Matematik Öğretmen Adaylarının, 6. Sınıf Öğrencilerinin Cebirsel Örüntüleri Genellemelerine İlişkin Farkındalıkları

Yıl 2019, Cilt: 27 Sayı: 4, 1713 - 1728, 15.07.2019

Seval Deniz Kılıç

https://doi.org/10.24106/kefdergi.3263

Cited By: 1

Öz

Matematik öğretmeninin sahip olması gereken bilgi, temel konu ve kavramları bilmenin ötesinde ayrıcalıklı bir bilgi türüdür. Bu bilginin bileşenlerinden birisi de öğrencinin matematiksel düşüncesini farketmektir. Özel olarak cebir alanında öğrencilerin örüntü genelleme süreçlerini anlamlandırmak ve hata kaynaklarını belirlemek için öğretmenin bu türde bir farkındalığa sahip olması gereklidir. Bu çalışmanın amacı matematik öğretmen adaylarının öğrencilerin örüntü genelleme süreçlerine ilişkin farkındalığını araştırmaktır. Bu amaca yönelik veri toplama aracı olarak farklı tipte yaklaşım ve stratejilerden oluşan gerçek öğrenci yanıtları kullanılmıştır. Nitel araştırma yöntemlerinin benimsendiği çalışmanın katılımcıları 2015-2016 eğitim-öğretim yılında bir devlet üniversitesinin matematik öğretmenliği bölümüne devam eden ve “cebirsel kavramlar ve öğretimi dersi”ni almakta olan 35 öğretmen adayıdır. Araştırma bulgularına göre, öğretmen adayları öğrencilerin görünür stratejilerini fark etme konusunda başarılı sayılabilirler. Ne var ki, adayların öğrencilerin hatalarının altında yatan nedenleri belirlemeye yönelik açıklamaları yeterli bulunmamıştır.

Anahtar Kelimeler

matematik öğretmen adayı, öğrenci bilgisi, örüntü genelleme

Teşekkür

Bu çalışma 26-28 Ekim tarihlerinde Muğla’da düzenlenen 5. Uluslar arası Eğitim Programları ve Öğretim Kongresi’nde sunulan sözlü bildirinin genişletilmiş halidir.

Prospective Mathematics Teachers’ Noticing On The Algebraic Pattern Generalisations Made By 6th Grade Students

Öz

The knowledge that the mathematics teachers should have is a privileged knowledge beyond the basic concepts and concepts. One of the components of this knowledge is noticing students’ mathematical thinking. In particular, in the field of algebra, it is necessary for the teacher to have this kind of awareness in order to make sense of pattern generalization processes and to identify sources of errors. The aim of this study is to investigate the awareness of mathematics teacher candidates about students pattern generalization processes. For this purpose, students’ real answers consisting of different types of approaches and strategies were used as the data collection tool. This study employs the qualitative research methods and the participants are 35 prospective teachers taking the “teaching algebraic concepts” course in mathematics teaching department at a state university in 2015 – 2016 academic year. According to the research findings, prospective teachers can be considered successful in recognising students’ visible strategies; nevertheless the explanations provided by the prospective teachers on finding out the reasons that lie beneath the student mistakes are unsatisfactory.

