Sınıf Ortamında Rutin Olmayan Matematik Problemi Çözme: Didaktik Durumlar Teorisine Dayalı Bir Uygulama Örneği

Abstract

Matematik öğretim programlarında ve matematik eğitimi literatüründe rutin olmayan problem çözme eylemine büyük önem verilmesine rağmen çalışmalar öğrencilerin rutin olmayan problemlerin çözümündeki başarılarının oldukça düşük olduğunu göstermektedir. Çıkış noktası kavramsal öğrenmenin şartlarını belirlemek olan Didaktik Durumlar Teorisi (DDT) rutin olmayan problem çözme etkinlikleri için önemli bir potansiyele sahiptir. Bu çalışmanın amacı teorinin söz konusu potansiyelini sınıf ortamı bağlamında incelemektir. Çalışmada öncelikle problem çözmeye ilişkin literatür, DDT’nin prensipleri ve kavramları verilerek, problem çözme yaklaşımı sınıf ortamı bağlamında tartışılmış, sonrasında bu prensip ve yaklaşımlar bir uygulama örneği ile desteklenmiştir. Nitel araştırma yöntemlerinin kullanıldığı bu uygulama bir devlet ortaokulunun 6. sınıfında okuyan 24 öğrenciyle gerçekleştirilmiştir. Yaklaşık 2 ders saatinde gerçekleştirilen uygulamanın verileri video kaydı ve öğrenci çalışma kağıtları aracılığıyla toplanmıştır. Veriler teorinin belirlediği aşamalara göre analiz edilmiştir. Tasarlanan ortamın öğrencilerin sezgisel stratejiler geliştirmesini desteklediği ve öğrencilerin tasarlanan ortamda karşılıklı etkileşim içinde ve muhakeme yoluyla yeni bilgilere ulaştıkları görülmüştür. Ayrıca DDT’nin sınıf ortamında öğrencilerin problem çözme yaklaşımlarıyla ilgili ortam tasarımı, öğretmen ve öğrencilerin rolleri açısından birçok avantaj sağladığı belirlenmiştir.

Keywords

• Didaktik Durumlar Teorisi,sınıf ortamında problem çözme,rutin olmayan problem,6. sınıf

Non-routine Mathematical Problem Solving in Classroom Environment: An Example Based Upon Theory of Didactical Situations

Abstract

Despite the fact that great importance is attached to the practice of solving non-routine problems in mathematics curriculums and literature of mathematical education, studies show that the success of the students in non-routine problem solving is considerably low. Theory of Didactical Situations (TDS), starting point of which is to define the conditions of meaningful learnings, has a substantial potential for non-routine problem solving activities. The aim of this study is to analyze the aforementioned potential of the theory in a classroom environment. Within the scope of the study, first of all, literature in relation to problem solving and the approach of problem solving were discussed in terms of classroom environment by giving the principles and concepts of TDS, and in the sequel, these principles and approaches were supported through an application example. This application through which qualitative research method were used was conducted with 24 students who studying their 6th grade education in a public school. Data of application which was performed in approximately 2 courses were collected via video records and students’ work sheets. The data were analyzed in accordance with the steps specified by theory. It was seen that the designed environment has supported the students in terms of developing heuristic problem solving strategies and students have reached new knowledge in the designed environment by interacting with each other and through the way of reasoning. Additionally, environment design of TDS in relation to problem solving activities in classroom environment is reported to have provided a lot of advantages for the roles of teachers and students.

