Profil Lapisan Pemahaman Konsep Turunan Fungsi dan Bentuk Folding Back Mahasiswa Calon Guru Berkemampuan Matematika Tinggi Berdasarkan Gender

Viktor Sagala (1)
(1) Universitas Negeri Surabaya, Indonesia


This research aimed to describe the profile of understanding layers of understanding the concept of the function’s derivative and folding back college student prospective teachers of mathematics by gender. This study used a qualitative descriptive approach. The data obtained is validated, then the analysis step-by- step reduction, data presentation, categorization, interpretation and inference. The analysis process is guided to the understanding of the model which hypothesizes Pirie&Kieren owned eight layers understanding students. The results showed that there was no difference between the achievement of a layers of understanding of the subject of women and man, both of them have an indicator layers of understanding ie; primitive knowing, image making, image having, property noticing, formalising, observing and structuring, then reaching also the first indicator (In1) of inventising layer, and indicators "ask questions about graphs the third-degree polynomial function" that leads to the second indicator (In2) of inventising layer. Based on the indicators of these, both subjects can be put in a category understanding layer ie oida inventising. But both subjects distinc 10 (ten) items the process of achieving this understanding, including in providing an example of a polynomial of fourth degree, woman began with equations, determining the intersections with the X-axis or the line x=k, drawing the X-axis and Y-axis, plot the points of intersection, divide into several intervals, then calculate some value functions to perform each test point intervals, and then describe the graph. Meanwhile, the man gave an example of a polynomial of fourth degree in the form of images, then determine the similarities, each interval point test done to test and verify that the correct graph drawn afterwards. Women made twice folding back the form of "off-topic", and man made that once. Instead of man performed twice folding back the form "working on the deeper layers", both subjects do not perform folding back the form "cause discontinuous".

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Asmaningtyas,Y.T (2012). Kemampuan Mathematika Laki-laki dan Perempuan, Jurnal PendidikanMatematika. article.php? article=115727&val=5278

Cai, Lane, Jacabcsin (1996). “Assesing Students’ Mathematical Communicationâ€. Official Journal of Science and Mathematics. 96 (5).

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

Dubinsky, E & Wilson,Robin (2013) “High School Students’ Understanding of the Function Conceptâ€. the Journal of Mathematical Behavior 32 (2013) 83 101.For a pre-publication draft PDF,

Herscovics, N.&Bergeson,J.C.(1983). Models of Understanding. Zentralblatt fur Didaktik der Mathematik (February), 75-88

Hudojo, Herman (2002). Representasi Belajar Berbasis Masalah. Jurnal Matematika dan Pembelajarannya. ISSN: 085-7792. Volume viii, edisi khusus.

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

Katsberg(2002) Understanding Mathematical Concepts : The Case of University Logaritmic Function. Dissertation. Departement of Mathematics Lulea. Online. http:/, diakses 20-01-2015

Maharaj, A.(2003) “An APOS Analysis of Students’ Understanding of the Concept of a Limit of a Function†, School of Mathematical Sciences University of KwaZuluâ€ ,

Manu(2005) Language Switching and Mathematical Understanding in Tongan Classrooms: An Investigation. Journal of Educational Studies. Vol 27, Nomor 2, diakses 6 Maret 2015

Martin, Lyndon (2008) Folding Back and Growth of Mathematical Understanding in Workplace Training, dimuat dalam Journal online Research Gate 239918621_ Folding_Back_and_the_Growth_of_Mathematical_Understanding_in_Workplace_Training. diakses 20 Januari 2015

Meel, D.E.(2003) Model and Theories of Mathematical Understanding: Comparing Pirie-Kieren’s Model of the Growth of Mathematical Understanding and APOS Theory. CMBS Issues in Mathematical Education.Volume 12, 2003

Moleong,J.(2010) Metodologi Penelitian Kualitatif. Edisi Revisi. Bandung. PT Remaja Rosdakarya

Mousley, J.(2005) What Does Mathematics Understanding Look Like? Makalah disajikan pada Annual Converence Held at RMIT, Melbourne, 7-9 Juli 2005 (Online), ( Diakses 12 Januari 2015.

Parameswaran, R(2010) Expert Mathematicians Approach to Understanding Definition, The Mathematic Educator Vol 20, Number I:45-51

Pegg, J. & Tall, D.(2005) The fundamental cycle of concept construction underlying various theoretical frameworksProceedings of PME Volume 37, Issue 6, pp 468-475 Online

Pirie,S.&Kieren,T. (1994) Growth in Mathematical Understanding: How we Can Characterize it an How can Represent it. Education Studies in Mathematics Volume 9:160-190

Radua, Joaquim; Phillips, Mary L.; Russell, Tamara; Lawrence, Natalia; Marshall, Nicolette; Kalidindi, Sridevi; El-Hage, Wissam;

McDonald, Colm; et al. (2010). "Neural response to specific components of fearful faces in healthy and schizophrenic adults".NeuroImage 491):939946. doi:10.1016/j.neuroimage.2009.08.030. PMID 19699306

Santos, A.G, Thomas, M.O.J (2003) “The Growth of Schematic Thinking about Derivativeâ€, The Journal of Mathematical Education University of Auckland

Sfard, Anna. (2000). On reform movement and the limits of mathematicaldiscourse. Mathematical Thinking and Learning, 157–189.

Skemp, R.(1976). Relational Understanding and Instrumental Understanding. Mathematics Teaching, 77:20-26

Skemp, R. (1987) Symbolic Understanding: Mathematics Teaching, 99:59-61

Slaten (2011) Effective Folding Back via Student Research of the History of Mathematics. Proceedings of the 13th Annual Converence of Research in Undergraduate Mathematics Education.Online., diakses 02-01-2015

Susiswo (2014) Folding back Mahasiswa dalam Menyelesaikan Masalah Limit, Disertasi, Universitas Negeri Malang. Jurnal online. 10-02-2015


Viktor Sagala (Primary Contact)
Sagala, V. (2016). Profil Lapisan Pemahaman Konsep Turunan Fungsi dan Bentuk Folding Back Mahasiswa Calon Guru Berkemampuan Matematika Tinggi Berdasarkan Gender. MUST: Journal of Mathematics Education, Science and Technology, 1(2), 183–198.

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