Developing a Model to Support Students in Solving Subtraction

Nila Mareta Murdiyani, Zulkardi Zulkardi, Ratu Ilma Indra Putri, Frans van Galen, Dolly van Eerde


Subtraction has two meanings and each meaning leads to the different strategies. The meaning of “taking away something†suggests a direct subtraction, while the meaning of “determining the difference between two numbers†is more likely to be modeled as indirect addition. Many prior researches found that the second meaning and second strategy rarely appeared in the mathematical textbooks and teacher explanations, including in Indonesia. Therefore, this study was conducted to contribute to the development of a local instruction theory for subtraction by designing instructional activities that can facilitate first grade of primary school students to develop a model in solving two digit numbers subtraction. Consequently, design research was chosen as an appropriate approach for achieving the research aim and Realistic Mathematics Education (RME) was used as a guide to design the lesson. This study involved 6 students in the pilot experiment, 31 students in the teaching experiment, and a first grade teacher of SDN 179 Palembang. The result of this study shows that the beads string could bridge students from the contextual problems (taking ginger candies and making grains bracelets) to the use of the empty number line. It also shows that the empty number line could promote students to use different strategies (direct subtraction, indirect addition, and indirect subtraction) in solving subtraction problems. Based on these findings, it is recommended to apply RME in the teaching learning process to make it more meaningful for students.


Subtraction; Design Research; Realistic Mathematics Education; The Beads String; The Empty Number Line

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Djaelani & Haryono. (2008). Matematika untuk SD/MI kelas 1 [Mathematics for grade 1 Primary School]. Jakarta: Departemen Pendidikan Nasional [Department of National Education].

Fosnot, C. T. & Dolk, M. (2001). Young Mathematicians at Work: Constructing Number Sense, Addition, and Subtraction. Portsmouth, NH: HEINEMENN.

Freudenthal, H. (1983). Didactical Phenomenology of Mathematical Structures. Dordrecht: D. Reidel.

Gravemeijer, K. & Cobb, P. (2006). Design research from the learning design perspective. Educational Design Research (pp. 17-51). London: Routledge.

Hadi, S., Zulkardi, & Hoogland, K. (2010). Quality assurance in PMRI. Design of standards for PMRI. In A Decade of PMRI in Indonesia (pp. 153-161). Bandung: Ten Brink Meppel.

Kamii, C. & Lewis, B. A. (1993). The harmful effects of algorithms…in primary arithmetic. Teaching pre-K-8, 23(4), 36-38.

Menne, J. J. M. (2001). A productive training program for mathematically weak children in the number domain up to 100 – A design study). Utrecht: CDBeta Press.

Torbeyns, J., De Smedt, B., Stassens, N., Ghesquiere, P., & Verschaffel, L. (2009). Solving subtraction problems by means of indirect addition. Mathematical Thinking and Learning, 11, 79-91. DOI: 10.1080/10986060802583998.

Treffers, A. (1987). Three Dimensions. A Model of Goal and Theory Description in Mathematics Instruction – The Wiskobas Project. Dordrecht, The Netherlands: Reidel Publishing Company.



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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

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