Investigating Students' Development of Learning Integer Concept and Integer Addition

Nenden Octavarulia Shanty


This research aimed at investigating students' development of learning integer concept and integer addition. The investigation was based on analyzing students' works in solving the given mathematical problems in each instructional activity designed based on Realistic Mathematics Education (RME) levels. Design research was chosen to achieve and to contribute in developing a local instruction theory for teaching and learning of integer concept and integer addition. In design research, the Hypothetical Learning Trajectory (HLT) plays important role as a design and research instrument. It was designed in the phase of preliminary design and tested to three students of grade six OASIS International School, Ankara – Turkey. The result of the experiments showed that temperature in the thermometer context could stimulate students’ informal knowledge of integer concept. Furthermore, strategies and tools used by the students in comparing and relating two temperatures were gradually be developed into a more formal mathematics. The representation of line inside thermometer which then called the number line could bring the students to the last activity levels, namely rules for adding integer, and became the model for more formal reasoning. Based on these findings, it can be concluded that students' learning integer concept and integer addition developed through RME levels.

Keywords: integer concept, integer addition, Realistic Mathematics Education

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Bakker, A. (2004). Design research in statistics education: on symbolizing and computer tools. Utrecht: CD-β Press.

Battista, M.T. (1983). A complete model for operations on integers. Arithmetic Teacher, 30(9), 26-31.

Doorman, L.M. (2005). Modelling motion: from trace graphs to instantaneous change. Amersfoort: Wilco Press.

Freudenthal, H. (1991). Revisiting mathematics education. Dordrecht: Kluwer Academic Publisher.

Gallardo, A. (2002). The extension o f the natural-number domain to the integers in the transition from arithmetic to algebra. Educational Studies in Mathematics, 49, 171-192.

Gravemeijer, K. (1994). Developing realistic mathematics education research group on mathematics education. Utrecht: CD β Press.

Gravemeijer, K. & Cobb, P. (2006). Educational design research: design research from a learning design perspective. UK: Routledge.

Liebeck, P. (1990). Scores and forfeits: An intuitive model for integer arithmetic. Educational Studies in Mathematics, 21, 221-239.

Smith, J.P. (1995). The effects of a computer microworld on middle school students’ use and understanding of integers. Unpublished doctoral dissertation. The Ohio State University, Columbus, Ohio. Retrieved from

Streefland, L. (1996). Negative numbers: Reflections of a learning researcher. Journal of Mathematical Behavior, 15, 57-79.

Stephan, M. & Akyuz, D. (2012). A proposed instructional theory for integer addition and subtraction. National Council of Teachers of Mathematics, 43, 428-464.

Swanson, P. E. (2010). The intersection of language and mathematics. Mathematics Teaching in the Middle School, 15 (9), 516-523.

Treffers, A. (1991). Didactical background of a mathematics program voor primary education. In: L. Streefland (ed.). Realistic Mathematics Education in Primary School. Utrecht: CD-β Press.

Van de Walle, et al. (2010). Elementary and middle school mathematics, teaching developmentally. Eight edition. United Stated of America: Pearson Education, Inc.



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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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