You are here

Types of Warrant in Mathematical Argumentations of Prospective-Teacher

Journal Name:

Publication Year:

Abstract (2. Language): 
This paper discusses types of warrant in mathematical argumentations stated by prospective-teacher. To solve mathematics problems, a problem solver needs argumentations to determine, yield, and bolster reasonable solution. Mathematical argumentations stated by students can be analyzed using Toulmin scheme that consists of data, claim, warrant, backing, rebuttal, and qualifier. This study focused on warrant because warrant is one of determinants of the quality of an argumentation. This study aims to describe types of warrant in mathematical argumentations. This study applied qualitative approach by collecting some data from written result, think aloud and interview. The subjects of this study are asked to investigate the truth of mathematical statements. Researchers choose prospective-teacher of Mathematics Education Study as subject, because they will be teachers of mathematics, who will give influences in the development of students’ thinking process in the mathematical argumentation. The result shows that there are three types of warrant in mathematical argumentation stated by the students, they are structural-intuitive, inductive and deductive. Both inductive and structural-intuitive warrants are considered as non-deductive. Non-deductive warrant-type is used to reduce uncertainty of the conclusion. Besides, the subjects used deductive warrant-type to remove uncertainty of the conclusion.
96
101

REFERENCES

References: 

[1] Tristanti, L.B., Sutawidjaja, A., As’ari, A.R., Muksar, M. 2015. Modelling Student Mathematical Argumentation with Structural-Intuitive and Deductive Warrant to Solve Mathematics Problem. Proceeding of ICERD 2015. ISBN: 978-979-028-799-0. pp. 130–139. Surabaya. Indonesia.
[2] Cerbin, B. 1988. The Nature and Development of Informal. Reasoning Skills in College Students. ERIC Document Reproduction Service. No. ED 298 805.
[3] Cho, K.L & Jonassen, D.H. 2002. The Effects of Argumenation Scaffolds on Argumenation and Problem Solving. ETR&D, Vol. 50, No. 3, 2002, pp. 5–22 ISSN 1042–1629. Seoul, South Korea.
[4] Krummheuer, G. 1999. The Narrative Character of Argumentative Mathematics Classroom Interaction in Primary Education. European Research in Mathematics Education I: Group 4. Berlin, Germany.
[5] Kuhn, D & Udell, W. 2003. The Development of Argument Skills. Blackwell Publishing and Society for Research in Child Development, Volume74, Number5, Pages 1245-1260. JSTOR. [6] Tristanti, L. B., Sutawidjaja, A., As’ari, A. R., & Muksar, M. 2016. The Construction of Deductive Warrant Derived from Inductive Warrant in Preservice-Teacher Mathematical Argumentations. Educational Research and Reviews, 11(17), 1696-1708.
[7] Jimenez Alexandre, M.P; Pereiro Munoz, C; & Aznar Cuadrado, V. 2000. 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. PB 98-0616. No. ED 493 960.
[8] Kuhn, D. 1992. Thinking as Argument. Harvard Educational Review, 62, 155-178.
[9] Brem, S.K & Rips, L.J. 2003. Explanation and Evidence in Informal Argument. Cognitive Science Vol 24 (4) 2000, pp. 573–604 ISSN 0364-021.
[10] Klaczynski, P. 2000. Motivated scientific reasoning biases, epistemological beliefs, and theory polarization: A two-process approach to adolescent cognition.Child Development, 71, 1347–1366.
[11] Walton, N.D. 1990. What is reasoning? What is an Argument?. The Journal of Philosophy. Vol. 87, Issue 8, 399-419. JSTOR.
[12] Toulmin, S. 2003. The uses of argumen. UK: Cambridge University Press.
[13] Weber, K & Alcock, L. 2005. Using Warranted Implications to Understand and Validate Proofs. For the Learning of Mathematics 25, 1 (March, 2005), pp. 34-51. Edmonton, Alberta, Canada: FLM Publishing Association.
[14] Inglis, M., Ramos, J.P.M., Simpson, A. 2007. Modelling mathematical argumentation: the importance of qualification. Educ Stud Math 66:3–21. Springer, Heidelberg.
[15] National Council of Teachers of Mathematics (NCTM). 2000. Principles and Standards of School Mathematics. Reston, VA: Author.
[16] Boero, P., Garuti, R., Lemut, E., & Mariotti, A. M. 1996. Challenging the traditional school approach to theorems: A hypothesis about the cognitive unity of theorems. In L. Puig & A. Gutiérrez (Eds.), Proceedings of the 20th Conference of the International Group for the Psychology of Mathematics Education, (Vol. 2, pp. 113−120). Valencia, Spain: PME.
[17] Miles & Huberman. 1992. Metode Penelitian Kualitatif. Jakarta: UI Press.
[18] Creswell, W.J. 2012. Educational Research Planning, Conducting and Evaluating Quantitative and Qualitative Research 4th Edition. Boston: Pearson Education.
[19] Hadamard, J.1945. The Psychology of Invention in the Mathematical Field, 1954 edn. New York: Dover.
[20] Hahn, H.1933. The crisis in intuition. In J. R. Newman (Ed.), The world of mathematics. Vol. 3 (pp.1956–1976). London: G. Allen.
[21] Poincar´e, H.1905. Science and hypothesis. London: Walter Scott Publishing.
[22] Feferman, S. 2000. Mathematical intuition vs. mathematical monsters. Synth`ese, 125, 317-332
[23] Fischbein, E. 1987. Intuition in Science and Mathematics. Dordrecht: Kluwer Academic Publihers.
[24] Harel, G., & Sowder, L. 1998. Students’ proof schemes: Results from exploratory studies. CBMS Issue in Mathematics Education.Volume 7. 234-283, 1998.
[25] Tall, D. O. 2004. Building theories: The Three Worlds of Mathematics. For the Learning of Mathematics, Vol. 23, No.3, 29–32.

Thank you for copying data from http://www.arastirmax.com