Yeliz Yazgan


This study aims to determine the explanatory and discriminative powers of non-routine problem solving strategies used by fourth graders. Six problems were asked to 240 pupils. After scoring answers between 0 and 10, bottom and top segments of 27% were determined based on total scores. Lastly, all scripts of students in these segments were re-scored with regard to strategy use. Multiple regression and discriminant analysis were utilized to evaluate data.

Results showed that strategies explain 84% of the problem solving success, and their importance order is as follows: look for a pattern, work backward, make a systematic list, make a drawing, guess and check and simplify the problem. Strategies which play a significant role in distinguishing students are look for a pattern, make a systematic list, work backward, simplify the problem, make a drawing, respectively. Further researches using more problems, and examining students of different grades are suggested. 


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non-routine problems, problem solving, problem solving strategies, fourth grade students, students’ success

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Altun, M., Bintas, J., Yazgan & Arslan, C. (2007). Examination of problem-solving development of elementary school students (Project No. AFP 2001/37). Bursa, Turkey: Uludag University, Academic Research Projects Department.

Altun, M., & Sezgin-Memnun, D. (2008). Mathematics teacher trainees’ skills and opinions on solving non-routine mathematical problems. Journal of Theory and Practice in Education, 4(2), 213–238.

Bilstein, R., Libeskind, S. & Lott, J. W. (1996). A Problem solving approach to mathematics for elementary school teachers, New York: Addison Wesley Longman Inc.

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.

Elia, I., Van den Heuvel-Panhuizen, M., & Kolovou, A. (2009). Exploring strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in mathematics. ZDM - The International Journal on Mathematics Education, 41, 605-618.

Fang, Y., Ho, K. F., Lioe, L. T., Wong, K. Y., & Tiong, Y. S. J. (2009). Developing the repertoire of heuristics for mathematical problem solving: Technical Report for Project CRP1/04 TSK/JH. Singapore: Centre for Research in Pedagogy and Practice, National Institute of Education, Nanyang Technological University.

Follmer, R. (2000). Reading, mathematics and problem solving: the effects of direct ınstruction in the development of fourth grade students’ strategic reading and problem solving approaches to textbased, nonroutine mathematics problems. (Unpublished doctoral thesis). Widener University, Chester PA.

Glass, G. V. & Hopkins, K. D. (1984). Statistical methods in education and psychology. 2nd Ed. Boston: Allyn and Bacon.

Hair, J.F., Anderson R.E., Tatham R.L., and. Black, W.C. (1998). Multivariate data analysis, 5th ed., NJ: Prentice-Hall.

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

Hok-Wing L. & Bin W. (2002). A comparison of strategies adopted by primary students in four cities of China in solving mathematical problems, Proceedings of The Mathematics Education into the 21st Century Project, Terrasini.

Ishida, J. (2002). Students’ evaluation of their strategies when they find several solution methods. The Journal of Mathematical Behavior, 21, 49–56.

Johnson, K., & Schmidt, A. (2006). The effects of teaching problem solving strategies to low achieving students. Action Research Projects. Paper 62.

Kolovou, A., van den Heuvel-Panhuizen, M. & Bakker, A. (2009). Non-routine problem solving tasks in primary school mathematics textbooks – a needle in a haystack. Mediterranean Journal for Research in Mathematics Education 8(2), 31-68. Lee, N. H., Yeo, J. S. D., & Hong, S. E. (2014). A metacognitive based instruction for primary four students to approach non-routine mathematical word problems. ZDM-The International Journal on Mathematics Education, 46 (3), 465-480.

Leng, N. W. (2008). Problem solving heuristics for primary school mathematics: a comprehensive guide. Singapore: Prentice Hall.

London, R. (2007). What is essential in mathematics education: A holistic view point. MSOR Connections, 7 (1), 30-34.

Mabilangan, R. A., Limjap, A. A., & Belecina, R. R. (2012). Problem solving strategies of high school students on non-routine problems. Alipato: A Journal of Basic Education, 5, 23-45.

Marchis, I (2012). Non-routine problems in primary mathematics workbooks from Romania. Acta Didactica Napocensia , 5(3), 49-56.

MoNE (2004). Talim ve Terbiye Kurulu Baskanlıgı, İlkögretim Matematik Dersi (1-4. Sınıflar) Ogretim Programı. (Board of Education, Elementary school mathematics curriculum: Grades 1- 4) Ankara: MEB Basimevi.

Muir, T., Beswick, K., & Williamson, J. (2008). “I’m not very good at solving problems”: An exploration of students’ problem solving behaviours. Journal of Mathematical Behavior, 22, 228–241.

Nancarrow, M. (2004). Exploration of metacognition and non-routine problem based mathematics instruction on undergraduate student problem-solving success (Unpublished doctoral thesis). The Florida State University, Florida.

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

Novick , L. R., Bassok, M (2005). Problem solving. In Holyoak, K. J. & Morrison, R. G. (ed.). The Cambridge Handbook of Thinking and Reasoning, New York: Cambridge University Press

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

Posamentier, A. S., Krulik, S. (2008). Problem solving strategies for efficient and elegant solutions, grades 6-12: a resource for the mathematics teacher. USA: Corwin Press.

Posamentier, A. S., Krulik, S. (2009). Problem solving in mathematics, grades 3-6: powerful strategies to deepen understanding. USA: Corwin Press.

Reys, R., Suydam, M., Lindquist, M. & Smith, N. L. (1998). Helping children learning mathematics. Boston: Allyn and Bacon.

Robinson, J.P., Shaver, P.R., & Wrightsman, L.S. (1991). Criteria for scale selection and evaluation, in Robinson, J.P., P.R. Shaver, L.S. Wrightsman, (Eds), Measures of Personality and Social Psychological Attitudes (pp. 1-13). San Diego: The Academic Press.

Salleh, F., & Zakaria, E. (2009). Non-routine problem-solving and attitudes toward problem-solving among high achievers. International Journal of Learning, 16(5), 549-559.

Schoenfeld, A. H. (1983). The wild, wild, wild, wild, wild world of problem solving: A review of sorts. For the Learning of Mathematics, 3, 40–47.

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.

Tiong, Y. S. J., Hedberg J., & Lioe L. T. (2005). A metacognitive approach to support heuristic solution of mathematical problems. Paper represented at International Conference on Education, Redesigning pedagogy: research, policy, practice, 30 May – 1 June 2005. Singapore: National Institute of Education.

Wong, K. Y., & Tiong, J. (2006). Diversity in heuristic use among Singapore pupils. Paper presented at ERAS Conference: Diversity for Excellence: Engaged Pedagogies. Singapore.

Wong, K. Y. (2008). Success and consistency in the use of heuristics to solve mathematics problems. Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australia, 589-595.

Van de Walle, J. A. (1994) Elementary school mathematics teaching developmentally. New York: Longman

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, Y., & Bintas, J. (2005). Fourth and fifth grade students’ levels of using problem solving strategies: a teaching experiment. Hacettepe University Education Faculty Journal, 28, 210-218.

Yazgan, Y., Arslan, C., Broutin, M. S. T, Memnun S. D., Akkaya, R., Celebioglu, B. (2013). Non-routine problem-solving skills of elementary and high school students (Project No. E(U)-2009/49. Bursa, Turkey: Uludag University, Academic Research Projects Department.



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