Keywords

• Theory of Didactical Situations,problem solving in classroom environment,non-routine problem,6th grade

References

1. Altun, M. (2011). Eğitim fakülteleri ve lise matematik öğretmenleri için liselerde matematik öğretimi (17. Baskı). Bursa: Aktüel Alfa.
2. Arslan, Ç. ve Altun, M. (2007). Learning to solve non-routine mathematical problems. İlköğretim Online, 6(1), 50-61.
3. Artigue, M. (1994). Didactical engineering as a framework for the conception of teaching products. R. Biehler, R. W. Scholz, R. Strasser ve B. Winkelmann (Ed.), Didactics of mathematics as a scientific discipline içinde (s. 27-39). New York: Kluwer.
4. Artut, P. D. ve Tarım, K. (2006). İlköğretim öğrencilerinin rutin olmayan sözel problemleri çözme düzeylerinin, çözüm stratejilerinin ve hata türlerinin incelenmesi. Çukurova Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 15(2), 39-50.
5. Baki, A. (2006). Kuramdan uygulamaya matematik eğitimi (3. Baskı). Trabzon: Derya.
6. Baykul, Y. (Ed.) (2010). Problem çözme stratejileri. Konya: Gençlik.
7. Bessot, A. (1994). Panorama del quadro teorico della didactica matematica. L’Educazione Matematica, 15(4).
8. Blum, W. ve Niss, M. (1991). Applied mathematical problem solving modelling, applications, and links to other subjects-state, trends and issues in mathematics instruction. Educational Studies in Mathematics, 22, 37-68.

