Cebir Eğitimi Almayan Öğrenciler Problem Çözümlerinde Denklemleri Kullanabiliyorlar mı?

Öz

Bu araştırmanın amacı, cebir eğitimi almamış öğrencilerin problem çözerken denklemleri kullanıp kullanamadıklarını araştırmaktır. Araştırmada nitel araştırma yöntemlerinden biri olan durum çalışması yöntemi uygulanmıştır. Amaçlı örnekleme yöntemlerinden ölçüt örnekleme yöntemi kullanılarak Bolu ilinin sosyo-ekonomik düzeyi orta seviyede olan bir ilçesindeki bir ilköğretim okulunun 5. sınıflarından 4’ü kız, 4’ü erkek olmak üzere 8 öğrenci araştırmaya katılmıştır. Verilerin toplanması için araştırmacılar tarafından doğru orantı, ters orantı, lineer ilişki ve üslü sayı konularını içeren birer tane sorudan oluşan 4 soruluk bir test hazırlanmıştır. Araştırma sonucunda öğrencilerin sorularda verilen sayısal durumlarda ters orantı hariç sorun yaşamadıkları, verdikleri cevapları sözel olarak açıklayabildikleri bulunmuştur. Ayrıca cebir eğitimi almamış bu öğrencilerin verilen sorularla ilgili denklemler kurabildikleri ve farklı sayısal durumlar için bu denklemleri kullanabildikleri ortaya çıkmıştır.

Anahtar Kelimeler

• Doğru-ters orantı, lineer ilişki, üslü sayılar, cebir öncesi, denklemler

Can the Students who haven't taken any Algebra Education Use Equations while Solving Problems?

Öz

The aim of the study is to investigate whether students who haven’t taken any algebra education use equations while solving problems or not. In the study, case study, one of the qualitative research methods, was used. Criterion sampling method of purposive sampling methods was used for selecting the participants. 8 students comprising of 4 girls and 4 boys of a 5th grade of an elementary school in a middle classed county of Bolu participated the study. A test including 4 questions namely, one right proportion, one inverse proportion, one linear relationship and one exponential number, was prepared by the researchers to collect data. As the result of the study it was found that while solving the questions, the students do not have any problems in numerical cases except inverse proportion and they can explain their answers orally. Additionally, it was appeared that the students who haven’t taken any algebra education can set up equations about the questions asked and use these equations for different numerical cases.

Anahtar Kelimeler

• Direct-inverse proportion, linear relationship, exponential numbers, pre-algebra, equations

Kaynakça

1. Barbosa, A., Palhares, P., Vale, I. (2007). Patterns and Generalization: The Influence of Visual Strategies. Paper presented at the Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education, Larnaca, Cyprus.
2. Baroudi, Z. (2006). Easing Students’ Transition to Algebra. Australian Mathematics Teacher, 62(2): 28-33.
3. Baş, S., Çetinkaya, B., Erbaş, A.K. (2011). Öğretmenlerin Dokuzuncu Sınıf Öğrencilerinin Cebirsel Düşünme Yapılarıyla İlgili Bilgileri. Eğitim ve Bilim, 36(159): 41-55.
4. Blanton, M., Schifter, D., Inge, V., Lofgren, P., Willis, C., Davis, F. Et al. (2007). Early algebra. In: V.J. Katz (Ed.), Algebra: Gateway to a Technological Future (7–25). Washington, DC: The Mathematics Association of America.
5. Behr, M. (1980). How Children View the Equals Sign. Mathematics Teaching, 92: 13-15.
6. Bellisio, C., Maher, C.A. (1998). What Kind of Notations do Children Build to Express Algebraic Thinking?. Paper presented at the Proceedings of the 20th Annual Conference of the North American Group for the Psychology of Mathematics Education, Raleigh, NC.
7. Booth, L.R., Johnson, D.C. (1984). Algebra: Children’ Strategies and Errors: A Report of the Strategies and Errors in Secondary Mathematics Project. Windsor, UK: Nfer-Nelson.
8. Büyüköztürk, Ş., Kılıç Çakmak, E., Akgün, Ö.E., Karadeniz, Ş., Demirel, F. (2012). Bilimsel Araştırma Yöntemleri (12. Baskı ed.). Ankara: Pegem Yayınları.

