AN INVESTIGATION OF STUDENTS’ ALGEBRAIC PROFICIENCY FROM A STRUCTURE SENSE PERSPECTIVE

Al Jupri, Ririn Sispiyati, Kin Eng Chin

Abstract


Structure sense can be interpreted as an intuitive ability towards symbolic expressions, including skills to perceive, to interpret, and to manipulate symbols in different roles. This ability shows student algebraic proficiency in dealing with various symbolic expressions and is considered important to be mastered by secondary school students for advanced study or professional work. This study, therefore, aims to investigate students’ algebraic proficiency in terms of structure sense. To reach this aim, we set up a qualitative case study with the following three steps. First, after conducting a literature study, we designed structure sense tasks according to structure sense characteristics for the topic of equations. Second, we administered an individual written test involving 28 grade XI students (16-17 year-old). Third, we analyzed students’ written work using a structure sense perspective. The results showed that about two-thirds of the participated students lack of structure sense in which they tend to use more procedural strategies than structure sense strategies in solving equations. We conclude that the perspective of structure sense provides a fruitful lens for assessing students’ algebraic proficiency.


Keywords


Algebraic Proficiency; Structure Sense; Equations; Procedural and Structure Sense Strategies

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References


Apsari, R. A., Putri, R. I. I., Sariyasa, Abels, M., & Prayitno, S. (2020). Geometry representation to develop algebraic thinking: A recommendation for a pattern investigation in pre-algebra class. Journal on Mathematics Education, 11(1), 45-58. http://doi.org/10.22342/jme.11.1.9535.45-58

Apsari, R. A., Sariyasa, S., Putri, R. I. I., Gunawan, G., & Prayitno, S. (2020). Understanding students’ transition from arithmetic to algebraic thinking in the pre-algebraic lesson. Journal of Physics: Conference Series, 1471(1), 012056. http://doi.org/10.1088/1742-6596/1471/1/012056

Arcavi, A. (1994). Symbol sense: Informal sense-making in formal mathematics. For the Learning of Mathematics, 14(3), 24–35. http://flm-journal.org/Articles/BFBFB3A8A2A03CF606513A05A22B

Arcavi, A. (2005). Developing and using symbol sense in mathematics. For the Learning of Mathematics, 25(2), 42–47. http://www.jstor.org/stable/40248497

Bednarz, N., Kieran, C., & Lee, L. (1996) Approaches to Algebra: Perspectives for research and teaching. In: Bernarz N., Kieran C., Lee L. (eds) Approaches to algebra. Mathematics education Library, vol 18. Springer, Dordrecht. http://doi.org/10.1007/978-94-009-1732-3_1

Bokhove, C., & Drijvers, P. (2010). Digital activities for capturing symbol sense. For the Learning of Mathematics, 30(3), 43-49. http://flm-journal.org/Articles/45D5ED606856931839C164A32C1092

Bokhove, C., & Drijvers, P. (2012). Effects of feedback in an online algebra intervention. Technology, Knowledge and Learning, 17(1), 43-59. https://doi.org/10.1007/s10758-012-9191-8

Carraher, D. W., Schliemann, A. D., Brizuela, B. M., & Earnest, D. (2006). Arithmetic and algebra in early mathematics education. Journal for Research in Mathematics Education, 37(2), 87-115. http://www.jstor.org/stable/30034843

De Lange, J. (2006). Mathematical literacy for living from OECD-PISA perspective. Tsukuba Journal of Educational Study in Mathematics, 25(1), 13–35. http://www.human.tsukuba.ac.jp/~mathedu/2503

Freudenthal, H. (1991). Revisiting mathematics education: China lectures. Dordrecht: Kluwer Academic Publishers. http://doi.org/10.1007/0-306-47202-3

Hoch, M., & Dreyfus, T. (2006). Structure sense versus manipulation skills: An unexpected result. In J. Novotna, H. Moraova, M. Kratka, & N. Stehlikova (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 305-312). Prague, Czech Republic: PME.

Hoch, M., & Dreyfus, T. (2010). Developing Katy’s algebraic structure sense. In Proceedings of the 6th Congress of the European Society for Research in Mathematics (pp. 529-538). Lyon, France: INRP.

