Research Article

The main purpose of this study was to investigate how well certain students in a high school solve non-routine problems. These problem situation required the use of their conceptual understanding of mathematics and their procedural knowledge of the algorithm involved in the solution. Results of analysis of students’ solutions showed that each student employed at least three problem solving strategies. Nine out of the ten possible problem solving strategies were used at least once to solve the eight non-routine problems. The most frequently used strategies were making systematic list, looking for patterns, logical reasoning and making a model or diagram. Those who performed well were also proficient in the use of solution strategies.

- Altun, M. (2005) İlköğretimde Matematik Öğretimi. Bursa. Aktüel Alfa Bas. Yay.
- Altun, M. , Bintas, J., Yazgan, Y., Arslan, C. (2007) Examination of problem solving development of elementary school students (Project No. AFP 2001/37). Bursa, Turkey: Uludağ University, Academic Research Projects Department.
- Artzt, A. ve Armour-Thomas, E. (1992) Development of A Cognitive - Metacognitive Framework for Protocol Analysis of Mathematical Problem Solving in Small Groups. Cognition and Instruction 9, 137-175.
- Baki, A. ve Kartal, T. (2004) Kavramsal ve Işlemsel Bilgi Bağlaminda Lise Öğrencilerinin Cebir Bilgilerinin Değerlendirilmesi. Türk Eğitim Bilimleri Dergisi, 2(1), 27-46.
- Ben-Hur, M. (2006) Concept-rich mathematics instruction: Building a strong foundation for reasoning and problem solving. Alexandria, Virginia: Association for Supervision and Curriculum Development. http://www.ascd.org/publications/books/106008/chapters/Conceptual-Understanding.aspx.
- Boesen, J., Lithner, J. & Palm, T. (2010) The relation between types of assessment tasks and the mathematical reasoning students use. Educational Studies in Mathematics, 75(1), 89–105.
- Cai, J and Lester, F. (2010) Why is Teaching with Problem Solving Important to Student Learning? Reston, VA: National Council of Teachers of Mathematics.
- Chicago Public Schools Bureau of Student Assessment (1991) Oregon Mathematics Problem Solving & Norwood Park Draft Math Problem Solving Rubric. Illinois: Chicago Public Schools Bureau of Student Assessment.
- Devlin, K. (2007) What is conceptual understanding? Washington DC: Mathematical Association of America. http://www.maa.org/devlin/ devlin_09_07.html.
- Elia I. , Van den Heuvel-Panhuizen M. , Kolovou A. (2009) Exploring 10.1016/j.jmathb.2008.04.003 strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in Mathematics. ZDM – Int. J. Math. problem based mathematics instruction on undergraduate student Educ. 41:605-618. http://dx.doi.org/ 10.1007/s11858-009-0184-6.
- Goos, M., Galbraith, P. ve Renshaw, P. 2000. A Money Problem: A Source of Insight into Problem Solving Action. International Journal For Mathematics Teaching and Learning, 80.
- Hartman, H. J. (1998). Metacognition in teaching and learning: An introduction. Instructional Science, 26, 1-3.
- Herr, T. and Johnson, K. (2002) Problem-solving strategies: Crossing the the river with dogs. USA: Key Curriculum Press.
- Inoue, N. (2005).The realistic reasons behind unrealistic solutions: The role of interpretive activity in word problem solving. Learning and Instruction, 15, 69 83.
- Kaur, B. ve Yeap, B. H. (2009) Mathematical Problem Solving in Singapore Schools. In B. Kaur, B. H. Yeap &Kapur, M., Mathematical Problem Solving: Yearbook 2009 (pp. 3-13). Singapore: Association of Mathematics Education and World Scientific.
- Koedinger, R. K. and Tabachneck, H. J. M. (1994) Two Strategies Are Better Than One: Multiply Strategy Use in Word Problem Solving. Paper Presented in Annual Meeting of The American Educational Research Education, New Orlans.
- Krulik, S. and Rudnick. J. A. (1996) The new source book for teaching reasoning and problem solving in junior and senior high schools. Boston, MA: Allyn and Bacon.
- Leng, N. W. (2008) Problem solving heuristics for primary school mathematics: a comprehensive guide. Singapore: Prentice Hall.
- London, R. (1993) A Curriculum of Non-Routine Problems. American Educational Research Association: Atalanta. April 12-16, 1993.
- Mabilangan, R. A., Limjap, A. A. & Belecina, R. R. (2011) Problem Solving Strategies of High School Students on Non-Routine Problems. Alipato: A Journal of Basic Education, Vol(5), 23-47.
- Mayer, R. E. (1985) Mathematical Ability. In R.J. Sternberg, Ed., Human Abilities: An Information Processing Approach (Pp. 127-150). New York: Freeman.
- Mayer, R. E., Sims, V., & Tajika, H. (1995). A comparison of how textbooks teaching mathematical problem solving in Japan and the United States. American Educational Research Journal, 35, 443-459.
- Milli Eğitim Bakanlığı (MEB) (2017) Ortaöğretim Kurumları Matematik dersi Öğretim Program Taslağı http://mufredat.meb.gov.tr Erişim Tarihi: 14.01.2017
- Nancarrow, M. (2004) Exploration of metacognition and non-routine problem based mathematics instruction on undergraduate student problem-solving success, Unpublished PhD thesis, the Florida State University, Florida.
- Olkun, S. and Toluk, Z. (2004) İlköğretimde Etkinlik Temelli Matematik Öğretimi. Ankara: Anı Yayıncılık.
- Polya, G. (1957) How to solve it: A new aspect of mathematical method. 2nd ed. New York: Double Day and Co.
- Polya, G. (1997). How to Solve It? (Feryal Halatçı, çev.).New York (Original work published 1957).
- 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.
- 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, MacMillan.
- Schoenfeld, A. H. (1999) Looking Toward The 21st Century: Challenges of Educational Theory and Practice. Educational Researcher, 28(7), 4-14.
- Tarım, K., Artut D. P. (2009) "Öğretmen Adaylarının Rutin Olmayan Sözel Problemleri Çözme Süreçlerinin Incelenmesi", Uludağ Üniversitesi Eğitim Fakültesi Dergisi , cilt.12, ss.53-70.
- Teong, K. S. (2000) The Effect of Metacognitive Training On The Mathematical Word Problem Solving of Singapore 11-12 Year Olds In A Computer Environment. Unpublished Phd Thesis: The University of Leeds.
- Yazgan, Y. (2007) Dördüncü ve Beşinci Sınıf Öğrencilerinin Rutin Olmayan Problem Çözme Stratejileriyle İlgili Gözlemler. İlköğretim Online, 6(2), 249-263. Xin, Z., Lin, C., Zhang, L.&Yan, R. (2007) The performance of Chinese Primary School students on realistic arithmetic word problems. Educational Psychology in Practice, 23 (2), 145 159.
- Wyndhamn, J.&Saljö, R. (1997) Word problems and mathematical reasoning. A study of children’s mastery of reference and meaning in textual realities. Learning and Instruction, 7 (4), 361 382.
- 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. Educator’s Practice Guide. U.S. Department of Education.

