GEOMETRY REPRESENTATION TO DEVELOP ALGEBRAIC THINKING: A RECOMMENDATION FOR A PATTERN INVESTIGATION IN PRE-ALGEBRA CLASS

Ratih Ayu Apsari, Ratu Ilma Indra Putri, Sariyasa Sariyasa, Mieke Abels, Sudi Prayitno

Abstract


The present study is a part of design research in local instructional theory in a pre-algebraic lesson using the Realistic Mathematics Education (RME) approach. The article will focus on recommendations for the type of pre-algebra class that supports elementary school students’ algebraic thinking. As design research study, it followed the three steps of preliminary studies, teaching experiment and retrospective analysis. The subject of the study is 32 fifth grade students of MIN 2 Palembang during the teaching experiment phase.  The data were gathered from students’ worksheets, lesson observation and interviews with the students. Data analysis was done using a constant comparative qualitative method. The results from the study indicate that pattern investigation in pre-algebra class that visualized geometrically supports the students to identify the form of the pattern and construct generalization.

Keywords


Pre-Algebra; Algebraic Thinking; Geometry Representation; Pattern Investigation; Realistic Mathematics Education

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References


Bakker, A., & Van Eerde, H.A. (2015). An introduction to design-based research with an example from statistics education. In A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Approaches to Qualitative Research in Mathematics Education (pp. 429-466). New York: Springer.

Ball, D.L. (2003). Mathematical proficiency for all students: Toward a strategic research and development program in mathematics education. Arlington: RAND.

Booth, J.L., Barbieri, C., Eyer, F., & Paré-Blagoev, E.J. (2014). Persistent and pernicious errors in algebraic problem solving. Journal of Problem Solving, 7(1), 10-23. http://dx.doi.org/10.7771/1932-6246.1161.

Brawner, B. (2012). Teaching and learning with technology: Reforming the algebra classroom. Southwest Teaching and Learning Conference (pp. 1-8). San Antonio: Texas A&M Univerisity.

Capraro, M.M., & Joffrion, H. (2006). Algebraic equations: Can middle-school students meaningfully translate from words to mathematical symbols? Reading Psychology, 27(2-3), 147-164. http://dx.doi.org/10.1080/02702710600642467.

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

Dekker, T., & Dolk, M. (2011). From Arithmetic to Algebra. In P. Drijvers (Ed.), Secondary algebra education: Revisiting topic and themes and exploring the unknowns (pp. 69-87). Rotterdam: Sense Publishers.

Drijvers, P., Dekker, T., & Wijers, M. (2011). Patterns and formulas. In P. Drijvers (Ed.), Secondary Algebra Education: Revisiting Topics and Themes and Exploring the Unknown (pp. 89-100). Rotterdam: Sense Publisher.

Drijvers, P., Goddijn, A., & Kindt, M. (2011). Algebra education: Exploring topics and themes. In P. Drijvers (Ed.), Secondary algebra education: Revisiting topics and themes and exploring the unknown (pp. 5-26). Rotterdam: Sense Publisher.

Ferryansyah, Widyawati, E., & Rahayu, S. (2018). The analysis of students’ difficulty in learning linear algebra. Journal of Physics: Conference Series, 1028(1), 012152. http://dx.doi.org/10.1088/1742-6596/1028/1/012152.

Gravemeijer, K. & Doorman, M. (1999). Context problems in realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics, 39(1-3), 111-129. https://doi.org/10.1023/A:1003749919816.

Gravemeijer, K., & Bakker, A. (2006). Design research and design heuristics in statistics education. In A. Rossman, & B. Chance (Ed.), Proceedings of the Seventh International Conference on Teaching Statistics (pp. 1-6). Voorburg: International Statistical Institute.

Güler, G. (2016). The difficulties experienced in teaching proof to prospective mathematics teachers: Academician views. Higher Education Studies, 6(1), 145-158. http://dx.doi.org/ 10.5539/hes.v6n1p145.

Hendroanto, A., van Galen, F., van Eerde, D., Prahmana, R.C.I., Setyawan, F., & Istiandaru, A. (2018). Photography activities for developing students’ spatial orientation and spatial visualization. Journal of Physics: Conference Series, 943(1), 012029. https://doi.org/10.1088/1742-6596/943/1/012029.

Jacobs, V.R., Franke, M.L., Carpenter, T.P., Levi, L., & Battey, D. (2007). Professional development focused on childrens' algebraic reasoning in elementary school. Journal for Research in Mathematics Education, 38(3), 258-288. http://dx.doi.org/10.2307/30034868.