Junarti, Sukestiyarno, Y. L., Mulyono, & Dwidayati, N. K. (2019). The profile of structure sense in abstract algebra instruction in an Indonesian mathematics education. European Journal of Educational Research, 8(4), 1081-1091. http://doi.org/10.12973/eu-jer.8.4.1081

Jupri, A., Drijvers, P., & Van den Heuvel-Panhuizen, M. (2014a). Difficulties in initial algebra learning in Indonesia. Mathematics Education Research Journal, 26(4), 683-710. http://doi.org/10.1007/s13394-013-0097-0

Jupri, A., Drijvers, P., & Van den Heuvel-Panhuizen, M. (2014b). Student difficulties in solving equations from an operational and a structural perspective. International Electronic Journal of Mathematics Education, 9(1), 39-55. https://www.iejme.com/article/student-difficulties-in-solving-equations-from-an-operational-and-a-structural-perspective

Jupri, A., Drijvers, P., & Van den Heuvel-Panhuizen, M. (2015). Improving grade 7 students’ achievement in initial algebra through a technology-based intervention. Digital Experiences in Mathematics Education, 1(1), 28-58. http://doi.org/10.1007/s40751-015-0004-2

Jupri, A., & Sispiyati, R. (2020). Students’ algebraic proficiency from the perspective of symbol sense. Indonesian Journal of Science and Technology, 5(1), 86-94. http://doi.org/10.17509/ijost.v5i1.23102

Katz, V. J. (Ed.) (2007). Algebra: Gateway to a technological future. The Mathematical Association of America. http://www.maa.org/news/new-report-algebra-gateway-technological-future

Kop, P. M., Janssen, F. J., Drijvers, P. H., & van Driel, J. H. (2020). The relation between graphing formulas by hand and students’ symbol sense. Educational Studies in Mathematics, 105(2), 137-161. http://doi.org/10.1007/s10649-020-09970-3

Kusumaningsih, W., Darhim, Herman, T., & Turmudi. (2018). Improvement algebraic thinking ability using multiple representation strategy on realistic mathematics education. Journal on Mathematics Education, 9(2), 281-290. https://doi.org/10.22342/jme.9.2.5404.281-290

Linchevski, L., & Livneh, D. (1999). Structure sense: The relationship between algebraic and numerical contexts. Educational Studies in Mathematics, 40(2), 173-196. http://doi.org/10.1023/A:1003606308064

MacGregor, M., & Price, E. (1999). An exploration of aspects of language proficiency and algebra learning. Journal for Research in Mathematics Education, 30(4), 449-467. http://doi.org/10.2307/749709

McCallum, W. G. (2007). Assessing the strands of student proficiency in elementary algebra. In A. H. Schoenfeld (Ed.), Assessing mathematical proficiency (pp. 157-162). Cambridge, New York: Cambridge University Press. http://doi.org/10.1017/CBO9780511755378

Mullis, I. V. S., Martin, M. O., Foy, P., & Arora, A. (2012). TIMSS 2011 international results in mathematics. Boston: TIMSS & PIRLS International Study Center. http://timss.bc.edu/timss2011/international-results-mathematics.html

Novotna, J., & Hoch, M. (2008). How structure sense for algebraic expressions or equations is related to structure sense for abstract algebra. Mathematics Education Research Journal, 20(2), 93-104. http://doi.org/10.1007/BF03217479

Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77(1), 20-26. https://www.atm.org.uk/write/MediaUploads/Resources/Richard_Skemp.pdf

Stiphout, I. V., Drijvers, P., & Gravemeijer, K. (2013). The development of students’ algebraic proficiency. International Electronic Journal of Mathematics Education, 8(2-3), 62-80. http://doi.org/10.29333/iejme

Sugiarti, L., & Retnawati, H. (2019). Analysis of student difficulties on algebra problem solving in junior high school. Journal of Physics: Conference Series, 1320(1), 012103. http://doi.org/10.1088/1742-6596/1320/1/012103

Van den Heuvel-Panhuizen, M., & Drijvers, P. (2014). Realistic mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education, 713-717. http://doi.org/10.1007/978-94-007-4978-8

Wahyuni, R., Prabawanto, S., & Herman, T. (2020). Students’ difficulties in solving algebra task in middle school. Journal of Physics: Conference Series, 1521(3), 032071. http://doi.org/10.1088/1742-6596/1521/3/032071

Widodo, S. A., Prahmana, R. C. I., Purnami, A. S., & Turmudi. (2018). Teaching materials of algebraic equation. Journal of Physics: Conference Series, 943(1), 012017. http://doi.org/10.1088/1742-6596/943/1/012017

Yin, R. K. (2015). Qualitative research from start to finish. New York, London: Guilford publications.




DOI: https://doi.org/10.22342/jme.12.1.13125.147-158

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Journal on Mathematics Education
Doctoral Program on Mathematics Education
Faculty of Teacher Training and Education, Universitas Sriwijaya
Kampus FKIP Bukit Besar
Jl. Srijaya Negara, Bukit Besar
Palembang - 30139
email: jme@unsri.ac.id

p-ISSN: 2087-8885 | e-ISSN: 2407-0610

Creative Commons License
Journal on Mathematics Education (JME) is licensed under a Creative Commons Attribution 4.0 International License.


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