Research Article
BibTex RIS Cite

Üstün Yetenekli Ortaokul Öğrencilerinin Rutin Olmayan Problemleri Çözerken Gösterdikleri Strateji Esnekliği

Year 2025, Volume: 8 Issue: 3, 214 - 228, 30.09.2025

Abstract

Bu çalışmanın amacı, üstün yetenekli ortaokul öğrencilerinin rutin dışı problemleri çözerken sergiledikleri stratejik esnekliği incelemektir. Araştırmaya, Bursa ili Yıldırım ilçesindeki ortaokullarda öğrenim gören ve üstün yetenekli olarak tanılanmış yedi altıncı sınıf, altı yedinci sınıf ve beş sekizinci sınıf öğrencisi yer almıştır. Her biriyle ayrı ayrı görüşmeler yapılmış ve öğrencilere yedi adet rutin olmayan problem yöneltilmiş, öğrencilerin çözüm süreçleri ve biçimleri incelenmiştir. Öğrencilerin problem çözme süreçleri üç temel kategori üzerinden değerlendirilmiştir: en uygun stratejiyi kullanma, görevler arası esneklik (inter-task flexibility) ve görev içi esneklik (intra-task flexibility). Bu kategorilerin her biri, 1 ile 4 arasında puanlanarak analiz edilmiştir. Araştırma bulguları, öğrencilerin uygun strateji seçimi ve farklı problemler karşısında strateji değiştirme konularında genel olarak başarılı olduklarını ortaya koymaktadır. Bununla birlikte, genel esneklik puanlarının yüksek olmasına rağmen, öğrencilerin tek bir problem üzerinde çalışırken strateji değiştirme veya birden fazla stratejiyi bir arada kullanma konusunda zorlandıkları görülmektedir. Elde edilen bulgular, stratejik esnekliğin boyutlarının birbirinden bağımsız gelişebileceğine işaret etmektedir.

