generic example? Educational Studies in Mathematics, 91(1), 37–53. https://doi.org/10.1007/s10649-015-9633-z

Yopp, D. A., Ely, R., & Johnson-Leung, J. (2015). Generic example proving criteria for all. For the Learning of Mathematics, 35(3), 8–13.


Article Metrics

Abstract has been read : 1008 times
PDF file viewed/downloaded: 0 times


DOI: http://doi.org/10.25273/jipm.v10i2.8903

Refbacks

  • There are currently no refbacks.


Copyright (c) 2021 JIPM (Jurnal Ilmiah Pendidikan Matematika)

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

 

View JIPM Stats

 

JIPM indexed by:

       

Copyright of JIPM (Jurnal Ilmiah Pendidikan Matematika) ISSN 2502-1745 (Online) and ISSN 2301-7929 (Print)