PROBLEM SOLVING STRATEGIES USED BY GIFTED SECONDARY SCHOOL STUDENTS TO SOLVE MATH PROBLEMS

Abstract

The general purpose of this study was to determine the strategies used by gifted secondary school students in solving mathematics problems. To collect data about the problem solving strategies of the gifted students, a case study was used. The research was performed at the Science and Arts Center of Ankara Province in Turkey. The study was conducted with five 7th grade secondary school students. In the sample chosen, first, the necessary permissions were obtained from the Ministry of National Education in Turkey, and then, the random sampling method was used. A problem solving test that was developed by the researcher was used as the measurement instrument. There were 5mathematics problems in the test, and each problem was checked whether specific problem solving strategies were used or not. Additionally, problems were developed by following the objectivesof the secondary mathematics curriculum. The responsesof the students were evaluated through semi-structured interviews for each problem according to the strategies used, and field notes were taken during the semi-structured interviews by the researcher. The data were analyzed using descriptive analyses and voice thinking techniques. The results of the study revealed that the students used 8 different strategies for solving the mathematics problems. They most frequently used logical reasoning and finding pattern problem solving strategies during the solution of these problems, however the working backward and considering extreme cases strategies were never used by the gifted students.

Keywords

• Gifted students
• problem solving strategies
• mathematics education

ÖZEL YETENEKLİ ORTAOKUL ÖĞRENCİLERİNİN PROBLEM ÇÖZMEDE KULLANDIKLARI PROBLEM ÇÖZME STRATEJİLERİ

Abstract

Bu çalışmanın genel amacı özel yetenekli ortaokul öğrencilerinin matematik problemlerini çözerken kullandıkları problem çözme stratejilerini belirlemektir. Çalışmada özel yeteneklilerin problem çözme stratejileri hakkında veri toplamak için durum çalışması yöntemi kullanılmıştır. Araştırma, Millî Eğitim Bakanlığından gerekli izinler alındıktan sonra Ankara ilinde yer alan bir Bilim Sanat Merkezinde öğrenim görmekte olan özel yetenekli beş öğrenci ile yürütülmüştür. Çalışmanın örneklemi, kurumda öğrenim görmekte olan yedinci sınıf öğrencileri arasından çalışmaya katılmaya gönüllü olan öğrencilerden oluşmaktadır. Çalışmanın verileri araştırmacı tarafından geliştirilen “Problem Çözme Testi” kullanılarak öğrencilerle yapılan yarı yapılandırılmış görüşmelerle elde edilmiştir. Test, her maddesi ilköğretim matematik öğretim programındayer alan hedefler doğrultusunda geliştirilen ve birden fazla problem çözme stratejisi kullanılmaya uygun olan beş matematik probleminden oluşmaktadır. Elde edilen veriler betimsel analiz ve sesli düşünme tekniği yöntemleri kullanılarak analiz edilmiştir. Araştırmanın sonucunda özel yetenekli öğrencilerin problemleri çözerken sekiz farklı problem çözme stratejisi kullandıkları ortaya çıkmıştır. Öğrenciler en fazla mantıksal akıl yürütme ve ilişki arama stratejilerini kullanmış, geriye doğru çalışma ve uç durumları düşünme stratejilerini hiç kullanmamıştır.

Keywords

• Özel yetenekli öğrenciler
• problem çözme stratejileri
• matematik eğitimi

References

1. Akkan, Y., Baki, A., & Çakıroğlu, Ü. (2012). Examination of the 5th-8th grade students’ transition process from arithmetic to algebra with regard problem solving. Hacettepe University Journal of Education Faculty, 2012(43), 1-13.
2. Altun, M. (2005). Teaching mathematics (13. baskı). Aktüel Publishing.
3. Azak, S. (2015). Determination of strategies and metacognitive skills used by secondary school 8th grade students in problem solving [Unpublished master's thesis]. Karadeniz Teknik University.
4. Billstein, R., Libeskind, S., & Lott, J. W. (2013). A problem solving approach to mathematics for elementary school teachers. Pearson New International Edition. Pearson Higher Ed.
5. Brown, P. A. (2008). A review of the literature on case study research. Canadian Journal for New Scholars in Education, 1(1), 1-13.
6. Creswell, J. W. (2013). Research design (S. B. Demir, Trans.). Eğiten Kitap.
7. Davis, G. A., & Rimm, S. B. (1998). Education of the gifted and talented (4th ed.). Allyn and Bacon.
8. Durmaz, B., & Altun, M. (2014). The usage of the problem solving strategies of the secondary students’. Mehmet Akif Ersoy University Journal of Education Faculty, 1(30), 73-94.

