Student Difficulties in Solving Equations from an Operational and a Structural Perspective

Al Jupri; Paul Drijvers; Marja van den Heuvel-Panhuizen

doi:10.29333/iejme/280

Full Text (PDF)

Al Jupri, Paul Drijvers, Marja van den Heuvel-Panhuizen

More Detail

Abstract

In Indonesia, as in many other countries, mathematics teachers, educators and researchers are confronted with student difficulties in initial algebra. To investigate and understand these difficulties, we carried out a pilot study involving 51 Indonesian grade seven students who use a digital mathematics environment for algebra. The notions of operational and structural conceptions offer a framework for explaining student difficulties in solving equations. These include difficulties with arithmetical skills, the use of the equal sign, understanding algebraic expressions, and understanding the concept of variable. The operational and structural perspectives provide guidelines for future task design and research.

Keywords

Algebra Education
Digital Mathematics Environment
Equations in One Variable
Operational and Structural Views

License

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

INT ELECT J MATH ED, Volume 9, Issue 1, January 2014, 39-55

https://doi.org/10.29333/iejme/280

Publication date: 02 Feb 2014

Article Views: 4221

Article Downloads: 3426

Open Access References How to cite this article

References

Arcavi, A. (1994). Symbol sense: Informal sensemaking in formal mathematics. For the Learning of Mathematics, 14(3), 24–35.
Arcavi, A. (2005). Developing and using symbol sense in mathematics. For the Learning of Mathematics, 14(3), 42–47.
Jupri, A., Drijvers, P., & Van den HeuvelPanhuizen, M. (2014). Difficulties in initial algebra learning in Indonesia. Mathematics Education Research Journal. DOI: 10.1007/s13394-013-0097-0.
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. (2010). Implementing feedback in a digital tool for symbol sense. International Journal for Technology in Mathematics Education, 17(3), 121–126.
Bokhove, C., & Drijvers, P. (2010). Symbol sense behavior in digital activities. For the Learning of Mathematics, 30(3), 43–49.
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/soft ware_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.
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.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. (Ed.) (2010). Secondary algebra education. Revisiting topics and themes and exploring the unknown. 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.
Herscovics, N., & Linchevski, L. (1994). A cognitive gap between arithmetic and algebra. Educational Studies in Mathematics, 27(1), 59–78.
Hoch, M., & Dreyfus, T. (2009). Developing Katy‘s algebraic structure sense. Proceedings of CERME 6; www.inrp.fr/editions/cerme6
Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12(3), 317–326.
Linchevski, L. (1995). Algebra with numbers and arithmetic with letters: A definition of prealgebra. Journal of Mathematical Behavior, 14(1), 113–120.
Linchevski, L., & Livneh, D. (1999). Structure sense: The relationship between algebraic and numerical contexts. Educational Studies in Mathematics, 40(2), 173–196.
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.
Mullis, I.V.S., Martin, M.O., Foy, P., & Arora, A. (2012). TIMSS 2011 international results in mathematics. Boston: TIMSS & PIRLS International Study Center.
Novotna, J., & Hoch, M. (2008). How structure sense for algebraic expressions of equations is related to structure sense for abstract algebra. Mathematics Education Research Journal, 20(2), 93–104.
Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22(1), 1–36.
Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20–26.
Tall, D., Thomas, M. (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 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– 35.
Warren, E. (2003). The role of arithmetic structure in the transition from arithmetic to algebra. Mathematics Education Research Journal, 15(2), 122–137.

How to cite this article

APA

Jupri, A., Drijvers, P., & Heuvel-Panhuizen, M. V. D. (2014). Student Difficulties in Solving Equations from an Operational and a Structural Perspective. International Electronic Journal of Mathematics Education, 9(1), 39-55. https://doi.org/10.29333/iejme/280

Vancouver

Jupri A, Drijvers P, Heuvel-Panhuizen MVD. Student Difficulties in Solving Equations from an Operational and a Structural Perspective. INT ELECT J MATH ED. 2014;9(1):39-55. https://doi.org/10.29333/iejme/280

AMA

Jupri A, Drijvers P, Heuvel-Panhuizen MVD. Student Difficulties in Solving Equations from an Operational and a Structural Perspective. INT ELECT J MATH ED. 2014;9(1), 39-55. https://doi.org/10.29333/iejme/280

Chicago

Jupri, Al, Paul Drijvers, and Marja van den Heuvel-Panhuizen. "Student Difficulties in Solving Equations from an Operational and a Structural Perspective". International Electronic Journal of Mathematics Education 2014 9 no. 1 (2014): 39-55. https://doi.org/10.29333/iejme/280

Harvard

Jupri, A., Drijvers, P., and Heuvel-Panhuizen, M. V. D. (2014). Student Difficulties in Solving Equations from an Operational and a Structural Perspective. International Electronic Journal of Mathematics Education, 9(1), pp. 39-55. https://doi.org/10.29333/iejme/280

MLA

Jupri, Al et al. "Student Difficulties in Solving Equations from an Operational and a Structural Perspective". International Electronic Journal of Mathematics Education, vol. 9, no. 1, 2014, pp. 39-55. https://doi.org/10.29333/iejme/280