Julius, E., Abdullah, A. H., & Suhairom, N. (2018). Attitude of students towards solving problems in algebra: A review of Nigeria secondary schools. IOSR Journal of Research & Method in Education, 8(1), 26-31. http://dx.doi.org/10.9790/7388-0801032631.

Jupri, A. & Drijvers, P. (2016). Student difficulties in mathematizing word problems in algebra. Eurasia Journal of M athematics, Science and Technology Education, 12(9), 2481-2502. http://dx.doi.org/10.12973/eurasia.2016.1299a.

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

Kenedi, A.K., Helsa, Y., Ariani, Y., Zainil, M., & Hendri, S. (2019). Mathematical connection of elementary school students to solve mathematical problems. Journal on Mathematics Education, 10(1), 69-80. http://dx.doi.org/10.22342/jme.10.1.5416.69-80.

Kieran, C. (2004). Algebraic thinking in the early grades: What is it? The Mathematics Educator, 8(1), 139-151.

Kieran, C. (2018). Seeking, using, and expressing structure in numbers and numerical operations: A fundamental path to developing early algebraic thinking. In Teaching and Learning Algebraic Thinking with 5-to 12-Year-Olds (pp. 79-105). Springer, Cham.

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.

Kvasz, L. (2006). The history of algebra and the development of the form of its language. Philosophia Mathematica, 14(3), 287-317. https://doi.org/10.1093/philmat/nkj017.

Lannin, J.K. (2005). Generalization and justification: The challenge of introducing algebraic reasoning through patterning activities. Mathematical Thinking and Learning, 7(3), 231-258. https://doi.org/10.1207/s15327833mtl0703_3.

Müller, T.J., Cury, H.N., & Valdeni, d.L. (2014). A discussion about errors in algebra for creation of learning object. International Journal of Contemporary Educational Research, 1(1), 42-50. http://ijcer.net/tr/issue/16050/167832.

Quinlan, C. (2001). From geometric patterns to symbolic algebra is too hard for many. In B. J., P. Perry, & M. M. (Ed.), Numeracy and Beyond, Proceedings of the Twenty-Fourth Annual Conference of the Mathematics Education Research Group of Australasia (pp. 426-433). Turramurra: MERGA Inc.

Radford, L. (2006). Algebraic thinking and the generalization of patterns: A semiotic perspective. In S. Alatorre, J. Cortina, M. Sáiz, & A. Méndez (Ed.), Proceedings of the 28th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Mérida, México (pp. 1-20). Universidad Pedagógica Nacional.

Rivera, F. (2011). Toward a Vvisually-Ooriented Sschool Mmathematics Ccurriculum. Mathematic Education Library Series. Dordrecht: Springer Science & Business Media. Mathematics Education Library, 49, 21-38.https://doi.org/10.1007/978-94-007-0014-7.

Salemeh, Z., & Etchells, M.J. (2016). A case study: Sources of difficulties in solving word problems in an International private school. Electronic International Journal of Education, Arts, and Science, 2 (Special Issue), 149-163. http://www.eijeas.com/index.php/EIJEAS/article/view/88

Sazhin, S. (1998). Teaching mathematics to engineering students. International Journal of Engineering Education, 14(2), 145-152. https://www.ijee.ie/articles/Vol14-2/ijee1007.pdf.

Treffers, A. (1987). Three dimensions: A model of goal and theory description in mathematics instruction - the Wiskobas project. Dordrecht: D. Reidel Publishing Company.

Usiskin, Z. (1988). Conceptions of school algebra and uses of variables. In A. F. Coxford (Ed.), The ideas of algebra: K-12 (pp. 8-19). Reston, VA: National Council of Teachers of Mathematics.

Venkat, H., Beckmann, S., Larsson, K., Xin, Y. P., Ramploud, A., & Chen, L. (2018). Connecting whole number arithmetic foundations to other parts of mathematics: Structure and structuring activity. In Building the Foundation: Whole Numbers in the Primary Grades (pp. 299-324). Springer, Cham.

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. https://doi.org/10.1088/1742-6596/943/1/012017.

Wijaya, A., Retnawati, H., Setyaningrum, W., Aoyama, K., & Sugiman. (2019). Diagnosing students' learning difficulties in the eyes of Indonesian mathematics teacher. Journal on Mathematics Education, 10(3), 357-364. http://dx.doi.org/10.22342/jme.10.3.7798.357-364.




DOI: https://doi.org/10.22342/jme.11.1.9535.45-58

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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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