### SUPPORTING STUDENTS' UNDERSTANDING OF LINEAR EQUATIONS WITH ONE VARIABLE USING ALGEBRA TILES

#### Abstract

This research aimed to describe how algebra tiles can support students' understanding of linear equations with one variable. This article is a part of a larger research on learning design of linear equations with one variable using algebra tiles combined with balancing method. Therefore, it will merely discuss one activity focused on how students use the algebra tiles to find a method to solve linear equations with one variable. Design research was used as an approach in this study. It consists of three phases, namely preliminary design, teaching experiment and retrospective analysis. Video registrations, students' written works, pre-test, post-test, field notes, and interview are technic to collect data. The data were analyzed by comparing the hypothetical learning trajectory (HLT) and the actual learning process. The result shows that algebra tiles could supports students' understanding to find the formal solution of linear equation with one variable.

Keywords: linear equation with one variable, algebra tiles, design research, balancing method, HLT

#### Full Text:

PDF#### References

Amerom, B.A. (2002). Reinvention of Early Algebra. Utrecht: Freudental Institut.

Bednarz, N., Kieran, C., & Lee, L. (1996). Approaches to Algebra Perspectives for Research and Teaching. Netherlands: Kluwer Academic Publishers.

Cai, J., et al. (2005). The Development of Studentsâ€™ Algebraic Thinking in Earlier Graders: A Cross-Cultural Comparative Perspective, Journal on National Science Foundation, ZDM 2005, 37 (1), 5-15.

Fachrudin, A., Putri, R.I.I., & Damawijoyo. (2014). Building Studentsâ€™ Understanding of Quadratic Equation Concept Using NaÃ¯ve Geometry. Journal on Mathematics Education, 5 (2), 192-202.

Fauvel, J. & van Maanen, J. (2002). History in Mathematics Education. New York: Kluwer Academic Publishers.

Freudenthal, H. (2002). Revisiting Mathematics Education: China Lectures. Dordrecht: Kluwer Academic Publishers.

Gravemeijer, K. (1994). Developing Realistic Mathematics Education. Utrecht: Technipress, Culemborg.

Gravemeijer, K. & Cobb, P. (2006). Design Research from a Learning Design Perspective. Educational Design Research. In Jan van den Akker, et.al. Educational Design Research. London: Routledge.

Gravemeijer, K. & van Eerde, D. (2009). Design Research as a Means for Building a Knowledge Base for Teaching in Mathematics Education. The Elementary School Journal, 109 (5).

Grugnetti, L. (2000). The History of Mathematics and its Influence on Pedagogical Problems. In Katz, V. (Ed), using history to teach mathematics: an international perspective (pp. 29-35) USA: The Mathematical Association of America.

Heddens, J.W. & Speer, W.R. (2001). Todayâ€™s Mathematics. John wlley & Sons, Inc.

Jupri, A., Drijvers, P., & Van den Heuvel-Panhuizen, M. (2014). Difficulties in initial algebra learning in Indonesia. Mathematics Education Research Journal, 1-28.

Jupri, Al. (2015). The Use of Applets to Improve Indonesian Student Performance in Algebra. Published Dissertation. Utrecht: Utrecht University.

Kemendikbud. (2013). Matematika SMP/MTs Kelas VII. Jakarta: Politeknik Negeri Media Kreatif.

Krantz, S.G. (2006). An Episodic History of Mathematics. MAA Textbooks.

Magruder, R.L. (2012). Solving Linear Equations: A Comparison of Concreate and Virtual Manipulatives in Middle School mathematics. University of Kentucky Acknowledge. Theses and Dissertations-Curriculum and Instruction, Paper 2: University of Kentucky.

Merzbach, U.C. & Boyer, C.B. (2010). A History of Mathematics. New Jersey: John Wiley & Sons, Inc. Hoboken.

Plomp & Nieven. (2007). an Introduction to Educational Design Research. Proceedings of the seminar conducted at the East China Normal University, Shanghai (PR China).

Radford, L. (1996). The roles of geometry and arithmetic in the development of algebra: Historical

remarks from a didactic perspective. In Approaches to algebra (pp. 39-53). Springer

Netherlands.

Sembiring, R.K. (2010). Pendidikan Matematika Realistik Indonesia (PMRI): Perkembangan dan Tantangannya. Journal on Mathematics Education, 1 (1), 11-16.

Tasman, F., den Hertog, J., Zulkardi, & Hartono, Y. (2011). Helping students acquainted with multiplication in rectangular model. Journal on Mathematics Education, 2 (2), 185-198.

Treffers, A. (1987). Three Dimensions. A Model of Goal and Theory Description in Mathematics Instruction â€“ The Wiskobas Project. Dordect: Reidel Publishing Company.

Van den Heuvel-Panhuizen, M. (1996). Assessment and Realistic Mathematics Education. Utrecht: Freudenthal Institute.

Van de Walle, J.A., Karp, K.S., & Williams, J.M.B. (2010). Elementary and Middle School Mathematics Teaching Development. Pearson Education, Inc.

Witzel, B.S., Mercer, C.D., & Miller, M.D. (2003). Teaching Algebra to Students with Learning Difficulties: An Investigation of an Explicit Instruction Model. The Division for Learning Disabilities of the Council for Exceptional Children. Learning Disabilities Research & Practice, 18 (2), 121â€“131.

Zulkardi. (2002). Developing a Learning Environment on Realistic Mathematics Education for Indonesian Student Teachers. Published Dissertation. Enschede: University of Twente.

DOI: https://doi.org/10.22342/jme.7.1.2814.19-30

### Refbacks

- There are currently no refbacks.

**Journal on Mathematics Education**

Kampus FKIP Bukit Besar

Jl. Srijaya Negara, Bukit Besar

Palembang - 30139

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

Journal on Mathematics Education is licensed under a Creative Commons Attribution 4.0 International License

View My Stats