Struktur Lapisan Pemahaman Konsep Turunan Fungsi Mahasiswa Calon Guru Matematika

Viktor Sagala


Prospective mathematics teachers should have met the Pirie-Kieren model of understanding indicators, to become professional teachers. The purpose of this research is to describe the layers of understanding structure that is filled by students of mathematics teacher prospectives. The description is based on a model hypothesized by Pirie-Kieren. Research subjects selected from female and male mathematics teacher prospective students have been given the task of understanding the concept of derivative functions and interviewed. Data collected from students’ answers from worksheets before the interview, students’ answers from worksheets during interviews, and interview transcripts. After the data were analyzed qualitatively, the description of the understanding layer structure of two subjects grouped by the original Pirie-Kieren Model was obtained. The subjects of female had met the indicators of primitive knowing, then there are the processes of image doing and image reviewing on the layer structure of image making towards image having, then image seeing and image saying on the layer of image having to property noticing, then there are the processes of property predicting and property recording on the layer of property noticing towards formalizing, then there are the processes of method applying and method justifying on the layer of formalizing  towards observing, then there are the processes of future identifying and feature prescribing on  the layer of observing towards structuring, and there are the prosesses of theorem conjecturing and theorem proving on the layer of structuring towards inventising. She almost fulfilled the inventising layer. Male subjects also meet the same understanding indicators as women. Both subjects have almost fulfilled a layer of creation, we called inventisingoid


understanding, understanding layers, structure of layers, structure of understanding, mathemathic teacher prospectives

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Asmaningtyias, Y.T. (2012). Kemampuan Mathematika Laki-laki dan Perempuan. Jurnal Pendidikan dan Pembelajaran Dasar, 1(2), 1-15.

Dubinsky, E., McDonald, M.A. (2001). APOS: A Constructivist Theory of Learning in Undergraduate Mathematics Education Research. Dalam D. Holton (Ed.) The Teaching and Learning of Mathematic at University Level: An ICMI Study. pp. 273-280. Dordrecht, NL: Kluwer.

Fitri, N., Munzir, S., & Duskri, M. (2017). Meningkatkan kemampuan Representasi Matematis melalui Penerapan Model Problem Based Learning, Jurnal Didaktik Matematika, 4(1), 59-67.

Halat, E., & Peker, M. (2011). The impacts of mathematical representations developed through WebQuest and spreadsheet activities on the motivation of pre-service elementary school teachers. TOJET: The Turkish Online Journal of Educational Technology, 10(2), 259-263.

Hwang, W. Y., Chen, N. S., Dung, J. J., & Yang, Y. L. (2007). Multiple Representation Skills and Creativity Effects on Mathematical Problem Solving using a Multimedia Whiteboard System. Journal of Educational Technology & Society, 10(2), 191-212.

Iswahyudi, G. (2012). Aktivitas Metakognisi dalam Memecahkan Masalah Pembuktian Langsung Ditinjau dari Gender dan Kemampuan Matematika. Makalah Seminar Nasional Program Studi Pendidikan Matematika. Surakarta: Universitas Negeri Surakarta.

Jones, B. F. & Knuth, R.A. (1991). What does Research Say about Mathematics? [on-line]. Tersedia di http://www.

Manu, S. S. (2005). Language switching and mathematical understanding in Tongan classrooms: An investigation. Direction: Journal of Educational Studies, 27(2), 47-70.

Martin, L., LaCroix, L., & Fownes, L. (2005). Folding Back and the Growth of Mathematical Understanding in Workplace Training. Adults Learning Mathematics, 1(1), 19-35.

Meel, D. E. (2003). Models and theories of mathematical understanding: Comparing Pirie and Kieren’s model of the growth of mathematical understanding and APOS theory. CBMS Issues in Mathematics Education, 12, 132-181.

Moleong, J.L . (2010). Metodologi Penelitian Kualitatif. Bandung: PT Remaja Rosdakarya.

Mousley, J. (2005). What does mathematics understanding look like?. In Building connections: research, theory and practice: proceedings of the annual conference held at RMIT. Melbourne, Merga.

Parameswaran, R. (2010). Expert Mathematics' Approach to Understanding Definitions. Mathematics Educator, 20(1), 43-51.

Pegg, J., & Tall, D. (2005). The fundamental cycle of concept construction underlying various theoretical frameworks. ZDM, 37(6), 468-475.

Pirie, S., & Kieren, T. (1994). Growth in mathematical understanding: How we can characterize it and how we can represent it. Educational Studies in Mathematics, 9, 160-190.

Sagala, V. (2017). “Profil Lapisan Pemahaman Konsep Turunan Fungsi Mahasiswa Calon Guru Berdasarkan Gender”. Disertasi. Pascasarjan UNESA Surabaya.

Schultz, J., & Waters, M. (2000). Why Representations? Mathematics Teacher, Procedia - Social and Behavioral Sciences, 93(6), 448-453.

Susiswo (2015). “Folding back Mahasiswa dalam Menyelesaikan Masalah Limit”. Disertasi. Universitas Negeri Malang.

Tall, D. (1992). The transition from arithmetic to algebra: Number patterns, or proceptual programming. Makalah di presentasikan pada Mathematics Teaching and Learning “From Numeracy to Algebra”, September 2-3, Queensland University of Teachnology, Brisbane.



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Jurnal Didaktik Matematika

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