İLKOKUL VE ORTAOKUL ÖĞRENCİLERİNİN ORANTISAL DURUMLARI ORANTISAL OLMAYAN DURUMLARDAN AYIRT EDEBİLME BECERİLERİ

Öz

Bu çalışmanın amacı, öğrencilerin orantısal ve orantısal olmayan durumları ayırt edebilme becerilerinin belirlenmesidir. Bu amaçla öğrencilerin orantısal ve orantısal olmayan problemlerin çözümünde kullandıkları stratejiler incelenmiştir. Araştırma, 4. , 5., 6. ve 7. sınıf ilkokul ve ortaokul öğrencileri olmak üzere toplam 320 öğrenci ile yürütülmüştür. Çalışmanın verileri, dört problemden oluşan bir test ile toplanmıştır. Testteki problemlerden iki tanesi toplamsal durumları orantısal olmayan ve iki tanesi ise çarpımsal durumları orantısal içermektedir. Öğrencilerin kullandıkları stratejiler çarpımsal ve toplamsal olmasına göre sınıflandırılmıştır. Araştırma sonuçları, bazı öğrencilerin iki problem durumunu ayırt edemediklerini, toplamsal durumu içeren problemlerde çarpımsal çözüm stratejilerini kullanma, çarpımsal durumu içeren problemlerde ise toplamsal çözüm stratejilerini kullanma eğilimini gösterdiği tespit edilmiştir.

Anahtar Kelimeler

• Oran-orantı,orantısal akıl yürütme,ilkokul ve ortaokul öğrencileri

Primary and Middle School Students’ Ability to Distinguish Proportional and Non-Proportional Situations

Öz

The aim of this study was to identify students’ ability to distinguish proportional and nonproportional situations. To accomplish the purpose of the study, the strategies used by primary and middle school students to solve proportional and non-proportional problems were examined. The study was conducted with a total of 320 students from 4th, 5th, 6th and 7th grades. Data was collected by a written test consisting of four problems. Two problems included additive situations non-proportional and two of them contained multiplicative situations proportional . Strategies used by the students were classified according to their types: multiplicative or additive. The results indicated that some of the students can not distinguish the two problem situations, and tend to use multiplicative strategies in additive situations and additive strategies in multiplicative situations

Anahtar Kelimeler

• Ratio-proportion,proportional reasoning,primary and middle school students

Kaynakça

1. Aladağ, A. (2009). İlköğretim Öğrencilerinin Orantısal Akıl Yürütmeye Dayalı Sözel Problemler İle Gerçekçi Cevap Gerektiren Problemleri Çözme Becerilerinin İncelenmesi. (Yüksek Lisans Tezi, Çukurova Üniversitesi Sosyal Bilimler Enstitüsü, Adana). https://tez.yok.gov.tr/ adresinden edinilmiştir.
2. Aladağ, A., & Artut, P. D. (2012). Examination of Students' Problem-Solving Skills of Proportional Reasoning Problems and Realistic Problems. Elementary Education Online, 11(4), 995-1009.
3. Avcu, R., & Doğan, M. (2014). What Are the Strategies Used by Seventh Grade Students While Solving Proportional Reasoning Problems?.International Journal of Educational Studies in Mathematics, 1(2), 34-55.
4. Ben-Chaim, D., Fey, J. T., Fitzgerald, W. M., Benedetto, C., & Miller, J. (1998). Proportional reasoning among 7th grade students with different curricular experiences. Educational Studies in Mathematics, 36(3), 247-273.
5. Clark, F. B., & Kamii, C. (1996). Identification of multiplicative thinking in children in grades 1-5. Journal for Research in Mathematics Education, 41-51.
6. Cramer, K., Post, T., & Currier, S. (1993). Learning and teaching ratio and proportion: Research implications. Middle grades mathematics (Research ideas for the classroom), 159-178.
7. Çelik, A. ve Özdemir, E. Y. (2011). İlköğretim Öğrencilerinin Orantısal Akıl Yürütme Becerileri İle Problem Kurma Becerileri Arasındaki İlişki. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 30(30), 1-11.
8. De Bock, D., Van Dooren, W., Janssens, D., & Verschaffel, L. (2002). Improper use of linear reasoning: An in-depth study of the nature and the irresistibility of secondary school students' errors. Educational Studies in Mathematics, 50(3), 311-334.

