Galuh Tyasing Swastika


Abstract: This qualitative research describes the representation of high school X students in solving non-routine math problems. The focus of the representation used in this study is the external representation in terms of differences in the ability of high, medium and low ability students. The method used in this research. The three subjects performed representations of algebraic symbols in solving non-routine problems. Two subjects directly represent the things related to the problem with. However, one subject is not appropriate in performing symbol representation because of an error in its form, not in its completion. In this study also found the number of students inset in non-routine problem solving.


Keyword: representation, non-routin problem


Abstrak: Penelitian kualitatif ini bertujuan mendeskripsikan representasi siswa kelas X SMA dalam menyelesaikan masalah non-rutin matematika. Fokus representasi yang digunakan dalam penelitian ini adalah representasi eksternal yang ditinjau dari perbedaan kemampuan matematika siswa berkemampuan tinggi, sedang dan rendah. Metode yang digunakan dalam penelitian ini wawancara berbasis tugas, dengan pemberian tes representasi masalah non-rutin. Ketiga subjek melakukan representasi berbentuk simbol aljabar dalam melakukan penyelesaian masalah non-rutin. Dua subjek secara langsung merepresentasikan hal-hal yang diketahui dalam masalah dengan simbol variabel secara tepat. Namun satu subjek tidak tepat dalam melakukan representasi simbol variabel karena mengalami kesalahan dalam menerjemahkan permasalahan ke dalam bentuk simbol, sehingga dalam penyelesaiannya pun didapatkan penyelesaian yang salah. Dalam penelitian ini juga ditemukan kurangnya number sense siswa dalam penyelesaian masalah non-rutin.


Kata kunci: representasi, masalah non-rutin


representasi, masalah non-rutin

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Bobis, J. (1996). Visualisation and the development of number sense with kindergarten children. Children’s number learning: A research monograph of MERGA/AAMT Adelaide: Australian Association of Mathematics teachers.

Cai, J. (2003). Singaporean students mathematical thinking in problem-solving and problem posing: An exploratory study. International Journal of Mathematical Education in Science and Technology, 34(5), 719-737.

English, L. (1996). Children’s Construction of Mathematical Knowledge in Solving Novel Isomorphic Problems in Concrete and Written Form. Journal of Mathematical Behavior 15, 81-112.

Eraslan, A. (2008). The notion of reducing abstraction in quadratic functions. International Journal of Mathematical Education in Science and Technology, 39(8), 1051–1060.

Herr, T., & Johnson, K. (2002). Problem-solving strategies: Crossing the river with dogs. USA: Key Curriculum Press.

Krulik, Stephen and Rudnick. Jesse A. (1996). The new sourcebook for teaching reasoning and problem solving in junior and senior high schools. Boston, MA: Allyn and Bacon.

Lesh, R., Post, T., & Behr, M. (1987). Representations and Translations Among Representations n Mathematics Learning and Problem Solving. In C. Janvier (Ed.), Problems of Representation in the Teaching and Learning of Mathematics (pp.33-40) Hillsdale, NJ: Laurence Eribaum.

Markmann, A.B. (1999). Knowledge Representation. Mahwah, NJ: Erlbaum.

Mabilangan, R. A., Limjap, A. A., & Belecina, R. R. (2011). Problem-solving strategies of high school students on non-routine problems: A case study. Alipato: A Journal of Basic Education, 5, 23-46.

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston/VA: National Council of Teachers of Mathematics.

Polya, G. (1957). How to solve it: A new aspect of mathematical method (2nd ed.). New York: Double Day and Co.

Polya, G. (1981). Mathematical Discovery on Understanding, Learning, and Teaching Problem Solving. United States of America.

Post, Thomas R. (1988). Teaching mathematics in grade K-8. USA. Allyn and Bacon. Inc

Reys, R., Lindquist, M., Lambdin, D., Smith & N. Suydam, M. (2004). Helping Children Learn Mathematics. Hoboken, NJ: John Wiley & Sons.

Rittle-Johnson, B., Siegler, R. ., & Alibali, M. . (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93(2), 346–362.

Saleh, Andri. (2009). Number sense, Belajar Matematika Selezat Cokelat. Bandung: Trans Media Pustaka

Schoenfeld, A. H. (1992). Learning to think mathematically: Problem-solving, metacognition and sense-making in mathematics. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 334-370). New York: Mac Millian.

Stylianou, D. A. (2011). An examination of middle school students’ representation practices in mathematical problem solving through the lens of expert work: Towards an organizing scheme. Educational Studies in Mathematics, 76(3), 265–280.

Woodward, J., Beckmann, S., Driscoll, M., Franke, M., Herzig, P., Jitendra, A., Koedinger, K. R., & Ogbuehi, P. (2012). Improving mathematical problem-solving in Grades 4 through 8: A practice guide. Washington, D.C.: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.

Yazgan, Yeliz. (2013). Non-routine Mathematical Problem-Solving at High School Level and Its Relation With Success on University Entrance Exam. US-China Education Review A, ISSN 2161-623X August 2013, 3(8), 571-57



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