STUDENTS’ THINKING PROCESS IN CREATING SCHEMATIC REPRESENTATION

rahmad bustanul anwar(1*), dwi rahmawati(2),

(1) Universitas Muhammadiyah Metro
(2) Universitas Muhammadiyah Metro
(*) Corresponding Author


Abstract


The aim of this study is to describe students’ thinking process in creating schematic representation. A describtive qualitative research is used in this paper along with case study approach. The examined case is students’ thinking process in creating schematic representation in solving word problem. The subjects are Junior High School students at grade VIII. Data collection were done by think aloud technique and interview. The result show that students’ thinking process in creating schematic representation is retrieved from processing theory started by taking the problem into account. Students read the problem based on its intonation with stress in each sentence. Then, students create a scheme and link all information they understand about. This scheme later is drawn into triangle form. By creating the scheme, students are able to comprehend the questions and problems proper. Students connect problems faced by theirself with the concept of Phytagoras stored in long-term memory. The students' understanding of the Phytagoras Theorem concept is well preserved so that students can solve the problem appropriately.


Keywords


Information Processing System; Schematic Representation; Students’ Thinking; Word Problem.

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References


Abdullah, N., Zakaria, E., & Halim, L. (2012). The Effect of a Thinking Strategy Approach through Visual Representation on Achievement and Conceptual Understanding in Solving Mathematical Word Problems. Asian Social Science, 8(16), 30. https://doi.org/10.5539/ass.v8n16p30

Amorapanth, P., Kranjec, A., Bromberger, B., Lehet, M., Widick, P., Woods, A. J., Chatterjee, A. (2011). Language, Perception, and the Schematic Representation of Spatial Relations. Brain and Language, 120(3), 226–236. https://doi.org/10.1016/j.bandl.2011.09.007

Anwar, R. B., Yuwono, I., As’ari, A. R., Sisworo, & Rahmawati, D. (2017). Identifikasi Representasi Skematis dalam Menyelesaikan Masalah Matematika. Retrieved March 12, 2018, from https://www.researchgate.net/publication/320696916_Identifikasi_Representasi_Skematis_Dalam_Menyelesaikan_Masalah_Matematika

Boonen, A. J. H., van Wesel, F., Jolles, J., & van der Schoot, M. (2014). The Role of Visual Representation Type, Spatial Ability, and Reading Comprehension in Word Problem Solving: An Item-Level Analysis in Elementary School Children. International Journal of Educational Research, 68, 15–26. https://doi.org/10.1016/j.ijer.2014.08.001

Cai, J. (2005). U.S. and Chinese Teachers’ Constructing, Knowing, and Evaluating Representations to Teach Mathematics. Mathematical Thinking and Learning: An International Journal, 7(2), 135–169.

Cobb, P. (2003). Modeling, Symbolizing, and Tool Use in Statistical Data Analysis. In Symbolizing, Modeling and Tool Use in Mathematics Education (pp. 171–195). Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3194-2_11

Cobb, P., Stephan, M., McClain, K., & Gravemeijer, K. (2002). Participating in Classroom Mathematical Practices. Journal of the Learning Sciences, 10, 113–163.

Corter, J. E., & Zahner, D. C. (2007). Use of External Visual Representations in Probability Problem Solving. Statistics Education Research Journal, 6(1), 22–50.

Creswell, J. W. (2012). Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research (4th ed). Boston: Pearson.

Dahlan, J. A., & Juandi, D. (2011). Analisis Representasi Matematika Siswa Sekolah Dasar dalam Penyelesaian Masalah Matematika Kontekstual. Jurnal Pengajaran MIPA, 16(1), 128–138. https://doi.org/10.18269/jpmipa.v16i1.273

Diezmann, C. M., & English, L. D. (2001). Promoting the Use of Diagrams as Tools for Thinking. In A. A. Cuoco (Ed.), 2001 National Council of Teachers of Mathematics Yearbook: The Role of Representation in School Mathematics (pp. 77–89). National Council of Teachers of Mathematics. Retrieved from http://eprints.qut.edu.au/1637/

Fagnant, A., & Vlassis, J. (2013). Schematic Representations in Arithmetical Problem Solving: Analysis of Their Impact on Grade 4 Students. Educational Studies in Mathematics, 84(1), 149–168. https://doi.org/10.1007/s10649-013-9476-4

Goldin, G. A. (1998). Representational Systems, Learning, and Problem Solving in Mathematics. The Journal of Mathematical Behavior, 17(2), 137–165. https://doi.org/10.1016/S0364-0213(99)80056-1

Goldin, G. A., & Shteingold, N. (2001). Systems of Representations and the Development of Mathematical Concepts. in: Cuoco, A.A. (Ed.), 2001 National Council of Teachers of Mathematics Yearbook: The Role of Representation in School Mathematics. National Council of Teachers of Mathematics, pp. 1–23. Retrieved March 12, 2018, from https://www.nctm.org/store/Products/Roles-of-Representation-in-School-Mathematics,-63rd-Yearbook-(2001)/

Gravemeijer, K. P., Lehrer, R., Oers, H. J. van, & Verschaffel, L. (2003). Symbolizing, Modeling and Tool Use in Mathematics Education. Springer Science & Business Media.

