Fragmentation of the Thinking Structure of Translation in Solving Mathematical Modelling Problems

Kadek Adi Wibawa


Fragmentation of the thinking structure is the process of construction of information in the brain that is inefficient, incomplete, and not interconnected, and hinders the process of mathematical problem solving. In solving mathematical modeling problems, students need to do translation thinking which is useful for changing the initial representation (source representation) into a new representation (target representation). This study aims to discover how the occurrence of the fragmentation of the thinking structure of translation within students in their solving of mathematical modeling problems. The method used is descriptive qualitative with the instrument in the form of one question for the mathematical modeling of necklace pendants and semi-structured interview sheets. The results showed that there were three errors that occurred in solving mathematical modeling problems. First, the error in changing a verbal representation to a graph. Secondly, errors in changing a graphical representation to symbols (algebraic form). Thirdly, errors in changing graphical representation and symbols into mathematical models. The three errors that occur are described based on the four categories of Bosse frameworks (Bosse, et al., 2014), namely: (1) unpacking the source (UtS), (2) preliminary coordination (PC), (3) constructing the target (CtT), and (4) determining equivalence (DE). In this study, there were 3 subjects who experienced fragmentation of the thinking structure in solving mathematical modeling problems. One of the highlights is the fragmentation of the structure of translation thinking often starts from the process of unpacking of the source due to the incompleteness of considering all the available source details.


Fragmentation of thinking structure; translation process; problem solving; mathematical modelling

Full Text:



Booth, J.L., Barbieri, C., Eyer, F., & Pare-Blagoev, E.J. (2014). Persistent and Pernicious Errors in Algebraic Problem Solving. Journal of Problem Solving, 7, 10-23.

Bosse, M.J., Adu-Gyamfi, K., & Chandler, K. (2014). Students’ Differentiated Translation Processes. International Journal for Mathematics Teaching and Learning. 1-28. Retrieved from

Bossé, M.J., Adu-Gyamfi, K., & Cheetham, M. (2011). Assessing the Difficulty of Mathematical Translations: Synthesizing the Literature and Novel Findings. International Electronic Journal of Mathematics Education, 6(3), 113-133.

Cobb, P., Yackel, E., & Wood, T. (1992). A Constructivist Alternative to the Representational View of Mind in Mathematics Education. Journal for Research in Mathematics Education, 23(1), 2-3.

Creswell, J.W. (2007). Qualitative Inquiry and Research Design. Choosing among Five Approaches (2nd ed.). Thousand Osks, CA: Sage.

Dorko, A. (2011). Calculus Student’ Understanding of Area and Volume in Non-Calculus Context. Unpublished Masters Thesis, University of Maine at Orono.

Kaput, J.J. (1987). Representation Systems and Mathematics. Janvier (Ed.), Problems of Representation in Teaching and Learning Mathematics, (19–26). Hillsdale, NJ: Erlbaum.

Kiat, S.E. (2005). Analysis of Student’ Difficulties in Solving Integration Problems. The Mathematics Educator, 9(1), 39-59.

Moleong, L.J. (2007). Metodologi Penelitian Kualitatif [Qualitative Research Methodology]. Bandung: PT Remaja Rosdakarya Offset.

Musser, G.L., Burger, W.F., & Peterson, B.E. (2011). Mathematics for Elementary Teachers a Contemporary Approach, Ninth Edition. United States of America: John Wiley & Sons, Inc.

Serhan, D. (2015). Students’ Understanding of the Definite Integral Concept. International Journal of Research in Education and Science (IJRES), 1(1), 84-88.

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

Skemp, R.R. (1982). Psychology of Learning Mathematics, 2nd Edition. London: Penguin Books.

Skemp, R.R. (2006). Relational Understanding and Instrumental Understanding. Mathematics Teaching in the Middle School, 12(2), 88-95.

Sternberg, R.J., & Sternberg, K. (2012). Cognitive Psychology, Sixth Edition. USA: Wadsworth Cengage Learning.

Subanji. (2015). Teori Kesalahan Konstruksi Konsep dan Pemecahan Masalah Matematika [Error Theory Construction Concepts and Mathematical Problem Solving]. Malang: Universitas Negeri Malang (UM Press).

Subanji. (2016). Teori Defragmentasi Struktur Berpikir dalam Mengonstruksi Konsep dan Pemecahan Masalah Matematika [Defragmentation Theory of Structure of Thinking in Constructing Concepts and Solving Mathematical Problems]. Malang: Universitas Negeri Malang (UM Press).

Veloo, A., Krishnasamy, H.N., & Abdullah, W.S.W. (2015). Types of Student Errors in Mathematical Symbols, Graphs, and Problem-Solving. Asian Social Science, 11(15), 324-334.

Wahono, R.S. (2009). Defragmentasi Otak: Cara Cerdas menjadi Cerdas [Brain Defragmentation: The Smart Way to Be Smart]. Universitas Bangka Belitung. Retrieved from menulengkap.php? judul=Defragmenting%20Otak%20:%20Cara%20Cerdas%20Menjadi%20Cerdas&&nomorurut_artikel=380.

Wibawa, K.A., Subanji, & Chandra, T.D. (2013). Defragmenting Berpikir Pseudo dalam Memecahkan Masalah Limit Fungsi [Defragmenting Pseudo Thinking in Solving Function Limit Problems]. Seminar Nasional Exchange of Experiences Teachers Quality Improvement Program (TEQIP). Malang: Universitas Negeri Malang.

Yin, R.K. (2011). Qualitative Research from Start to Finish. New York: The Guilford Press.

Yost, D. (2009). Integration: Reversing Traditional Pedagogy. Australian Senior Mathematics Journal, 22, 37-40.

Zakaria, E., Ibrahim, & Maat, S.M. (2010). Analysis of Students’ Error in Learning of Quadratic Equations. International Education Studies, 3(3), 105-110.



  • There are currently no refbacks.

Indexed by:


Southeast Asian Mathematics Education Journal
SEAMEO Regional Centre for QITEP in Mathematics
Jl. Kaliurang Km 6, Sambisari, Condongcatur, Depok, Sleman
Yogyakarta, Indonesia
Telp. +62 274 889955

p-ISSN: 2089-4716 | e-ISSN: 2721-8546

Southeast Asian Mathematics Education Journal is licensed under a Creative Commons Attribution 4.0 International License

View My Stats

Supported by: