Ortaokul 7. Sınıf Öğrencilerinin Cebirsel İfadeleri ve Değişkenleri Yorumlama Sürecinde Yaptıkları Hatalar

Öz

Bu çalışmanın amacı öğrencilerin cebirsel ifadeleri ve değişkenleri yorumlama sürecinde yaşadıkları zorlukları ve yaptıkları hataları belirlemektir. Öğrencilerin cebirsel ifadeleri ve değişkenleri nasıl yorumladıkları ve bu süreçte karşılaştıkları zorlukların belirlenmesinin amaçlandığı bu araştırmada nitel araştırma desenlerinden, vaka çalışması modeli [case study] kullanılmıştır. Araştırma ortaokulda öğrenim gören ve amaçlı örnekleme yöntemlerinden maksimum çeşitlilik örneklemesi kullanılarak belirlenen farklı başarı düzeylerine sahip dört yedinci sınıf öğrencisiyle yürütülmüştür. Araştırma sürecinde elde edilen veriler içerik analizi ve betimsel analiz kullanılarak analiz edilmiştir. Yapılan analizler sonucunda elde edilen veriler ışığında öğrencilerin yaptıkları hatalar; (i) cebirsel ifadeyi bilinmeyen olarak görme, (ii) cebirsel ilişkileri yanlış kullanma, (iii) cebirsel ifadeleri birleştirme ve sonlandırma, (iv) değişkenlerin sayısal bir değeri değil nesneleri temsil ettiklerini düşünme, (v) değişkenleri sadece bilinmeyen olarak düşünme temaları altında sunulmuştur.

Kaynakça

1. Akkuş, O. (2004). The effects of multiple representations-based instruction on seventh grade students’ algebra performance, attitude toward mathematics, and representation preference. Unpublished doctoral dissertation. Middle East Techinal University, Ankara.
2. Asquith, P., Stephens, A. C., Knuth, E. J., & Alibali, M. W. (2007). Middle school mathematics teachers’ knowledge of students’ understanding of core algebraic concepts: Equal sign and variable. Mathematical Thinking and Learning, 9(3), 249-272.
3. Baroody, A.J., & Ginsburg, H. P. (1983). The effects of instruction on children’s understanding of the “equals” sign. The Elementary School Journal, 84(2), 198-212.
4. Behr, M., Erlwanger, S., & Nichols, E. (1980). How children view the equals sign. Mathematics Teaching, 92, 13-15.
5. Booth, L. (1988). Children’s difficulties in beginning algebra. A. F. Coxford, & A. P. Shulte (Ed.), The ideas of algebra. K–12. VA: Yearbook. Reston.
6. Collis, K.F. (1975). A study of concrete and formal operations in school mathematics: A Piegatian Viewpoint. Australian Council for Educational Research: Melbourne
7. Davis, R. B. (1975). Cognitive process inveolved in simple algebraic equations. Journal of Children’s Mathematical Behaviour, 1(3), 7-35.
8. Creswell, J. W. (1998). Qualitative inquiry and research design: Choosing among five traditions. Thousand Oaks, CA: Sage Publications.

9. Dede, Y. ve Argün, Z. (2003). Cebir, Öğrencilere niçin zor gelmektedir?. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 24, 180-185.
10. Falkner, K.P., Levi, L., & Carpenter, T. P. (1999). Childrens understanding of equality: A foundation for algebra. Teaching Children Mathematics, 6, 231-236.
11. Hattikudur, S., & Alibali, M. W. (2010). Learning about the equal sign: Does comparing with inequality symbols help?. Journal of experimental child psychology, 107(1), 15-30.
12. Herscovics, N., & Linchevski, L. (1994). A cognitive gap between arithmetic and algebra. Educational Studies in Mathematics, 27(1), 59-78.
13. Jones, I., Inglis, M., Gilmore, C., & Dowens, M. (2012). Substitution and sameness: Two components of a relational conception of the equals sign. Journal of experimental child psychology, 113(1), 166-176.
14. Kaput, J. (1998). Transforming algebra from an engine of inequity to an engine of mathematical power by “algebrafying” the K-12 curriculum. Paper presented at the Algebra Symposium, Washington, DC, May, 1998.
15. Kieran, C. (1992). The learning and teaching of school algebra. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 390-419). New York: Macmillan.
16. Kuchemann, D. (1978). Children’s understanding of numerical variables. Mathematics in Scholl, 7(4), 23-26.
17. Kuchemann, D. (1981). 'Algebra' in Children's Understanding of Mathematics; 11-16, K. Hart (Ed.). Alden Press, Oxford, London.
18. MacGregor, M., & Price, E. (1999). An exploration of aspects of language proficiency and algebra learning. Journal for Research in Mathematics Education, 449-467.
19. MacGregor, M., & Stacey, K. (1997). Students' understanding of algebraic notation: 11–16. Educational Studies in Mathematics, 33, 1–19.
20. Malisani, E., & Spagnolo, F. (2009). From arithmetical thought to algebraic thought: The role of the variable. Educational studies in mathematics, 71, 19–41.
21. McNeil, N. M. (2008). Limitations to teaching children 2+ 2= 4: Typical arithmetic problems can hinder learning of mathematical equivalence. Child Development, 79(5), 1524-1537.
22. Rosnick, P. (1981). Some misconceptions concerning the concept of variable. Are you careful about defining your variables?.. Mathematics Teacher, 74(6), 418–420.
23. Stacey, K., & MacGregor, M. (1997).Ideas about symbolism that students bring to algebra. The Mathematics Teacher, 90(2), 110-113.
24. Tirosh, D., Even, R., & Robinson, N. (1998). Simplifying algebraic expressions: Teacher awareness and teaching approaches. Educational Studies in Mathematics, 35(1), 51-64.
25. Usiskin, Z. (1999). Conceptions of school algebra and uses variables. In Allgebraic Thinking, Grades K-12: Readings from NCTM’s School-Based Journals and Other Publications, edited by Barbara Moses, pp. 7-13. Reston, Va: Natinoal Council of Teachers Mathematics.
26. Vance, J. (1988). Number operations from an algebraic perspective. Teaching Children Mathematics, 4, 282–285.
27. Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics: Teaching developmentally. Pearson Education, Inc.
28. Yıldırım, A. ve Şimşek, H. (2011). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin Yayıncılık.