Hegarty, M., & Kozhevnikov, M. (1999). Types of Visual–Spatial Representations and Mathematical Problem Solving. Journal of Educational Psychology, 91(4), 684.

Kaput, J., Noss, R., & Hoyles, C. (2008). Developing New Notations for a Learnable Mathematics in the Computational Era. In L. English (Ed.), Handbook of international research in mathematics education (pp. 51–75). Mahwah, NJ; London: Lawrence Erlbaum. Retrieved from http://discovery.ucl.ac.uk/1515590/

Krawec, J. L. (2014). Problem Representation and Mathematical Problem Solving of Students of Varying Math Ability. Journal of Learning Disabilities, 47(2), 103–115. https://doi.org/10.1177/0022219412436976

Meira, L. R. D. L. (2003). Mathematical Representations as Systems of Notations-In-Use. In Symbolizing, Modeling and Tool Use in Mathematics Education (pp. 87–103). Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3194-2_6

National Council of Teachers of Mathematics (NCTM) (Ed.). (2000). Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics.

Nizarudin. (2014). Role of Multiple Representations in Mathematical Problem Solving. Retrieved March 12, 2018, from http://webcache.googleusercontent.com/search?q=cache:jcXXjvNpH8gJ:icmseunnes.com/2015/wp-content/uploads/2015/10/28.pdf+&cd=2&hl=en&ct=clnk&gl=id

Novick, L. R., Hurley, S. M., & Francis, M. (1999). Evidence for Abstract, Schematic Knowledge of Three Spatial Diagram Representations. Memory & Cognition, 27(2), 288–308. https://doi.org/10.3758/BF03211413

Panjaitan, B. (2013). PROSES KOGNITIF Siswa Dalam Pemecahan Masalah Matematika. Jurnal Ilmu Pendidikan, 19(1). https://doi.org/10.17977/jip.v19i1.3751

Pape, S. J., & Tchoshanov, M. A. (2001). The Role of Representation(s) in Developing Mathematical Understanding. Theory into Practice, 40(2), 118–127.

Pemendikbud No. 24. (2016). Tentang KI KD Kurikulum 2013. Retrieved April 8, 2018, from https://www.gurupembelajar.net/2016/07/permendikbud-no-24-tahun-2016-tentang.html

Polya, G. (1973). How To Solve It : A New Aspect of Mathematical Method. Retrieved March 7, 2018, from http://www.philosciences.org/notices/document.php?id_document=583

Sari, D. P., Darhim, D., & Rosjanuardi, R. (2018). Errors of Students Learning With React Strategy in Solving the Problems of Mathematical Representation Ability. Journal on Mathematics Education, 9(1), 121–128. https://doi.org/10.22342/jme.9.1.4301.

Slavin, R. E. (1997). Educational psychology theory and practice (5th ed). Boston Allyn and Bacon. Retrieved from https://trove.nla.gov.au/version/207898716

Stylianou, D. A. (2010). Teachers’ Conceptions of Representation in Middle School Mathematics. Journal of Mathematics Teacher Education, 13(4), 325–343. https://doi.org/10.1007/s10857-010-9143-y

Surya, E., Sabandar, J., Kusumah, Y., S., & Darhim, D. (2013). Improving of Junior High School Visual Thinking Representation Ability in Mathematical Problem Solving by CTL. Journal on Mathematics Education, 4(1), 113–126. https://doi.org/10.22342/jme.4.1.568.113 - 126

Talmy, L. (2000). Toward a Cognitive Semantics. MIT Press.

Van Garderen, D., & Montague, M. (2003). Visual-Spatial Representation, Mathematical Problem Solving, and Students of Varying Abilities. Learning Disabilities Research & Practice, 18(4), 246–254. https://doi.org/10.1111/1540-5826.00079

Zahner, D., & Corter, J. E. (2010). The Process of Probability Problem Solving: Use of External Visual Representations. Mathematical Thinking and Learning, 12(2), 177–204. https://doi.org/10.1080/10986061003654240




DOI: http://dx.doi.org/10.24127/ajpm.v7i2.1480

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