Student Difficulties in Mathematizing Word Problems in Algebra

Al Jupri; Paul Drijvers

doi:10.12973/eurasia.2016.1299a

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Al Jupri ¹ ^* , Paul Drijvers ²

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¹ Universitas Pendidikan Indonesia, INDONESIA² Utrecht University, the NETHERLANDS^* Corresponding Author

Abstract

To investigate student difficulties in solving word problems in algebra, we carried out a teaching experiment involving 51 Indonesian students (12/13 year-old) who used a digital mathematics environment. The findings were backed up by an interview study, in which eighteen students (13/14 year-old) were involved. The perspective of mathematization, i.e., the activity to transform a problem into a symbolic mathematical problem, and to reorganize the mathematical system, was used to identify student difficulties on the topic of linear equations in one variable. The results show that formulating a mathematical model—evidenced by errors in formulating equations, schemas or diagrams—is the main difficulty. This highlights the importance of mathematization as a crucial process in the learning and teaching of algebra.

Keywords

algebra education
digital mathematics environment
linear equations in one variable
mathematization
word problems

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 12, Issue 9, September 2016, 2481-2502

https://doi.org/10.12973/eurasia.2016.1299a

Publication date: 17 Jul 2016

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Article Downloads: 12020

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References

Arcavi, A. (1994). Symbol sense: Informal sense-making in formal mathematics. For the Learning of Mathematics, 14(3), 24–35.
Barkatsas, A., Kasimatis, K., & Gialamas, V. (2009). Learning secondary mathematics with technology: Exploring the complex interrelationship between students’ attitudes, engagement, gender and achievement. Computers & Education, 52(3), 562–570.
Bokhove, C., & Drijvers, P. (2010). Symbol sense behavior in digital activities. For the Learning of Mathematics, 30(3), 43–49.
Bokhove, C., & Drijvers, P. (2012). Effects of feedback in an online algebra intervention. Technology, Knowledge and Learning, 17(1-2), 43–59.
Boon, P. (2006). Designing didactical tools and micro-worlds for mathematics education. In C. Hoyles, J. B. Lagrange, L. H. Son, & N. Sinclair, Proceedings of the 17th ICMI Study Conference; http://www.fi.uu.nl/isdde/documents/software_boon.pdf
Booth, L. R. (1988). Children’s difficulties in beginning algebra. In A.F. Coxford (Ed.), The ideas of algebra, K–12(1988 Yearbook) (pp. 20–32). Reston, VA: National Council of Teachers of Mathematics.
Bush, S. B., & Karp, K. S. (2013). Prerequisite algebra skills and associated misconceptions of middle grade students: A review. Journal of Mathematical Behavior, 32(3), 613–632.
Carpraro, M. M., & Joffrion, H. (2006). Algebraic equations: Can middle school students meaningfully translate from words to mathematical symbols? Reading Psychology, 27(2) 147–164.
Clement, J. (1982). Algebra word problem solutions: Thought processes underlying a common misconception. Journal for Research in Mathematics Education, 13(1), 16–30.
De Lange, J. (1987). Mathematics insight and meaning. Dissertation. Utrecht, the Netherlands: OW & OC.
De Lange, J. (2006). Mathematical literacy for living from OECD-PISA perspective. Tsukuba Journal of Educational Study in Mathematics. Vol. 25. Special Issue on The APEC-TSUKUBA International Conference "Innovative Teaching Mathematics through Lesson Study" (pp. 13-35). Tokyo, Japan: University of Tsukuba.
Doorman, M., Drijvers, P., Gravemeijer, K., Boon, P., & Reed, H. (2012). Tool use and the development of the function concept: from repeated calculations to functional thinking. International Journal of Science and Mathematics Education, 10(6), 1243–1267.
Drijvers, P., & Doorman, M. (1996). The graphics calculator in mathematics education. Journal of Mathematical Behavior, 15(4), 425–440.
Drijvers, P. (2000). Students encountering obstacles using a CAS. International Journal of Computers for Mathematical Learning, 5(3), 189–209.
Drijvers, P. H. M. (2003). Learning algebra in a computer algebra environment: Design research on the understanding of the concept of parameter. Dissertation. Utrecht, the Netherlands: CD-B Press.
Drijvers, P., Boon, P., & Van Reeuwijk, M. (2010). Algebra and technology. In P. Drijvers (Ed.), Secondary algebra education. Revisiting topics and themes and exploring the unknown (pp. 179–202). Rotterdam, the Netherlands: Sense.
Drijvers, P., Boon, P., Doorman, M., Bokhove, C., Tacoma, S. (2013). Digital design: RME principles for designing online tasks. ICMI Study 22.
Freudenthal, H. (1991). Revisiting mathematics education: China lectures. Dordrecht: Kluwer Academic Publishers.
Ghosh, J. B. (2012). Learning mathematics in secondary school: The case of mathematical modeling enabled by technology. Regular lecture 12th ICME conference; http://nime.hbcse.tifr.res.in/indian-participants-at-icme2012/JonakiG_RL612Mathematicalmodellingenabledbytechnonlogy.pdf
Gravemeijer, K. P. E. (1994). Developing realistic mathematics education. Utrecht: CD-B Press.
Herscovics, N., & Linchevski, L. (1994). A cognitive gap between arithmetic and algebra. Educational Studies in Mathematics, 27(1), 59–78.
Jupri, A., Drijvers, P., & Van den Heuvel-Panhuizen, M. (2014). Difficulties in initial algebra learning in Indonesia. Mathematics Education Research Journal, 26(4), 683-710.
Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12(3), 317–326.
Landis, J. R., & Koch, G. G. (1977). The measurement of observer agreement for categorial data. Biometrics, 33(1), 159–174.
Li, Q., & Ma, X. (2010). A meta-analysis of the effects of computer technology on school students’ mathematics learning. Educational Psychology Review, 22(3), 215–243.
Linchevski, L. (1995). Algebra with numbers and arithmetic with letters: A definition of prealgebra. Journal of Mathematical Behavior, 14(1), 113–120.
MacGregor, M., & Stacey, K. (1998). Cognitive models underlying algebraic and non-algebraic solutions to unequal partition problems. Mathematics Education Research Journal, 10(2), 46-60.
Mullis, I. V. S., Martin, M. O., Foy, P., in collaboration with Olson, J. F., Preuschoff, C., Erberber, E., Arora, A., & Galia, J. (2008). TIMSS 2007 international mathematics report: Findings from IEA’s trends in international mathematics and science study at the fourth and eighth grades. Boston: TIMSS & PIRLS International Study Center.
Sembiring, R. K., Hadi, S., & Dolk, M. (2008). Reforming mathematics learning in Indonesian classrooms through RME. ZDM, The International Journal on Mathematics Education, 40(6), 927–939.
Stacey, K., & MacGregor, M. (2000). Learning the algebraic method of solving problems. Journal of Mathematical Behavior, 18(2), 149–167.
Thomas, M., & Tall, D. (1991). Encouraging versatile thinking in algebra using the computer. Educational Studies in Mathematics, 22(2), 125–147.
Treffers, A. (1987). Three dimensions. A model of goal and theory description in mathematics instruction-The Wiskobas project. Dordrecht, the Netherlands: Kluwer Academic Publishers.
Van Amerom, B. A. (2003). Focusing on informal strategies when linking arithmetic to early algebra. Educational Studies in Mathematics, 54(1), 63-75.
Van den Heuvel-Panhuizen, M. (2000). Mathematics education in the Netherlands: A guided tour. Freudenthal Institute Cd-rom for ICME9. Utrecht: Utrecht University.
Van den Heuvel-Panhuizen, M. (2003). The didactical use of models in realistic mathematics education: An example from a longitudinal trajectory on percentage. Educational Studies in Mathematics, 54(1) 9–3.
Van den Heuvel-Panhuizen, M., & Drijvers, P. (2013). Realistic Mathematics Education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education. Dordrecht, Heidelberg, New York, London: Springer.
Warren, E. (2003). The role of arithmetic structure in the transition from arithmetic to algebra. Mathematics Education Research Journal, 15(2), 122–137.
Zulkardi. (2002). Developing a learning environment on realistic mathematics education for Indonesian student teachers. Dissertation. Enschede: University of Twente.