References

  • Assmus, J., Ertküçük, A., & Grigutsch, S. (2022). Gifted students’ approaches to solving non-routine mathematical problems: Insights from a process-oriented perspective. International Journal of Science and Mathematics Education, 20(4), 789–812. https://doi.org/10.1007/s10763-021-10189-9
  • Altun M. (2016). Ortaokullarda (5, 6, 7 ve 8. sınıflarda) matematik öğretimi. Bursa: Aktüel Yayıncılık.
  • Altun, M., Bintas, J., Yazgan, Y. & Arslan, C. (2004). İlköğretim çağındaki çocuklarda problem çözme gelişiminin incelenmesi. Uludağ Üniversitesi Bilimsel Araştırma Projeleri Birimi. https://www.researchgate.net/profile/Yeliz-Yazgan-2/publication/305769065_ILKOGRETIM_CAGINDAKI_COCUKLARDA_PROBLEM_COZME_GELISIMININ_INCELENMESI/links/57a0602a08aec29aed23755e/ILKOGRETIM-CAGINDAKI-COCUKLARDA-PROBLEM-COeZME-GELISIMININ-INCELENMESI.pdf
  • Arslan, C., & Yazgan, Y. (2015). Common and flexible use of mathematical non routine problem solving strategies. American Journal of Educational Research, 3(12), 1519-1523. doi:10.12691/education-3-12-6.
  • Bräuning, K. (2016). Investigating multiple strategy use and strategy flexibility in problem solving by pre-service teachers. In T. Fritzlar, D. Aßmus, K. Bräuning, A. Kuzle, & B. Rott (Eds.), Problem solving in mathematics education. Proceedings of the 2015 joint conference of ProMath and the GDM working group on problem solving (pp. 41-55). Münster: WTM.
  • Boesen, J., Lithner, J., & Palm, T. (2023). Students' creative reasoning and mathematical problem solving: New insights from classroom settings. Educational Studies in Mathematics, 112(1), 45–67. https://doi.org/10.1007/s10649-022-10154-4
  • Boaler, J. (2022). Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages and innovative teaching. Jossey-Bass.
  • Bulgar, S. (2008). Enabling more students to achieve mathematical success; a case study of Sarah. In B. Sriraman (Ed.), Creativity, giftedness, and talent development in mathematics (133-154). Charlotte, NC: Age Publishing Inc.
  • Er, F. S. K., Selek, H. K. G., & Yazgan, Y. (2024). Beşinci Sınıf Öğrencilerinin Problem Çözmede Stratejik Esnekliklerinin Matematiğin Doğasına İlişkin Görüşleri Çerçevesinde İncelenmesi. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi, (59), 98-119.
  • Elia, I., Van den Heuvel-Panhuizen, M., & Kolovou, A. (2009). Exploring strategy use and strategy flexibility in nonroutine problem solving by primary school high achievers in mathematics. Zentralblatt Didaktik für Mathematik (ZDM), 41(5), 605-618. doi:10.1007/s11858-009-0184-6
  • Gavaz, H. O., Yazgan, Y., & Arslan, Y. (2021). Non-routine problem solving and strategy flexibility: A quasi-experimental study. Journal of Pedagogical Research, 5(3), 40-54. doi:10.33902/JPR.2021370581.
  • Greenes, C. (1981). Identifying the gifted student in mathematics. Arithmetic Teacher, 28(6), 14–17. doi:10.5951/AT.28.6.0014
  • Hatano, G. (2003). Foreword. In A.J. Baroody & A. Dowker (Eds), The development of arithmetic concepts and skills (pp. xi-xiii). New Jersey, NJ: Lawrence Erlbaum Associates.
  • Herr, T., & Johnson, K. (2002). Problem-solving strategies: Crossing the river with dogs. Emeryville: Key Curriculum Press.
  • Hong, W., Star, J. R., Liu, R., Jiang, R. & Fu, X. (2023). A Systematic Review of Mathematical Flexibility: Concepts, Measurements, and Related Research. Educational Psychology Review. 35:104 https://doi.org/10.1007/s10648-023-09825-2.
  • Karabulut, T. (2019). Altıncı sınıf öğrencilerinin matematiksel problem çözmedeki stratejik esneklikleri ve bu konuyla ilgili öğretmen görüşleri.(Yüksek Lisans Tezi). Bursa Uludağ Üniversitesi.
  • Keleş, T., & Yazgan, Y. (2021). Gifted eighth, ninth, tenth and eleventh graders’ strategic flexibility in non-routine problem solving. The Journal of Educational Research, 1-14. doi:10.1080/00220671.2021.1937913