9. Heinze, A. (2005). Differences in problem solving strategies of mathematically gifted and non-gifted elementary students. International Education Journal, 6(2), 175-183.
10. Huberman, A. M., & Miles, M. B. (1994). Data management and analysis methods. In N. K. Denzin & Y. S. Lincoln (Eds.), Handbook of qualitative research (pp. 428–444). Sage Publications.
11. Intaros, P., Inprasitha, M., & Srisawadi, N. (2014). Students’ problem solving strategies in problem solving-mathematics classroom. Procedia-Social and Behavioral Sciences, 116(1), 4119-4123. https://doi.org/10.1016/j.sbspro.2014.01.901
12. Karaca, T. E. (2012). An analysis of elementary school 5th grade students’ problem solving performance on non-routine open-ended questions (Publication No. 317142) [Master's thesis, Gazi University]. https://tez.yok.gov.tr/UlusalTezMerkezi/tezSorguSonucYeni.jsp
13. Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. University of Chicago Press.
14. Lee, K. H. (2005). Mathematically gifted students' geometrical reasoning and informal proof. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (vol. 3, pp. 241-248). PME.
15. Lee, N. H., Yeo, D. J. S., & Hong, S. E. (2014). A metacognitive-based instruction for primary four students to approach non-routine mathematical word problems. ZDM, 46(3), 465-480. https://doi.org/10.1007/s11858-014-0599-6
16. Millî Eğitim Bakanlığı. (2013). Ortaokul matematik dersi 5-8. sınıflar öğretim programı. MEB.
17. Merriam, S.B. (1998). Qualitative research and case study applications in education. Jossey-Bass Inc.
18. Miller, R. C. (1990). Discovering mathematical talent (Report No. ED321487). ERIC. https://eric.ed.gov/?id=ED321487
19. Montgomery, D. (1996). Educating the able. Cassell.
20. Mönks, F. J. (1992). Development of gifted children: The issue of identification and programming. In F. J. Mönks & W. A. M. Peters (Eds.), Talent for the future (pp. 191–202). Proceedings of the Ninth World Conference on Gifted and Talented Children, Van Gorcum.
21. Özmen, Z. M., Aydın, F., & Güven, B. (2011, October 5-8). The relationship between the strategies used by prospective mathematics teachers and their problem solving success. 1th International Congress on Curriculum and Instruction, Anadolu University, Eskişehir.
22. Pilten, P. (2008). The effect of metacognitive instruction on mathematical reasoning of fifth grade primary school students (Publication No. 214521) [Doctoral dissertation, Gazi University]. https://tez.yok.gov.tr/UlusalTezMerkezi/tezSorguSonucYeni.jsp
23. Posamentier, A., & Krulik, S. (1998). Problem solving strategies for efficient and elegant solutions. Corwin Press.
24. Renzulli, J. S. (Ed.). (1986). Systems and models for developing programs for the gifted and talented. Creative Learning Pr.
25. Renzulli, J. S. (2002a). Emerging conceptions of giftedness: Building a bridge to the new century. Exceptionality 10, 67–75. https://doi.org/10.1207/S15327035EX1002_2
26. Renzulli, J. S. (2002b). Expanding the conception of giftedness to include cocognitive traits and to promote social capital. Phi Delta Kappan, 84, 33–58. https://doi.org/10.1177/003172170208400109
27. Renzulli, J. S. (2003). The three-ring conception of giftedness: Its implications for understanding the nature of innovation. In L. V. Shavinina (Ed.), The international handbook on innovation (pp. 79–96). Elsevier Science. https://doi.org/10.1016/B978-008044198-6/50007-3
28. Rotigel, J. V., & Fello, S. (2004). Mathematically gifted students: How can we meet their needs? Gifted Child Today, 27(4), 46-51.
29. Singer, F. M., Sheffield, L. J., Freiman, V., & Brandl, M. (2016). Research on and activities for mathematically gifted students. In Research on and activities for mathematically gifted students (pp. 1-41). Springer International Publishing.
30. Sousa, D. A. (2003). How the gifted brain learners. Corwin Press.
31. 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.
32. Stanic, G. M., & Kilpatrick, J. (1992). Mathematics curriculum reform in the United States: A historical perspective. International Journal of Educational Research, 17(5), 407-417. https://doi.org/10.1016/S0883-0355(05)80002-3
33. Sternberg, R. J., Jarvin, L., & Grigorenko, E. L. (2011). Explorations in giftedness. Cambridge University Press. Tannenbaum, A. (2004). Unmasking and unmaking underachievement among the gifted. Freund Publishing House, Ltd.
34. Tertemiz, N. I., Doğan, A., & Karakaş, H. (2017). A comparative study on problem solving strategies of gifted 4th grade students and their high-achieving counterparts. International Journal of Curriculum and Instructional Studies, 7(13), 161-188.
35. Verschaffel, L., De Corte, E., Lasure, S., Van Vaerenbergh, G., Bogaerts, H., & Ratinckx, E. (1999). Learning to solve mathematical application problems: A design experiment with fifth graders. Mathematical Thinking and Learning, 1(3), 195-229. https://doi.org/10.1207/s15327833mtl0103_2
36. Wallace, B., & Adams, H. B. (Eds.). (1993). Worldwide perspectives on the gifted disadvantaged. AB Academic Publishers.
37. Wallace, B., & Adams, H. B. (2018). TASC: Thinking actively in a social context: A universal framework for developing thinking skills and problem-solving across the curriculum. The SAGE Handbook of Gifted and Talented Education.
38. Webb-Johnson, G. C. (2006). To be young, gifted, emotionally challenged and black: A principal’s role in providing a culturally responsive context. Voices in Urban Education, 12, 20-27.
39. Yazgan, Y. (2007). Observations about fourth and fifth grade students’ strategies to solve non-routine problems. Elementary Education Online, 6(2), 249-263.
40. Yazgan, Y., & Bintaş, J. (2005). Fourth and fifth grade students’ levels of using problem solving strategies: A teaching experiment. Hacettepe University Journal of Education Faculty, 28(28), 210-218.
41. Yıldız, A., Baltacı, S., Kurak, Y., & Güven, B. (2012). Examining the usage of problem-solving strategies by the eighth grade gifted and non-gifted students. Uludağ University Journal of Education Faculty, 25(1), 123-143.