Anahtar Kelimeler

prospective mathematics teacher, student knowledge, pattern generalization

Kaynakça

• Amit, M &Neria, D. (2008). Rising to the challenge: using generalization in pattern prob-lems to unearth the algebraic skills of talented pre-algebra students. ZDM Mathema-tics Education, 40, 111–129.
• An, S. & Wu, Z. (2012). Enhancing mathematics teachers’ knowledge of students’ thinking from assessing and analysis misconceptions in homework. International Journal of Science and Mathematics Education, 10, 717–753.
• Ball, D.L.,Thames, M.H., &Phelps, G. (2008). Content knowledge for teaching. What makes it special? Journal of Teacher Education, 59(5), 389–407.
• Baş, S., Erbaş, A. K. ve Çetinkaya, B. (2011). Öğretmenlerin dokuzuncu sınıf öğrencilerinin cebirsel düşünme yapılarıyla ilgili bilgileri. Eğitim ve Bilim, 36(159), 41-55.
• Bartell, T. G., Webel, C., Bowen, B., Dyson, N. (2013). Prospective teacher learning: re-cognizing evidence of conceptual understanding. Journal of Mathematics Teacher Education.16:57–79
• Becker, J. R.& Rivera, F. (2005). Generalizationstrategies of beginning high school algebra students. ınchick, h. l. &vincent, j. l. (eds.). Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, pp. 121-128. Melbourne: PME.
• Becker, J. R., & Rivera, F. (2006). Sixth graders’ figural and numerical strategies for genera-lizing patterns in algebra (1). In Alatorre, S., Cortina, J.L., Sáiz, M., & Méndez, A. (Eds), Proceedings of the 28th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Vol. 2 (pp. 95-101). Mérida, México: Universidad Pedagógica Nacional.
• Callejo, M.L. & Zapatera, A. (2016). Prospective primary teachers’ noticing of students’ un-derstanding of pattern generalization. Journal of Mathematics Teacher Education, 20(4), 309-333.
• Fernández, C., Llinares, S. & Valls, J. (2012). Learning to notice students’ mathematical thinking through on-line discussions. ZDM Mathematics Education, 44, 747–759
• Fernández, C., Llinares, S., & Valls, J. (2013). Primary teacher’s Professional noticing of students’ mathematical thinking. The Mathematics Enthusiast, 10(1&2), 441-468.
• Gall, M. D.,Borg, W. R., &Gall, J. P.(1996). Educational Research(6th ed.). White Plains, NY:Longman Publishers USA.
• Hines, E., & McMahon, M. T. (2005). Interpreting middle school students’ proportional rea-soning strategies:observations from prospective teachers. School Science and Mathe-matics, 105(2), 88–105.
• Holt, P., Mojica, G., & Confrey, J. (2013). Learning trajectories in teacher education: Sup-porting teachers’ understandings of students’ mathematical thinking. Journal of Mat-hematical Behavior, 32, 103-121.
• Jacobs, V. A., Lamb, L. L. C., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169–202.
• Kılıç, Ç. (2017). Analyzing middle school students’ figural pattern generating strategies con-sidering a quadratic number pattern. Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi,17 (1), 250-267.
• Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. Chica-go: University of Chicago Press.
• Lannin, J. K. (2005). Generalization and justification: Thechallenge of introducing algebraic reasoning through patterning activities. Mathematical Thinking and Learning, 7(3), 231-258.
• Lesley, L. &Freiman, V. (2004). Tracking primary students’ understanding of patterns. In M. J. Hoines, & A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the Inter-national Group for the Psychology of Mathematics Education(Vol. 2, pp. 415-422). Bergen, Norway: PME.
• Llinares, S. (2013). Professional noticing: A component of the mathematics teacher’s profes-sional noticing.Sisyphus Journal of Education, 1(3), 76–93.
• Magiera, M., van der Kieboom, L., & Moyer, J. (2013). An exploratory study of pre-service middle school teachers’ knowledge of algebraic thinking. Educational Studies in Mathematics, 84(1), 93–113.
• Mason, J. (2002). Researching your own practice. The discipline of noticing. London: Rout-ledge-Falmer.
• Morris, A. K. (2006). Assessing pre-service teachers’ skills for analyzing teaching. Journal of Mathematics Teacher Education, 9:471–505.m
• Mouhayar, R.R. & Jurdak, M.E. (2012). Teachers’ ability to identify and explain students’ actions in near and far figural pattern generalization tasks. Educational Studies in Mathematics, 82, 379-396.
• Polya, G. (1957). How to solve it (2nd ed.). Princeton: Princeton University Press.
• Ponte, J. P., & Chapman, O. (2006). Mathematics teachers’ knowledge and practices. In A. Gutierrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 461-494). Rotterdam/Taipei: Sense Publis-hers.
• Rivera, F. (2007). Visualizing as a mathematical way of knowing: understanding figural ge-neralization. MathematicsTeacher. 101(1), 69–75.
• Rivera, F. (2010). Visual templates in pattern generalization activity. Educational Studies in Mathematics, 73, 297–328.
• Sa´nchez-Matamoros, G., Ferna´ndez, C., & Llinares, S. (2014). Developing Prospective Te-achers’ Noticing of Students’ understanding of the derivative concept. International Journal of Science and Mathematics Education. doi:10.1007/s10763-014-9544-y.
• Schack, E., Fisher, M., Thomas, J., Eisenhardt, S., Tassell, J., & Yoder, M. (2013). Prospec-tive elementary school teachers’ professional noticing of children’s early numeracy. Journal of Mathematics Teacher Education, 16, 379-397.
• Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (Eds.) (2010). Mathematics teacher noticing: Seeing through teachers’ eyes. New York, NY: Routledge.
• Shulman, L.S. (1986). Those who understand: knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
• Shulman, L. S. (1987). Knowledge andteaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-22.
• Spitzer, S., Phelps, C. M., Beyers, J. E. R., Johnson, D. Y. & Sieminski, E. M. (2011). Deve-loping prospective elementary teachers’ ability to identify evidence of student mat-hematical achievement. Journal of Mathematics Teacher Education, 14, 67–87
• Stacey, K. (1989). Finding and using patterns in linear generalizing problems. Educational Studies in Mathematics, 20 (2), 147–164.
• Tanışlı, D. ve Yavuzsoy Köse, N. (2011). Lineer şekil örüntülerine ilişkin genelleme strateji-leri: görsel ve sayısal ipuçlarının etkisi. Eğitim ve Bilim, 36(160), 184-198.
• Tanışlı, D. ve Köse, N.(2013) Sınıf öğretmeni adaylarının genelleme sürecindeki bilişsel yapıları: bir öğretim deneyi. Elektronik Sosyal Bilimler Dergisi. 12(44), 255-283.
• Yıldırım, A. ve Şimşek, H. (2013). Sosyal bilimlerde nitel araştırma yöntemleri (9. baskı). Ankara: Seçkin Yayıncılık.
• Warren, E.(2005). In Chick, H. L. & Vincent, J. L. (Eds.). Young children’s ability to genera-lise the pattern rule for growing patterns. Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, pp. 305-312. Melbourne: PME.
• Wilson, P. H.,Mojica, G., &Confrey, J. (2013). Learning trajectories in teachereducation: supportingteachers’ understanding of students’ mathematicalthinking. Journal of Mathematical Behavior, 32, 103–121.