  • Kılıç, H., & Uçar, Z. (2023). Secondary school students’ flexibility in mathematical problem solving: An analysis of strategies. International Journal of Educational Research, 118, 102106. https://doi.org/10.1016/j.ijer.2023.102106
  • Kitchener, R.F (2011). Personal epistemology and philosophical epistemology: The view of a philosopher. In J. Elen, E. Stahl, R. Bromme, & G. Clarebout, (Eds.), Links between beliefs and cognitive flexibility: Lessons learned (pp. 79– 103). Rotterdam: Springer
  • 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.
  • Kramarski, B., & Michalsky, T. (2015). Enhancing mathematical reasoning and metacognitive awareness through computerized collaborative learning. Learning and Instruction, 39, 1-11. https://doi.org/10.1016/j.learninstruc.2015.05.002
  • Krems, J. F. (2014). Cognitive flexibility and complex problem solving. In P.A. Frensch and J. Funke (ed.), Complex problem solving the European perspective (pp. 206-223). New York, NY: Psychology Press.
  • 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, 46 (3), 465-480. doi:10.1007/s11858-014-0599-6
  • Leikin, R., Koichu, B., & Berman, A. (2009). Mathematical giftedness as a quality of problem-solving acts. In R. Leikin, A. Berman and B. Koichu, (Eds.), Creativity in mathematics and the education of gifted students (115-127). Rotterdam: Sense Publishers.
  • Leikin, R. (2020). Advanced mathematical thinking and creativity: A look at high achieving learners. ZDM–Mathematics Education, 52(1), 3–13. https://doi.org/10.1007/s11858-019-01088-5
  • Leikin, R., & Levav-Waynberg, A. (2020). Characteristics of gifted students’ mathematical creativity: Connections to flexibility and multiple solution strategies. ZDM–Mathematics Education, 52(1), 25–37. https://doi.org/10.1007/s11858-019-01107-5
  • Maker, J. (2003). New directions in enrichment and acceleration. In N. Colangelo & G. Davis (Eds.). Handbook of gifted education (pp. 163-173). Boston, MA: Allyn and Bacon.
  • McMillian, J. H. (2004). Educational research: Fundamentals for the consumer. New York, NY: HarperCollins College Publishers.
  • Ministry of National Education (2019). Bilim ve sanat merkezi matematik dersi öğretim programı etkinlik kitabı. Ankara: Milli Eğitim Bakanlığı. Özel Eğitim ve Rehberlik Hizmetleri Genel Müdürlüğü.
  • Mok, I. A. C., & Lam, S. F., Cheng, M. M. H., & Ho, S. K. W. (2020). Standardized testing and creativity: The impact of test preparation on students’ problem-solving skills. Journal of Educational Psychology, 112(7), 1349–1360. https://doi.org/10.1037/edu0000421
  • NCTM (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
  • NCTM(2010). Why is teaching with problem solving important to student learning? Reston, VA: NCTM
  • NCTM. (2023). Catalyzing change in early childhood and elementary mathematics: Initiating critical conversations. National Council of Teachers of Mathematics.
  • Niederer, K., Irwin, R. J., Irwin, K. C., & Reilly, I. L. (2003). Identification of mathematically gifted children in New Zealand, High Ability Studies, 14(1), 71-84. doi:10.1080/13598130304088 Patton, M. Q. (1987). How to use qualitative methods in evaluation.
  • Newsbury Park, London, New Dehli: Sage Publications. Patton, M. Q. (2014). Qualitative research & evaluation methods: Integrating theory and practice (4. ed.), Thousand Oaks, CA: Sage Publications.
  • Polya, G. (1945). How to solve it: A new aspect of mathematical method. Princeton, NJ: Princeton University Press.
  • 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.
  • Schoenfeld, A. (1985). Mathematical problem solving. USA: Lawrence Erlbaum Associates.
  • Schoenfeld, A. H. (2021). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. Educational Psychologist, 56(4), 261–278. https://doi.org/10.1080/00461520.2021.1902311