Bu araştırmanın amacı lise öğrencilerinin rutin olmayan problem çözme beceri düzeylerinin ve kullandıkları stratejilerin başarı durumlarına göre dağılımını saptamak amaçlanmaktadır. Bu amaç doğrultusunda öğrencilerin kavramsal anlama, işlemsel bilgi düzeyleri ve problem çözme becerileri incelenmiştir. Durum çalışması deseninin kullanıldığı bu araştırma 18 öğrenci ile yürütülmüştür. Araştırma sonuçları her bir öğrenci en az üç farklı problem çözme stratejisi kullandığını göstermektedir. Araştırmadaki rutin olmayan sekiz problemde kullanılması muhtemel olan on stratejiden dokuzunu öğrenciler en az bir kez kullandıkları görülmüştür. En çok birlikte kullanılan stratejiler sistematik liste yapma, örüntü-bağıntı bulma, mantıksal düşünme, şema çizmedir. Problem çözme becerisi usta düzeyinde olan öğrencilerin stratejileri etkin bir şekilde kullandıkları görülmüştür.

- Altun, M. (2005) İlköğretimde Matematik Öğretimi. Bursa. Aktüel Alfa Bas. Yay.
- Altun, M. , Bintas, J., Yazgan, Y., Arslan, C. (2007) Examination of problem solving development of elementary school students (Project No. AFP 2001/37). Bursa, Turkey: Uludağ University, Academic Research Projects Department.
- Artzt, A. ve Armour-Thomas, E. (1992) Development of A Cognitive - Metacognitive Framework for Protocol Analysis of Mathematical Problem Solving in Small Groups. Cognition and Instruction 9, 137-175.
- Baki, A. ve Kartal, T. (2004) Kavramsal ve Işlemsel Bilgi Bağlaminda Lise Öğrencilerinin Cebir Bilgilerinin Değerlendirilmesi. Türk Eğitim Bilimleri Dergisi, 2(1), 27-46.
- Ben-Hur, M. (2006) Concept-rich mathematics instruction: Building a strong foundation for reasoning and problem solving. Alexandria, Virginia: Association for Supervision and Curriculum Development. http://www.ascd.org/publications/books/106008/chapters/Conceptual-Understanding.aspx.
- Boesen, J., Lithner, J. & Palm, T. (2010) The relation between types of assessment tasks and the mathematical reasoning students use. Educational Studies in Mathematics, 75(1), 89–105.
- Cai, J and Lester, F. (2010) Why is Teaching with Problem Solving Important to Student Learning? Reston, VA: National Council of Teachers of Mathematics.
- Chicago Public Schools Bureau of Student Assessment (1991) Oregon Mathematics Problem Solving & Norwood Park Draft Math Problem Solving Rubric. Illinois: Chicago Public Schools Bureau of Student Assessment.
- Devlin, K. (2007) What is conceptual understanding? Washington DC: Mathematical Association of America. http://www.maa.org/devlin/ devlin_09_07.html.
- Elia I. , Van den Heuvel-Panhuizen M. , Kolovou A. (2009) Exploring 10.1016/j.jmathb.2008.04.003 strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in Mathematics. ZDM – Int. J. Math. problem based mathematics instruction on undergraduate student Educ. 41:605-618. http://dx.doi.org/ 10.1007/s11858-009-0184-6.
- Goos, M., Galbraith, P. ve Renshaw, P. 2000. A Money Problem: A Source of Insight into Problem Solving Action. International Journal For Mathematics Teaching and Learning, 80.
- Hartman, H. J. (1998). Metacognition in teaching and learning: An introduction. Instructional Science, 26, 1-3.
- Herr, T. and Johnson, K. (2002) Problem-solving strategies: Crossing the the river with dogs. USA: Key Curriculum Press.
- Inoue, N. (2005).The realistic reasons behind unrealistic solutions: The role of interpretive activity in word problem solving. Learning and Instruction, 15, 69 83.
- Kaur, B. ve Yeap, B. H. (2009) Mathematical Problem Solving in Singapore Schools. In B. Kaur, B. H. Yeap &Kapur, M., Mathematical Problem Solving: Yearbook 2009 (pp. 3-13). Singapore: Association of Mathematics Education and World Scientific.
