The Representation of Students' Mathematical Concepts in Algebraic Problems Solving Based on Mathematical Ability

Mustangin Mustangin(1Mail), St Suwarsono(2), Agung Lukito(3),
(1) University of Islam Malang (UNISMA), Malang, Indonesia
(2) Sanata Dharma University, Yogjakarta, 55002, Indonesia
(3) Surabaya State University, Surabaya, 60231, Indonesia

Mail Corresponding Author
Copyright (c) 2020 Mustangin Juwaini



This study aims to describe the representation of students' mathematical concepts in solving algebraic problems based on mathematical ability. This study is exploratory descriptive qualitative with four junior high school students as subjects. Data were collected using a task-based interview and analyzed using qualitative data analysis techniques through data reduction, data presentation, and drawing conclusions. The mathematical ability is categorized into high and low.  The results show that differences in mathematical ability has no real effect on the representation of mathematical concepts of students in algebraic problem solving. Proved by all subjects (low and high mathematical abilities) are able to solve algebraic problems using verbal, symbolic, imagistic, and notational formal representations. However, there is a difference on the model of mathematical representation used. Students with high ability prefer to use conceptual representations using conventional standard notations, while those with low mathematical ability tend to use pictorial representations using non-standard illustrations.


Mathematical Ability, Mathematical Concept Representation, Algebraic Problem-Solving


Anwar, R.B. & Rahmawati, D. (2017). Symbolic and Verbal Repre-sentation Process of Student in Solving Mathematics Problem Based Polya’s Stages. International Education Studies. Vol. 10, No. 10; 2017. p-ISSN 1913-9020, e-ISSN 1913-9039. Published by Canadian Center of Science and Education.

Bogdan, R.C. & Biklen, S.K. (1992). Qualitative Research for Education, An Introduction to Theory and Methods. Boston: Allyn and Bacon Inc.

Booker, G. (2009). Algebraic Thinking: Generalising Number and Geometrry to Express Patterns and Properties Succinetly. Brisbane: Griffith University.

Borg, W.R. & Gall, M.D. (1983). Educational Research: An Intro-duction. Fourth Edition. New York: Longman, Inc.

Bossé, M.J., Bayaga, A., Fountain, C., & Young, E.S. (2019). Mathe-matical Representational Code Switching. International Journal For Mathematics Teaching And Learning 2019, Vol. 20.1.

Cuoco, A.A. (2001). The Roles of Representation in School Mathe-matics 2001 Year Book. Reston, VA: NCTM.

Dendane, A. (2009). Skills Needed for Mathematical Problem Solving. Paper presented at the 10th Annual Research Conference - UAE University - 13th -16th April, 2009.

Fiedlander A. & Tabach, M. (2001). Promoting Multiple Represen-tations in Algebra. In Cuoco, Albert A. The Roles of Repre-sentation in School Mathematics 2001 Year Book. Reston, VA: NCTM.

Fonna & Mursalin. (2018). Role of Self-Efficacy toward Students’ Achievement in Mathematical Multiple Representation Ability (MMRA). JIP-The International Journal of Social Science. Vol. 6, No. 1, January 2018 p-ISSN:2338-8617, e-ISSN: 2443-2067. doi: 10.26811/peuradeun.v6i1.174.

Goldin, G. A. (2002). Representation in Mathematical Learning and Problem Solving. In L. D. English (Ed.), Handbook of Inter-national Research in Mathematics Education . Mahwah, NJ: Lawrence Erlbaum Associates, Publishers.

Goldin, G.A. & Shteingold, N. (2001). System of Representation and the Development of Mathematical Concept. In Cuoco, Albert A. (Ed). The Roles of Representation in School Mathematics 2001 Yearbook. Reston, VA: NCTM.

Helingo, D.D.Z, Amin, S.M., & Masriyah, M. (2019). D D Z Helingo, S M Amin and M Masriyah. Journal of Physics: Conf. Series 1188 (2019) 012055. IOP Publishing doi:10.1088/1742-6596/1188/1/012055.

Hitt, F. (Eds). (2002). Representations and Mathematics Visualization. Mexico: Departamento Dematemática Educativa, Cinvestav-IPN.

Kieran, C. (2004). Algebraic Thinking in the Early Grades: What Is It?. The Mathematics Educator, Vol.8, No.1.

Kilpatrick, J., Swafford, J. & Findell, B. (2001). Adding it up. Helping Children Learn Mathematics. Washington: National Academy Press.

