Profile of Understanding Layers of Function Derivatives and Folding Back of College Student Prospective Teachers of Mathematics by Gender

Viktor Sagala


This research aimed to describe the profile of understanding layers 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 .
The results showed that there was no difference between the achievement of a layers 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 understanding layer ie inventisingoid. But both subjects distinc 10 (ten) items the process of achieving this understanding. Women performed 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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Pirie,S.&Kieren,T, Growth in Mathematical Understanding: How we

Can Characterize it an How can Represent it, Education Studies in

Mathematics Volume 9:160-190A, 1994.

Skemp, R, Relational Understanding and Instrumental Understanding,

Mathematics Teaching, 77:20-26, 1976.

Skemp, R, Symbolic Understanding: Mathematics Teaching, 99:59-61,

Mousley, J. (2005). What Does Mathematics Understanding Look Like?

Makalah disajikan pada Annual Converence Held at RMIT, Melbourne,

-9 Juli 2005. [Online]. Available: Diakses 12 Januari 2015

Pegg, J. & Tall, D. (2005). The fundamental cycle of concept

construction underlying various theoretical frameworks

Proceedings of PME Volume 37, Issue 6, pp 468-475. [Online].


Herscovics, N.&Bergeson,J.C, Models of Understanding. Zentralblatt

fur Didaktik der Mathematik (February), 75-88, 1983.

Cai,J; Lane,S; Jacabcsin,M, “Assesing Students Mathematical

Communication”, Official Journal of Science and Mathematics. 96(5),

Hudojo, Herman, Representasi Belajar Berbasis Masalah. Jurnal

Matematika dan Pembelajarannya, ISSN: 085-7792, Volume viii, edisi

khusus, 2002.

Parameswaran, R, Expert Mathematicians Approach to Understanding

Definition, The Mathematic Educator Vol 20, Number I:45-51, 2010.

Dubinsky & McDonald, 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, 2001.

Dubinsky, E & Wilson,Robin. (2013). “High School Students’

Understanding of the Function Concept”. the Journal of Mathematical

Behavior 32 (2013) 83 101.For a pre-publication draft PDF. [Online].


Katsberg. (2002). Understanding Mathematical Concepts : The Case of

University Logaritmic Function. Dissertation. Departement of

Mathematics Lulea. [Online]. Available:


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 KwaZulu‐

[Online]. Available:

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. diakses 20 Januari 2015

Meel, D.E, 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, Metodologi Penelitian Kualitatif. Edisi Revisi, Bandung.

PT Remaja Rosdakarya, 2010.

smaningtyas,Y.T. (2012). Kemampuan Mathematika Laki-laki dan

Perempuan, Jurnal PendidikanMatematika. [Online]. Available: article.php? article=115727&val=5278

Radua, Joaquim; Phillips, Mary L.; Russell, Tamara; Lawrence, Natalia;

Marshall, Nicolette; Kalidindi, Sridevi; El-Hage, Wissam; McDonald,

Colm; et al, "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, 2010.

Santos, A.G, Thomas, M.O.J, “The Growth of Schematic Thinking

about Derivative”, The Journal of Mathematical Education University

of Auckland, 2003.

Susiswo (2014) Folding back Mahasiswa dalam Menyelesaikan

Masalah Limit, Disertasi, Universitas Negeri Malang. [Online].


-153.pdfdiakses 10-02-2015


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