9. De Bock, D. (2008). Operations in the number systems: Towards a modelling perspective. Proceedings of ICMI-11–Topic Study Group 10: Research and Development in the Teaching and Learning of Number Systems and Arithmetic, 125-130.
10. Dole, S., Wright, T. & Clarke (2013). Proportional Reasoning. 07.08.2015 tarihinde http://www.proportionalreasoning.com/uploads/1/1/9/7/11976360/proportional_re asoning.pdf alınmıştır.
11. Fernández C., & Llinares, S. (2009). Understanding additive and multiplicative structures: the effect of number structure and nature of quantities on primary school students' performance. In First French-Cypriot Conference of Mathematics Education, 1- 18.
12. Fernández C., Llinares S., Modestou, M., & Gagatsis, A. (2010). Proportional reasoning: how task variables influence the development of students' strategies from primary to secondary school. Acta Didactica Universitatis Comenianae Mathematics- ADUC, 10, 1-18.
13. Fernández, C., Llinares, S., Van Dooren, W., De Bock, D., & Verschaffel, L. (2012). The development of students’ use of additive and proportional methods along primary and secondary school. European Journal of Psychology of Education, 27(3), 421- 438.
14. Fernández, C., Llinares, S., & Valls, J. (2013). Primary school teacher's noticing of students' mathematical thinking in problem solving. The Mathematics Enthusiast, 10(1/2), 441.
15. Hart, K.M. (1994). Ratios: Children’s strategies and errors. Windsor, UK: TheNFER- Nelson Publishing Company.
16. Hiebert, J. & Behr, M. (1988). Introduction: Capturing the major themes. In J.Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 1–18). Hillsdale, NJ: Erlbaum and Reston, VA: National Council of Teachers of Mathematics.
17. Işık, C. (2011). İlköğretim matematik öğretmeni adaylarının kesirlerde çarpma ve bölmeye yönelik kurdukları problemlerin kavramsal analizi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 41(41).
18. Jeong, Y., Levine, S. C., & Huttenlocher, J. (2007). The development of proportional reasoning: Effect of continuous versus discrete quantities. Journal of Cognition and Development, 8(2), 237-256.
19. Kaput, J., & West, M. M. (1994). Missing-Value Proportional Reasoning Problems: Factors Affecting Informal Reasoning Patterns. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 237–287). Albany, New York: SUNY Press.
20. Lamon, S. (1999). Teaching fractions and ratios for understanding. Mahwah, NJ: Lawrence Erlbaum Associates.
21. Langrall, C., & Swafford, J. (2000). Three balloons for two dollars: Developing proportional reasoning. Mathematics Teaching in the Middle School, 6, 254-261.
22. Lesh, R., Post, T., & Behr, M. (1988). Proportional reasoning. In J. Hiebert & M. Behr
23. (Eds.),Number concepts and operations in the middle grades(pp. 93-118). Reston, VA: Lawrence Erlbaum & National Council of Teachers of Mathematics.
24. Lim, K. H. (2009). Burning the candle at just one end: Using nonproportional examples helps students determine when proportional strategies apply. Mathematics Teaching in the Middle School, 14, 492-500.
25. Lin, F.-L. (1991). Understanding in multiple ratio and non-linear ratio. Proceedings of the National Science Council ROC(D), 1(2), 14–30.
26. Misailidou, C., & Williams, J. (2003). Diagnostic assessment of children’s proportional reasoning. The Journal of Mathematical Behavior, 22(3), 335-368.
27. Modestou, M., & Gagatsis, A. (2009). Proportional reasoning: the strategies behind the percentages. Acta Didactica Universitatis Comenianae–Mathematics, 9, 25-40.
28. Peled, I., Levenberg, L., Mekhmandarov, I., Meron R., & Ulitsin A. (1999). Obstacles in applying a mathematical model: The Case of the Multiplicative Structure. In O. Zaslavsky (Ed.), Proceedings of the 23rd International Conference for the Psychology of Mathematics Education. Haifa, Israel: Technion – Israel Institute of Technology.
29. Piaget, J., & Inhelder, B. (1975). The origin of the idea of chance in children. New York: W. W Norton.
30. Pittalis, M., Christou, C., & Papageorgiou, E. (2003). Students’ ability in solving proportional problems. Proceedings of the 3rd European Research Conference in Mathematics Education: Bellaria: Italy, 3.
31. Slovin, H. (2000). Moving to proportional reasoning. Mathematics Teaching in the Middle School, 6, 58-60.
32. Sowder, J., Aarmstrong, B., Lamon, S., Simon, M., Sowder, L., & Thompson, A. (1998). Educating teachers to teach multiplicative structures in the middle grades. Journal of Mathematics Teacher Education, 1, 127- 155.
33. Thompson, P. W. & Saldanha, L. A. (2003). Fractions and multiplicative reasoning. In Kilpatrick, J., Martin, G. W., and Schifter D. (Eds.) A research companion to Principles and Standards for School Mathematic (pp. 95-113). Reston, VA: National Council of Teachers of Mathematics.
34. Tourniaire, F., & Pulos, S. (1985). Proportional reasoning: A review of the literature. Educational studies in mathematics, 16(2), 181-204
35. Van De Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2012). İlkokul ve ortaokul matematiği: Gelişimsel yaklaşımla öğretim (Çev. S. Durmuş). Ankara: Nobel Yayıncılık.
36. Van Dooren, W., De Bock, D., Hessels, A., Janssens, D., & Verschaffel, L. (2005). Not everything is proportional: Effects of age and problem type on propensities for overgeneralization. Cognition and Instruction, 23(1), 57-86.
37. Van Dooren, W., De Bock, D., Gillard, E., & Verschaffel, L. (2009). Add? Or multiply? A study on the develpment of primary school students’ proportional reasoning skills. In M. Tzekaki, M. Kaldrimidou, & C. Sakonidis (Eds.). Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (vol. 5, pp. 281- 288). Thessaloniki, Greece: PME.
38. Van Dooren, V., De Bock, D., & Verschaffel, L. (2010). From addition to multiplication… and back: The development of students’ additive and multiplicative reasoning skills. Cognition and Instruction, 28(3), 360-381.