### Supporting Students’ Reasoning About Multiplication of Fractions by Constructing an Array Model

DOI: https://doi.org/10.23917/jramathedu.v1i2.3385

#### Abstract

*The aim of the research is to support students in constructing an array model as a bridge from their informal knowledge to the formal one in understanding the part-whole relation concept. The part-whole relation concept is important for students to reason about multiplication of fractions. Realistic Mathematics Education which is in Indonesia adapted as Pendidikan Matematika Realistik Indonesia (PMRI) is used as an approach in designing a series of lessons. For this purpose, hypothetical learning trajectory (HLT) became the base for conducting a teaching experiment and designing its learning materials. The research was conducted in the fifth grade of SD Al Hikmah Surabaya, an elementary school in Indonesia, with five students as the participants. The collected data were qualitative data in the form of students’ written works and the transcript of video recording during the lesson. The data were analyzed retrospectively by confronting the conjecture of students’ thinking in the HLT with the fact in the teaching experiment. The result of the research shows that most students could use the contextual problem in promoting their ability on constructing their own array model to reason about part-whole relation.*

#### Keywords

#### Full Text:

PDF#### References

Bakker, A., & van Eerde, D. (2015). An introduction to design-based research with an example from statistics education. In Approaches to qualitative research in mathematics education (pp. 429-466). Springer Netherlands.

Behr, M. J., Harel, G., Post, T., & Lesh, R. (1992). Rational number, ratio, and proportion. Handbook of research on mathematics teaching and learning, 296-333.

Charalambous, C. Y., & Pitta-Pantazi, D. (2007). Drawing on a theoretical model to study students’ understandings of fractions. Educational Studies in Mathematics, 64(3), 293-316.

Fosnot, C. T., & Dolk, M. L. A. M. (2002). Young mathematicians at work: Constructing fractions, decimals, and percents. Portsmouth: Heinemann.

Freudenthal, H. (1983). Didactical phenomenology of mathematical structures (Vol. 1). Springer.

Freudenthal, H. (1991). Revisiting mathematics education-china lectures. Dordrecht: Kluwer Academic Publishers.

Gravemeijer, K. (1994). Developing realistic mathematics education. Utrecht: CD-ß press/ Freudenthal Institute.

Gravemeijer, K.P.E & Cobb, P. (2006). Design research from a learning design perspective. In: Van Den Akker, J., Gravemeijer, K.P.E McKenny, S. & Nieveen, N (Eds.). Educational Design Research. New York: Routledge.

Keijzer, R. (2003). Teaching formal mathematics in primary education. Fraction learning as mathematising process. CD-Beta Press, Center for Science and Mathematics Education.

Lestiana, H. T., Abadi, Budiarto, M. T., Abels, M. J., van Eerde, D. (2014). Promoting students’ understanding of the addition of fractions. In R. I. I., Putri (Ed.), The second South East Asia Design/ Development Research (SEA-DR) International Conference (pp. 142-151). Palembang: Sriwijaya University.

Nasution, A. A., Amin, S. M., Lukito, A., Abels, M. J., Dolk, M. (2014). Educational Design Research: Supporting fifth-grade students to learn about proportion . In R. I. I., Putri (Ed.), The second South East Asia Design/ Development Research (SEA-DR) International Conference (pp. 43-51). Palembang: Sriwijaya University.

Pantziara, M., & Philippou, G. (2012). Levels of students’“conception” of fractions. Educational Studies in Mathematics, 79(1), 61-83.

Rifandi, R., Budiarto, M. T., Lukito, A., Abels, M. J., Dolk, M. (2014). Developing grade five students understanding of multiplication of two fractions trough taking a part of a part of a whole activity. In R. I. I., Putri (Ed.), The second South East Asia Design/ Development Research (SEA-DR) International Conference (pp. 272-278). Palembang: Sriwijaya University.

Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for research in mathematics education, 114-145.

Smith, J. P. (2002). The development of students' knowledge of fractions and ratios. In B. Litwiller, & G. Bright, Make Sense of Fractions, Ratios, and Proportions (pp. 3-17). Reston, VA: National Council of Teachers of Mathematics.

Vale, C., Widjaja, W., Herbert, S., Bragg, L. A., & Loong, E. Y. K. (2016). Mapping Variation in Children’s Mathematical Reasoning: The Case of ‘What Else Belongs?’. International Journal of Science and Mathematics Education, 1-22.

Van den Heuvel-Panhuizen, M. (1996). Assessment and realistic mathematics education. Utrecht: CD-ß Press / Freudenthal Institute, Utrecht University.

Wright, Vince. (2014). Towards a hypothetical learning trajectory for rational number. MathematicsEducation Research Journal, 635- 657.

### Refbacks

- There are currently no refbacks.