Nonik Indrawatiningsih(1*), Andika Setyo Budi Lestari(2),

(1) Universitas Negeri Surabaya
(2) Universitas PGRI Wiranegara
(*) Corresponding Author


The structure of thinking is a representation of the thought process in the form of a problem-solving flow that is carried out by a person when he resolves a problem. many students make mistakes in solving problems. One way that can be done to overcome these errors is to defragment the structure of thought. This study aims to describe the students’ erroneous thinking structure in solving mathematical argument and the defragmenting efforts. The students of 10th Grade of high school in Pasuruan, East Java, Indonesia, were involved as research subjects. They were selected based on three criteria, namely low, moderate and high level of procedural error. The activity of ‘think out loud’ was used to observe the errors made by students in solving mathematical argument. The data obtained from this activity were codified and later used as a basis to perform the defragmenting process. Based on the findings of this study, it can be concluded that procedural errors in solving mathematical argument are in the form of error in determining the value of x from an equation, modeling an argument, and proving a valid argument. Defragmenting was done using scaffolding approach to improve students' thinking structure in solving mathematical problems


Defragmenting; Thinking Structure; Mathematical argument; Scaffolding

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A. Karal, M., & Riccomini, P. J. (2016). General Education Teachers ’ Perceptions About Students With. International Journal of Special Education, 31, 23–31.

Anghileri, J. (2006). Scaffolding Practices that Enhance Mathematics. Journal of Mathematics Teacher Education, 33–52.

Bahrudin, M. A., Indrawatiningsih, N. &, & Nazihah, Z. (2019). Defragmenting Struktur Berpikir Siswa SMP dalam Menyelesaikan Masalah Bangun Datar. Indonesia Mathematics Education (IndoMath), 2(2), 127–140.

Bulent, D., Erdal, B., Ceyda, A., Betul, T., Nurgul, C., & Cevahir, D. (2016). An analysis of teachers questioning strategies. Educational Research and Reviews, 11(22), 2065–2078.

Chick, H., & Mccrae, B. (2005). Argumentation Profile Charts As Tools For Analysing Students ’ Argumentations. Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, Pp. 281-288. Melbourne: PME, 4, 281–288.

Conner, A., 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. 2014.

Creswell, J. (2012). Educational Research. Pearson Education, Inc., 501 Boylston Street, Boston, MA 02116.

Das, R., & Chandra, D. G. (2013). Math Anxiety : The Poor Problem Solving Factor in. International Journal of Scientific and Research Publications, 3(4), 1–5.

Indrawatiningsih, N. (2018). Arguments in Critical Thinking Ability.IcoMse (2018)

Jorczak, R. L. (2011). An information processing perspective on divergence and convergence in collaborative learning. Computer-Supported Collaborative Learning, 207–221.

Kirshner, D. (2014). Interference of Instrumental Instruction in Subsequent Relational Learning. JRME, November 2000.

Lee, Kosze & Smith III, J. P. (2009). Cognitive and Linguistic Challenges in Understanding Proving. Proceedings of the ICMI Study 19 Conference: Proof and Proving in Mathematics Education, 2, 2–21.

Legutko, M. (2008). of Mathematics Teaching Research : (Issue 226685).

NCTM. (2000). Introduction: Perspectives on Principles and Standards for School Mathematics. School Science and Mathematics, 101(6), 277–279.

Pape, S. J. (2012). Middle School Children ’ s Behavior : A Cognitive Analysis from a Reading Comprehension Perspective. Journal for Research in Mathematics Education, 35(3).

Sakif, S. (2014). E – 58 Defragmenting Of Thinking Process Through Cognitive Mapping To Fix S tudent ’ s Error In Solving The Problem Of Algebra. This Paper Has Been Presented at International Seminar on Innovation in Mathematics and Mathematics Education 1st ISIM-MED 2014 “Innovation and Technology for Mathematics and Mathematics Education” Department of Mathematics Education,Yogyakarta State Univ.

Salma, J., & Sherwin, R. (2012). Students ’ difficulties in comprehending. International researchers, 1.

Stylianides, A. J., & Bieda, K. N. (2016). Proof and Argumentation In Mathematics Education Research. Icmi, 315–351.

Subanji, & Nusantara, T. (2018). Defragmenting Proses Berpikir Matematik melalui Pemetaan Kognitif untuk Memperbaiki Kesalahan Matematika Siswa. Ditlitabmas Ditjen DIKTI, 9(2), 2–4.

Supiarmo, M. G. (2021). Defragmenting Student’s Thinking Structures in Solving Mathematical Problems on Pisa Model. (JIML) Journal of Innovative Mathematics Learning, 4(4), 167–177.

Van Ness, C. K., & Maher, C. A. (2018). Analysis of the argumentation of nine-year-olds engaged in discourse about comparing fraction models. Journal of Mathematical Behavior, January, 0–1.

Whitenack, J. W., & Knipping, N. (2002). Argumentation, instructional design theory and students’ mathematical learning: A case for coordinating interpretive lenses. Journal of Mathematical Behavior, 21(4), 441–457.

Wibawa, K A, Nusantara, T., Subanji, & Parta, I. N. (2018). Defragmentation of Student ’ s Thinking Structures in Solving Mathematical Problems based on CRA Framework Defragmentation of Student ’ s Thinking Structures in Solving Mathematical Problems based on CRA Framework. IOP Conf. Series: Journal of Physics: Conf. Series 1028.

Wibawa, Kadek Adi, Nusantara, T., Subanji, & Nengah Parta, I. (2018). Defragmentation of Student’s Thinking Structures in Solving Mathematical Problems based on CRA Framework. Journal of Physics: Conference Series, 1028(1).

Wibawa, Kadek Adi, Payadnya, I. P. A. A., Atmaja, I. M. D., & Simons, M. D. (2020). Defragmenting structures of students’ translational thinking in solving mathematical modeling problems based on CRA framework. Beta: Jurnal Tadris Matematika, 13(2), 130–151.

Wulandari, S., & Gusteti, M. U. (2021). Defragmentation of Preservice Teacher’s Thinking Structures in Solving Higher Order Mathematics Problem. Journal of Physics: Conference Series, 1940(1).

Yackel, E. (2002). What we can learn from analyzing the teacher’s role in collective argumentation. Journal of Mathematical Behavior, 21(4), 423–440.

Yackel, E., & Cobb, P. (1996). Sociomathematical Norms, Argumentation, and Autonomy in Mathematics. Journal for Research in Mathematics Education, 27(4), 458.

Yackel, E., Rasmussen, C., & King, K. (2000). Social and sociomathematical norms in an advanced undergraduate mathematics course. The Journal of Mathematical Behavior, 19(3), 275–287.

Zazkis, R., & Chernoff, E. J. (2015). What makes a counterexample exemplary ? What makes a counterexample exemplary ? July 2008.



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