### BUILDING STUDENTS' UNDERSTANDING OF QUADRATIC EQUATION CONCEPT USING NAÏVE GEOMETRY

#### Abstract

The purpose of this research is to know how Naive Geometry method can support students' understanding about the concept of solving quadratic equations. In this article we will discussÂ one activities of the four activities we developed. This activity focused on how students linking the Naive Geometry method with the solving of the quadratic equation especially on how student bring geometric solution into algebraic form. This research was conducted in SMPÂ Negeri 1 Palembang. Design research was chosen as method used in this research that have three main phases. The results of this research showed that manipulating and reshaping theÂ rectangle into square could stimulate students to acquire the idea of solving quadratic equations using completing perfect square method. In the end of the meeting, students are also guided to reinvent the general formula to solve quadratic equations.

Keywords: Quadratic Equations, Design Research, Naive Geometry, PMRI

#### Full Text:

PDF#### References

Bakker, A. (2004). Design Research in Statistics Education on Symbolizing and Computer Tools. Amersfoort: Wilco Press.

Boyer, C. B., & Merzbach, U. C. (2011). A history of mathematics. John Wiley & Sons.

Fauvel, J., & Van Maanen, J. (Eds.). (2000). History in mathematics education. Dordrecht, theNetherlands: Kluwer Academic Publishers.

French, D. (2002). Teaching and Learning Algebra. London: Continuum.

Gravemeijer, K. (2004). Local instruction theories as means of support for teachers in reform mathematics education. Mathematical thinking and learning,6(2), 105-128.

Gravemeijer, K., & Cobb, P. (2006). Design research from a learning design perspective. Educational design research, 17-51.

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.

HÇ¿yrup, J. (1990b). Algebra and naive geometry. An investigation of some basic aspects of old babylonian mathematical thought II. Altorientalische Forschungen, 17, 262-254.

Krantz, S. G. (2006). An Episodic History of Mathematics: Mathematical Culture through Problem Solving. Mathematical Association of America.

Panasuk, R. M., & Horton, L. B. (2012). Integrating History of Mathematics into Curriculum: What are the Chances and Constraints?. International Electronic Journal of Mathematics Education, 7(1)

Radford, L. & Guerette, G. (2000). Second degree equations in the classroom: a Babylonian approach. In Katz, V. (Ed), Using history to teach mathematics: an international perspective (pp. 69-75). USA: The Mathematical Association of America.

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.

Radford, L. (2002). The historical origins of algebraic thinking. Perspectives on school algebra, 13- 36.

Wijaya, A. (2008). Design Research in Mathematics Education: Indonesian Traditional Games as Means to Support Second Gradersâ€™ Learning of Linear Mesurement. Master Thesis of Utrecht University. The Netherlands: Utrecht University.

Simon, M. A., & Tzur, R. (2004). Explicating the role of mathematical tasks in conceptual learning: An elaboration of the hypothetical learning trajectory.Mathematical Thinking and Learning, 6(2), 91-104.

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

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.

Zakaria, E., & Maat, S. M. (2010). Analysis of Studentsâ€™ Error in Learning of Quadratic Equations. International Education Studies, 3(3), P105.

DOI: https://doi.org/10.22342/jme.5.2.1502.191-202

### 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