  • Selter, C. (2001). Addition and subtraction of three-digit numbers: German elementary children's success, methods and strategies. Educational Studies in Mathematics, 47(2), 145-173. doi:10.1023/a:1014521221809
  • Sheffield, L. J. (2003). Extending the challenge in mathematics: Developing mathematical promise in K-8 students. USA: Corwin Press.
  • Sriraman, B. (2003). Mathematical giftedness, problem solving, and the ability to formulate generalizations: The problem-solving experiences of four gifted students. Journal of Secondary Gifted Education, 14(3), 151-165. doi:10.4219/jsge-2003-425.
  • Star, J. (2018). Flexibility in mathematical problem solving: The state of the field. In F. J. Hsieh, (Ed.) Proceedings of the 8th ICMI-East Asia Regional Conference on Mathematics Education: Vol. 1 (pp. 15-25). EARCOME8-National University of Taiwan.
  • Star, J. R., & Rittle-Johnson, B. (2008). Flexibility in problem solving: The case of equation solving. Learning and Instruction, 18(6), 565-579. doi:10.1016/j.learninstruc.2007.09.018
  • Star, J. R., & Rittle-Johnson, B. (2022). Promoting flexibility in mathematics: A review of instructional approaches and practices. Journal for Research in Mathematics Education, 53(2), 123–148. https://doi.org/10.5951/jresematheduc-2022-0010
  • Threlfall, J., (2009). Strategies and flexibility in mental calculation. ZDM, 41(5), 541-555. doi:10.1007/s11858-009-0195-3
  • Threlfall, J., & Hargreaves, M. (2008). The problem-solving methods of mathematicallygifted and older average-attaining students. High Ability Studies, 19,83–98. doi:10.1080/13598130801990967
  • Tiong, J. Y. S., Hedberg, J. G., & Lioe, L. T. (2005). A metacognitive approach to support heuristic solution of mathematical problems. Proceedings of the Redesigning Pedagogy: Research, Policy, Practice Conference. Singapore National Institute of Education. https://repository.nie.edu.sg/bitstream/10497/141/1/2005a15.pdf
  • Torbeyns, J., Schneider, M., Xin, Z., & Siegler, R. S. (2021). Bridging the gap between numerical understanding and strategic flexibility: Recent insights. Cognitive Development, 59, 101063. https://doi.org/10.1016/j.cogdev.2021.101063
  • OECD. (2023). OECD Future of Education and Skills 2030: Curriculum analysis. https://www.oecd.org/education/2030-project/
  • OECD. (2023). Mathematics curriculum redesign: Toward 21st century learning. OECD Publishing. https://www.oecd.org/education
  • Van de Walle, J. A. (1990). Elementary school mathematics, teaching developmentally. Newyork, NY: Addison-Wesley/Longman.
  • Verhage, H., & de Lange, J. (1997). Mathematics education and assessment. Pythagoras, 42, 14-20.
  • Verschaffel, L. (2023). Strategy flexibility in mathematics. ZDM – Mathematics Education https://doi.org/10.1007/s11858-023-01491-6.
  • Verschaffel, L., Luwel, K., Torbeyns, J., & Van Dooren, W. (2009). Conceptualizing, investigating, and enhancing adaptive expertise in elementary mathematics education. European Journal of Psychology of Education, 24(3), 335–359. doi:10.1007/bf03174765.
  • Vural, E. (2019). İlkokul 4. sınıf düzeyinde doğal sayılarla ilgili rutin ve rutin olmayan problemlerin öğrenim ve öğretim durumları (Master's thesis, Lisansüstü Eğitim Enstitüsü).
  • World Economic Forum. (2024). Future of Jobs Report 2024. https://www.weforum.org/reports/future-of-jobs-report-2024
  • 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. National Center for Education Evaluation and Regional Assistance. https://ies.ed.gov/ncee/wwc/Docs/PracticeGuide/MPS_PG_043012.pdf
  • Yeo, K. K. J. (2009). Secondary 2 students’ difficulties in solving non-routine problems. International Journal for Mathematics Teaching and Learning, 10, 1–30.
  • Zhou, Z., Sun, Y., & Wang, S. (2021). Strategy use and metacognitive monitoring in mathematical problem solving among high-achieving students. Journal of Educational Psychology, 113(8), 1471–1487. https://doi.org/10.1037/edu0000674