9. Cai, J., Moyer, J. (2007). Developing Algebraic Thinking in Earlier Grades: Some Insights from International Comparative Studies. Reston, VA: NCTM.
10. Carpenter, T.P., Levi, L. (2000). Developing Conceptions of Algebraic Reasoning in the Primary Grades. Wisconsin, Madison: National Center for Improving Student Learning and Achievement in Mathematics and Science.
11. Cuoco, A., Goldenberg, E.P., Mark, J. (2010). Organizing a Curriculum Around Mathematical Habits of Mind. Mathematics Teacher, 103(9): 682–688.
12. Dettori, G., Garuti, R., Lemut, E. (2001). From Arithmetic to Algebraic Thinking by Using a Spreadsheet. In: A.B.T. Rojano, R. Ling (Ed.), Perspectives on School Algebra (pp. 191-207). Dordrecht, The Netherlands: Kluwer: Springer.
13. Doğan, A., Çetin, İ. (2009). Doğru ve Ters Orantı Konusundaki 7. ve 9. Sınıf Öğrencilerinin Kavram Yanılgıları. Uşak Üniversitesi Sosyal Bilimler Dergisi, 2(2): 118-128.
14. Duatepe, A., Akkuş Çıkla, O., Kayhan, M. (2005). Orantısal Akıl Yürütme Gerektiren Sorularda Öğrencilerin Kullandıkları Çözüm Stratejilerinin Soru Türlerine Göre Değişiminin İncelenmesi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 28: 73-81.
15. Falkner, K.P., Levi, L., Carpenter, T.P. (1999). Children’s Understanding of Equality: A Foundation for Algebra. Teaching children mathematics, 6(4): 232-236.
16. Fisher, L.C. (1988). Strategies Used by Secondary Mathematics Teachers to Solve Proportion Problems. Journal for Research in Mathematics Education, 19(2): 157-168.
17. Greer, B. (1997). Modelling Reality in Mathematics Classrooms: The Case of Word Problems. Learning and instruction, 7(4): 293-307.
18. Gürbüz, R., Akkan, Y. (2010). Farklı Öğrenim Seviyesindeki Öğrencilerin Aritmetikten Cebire Geçiş Düzeylerinin Karşılaştırılması: Denklem Örneği. Eğitim ve Bilim, 33(148): 64-76.
19. Herscovics, N., Chalouh, L. (1984). Using Literal Symbols to Represent Hidden Quantities. Paper presented at the Proceedings of the Sixth Annual Meeting of PME-NA, Madison: University of Wisconsin.
20. Herscovics, N., Linchevski, L. (1994). A Cognitive Gap between Arithmetic and Algebra. Educational Studies in Mathematics, 27(1): 59-78.
21. Kieran, C. (1992). The Learning and Teaching of School Algebra (I.D.L. Grouws Ed.). Reston, VA: National Council of Teachers of Mathematics: Handbook of Mathematics Teaching and Learning.
22. Kieran, C. (2004). Algebraic Thinking in the Early Grades: What is It. The Mathematics Educator, 8(1): 139-151.
23. Lacampagne, C.B., Blair, W.D. Kaput, J.J. (1995). The Algebra Initiative Colloquium: Papers Presented at a Conference on Reform in Algebra, December 9-12, 1993. US Department of Education, Office of Educational Research and Improvement, National Institute on Student Achievement, Curriculum, and Assessment.
24. Lundberg, Anna L.V. (2011). Proportion in Mathematics Textbooks in Upper Secondary School. Paper presented at the Proceedings of the CERME7 (Teaching and Learning of Number Systems and Arithmetic), Rzeszow, Poland.
25. Milli Eğitim Bakanlığı (MEB) (2013). İlköğretim 5-8 Matematik Dersi Öğretim Programı. TTKB.
26. National Council of Teachers of Mathematics (NCTM) (2000). Principles and Standards for School Mathematics. Reston, Va.; NCTM.
27. Nickson, M. (2004). Teaching and Learning Mathematics: A Teacher’s Guide to Recent Research and its Application (2nd ed.). New York: Continuum International Publishing Group.
28. Post, T.R. (1992). Teaching Mathematics in Grades K-8. Research Based Methods (Second Edition ed.): Allyon and Bacon.
29. Singh, P. (2000). Understanding the Concepts of Proportion and Ratio among Grade Nine Students in Malaysia. International Journal of Mathematical Education in Science and Technology, 31: 579-599.
30. Swafford, J.O., Langrall, C.W. (2000). Grade 6 Students’ Preinstructional Use of Equations to Describe and Represent Problem Situations. Journal for Research in Mathematics Education, 89-112.
31. Maria Teresa Munoz, S., Mullet, E. (1998). Evolution of the Intuitive Mastery of the Relationship between Base, Exponent, and Number Magnitude in High-School Students. Mathematical cognition, 4(1): 67- 77.
32. Wagner, S., Kieran, C. (1989). An Agenda for Research on the Learning and Teaching of Algebra. Reston, VA.: NCTM; Hillsdale, NJ: Lawrence Erlbaum and Associates.
33. Xin, Y., Wiles, B., Lin, Y. (2008). Teaching Conceptual Model—Based Word Problem Story Grammar to Enhance Mathematics Problem Solving. The Journal of Special Education, 42(3): 163-178.
34. Yaman, H., Toluk, Z., Olkun, S. (2003). İlköğretim Öğrencileri Eşit İşaretini Nasıl Algılamaktadırlar?. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 24: 142-151.
35. Yıldırım, A., Şimşek, H. (2011). Sosyal Bilimlerde Nitel Araştırma Yöntemleri. Ankara: Seçkin Yayınevi.