9. Bosch, M., Chevallard, Y. ve Gascon, J. (2005). Science or magic? The us of models and theories in didactics of mathematics. M. Bosch (Ed.), Proceeding of the fourth congress of the European Society for Research in Mathematics Education içinde (s.1254-1263), Sant Feliu de Guixols: Universitat Ramon Llull.
10. Brousseau, G. (1997). Theory of didactical situations in mathematics: Didactique des mathématiques, 1970- 1990. Dordrecht: Kluwer.
11. Brousseau, G. (2002). Theory of didactical situations in mathematics, Didactique des Mathématiques, 1970-1990. New York: Kluwer.
12. Brousseau, G. ve Gibel, P. (2005). Didactical handling of students' reasoning processes in problem solving situations. Educational Studies in Mathematics, 59, 13-58.
13. Buchanan, N. K. (1987). Factors contributing to mathematical problem-solving performance: An exploratory study. Educational Studies in Mathematics, 18(4), 399-415.
14. De Bock, D., Verschaffel, L. ve Janssens, D. (1998). The predominance of the linear model in secondary school students’ solutions of word problems involving length and area of similar plane figures. Educational Studies in Mathematics, 35, 65-83.
15. Denzin, N. K. ve Lincoln, Y. S. (2005). The sage handbook of qualitative research (3. Baskı). Thousand Oaks: Sage. Durmaz, B. ve Altun, M. (2014). Ortaokul öğrencilerinin problem çözme stratejilerini kullanma düzeyleri. Mehmet Akif Ersoy Üniversitesi Eğitim Fakültesi Dergisi, 30, 73-94.
16. Elia, I., van den Heuvel-Panhuizen, M. ve 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 of Mathematics Education, 41, 605-618.
17. English, L. D. (1996). Children's construction of mathematical knowledge in solving novel isomorphic problems in concrete and written form. The Journal of Mathematical Behavior, 15(1), 81-112.
18. Erdoğan, A. (2016). Didaktik durumlar teorisi. E. Bingölbali, S. Arslan, ve İ. Ö. Zembat (Ed.), Matematik eğitiminde teoriler içinde (s. 413-430). Ankara: Pegem.
19. Erdoğan, A. (2015). Turkish primary school students’ strategies in solving a non-routine mathematical problem and some implications for the curriculum design and implementation. International Journal forMathematics Teaching and Learning, 1-27.
20. Erdoğan, A. ve Özdemir Erdoğan, E. (2013). Didaktik durumlar teorisi ışığında ilköğretim öğrencilerine matematiksel süreçlerin yaşatılması. Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi, 14(1), 17-34.
21. Ernest, P. (1992). Problem solving: Its assimilation to the teacher's perspective. J. P. Ponte, J. F. Matos, J. M. Matos, ve D. Fernandes (Ed.), Mathematical problem solving and new information technologies research in contexts of practice içinde (s. 287-300). Berlin: Springer-Verlag .
22. Jonassen, D. H. (2011). Learning to solve problems: A handbook for designing problem-solving learning environments. New York: Routledge.
23. Laborde, C. (2007). Towards theoretical foundations of mathematics education. ZDM Mathematics Education, 39, 137-144.
24. Laborde, C. ve Perrin-Glorian, M. J. (2005). Introduction teaching situations as object of research: Empirical studies within theoretical perspectives. Educational Studies in Mathematics, 59, 1-12.
25. Lester, F. K. (1994). Musings about mathematical problem-solving research: 1970-1994. Journal for Research in Mathematics Education, 25(6), 660-675.
26. Lester, F. K., Garofalo, J. ve Kroll, D. (1989). The role of metacognition in mathematical problem solving: A study of two grade seven classes (Final report to the National Science Foundation, NSF Project No. MDR 85-50346). Bloomington: Indiana University, Mathematics Education Development Center.
27. Lester, F. K. ve Mau, S. T. (1993). Teaching mathematics via problem solving: A course for prospective elementary teachers. For the Learning of Mathematics, 13(2), 8-11.
28. Lesh, R. ve Zawojewski, J. (2007). Problem solving and modeling. F. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning içinde (2nd ed., s. 763–804). National Council of Teachers of Mathematics.
29. Ligozat, F. ve Schubauer-Leoni, M.-L. (2010). The joint action theory in didactics: Why do we need it in the case of teaching and learning mathematics? V. Durand-Guerrier, S. Soury-Lavergne ve F. Arzarello (Ed.), Proceedings of the 6th Conference of European Research in Mathematics Education (CERME 6) içinde (s. 1615–1624). Lyon: Institut National de la Recherche Pédagogique.
30. Milli Eğitim Bakanlığı [MEB]. (2013). Ortaokul matematik dersi 5-8. sınıflar öğretim programı. Ankara: Milli Eğitim Bakanlığı.
31. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematic. Reston, VA: National Council of Teachers of Mathematics.
32. OECD (2014). PISA 2012 results: Creative problem solving: Students' skills in tackling real-life problems (Volume V). Paris: OECD Publishing.
33. Pantziara , M., Gagatsis, A. ve Elia, I. (2009). Using diagrams as tools for the solution of non-routine mathematical problems. Educational Studies in Mathematics, 72, 39–60.
34. Polya, G. (1957). How to solve It. New Jersey: Princeton University.
35. Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. D. Grouws (Ed.), Handbook for research on mathematics Teachingand Learning içinde (s. 334-370). New York: MacMillan.
36. Sensevy, G. ve Mercier, A. (2007). Agir ensemble: L’action didactique conjointe du professeur et des élèves. Rennes: PUR.
37. Stacey, K. (1989). Finding and using patterns in linear generalizing problems. Educational Studies in Mathematics 20, 147–164.
38. Stanic, G. ve Kilpatrick, J. (1989). Historical perspectives on problem solving in the mathematics curriculum. R. Charles, ve E. Silver (Ed.), The teaching and assessing of mathematical problem solving içinde (s. 1-22). Reston, VA: National Council of Teachers of Mathematics.
39. Verschaffel, L., De Corte, E., Lasure, S., Van Vaerenbergh, G., Bogaerts, H. ve Ratinckx, E. (1999). Learning to solve mathematical application problems: A design Experiment With Fifth Graders. Mathematical Thinking and Learning, 1(3), 195-229.
40. Warfield, V., M. (2014). Invitationto didactique. New York: Springer.
41. Yazgan, Y. (2007). Observations about fourth and fifth grade students’ strategies to solve non-routine problems. Elementary Education Online 6(2), 249-263.
42. Zembat, İ. Ö. (2008). Sayıların farklı algılanması-sorun sayılarda mı, öğrencilerde mi, yoksa öğretmenlerde mi? M. F. Özmantar, E. Bingölbali, ve H. Akkoç (Ed.), Matematiksel kavram yanılgıları ve çözüm önerileri içinde (s. 41-60). Ankara: Pegem.