Strategy Flexibility Exhibited by Gifted Middle Schoolers While Solving Non-Routine Problems

Year 2025, Volume: 8 Issue: 3, 214 - 228, 30.09.2025

Abstract

The aim of this study is to examine the strategic flexibility demonstrated by gifted middle school students while solving non-routine problems. The study involved seven sixth-grade, six seventh-grade, and five eighth-grade students who were identified as gifted and were attending middle schools in the Yıldırım district of Bursa, Turkey. Individual interviews were conducted with each student, during which they were presented with seven non-routine problems. The students’ problem-solving processes and approaches were analyzed. Their performances were evaluated based on three main categories: selecting the most appropriate strategy, inter-task flexibility, and intra-task flexibility. Each category was scored on a scale from 1 to 4. The findings reveal that students were generally successful in selecting suitable strategies and in shifting strategies across different tasks. However, despite their overall high flexibility scores, it was observed that they struggled to change strategies or use multiple strategies simultaneously within a single problem. These findings suggest that the components of strategic flexibility may develop independently from one another.

References

  • Assmus, J., Ertküçük, A., & Grigutsch, S. (2022). Gifted students’ approaches to solving non-routine mathematical problems: Insights from a process-oriented perspective. International Journal of Science and Mathematics Education, 20(4), 789–812. https://doi.org/10.1007/s10763-021-10189-9
  • Altun M. (2016). Ortaokullarda (5, 6, 7 ve 8. sınıflarda) matematik öğretimi. Bursa: Aktüel Yayıncılık.
  • Altun, M., Bintas, J., Yazgan, Y. & Arslan, C. (2004). İlköğretim çağındaki çocuklarda problem çözme gelişiminin incelenmesi. Uludağ Üniversitesi Bilimsel Araştırma Projeleri Birimi. https://www.researchgate.net/profile/Yeliz-Yazgan-2/publication/305769065_ILKOGRETIM_CAGINDAKI_COCUKLARDA_PROBLEM_COZME_GELISIMININ_INCELENMESI/links/57a0602a08aec29aed23755e/ILKOGRETIM-CAGINDAKI-COCUKLARDA-PROBLEM-COeZME-GELISIMININ-INCELENMESI.pdf
  • Arslan, C., & Yazgan, Y. (2015). Common and flexible use of mathematical non routine problem solving strategies. American Journal of Educational Research, 3(12), 1519-1523. doi:10.12691/education-3-12-6.
  • Bräuning, K. (2016). Investigating multiple strategy use and strategy flexibility in problem solving by pre-service teachers. In T. Fritzlar, D. Aßmus, K. Bräuning, A. Kuzle, & B. Rott (Eds.), Problem solving in mathematics education. Proceedings of the 2015 joint conference of ProMath and the GDM working group on problem solving (pp. 41-55). Münster: WTM.
  • Boesen, J., Lithner, J., & Palm, T. (2023). Students' creative reasoning and mathematical problem solving: New insights from classroom settings. Educational Studies in Mathematics, 112(1), 45–67. https://doi.org/10.1007/s10649-022-10154-4
  • Boaler, J. (2022). Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages and innovative teaching. Jossey-Bass.
  • Bulgar, S. (2008). Enabling more students to achieve mathematical success; a case study of Sarah. In B. Sriraman (Ed.), Creativity, giftedness, and talent development in mathematics (133-154). Charlotte, NC: Age Publishing Inc.
  • Er, F. S. K., Selek, H. K. G., & Yazgan, Y. (2024). Beşinci Sınıf Öğrencilerinin Problem Çözmede Stratejik Esnekliklerinin Matematiğin Doğasına İlişkin Görüşleri Çerçevesinde İncelenmesi. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi, (59), 98-119.
  • Elia, I., Van den Heuvel-Panhuizen, M., & Kolovou, A. (2009). Exploring strategy use and strategy flexibility in nonroutine problem solving by primary school high achievers in mathematics. Zentralblatt Didaktik für Mathematik (ZDM), 41(5), 605-618. doi:10.1007/s11858-009-0184-6
  • Gavaz, H. O., Yazgan, Y., & Arslan, Y. (2021). Non-routine problem solving and strategy flexibility: A quasi-experimental study. Journal of Pedagogical Research, 5(3), 40-54. doi:10.33902/JPR.2021370581.
  • Greenes, C. (1981). Identifying the gifted student in mathematics. Arithmetic Teacher, 28(6), 14–17. doi:10.5951/AT.28.6.0014
  • Hatano, G. (2003). Foreword. In A.J. Baroody & A. Dowker (Eds), The development of arithmetic concepts and skills (pp. xi-xiii). New Jersey, NJ: Lawrence Erlbaum Associates.
  • Herr, T., & Johnson, K. (2002). Problem-solving strategies: Crossing the river with dogs. Emeryville: Key Curriculum Press.
