Öğretmen Adaylarının Birinci Dereceden İki Bilinmeyenli Denklem Sistemini Yorumlama Biçimleri

Yıl 2018, Cilt: 51 Sayı: 3, 127 - 144, 01.12.2018

Zeynep Akkurt Denizli

https://doi.org/10.30964/auebfd.440349

Öz

Bu araştırmanın amacı, öğretmen adaylarının
birinci dereceden iki bilinmeyenli denklem sistemlerini yorumlarken ilgili
kavramsal anlamalarını ve ne tür güçlükler yaşadıklarını incelemektir.
Araştırmaya, Türkiye’de büyükşehirdeki bir devlet üniversitesinin 3. sınıfında
okuyan 162 sınıf öğretmeni adayı katılmıştır. Öğretmen adaylarından, 2x-3y=19 ……………………………………………….
                                                                                                                                                                                                                     3x+6y=18
denklem sistemi ile çözülebilen bir gerçek yaşam problemi yazmaları
istenmiştir. Böylece, yazdıkları problemlerle, öğretmen adaylarının denklem
sistemini nasıl analiz ettiklerini ve sistemdeki kavramları nasıl ele
aldıklarını ortaya çıkarmak amaçlanmıştır. Sonuç olarak; öğretmen adaylarının,
birinci dereceden iki bilinmeyenli denklem sistemlerini yorumlamada ve ilgili
kavramları anlamlandırmada güçlük yaşadıkları ve bu kavramlarla ilgili önemli
eksikliklerinin olduğu belirlenmiştir. 

Anahtar Kelimeler

Cebir, birinci dereceden iki bilinmeyenli denklem sistemi, kavramsal anlama, öğretmen adayları

Kaynakça

• Arcavi, A., & Schoenfeld, A. (1988). On the meaning of variable. Mathematics Teacher, 81 (6), 420-427.
• Booth, L. (1988). Children's difficulties in beginning algebra. In A. F. Coxford (Eds.), The ideas of algebra, K-12 (pp. 20–32). Reston, VA: NCTM.
• Carpenter, T.P., & Levi, L. (2000). Developing conceptions of algebraic reasoning in the primary grades. National Center for Improving Student Learning and Achievement in Mathematics and Science. 5 Mayıs 2018 tarihinde https://files.eric.ed.gov/fulltext/ED470471.pdf adresinden alınmıştır.
• Chow, T. F. (2011). Students’ difficulties, conceptions and attitudes towards learning algebra: an ıntervention study to ımprove teaching and learning. Unpublished doctoral dissertation, Curtin University.
• Dede, Y. (2004). Değişken kavramı ve öğrenimindeki zorlukların belirlenmesi. Kuram ve Uygulamada Eğitim Bilimleri Dergisi, 4 (1), 24-56.
• Dede, Y. (2005). I. Dereceden denklemlerin yorumlanması: Eğitim fakültesi 1. sınıf öğrencileri üzerine bir çalışma. C.Ü. Sosyal Bilimler Dergisi, 29(2), 197- 205.
• Drijvers, P., Goddijn, A., & Kindt, M. (2011). Algebra education: Exploring topics and themes. In P. Drijvers (Eds.), Secondary algebra education: Revisiting topics and themes and exploring the unknown (pp. 5-26). Rotterdam, The Netherlands: Sense Publishers.
• 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.
• Harper, E. (1987). Ghosts of diophantus. Educational Studies in Mathematics, 28, 75-90.
• Herscovics, N., & Linchevski, L. (1994). A cognitive gap between arithmetic and algebra. Educational Studies in Mathematics, 27, 59-78.
• Kieran, C. (1992). The learning and teaching of school algebra. In D. Grouws (Eds.), Handbook of research on mathematics teaching and learning (pp.390-419). Macmillan Library Reference, New York.
• Krippendorff, K. (2004). Content analysis: An introduction to its methodology (2nd Ed.). Thousand Oaks, California: Sage Publications.
• Küchemann, D. (1978). Children’s understanding of numerical variables. Mathematics in Scholl, 7(4), 23-26.
• Kücherman, D. (1981). Algebra. In K. M. Hart (Eds.), Children’s understanding of mathematics: 11–16 (pp. 102–119). London: John Murray.
• Laughbaum, E. (2003). Developmental algebra with function as the underlying theme. Mathematics and Computer Education, 37 (1), 63-71.
• Linchevski, L. (1995). Algebra with numbers and arithmetic with letters: A definition of prealgebra. The Journal of Mathematical Behaviour, 14, 113-120.
• Linchevski, L., & Livneh, D. (1999). Structure sense: The relationship between algebraic and numerical contexts. Educational Studies in Mathematics, 40, 173–196.
• MacGregor, M., & Stacey, K. (1997). Students’ understanding of algebraic notation. 11-15. Educational Studies in Mathematics, 33, 1-19.
• Marcus, R., & Chazan, D. (2005). Introducing solving equations: teachers and the one variable first [algebra] curriculum. 2 Mayıs 2018 tarihinde https://www.researchgate.net/profile/Daniel_Chazan/publication/242091175_Introducing_solving_equations_Teachers_and_the_one-variable first_curriculum/links/00463528df7d866ed8000000/Introducing-solving-equations-Teachers-and-the-one-variable-first-curriculum.pdf adresinden alınmıştır.
• Miles, M.B., & Huberman, A.M. (1994). Qualitative data analysis: An expanded sourcebook (2nd ed.). Newbury Park, CA: Sage.
• National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
• Real, L. F. (1996). Secondary pupils’ translation of algebraic relationships into everyday language: A Hong Kong Study, (Eds. Luis, P. and Angel, G.). Paper presented at PME 20, Valencia, Spain, 3, pp.280-287.
• Sfard, A. (1995). The development of algebra: confront historical and psychological perspectives. Journal of Mathematical Behavior, 14, 15-39.
• Stacey, K., & MacGregor M. (2000). Learning the algebraic method of solving problems. Journal of Mathematical Behavior, 18 (2), 149-167.
• Usiskin, Z. (1999). Conceptions of school algebra and uses of variables. In B. Moses (Eds.), Algebraic thinking, grades K–12: Readings from NCTM’s school-based journals and other publications (pp. 7–13.). Reston, Va.: National Council of Teachers of Mathematics, 1999.
• Yahya, N., & Shahrill, M. (2015). The strategies used in solving algebra by secondary school repeating students. Procedia- Social and Behavioral Sciences, 186 (2015), 1192 – 1200.