The Process of Thinking by Prospective Teachers of Mathematics in Making Arguments

Lia Budi Tristanti


This study aimed to describe the process of thinking by prospective teachers of mathematics in making arguments. It was a qualitative research involving the mathematics students of STKIP PGRI Jombang as the subject of the study. Test and task-based semi structural interview were conducted for data collection. The result showed that 163 of 260 mathematics students argued using inductive and deductive warrants. The process of thinking by the prospective teachers of mathematics in making arguments had begun since they constructed their very first idea by figuring out some objects to make a conclusion. However, they also found a rebuttal from that conclusion, though they did not further describe what such rebuttal was. Therefore, they decided to construct the second ideas in order to verify the first ones through some pieces of definition.


Thinking, Argument, Warrant, Inductive, Deductive


A. Ahmadi and W. Supriyadi, “Psikologi Belajar”. Jakarta: Rineka Cipta, 2004.

D. McGregor, “Developing Thinking; Developing Learning”. New York: The McGraw-Hill Companies, 2007.

W.S. Kuswana, “Taksonomi Berpikir”. Bandung: Remaja Rosdakarya, 2013.

T. Y. E. Siswono, “Model Pembelajaran Matematika Berbasis Pengajuan dan Pemecahan Masalah untuk Meningkatkan Kemampuan Berpikir Kreatif”. Surabaya: Unesa University Press, 2008.

Subanji, “Teori Berpikir Pseudo Penalaran Kovariasonal”. Malang: Penerbit Universitas Negeri Malang (UM Press), 2011.

R. Swartz and C. McGuinness, “Developing and Assessing Thinking Skills Project”, 2014.. Tersedia di 198aa56ce2f8b5ab2/finalreportpart1.pdf. accessed on 11th May 2017, at 08.31 pm.

R.J. Swartz, S.D. Fisher, and S. Park, “Infusing the Teaching of Critical and Crative Thinking into Secondary Science”. United State of America, 1998.

J.M.P. Alexandre, P. Munoz. Cristina, A. Cuadrado, and Virginia, “Expertise, Argumenation and Scientific Practice: A Case Study about Environmental Education in the 11th Grade”. The National Association for Research in Science Teaching (NARST) annual meeting, New Orleans, April-May 2000.

B. Cerbin, “The Nature and Development of Informal”. Reasoning Skills in College Students. ERIC Document Reproduction Service No. ED 298 805, 1988.

K.L Cho and D.H Jonassen, “The Effects of Argumenation Scaffolds on Argumenation and Problem Solving”. ETR&D, Vol. 50, No. 3, 2002, pp. 5–22 ISSN 1042–1629, 2002.

G. Krummheuer, “The Narrative Character of Argumentative Mathematics Classroom Interaction in Primary Education”. European Research in Mathematics Education I: Group 4, pp. 331-341, 1999.

D. Kuhn and W. Udell, “The Development of Argument Skills”. Child Development, 74(5), 1245-1260, 2003.

L.B. Tristanti, A. Sutawidjaja, A.R. As’ari, and M. Muksar, “Modelling Student Mathematical Argumentation With Structural-Intuitive and Deductive Warrant to Solve Mathematics Problem”. Proceeding of International Conference on Educational Research and Development (ICERD 2015), pp. 130-139. ISBN 978-979-028-799-0. 130–139, 2015.

L.B. Tristanti, A. Sutawidjaja, A.R. As’ari, and M. Muksar, “Warrant Deduktif dalam Argumentasi Matematis Mahasiswa Calon Guru”. Prosiding Seminar Nasional Hasil Penelitian Pendidikan dan Pembelajaran. ISSN: 2443-1923, Vol. 2 No. 1, pp. 230-236, 2016.

L.B. Tristanti, A. Sutawidjaja, A.R. As’ari, and M. Muksar, “The Construction of Deductive Warrant Derived from Inductive Warrant in Preservice-Teacher Mathematical Argumentations”. Educational Research and Reviews, 11(17), 1696-1708, 2016.

L.B. Tristanti, A. Sutawidjaja, A.R. As’ari, and M. Muksar, “Types of Warrant in Mathematical Argumentations of Prospective-Teacher”. International Journal of Science and Engineering Investigation. 6, 68, pp 96-101, 2017.

C. D. Rosita, “Meningkatkan Kemampuan Argumentasi Matematis Melalui Pembelajaran CIRC”. Proseding Seminar Nasional Matematika dan Pendidikan Matematika STKIP Siliwangi Bandung. Volume 1, ISSN 977-2338831, 2013.

S. Toulmin, The Uses of Argument. UK: Cambridge University Press, 2003.

M. Inglis, “Dual Processes in Mathematics: Reasoning about Conditionals”. University of Warwick: A thesis submitted for the degree of Doctor of Philosophy, 2006.

M. Inglis, J.P. Mejia-Ramos, and A. Simpson, “Modelling Mathematical Argumentation: The Importance of Qualification”. Educational Studies in Mathematics, 66(1), 3-21. DOI 10.1007/s10649-006-9059-8. Published online: 5 April 2007 © Springer Science + Business Media B.V. 2007.

R. Soedjadi, “Kiat Pendidikan Matematika di Indonesia”. Jakarta: Direktorat Jenderal Pendidikan Tinggi Departemen Pendidikan Nasional, 2000.

G. Keraf, “Argumentasi dan Narasi”. Jakarta: PT Gramedia Pustaka Utama, 2010.

J. Vincent, H. Chick, and B. McCrae, “Argumenation Profile Charts as Toll for Analysing Student’s Argumenations”. Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, pp. 281-288. Melbourne: PME, 2005.

A.M. Conner, “Student Teachers’ Conceptions of Proof and Facilitation of Argumentation in Secondary Mathematics Classrooms. The Pennsylvania State University: Disertasion, 2007.

H. B. Verheij, “Evaluating Argumens Based on Toulmin’s Scheme”. Argumenation. 19: 347–371. Springer 2006. DOI 10.1007/s10503-005-4421-z, 2005.

P. Boero, “Argumentation and Mathematical Proof: A Complex, Productive, Unavoidable Relationship in Mathematics and Mathematics Education”. International Newsletter on the Teaching and Learning of Mathematical Proof, 7(8), 1999.

J. Whitenack, and E. Yackel, “Making Mathematical Argumens in the Primary Grades: The Importance of Explaining and Justifying Ideas”. Teaching Children Mathematics. Volume 8, Issue 9, pp. 524-527, May 2002.

S. Krulik, J. A. Rudnick, and E. Milou, “Teaching Mathematics in Middle School: A practical Guide”. Allyn and Bacon, 2003.

N. Balacheff, “Aspects of Proof in Pupils’ Practice of School Mathematics”. In D. Pimm (Ed.), Mathematics, Teachers and Children, (pp. 216–235). London, UK: Hodder, 1988.

A. Viholainen, “The View of Mathematics and Argumentation”. Proceedings of The Seventh Congress of The European Society For Research In Mathematics Education, CERME 7, 243-252, 2011.

W. G. Martin, and G. Harel, “Proof Frames of Preservice Elementary Teachers”. Journal For Research in Mathematics Education. Vol. 20, No 1, 41 -51, 1989.



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