Muchamad Subali Noto, Nanang Priatna, Jarnawi Afgani Dahlan


Several studies related to mathematical proof have been done by many researchers on high-level materials, but not yet examined on the material of transformation geometry. The aim of this research is identification learning obstacles pre-service teachers on transformation geometry. This study is qualitative research; data were collected from interview sheets and test. There were four problems given to 9 pre-service mathematics teachers. The results of this research were as follows: learning obstacles related to the difficulty in applying the concept; related to visualize the geometry object; related to obstacles in determining principle; related to understanding the problem and related obstacles in mathematical proofs such as not understanding and unable to express a definition, not knowing to use the definition to construct the proof, not understanding the use of language and mathematical notation, not knowing how to start the proof.


Mathematical proof; Pre-service mathematics teachers; Geometry

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Ahamad, S. N. S. H., Li, H. C., Shahrill, M., & Prahmana, R. C. I. (2018). Implementation of problem-based learning in geometry lessons. Journal of Physics: Conference Series, 943(1), 012008.

Antonini, S., & Mariotti, M. A. (2008). Indirect proof: What is specific to this way of proving? ZDM International Journal on Mathematics Education, 40(3), 401–412.

Arzarello, F., Micheletti, C., Olivero, F., & Robutti, O. (1998). A model for analyzing the transition to formal proofs in geometry. In A. Olivier & K. Newstead (Eds.), Proceedings of the 22nd PME Conference, 24–31. Stellenbosch, Republic of South Africa: PME.

Balacheff, N. (1988). Aspects of proof in pupils’ practice of school mathematics. In D. Pimm (Ed.), Mathematics, teachers and children, 216–235. London: Hodder & Stoughton.

Christou, C., Mousoulides, N., Pittalis, M and Pantazi, D.P. (2004). Proofs Through Exploration In Dynamic Geometry Environments. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education 2004, 215–222.

Duval, R. (1991). Structure du raisonnement déductif et apprentissage de la démonstration. Educational Studies in Mathematics, 22(3), 233–261.

Fachrudin, A. D., Putri, R. I. I., & Darmawijoyo. (2014). Building Students' Understanding of Quadratic Equation Concept Using Naïve Geometry. Journal on Mathematics Education, 5(2), 192-202.

Hanna, G., & de Villiers, M. (Eds.). (2012). Proof and proving in mathematics education. Dordrecht, The Netherlands: Springer.

Harel, G., & Sowder, L. (1998). Students’ proof schemes: Results from exploratory studies. In A. H. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), Research in collegiate mathematics education, 234–283. Providence, RI: American Mathematical Society.

Heinze, A., & Reiss, K. (2003). Reasoning and proof: Methodological knowledge as a component of proof competence. Proceedings of the third conference of the European Society for Research in mathematics education, 1-10.

Jones, K & Rodd, M. (2001). Geometry and Proof. Proceedings of the British Society for Research into Learning Mathematics 21(1), 95-100.

Komatsu, K. (2017). Fostering empirical examination after proof construction in secondary school geometry. Educational Studies in Mathematics, 96(2), 129–144.

Knuth, E.J. (2002). Teachers’ Conception of Proof in the Context of Secondary School Mathematics. Journal of Mathematics Teacher Education 5(1), 61–88.

Marrades, R., & Gutiérrez, A. (2000). Proofs produced by secondary school students learning geometry in a dynamic computer environment. Educational Studies in Mathematics, 44(2), 87–125.

Mariotti, M. A. (2001). Introduction To Proof: The Mediation Of A Dynamic Software Environment. Educational Studies in Mathematics 44(1), 25–53.

Mariotti, M. A. (2006). Proof and proving in mathematics education. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education. Rotterdam. The Netherlands: Sense.

Mata-pereira, J., & Ponte, J. (2017). Enhancing students’ mathematical reasoning in the classroom: teacher actions facilitating generalization and justification. Educational Studies in Mathematics, 96(2), 169–186.

Maya, R., & Sumarmo, U. (2014). Mathematical Understanding and Proving Abilities: Experiment With Undergraduate Student By Using Modified Moore Learning Approach. Journal on Mathematics Education, 2(2), 231-250

Novita, R., Prahmana, R. C. I., Fajri, N., & Putra, M. (2018). Penyebab kesulitan belajar geometri dimensi tiga. Jurnal Riset Pendidikan Matematika, 5(1), 18-29.

Nurhasanah, F., Kusumah, Y. S., & Sabandar, J. (2017). Concept of triangle: Examples of mathematical abstraction in two different contexts. International Journal on Emerging Mathematics Education, 1(1), 53-70.

Rizkianto, I., Zulkardi, & Darmawijaya. (2013). Constructing Geometric Properties of Rectangle, Square, and Triangle in the Third Grade of Indonesian Primary Schools. Journal on Mathematics Education, 4(2), 160-171.

Reid, D. A., & Knipping, C. (2010). Proof in mathematics education. Rotterdam, The Netherlands: Sense.

Stefanowicz, A., & Kyle, J. (2014). Proofs and Mathematical Reasoning. University of Birmingham. Retrieved from

Stylianides, G. J., Stylianides, A. J., & Philippou, G. N. (2007). Preservice teachers’ knowledge of proof by mathematical induction. Journal of Mathematics Teacher Education, 10(3), 145–166.

Sukirwan, Darhim, Herman, T., & Prahmana, R. C. I. (2018). The students’ mathematical argumentation in geometry. Journal of Physics: Conference Series, 943(1), 012026.

Suryadi, D. (2007). Model Bahan Ajar dan Kerangka-Kerja Pedagogis Matematika Untuk Menumbuhkembangkan Kemampuan Berpikir Matematik Tingkat Tinggi [Model of Teaching Materials and Framework of Mathematical Pedagogy for Developing Higher Mathematical Thinking Ability]. Unpublished Research Report. Bandung: SPS UPI.



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