- Koedinger, R. K. and Tabachneck, H. J. M. (1994) Two Strategies Are Better Than One: Multiply Strategy Use in Word Problem Solving. Paper Presented in Annual Meeting of The American Educational Research Education, New Orlans.
- Krulik, S. and Rudnick. J. A. (1996) The new source book for teaching reasoning and problem solving in junior and senior high schools. Boston, MA: Allyn and Bacon.
- Leng, N. W. (2008) Problem solving heuristics for primary school mathematics: a comprehensive guide. Singapore: Prentice Hall.
- London, R. (1993) A Curriculum of Non-Routine Problems. American Educational Research Association: Atalanta. April 12-16, 1993.
- Mabilangan, R. A., Limjap, A. A. & Belecina, R. R. (2011) Problem Solving Strategies of High School Students on Non-Routine Problems. Alipato: A Journal of Basic Education, Vol(5), 23-47.
- Mayer, R. E. (1985) Mathematical Ability. In R.J. Sternberg, Ed., Human Abilities: An Information Processing Approach (Pp. 127-150). New York: Freeman.
- Mayer, R. E., Sims, V., & Tajika, H. (1995). A comparison of how textbooks teaching mathematical problem solving in Japan and the United States. American Educational Research Journal, 35, 443-459.
- Milli Eğitim Bakanlığı (MEB) (2017) Ortaöğretim Kurumları Matematik dersi Öğretim Program Taslağı http://mufredat.meb.gov.tr Erişim Tarihi: 14.01.2017
- Nancarrow, M. (2004) Exploration of metacognition and non-routine problem based mathematics instruction on undergraduate student problem-solving success, Unpublished PhD thesis, the Florida State University, Florida.
- Olkun, S. and Toluk, Z. (2004) İlköğretimde Etkinlik Temelli Matematik Öğretimi. Ankara: Anı Yayıncılık.
- Polya, G. (1957) How to solve it: A new aspect of mathematical method. 2nd ed. New York: Double Day and Co.
- Polya, G. (1997). How to Solve It? (Feryal Halatçı, çev.).New York (Original work published 1957).
- 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.
- 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, MacMillan.
- Schoenfeld, A. H. (1999) Looking Toward The 21st Century: Challenges of Educational Theory and Practice. Educational Researcher, 28(7), 4-14.
- Tarım, K., Artut D. P. (2009) "Öğretmen Adaylarının Rutin Olmayan Sözel Problemleri Çözme Süreçlerinin Incelenmesi", Uludağ Üniversitesi Eğitim Fakültesi Dergisi , cilt.12, ss.53-70.
- Teong, K. S. (2000) The Effect of Metacognitive Training On The Mathematical Word Problem Solving of Singapore 11-12 Year Olds In A Computer Environment. Unpublished Phd Thesis: The University of Leeds.
- Yazgan, Y. (2007) Dördüncü ve Beşinci Sınıf Öğrencilerinin Rutin Olmayan Problem Çözme Stratejileriyle İlgili Gözlemler. İlköğretim Online, 6(2), 249-263. Xin, Z., Lin, C., Zhang, L.&Yan, R. (2007) The performance of Chinese Primary School students on realistic arithmetic word problems. Educational Psychology in Practice, 23 (2), 145 159.
- Wyndhamn, J.&Saljö, R. (1997) Word problems and mathematical reasoning. A study of children’s mastery of reference and meaning in textual realities. Learning and Instruction, 7 (4), 361 382.
- 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. Educator’s Practice Guide. U.S. Department of Education.

Primary Language | English |
---|---|

Subjects | Studies on Education |

Journal Section | Educational Sciences and Sciences of Field Education |

Authors | |

Publication Date | August 22, 2017 |

Published in Issue | Year 2017Volume: 8 Issue: 2 |

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