  • Hong, W., Star, J. R., Liu, R., Jiang, R. & Fu, X. (2023). A Systematic Review of Mathematical Flexibility: Concepts, Measurements, and Related Research. Educational Psychology Review. 35:104 https://doi.org/10.1007/s10648-023-09825-2.
  • Karabulut, T. (2019). Altıncı sınıf öğrencilerinin matematiksel problem çözmedeki stratejik esneklikleri ve bu konuyla ilgili öğretmen görüşleri.(Yüksek Lisans Tezi). Bursa Uludağ Üniversitesi.
  • Keleş, T., & Yazgan, Y. (2021). Gifted eighth, ninth, tenth and eleventh graders’ strategic flexibility in non-routine problem solving. The Journal of Educational Research, 1-14. doi:10.1080/00220671.2021.1937913
  • Kılıç, H., & Uçar, Z. (2023). Secondary school students’ flexibility in mathematical problem solving: An analysis of strategies. International Journal of Educational Research, 118, 102106. https://doi.org/10.1016/j.ijer.2023.102106
  • Kitchener, R.F (2011). Personal epistemology and philosophical epistemology: The view of a philosopher. In J. Elen, E. Stahl, R. Bromme, & G. Clarebout, (Eds.), Links between beliefs and cognitive flexibility: Lessons learned (pp. 79– 103). Rotterdam: Springer
  • 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.
  • Kramarski, B., & Michalsky, T. (2015). Enhancing mathematical reasoning and metacognitive awareness through computerized collaborative learning. Learning and Instruction, 39, 1-11. https://doi.org/10.1016/j.learninstruc.2015.05.002
  • Krems, J. F. (2014). Cognitive flexibility and complex problem solving. In P.A. Frensch and J. Funke (ed.), Complex problem solving the European perspective (pp. 206-223). New York, NY: Psychology Press.
  • 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, 46 (3), 465-480. doi:10.1007/s11858-014-0599-6
  • Leikin, R., Koichu, B., & Berman, A. (2009). Mathematical giftedness as a quality of problem-solving acts. In R. Leikin, A. Berman and B. Koichu, (Eds.), Creativity in mathematics and the education of gifted students (115-127). Rotterdam: Sense Publishers.
  • Leikin, R. (2020). Advanced mathematical thinking and creativity: A look at high achieving learners. ZDM–Mathematics Education, 52(1), 3–13. https://doi.org/10.1007/s11858-019-01088-5
  • Leikin, R., & Levav-Waynberg, A. (2020). Characteristics of gifted students’ mathematical creativity: Connections to flexibility and multiple solution strategies. ZDM–Mathematics Education, 52(1), 25–37. https://doi.org/10.1007/s11858-019-01107-5
  • Maker, J. (2003). New directions in enrichment and acceleration. In N. Colangelo & G. Davis (Eds.). Handbook of gifted education (pp. 163-173). Boston, MA: Allyn and Bacon.
  • McMillian, J. H. (2004). Educational research: Fundamentals for the consumer. New York, NY: HarperCollins College Publishers.
  • Ministry of National Education (2019). Bilim ve sanat merkezi matematik dersi öğretim programı etkinlik kitabı. Ankara: Milli Eğitim Bakanlığı. Özel Eğitim ve Rehberlik Hizmetleri Genel Müdürlüğü.
  • Mok, I. A. C., & Lam, S. F., Cheng, M. M. H., & Ho, S. K. W. (2020). Standardized testing and creativity: The impact of test preparation on students’ problem-solving skills. Journal of Educational Psychology, 112(7), 1349–1360. https://doi.org/10.1037/edu0000421
  • NCTM (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
  • NCTM(2010). Why is teaching with problem solving important to student learning? Reston, VA: NCTM
  • NCTM. (2023). Catalyzing change in early childhood and elementary mathematics: Initiating critical conversations. National Council of Teachers of Mathematics.
  • Niederer, K., Irwin, R. J., Irwin, K. C., & Reilly, I. L. (2003). Identification of mathematically gifted children in New Zealand, High Ability Studies, 14(1), 71-84. doi:10.1080/13598130304088 Patton, M. Q. (1987). How to use qualitative methods in evaluation.
  • Newsbury Park, London, New Dehli: Sage Publications. Patton, M. Q. (2014). Qualitative research & evaluation methods: Integrating theory and practice (4. ed.), Thousand Oaks, CA: Sage Publications.
  • Polya, G. (1945). How to solve it: A new aspect of mathematical method. Princeton, NJ: Princeton University Press.
  • 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.
  • Schoenfeld, A. (1985). Mathematical problem solving. USA: Lawrence Erlbaum Associates.
  • Schoenfeld, A. H. (2021). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. Educational Psychologist, 56(4), 261–278. https://doi.org/10.1080/00461520.2021.1902311