Miles, B.M. & Huberman, M.A. (1994). Qualitative Data Analysis: an Expanded Sourcebook, 2ndEd. New Delhi: Sage Publications, Inc.

Minarni, A., Napitupulu, E.E., & Husein, R. (2016). Mathematical Understanding And Representation Ability Of Public Junior High School In North Sumatra. Journal on Mathematics Education. Volume 7, No. 1, January 2016. p-ISSN 2087-8885, e-ISSN 2407-0610.

Miura, I.T. (2001). The Influence of Language on Mathematical Representations. In Cuoco, Albert A. The Roles of Represen-tation in School Mathematics 2001 Year Book. Reston, VA: NCTM.

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

National Council of Teachers of Mathematics. (2008). Principles and Standards for School Mathematics. Reston, VA: NCTM.

Nizaruddin, Muhtarom, & Murtianto, Y.H. (2017). Exploring of Multi Mathematical Representation Capability in Problem Solving on Senior High School Students. Problems of Education in The 21st Century Vol. 75, No. 6, 2017 591, ISSN 1822-7864 (Print) ISSN 2538-7111 (Online).

Nizarudin. (2014). Role of Multiple Representations in Mathematical Problem Solving. Proceeding of International Conference on Mathematics, Science, and Education 2014 (ICMSE2014).

Nurrahmawati, Sa’dijah, C., Sudirman, Muksar, M., As’ari, A.R., & Nusantara, T. (2018). Pre-Service Mathemathics Teachers’ Preferences in Using Multiple Representation of Word Problem Solving. International Journal of Insight for Mathematics Teaching Volume 01, No. 2, October 2018.

Ollerton, M. (2007). Teaching and Learning Through Problem Solving. Mathematics Teaching Incorporating Micromath 20.

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

Putra, I.S., Masriyah, & Sulaiman, R. (2018). Students Translation Ability of Mathematical Representation (Symbolic and Visual) Based on Their Learning Styles. Journal of Physics: Conf. Series 1108 (2018) 012079. doi:10.1088/1742-6596/1108/1/012079.

Rahmawati, D., Purwanto, Subanji, Hidayanto, E., & Anwar, R.B. (2017). Process of Mathematical Representation Translation from Verbal into Graphic. IEJME- Mathematics Education 2017, VOL. 12, NO. 4.

Rakes, C.R. (2010). Misconception in Rational Numbers, Probability, Algebra, and Geometry. USA: The University of Louisville.

Rohmah, M. & Sutiarso, S. (2018). Analysis Problem Solving in Mathematical Using Theory Newman. EURASIA Journal of Mathematics, Science and Technology Education. ISSN: 1305-8223 (online) 1305-8215 (print) 2018 14(2). DOI: 10.12973/ejmste/80630.

Sahendra, A., Budiarto, M.T., & Fuad, Y. (2017). Students’ Repre-sentation in Mathematical Word Problem Solving: Exploring Student Self-efficay. Journal of Physics: Conf. Series 947 (2017) 012059. doi:10.1088/1742-6596/947/1/012059.

Tchoshanov, M.A. (2002). Representation and Cognition: Internalizing Mathematical Concept. In Hitt, F. (Eds). Representations and Mathematics Visualization. Mexico: Departamento Dematemática Educativa, Cinvestav-IPN.

The Vermont Department of Education. (2007). Vermont Elementary and Middle Level Mathematics Problem Solving Assessment Guide. Vermont: Vermont Institue for Science, Math and Technology.

Ulfatin, N. (2013). Metode Penelitian Kualitatif di Bidang Pendidikan: Teori dan Aplikasinya. Malang: Bayumedia Publishing.

Villegas, J.L., Castro, E., & Gutiérrez, J. (2009). Representations in Problem Solving: A Case Study with Optimization Problems. Electronic Journal of Research in Educational Psychology. ISSN. 1696-2095. No 17, Vol 7 (1).

Warren, E. (2003). The Role of Arithmetic Structure in the Transition from Arithmetic to Algebra. Australian Catholic University Mathematics Education Research Journal, Vol. 15, No. 2.

Yanti, R.M., Amin, S.M., & Sulaiman, R. (2017). Representation of Students in Solving Simultaneous Linear Equation Problems Based on Multiple Intelligence. Journal of Physics: Conf. Series 947 (2017) 012038. doi:10.1088/1742-6596/947/1/012038.

Article Metrics

 Abstract Views : 116 times


  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.