How to cite this article

APA

Jupri, A., & Drijvers, P. (2016). Student Difficulties in Mathematizing Word Problems in Algebra. Eurasia Journal of Mathematics, Science and Technology Education, 12(9), 2481-2502. https://doi.org/10.12973/eurasia.2016.1299a

Vancouver

Jupri A, Drijvers P. Student Difficulties in Mathematizing Word Problems in Algebra. EURASIA J Math Sci Tech Ed. 2016;12(9):2481-502. https://doi.org/10.12973/eurasia.2016.1299a

AMA

Jupri A, Drijvers P. Student Difficulties in Mathematizing Word Problems in Algebra. EURASIA J Math Sci Tech Ed. 2016;12(9), 2481-2502. https://doi.org/10.12973/eurasia.2016.1299a

Chicago

Jupri, Al, and Paul Drijvers. "Student Difficulties in Mathematizing Word Problems in Algebra". Eurasia Journal of Mathematics, Science and Technology Education 2016 12 no. 9 (2016): 2481-2502. https://doi.org/10.12973/eurasia.2016.1299a

Harvard

Jupri, A., and Drijvers, P. (2016). Student Difficulties in Mathematizing Word Problems in Algebra. Eurasia Journal of Mathematics, Science and Technology Education, 12(9), pp. 2481-2502. https://doi.org/10.12973/eurasia.2016.1299a

MLA

Jupri, Al et al. "Student Difficulties in Mathematizing Word Problems in Algebra". Eurasia Journal of Mathematics, Science and Technology Education, vol. 12, no. 9, 2016, pp. 2481-2502. https://doi.org/10.12973/eurasia.2016.1299a