  • Selter, C. (2001). Addition and subtraction of three-digit numbers: German elementary children's success, methods and strategies. Educational Studies in Mathematics, 47(2), 145-173. doi:10.1023/a:1014521221809
  • Sheffield, L. J. (2003). Extending the challenge in mathematics: Developing mathematical promise in K-8 students. USA: Corwin Press.
  • Sriraman, B. (2003). Mathematical giftedness, problem solving, and the ability to formulate generalizations: The problem-solving experiences of four gifted students. Journal of Secondary Gifted Education, 14(3), 151-165. doi:10.4219/jsge-2003-425.
  • Star, J. (2018). Flexibility in mathematical problem solving: The state of the field. In F. J. Hsieh, (Ed.) Proceedings of the 8th ICMI-East Asia Regional Conference on Mathematics Education: Vol. 1 (pp. 15-25). EARCOME8-National University of Taiwan.
  • Star, J. R., & Rittle-Johnson, B. (2008). Flexibility in problem solving: The case of equation solving. Learning and Instruction, 18(6), 565-579. doi:10.1016/j.learninstruc.2007.09.018
  • Star, J. R., & Rittle-Johnson, B. (2022). Promoting flexibility in mathematics: A review of instructional approaches and practices. Journal for Research in Mathematics Education, 53(2), 123–148. https://doi.org/10.5951/jresematheduc-2022-0010
  • Threlfall, J., (2009). Strategies and flexibility in mental calculation. ZDM, 41(5), 541-555. doi:10.1007/s11858-009-0195-3
  • Threlfall, J., & Hargreaves, M. (2008). The problem-solving methods of mathematicallygifted and older average-attaining students. High Ability Studies, 19,83–98. doi:10.1080/13598130801990967
  • Tiong, J. Y. S., Hedberg, J. G., & Lioe, L. T. (2005). A metacognitive approach to support heuristic solution of mathematical problems. Proceedings of the Redesigning Pedagogy: Research, Policy, Practice Conference. Singapore National Institute of Education. https://repository.nie.edu.sg/bitstream/10497/141/1/2005a15.pdf
  • Torbeyns, J., Schneider, M., Xin, Z., & Siegler, R. S. (2021). Bridging the gap between numerical understanding and strategic flexibility: Recent insights. Cognitive Development, 59, 101063. https://doi.org/10.1016/j.cogdev.2021.101063
  • OECD. (2023). OECD Future of Education and Skills 2030: Curriculum analysis. https://www.oecd.org/education/2030-project/
  • OECD. (2023). Mathematics curriculum redesign: Toward 21st century learning. OECD Publishing. https://www.oecd.org/education
  • Van de Walle, J. A. (1990). Elementary school mathematics, teaching developmentally. Newyork, NY: Addison-Wesley/Longman.
  • Verhage, H., & de Lange, J. (1997). Mathematics education and assessment. Pythagoras, 42, 14-20.
  • Verschaffel, L. (2023). Strategy flexibility in mathematics. ZDM – Mathematics Education https://doi.org/10.1007/s11858-023-01491-6.
  • Verschaffel, L., Luwel, K., Torbeyns, J., & Van Dooren, W. (2009). Conceptualizing, investigating, and enhancing adaptive expertise in elementary mathematics education. European Journal of Psychology of Education, 24(3), 335–359. doi:10.1007/bf03174765.
  • Vural, E. (2019). İlkokul 4. sınıf düzeyinde doğal sayılarla ilgili rutin ve rutin olmayan problemlerin öğrenim ve öğretim durumları (Master's thesis, Lisansüstü Eğitim Enstitüsü).
  • World Economic Forum. (2024). Future of Jobs Report 2024. https://www.weforum.org/reports/future-of-jobs-report-2024
  • 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. National Center for Education Evaluation and Regional Assistance. https://ies.ed.gov/ncee/wwc/Docs/PracticeGuide/MPS_PG_043012.pdf
  • Yeo, K. K. J. (2009). Secondary 2 students’ difficulties in solving non-routine problems. International Journal for Mathematics Teaching and Learning, 10, 1–30.
  • Zhou, Z., Sun, Y., & Wang, S. (2021). Strategy use and metacognitive monitoring in mathematical problem solving among high-achieving students. Journal of Educational Psychology, 113(8), 1471–1487. https://doi.org/10.1037/edu0000674
There are 60 citations in total.

Details

Primary Language English
Subjects Mathematics Education
Journal Section Research Articles
Authors

Sümeyra Balikçi

Yeliz Yazgan 0000-0002-8417-1100

Gizem Yapar Söğüt 0000-0001-8157-402X

Publication Date September 30, 2025
Submission Date May 29, 2025
Acceptance Date July 17, 2025
Published in Issue Year 2025 Volume: 8 Issue: 3

Cite

APA Balikçi, S., Yazgan, Y., & Yapar Söğüt, G. (2025). Strategy Flexibility Exhibited by Gifted Middle Schoolers While Solving Non-Routine Problems. Fen Matematik Girişimcilik Ve Teknoloji Eğitimi Dergisi, 8(3), 214-228.