Middle School Mathematics Teachers’ Pedagogical Content Knowledge Regarding Student Knowledge about Quadrilaterals

Yıl 2015, , 744 - 756, 26.04.2015

Elif Akkaş , Elif Türnüklü

https://doi.org/10.17051/io.2015.12002

Cited By: 9

Öz

Abstract

Pedagogical content knowledge is consisted of two components: student knowledge and teaching strategies. Student knowledge was defined to sub-categories as connecting prior knowledge to new knowledge, noticing students’ mistakes, identifying students’ difficulties of understanding. The aim of this study is to examine middle school mathematics teachers’ pedagogical content knowledge in terms of student knowledge regarding quadrilaterals.

Interview method was used for data acquisition. 30 middle school mathematics teachers working at 12 different schools in Turkey participated in this study. The questions asked the teachers during interviews were prepared by researchers in accordance with student knowledge component of the pedagogical content knowledge. Content analysis was used to analyze the data acquired in this study.

The study results show that teachers pointed out that they teach lessons taking into consideration their students’ previous knowledge and  new knowledge they do by “reminding quadrilaterals students previously learnt” or “making association between similar quadrilaterals. Based on the data, the teachers pointed out the students’ mistakes about quadrilaterals were group under three headings. These are, mistakes regarding defining quadrilaterals, mistakes regarding visual property and, classification of quadrilaterals and family relation within quadrilaterals.  The students’ difficulties inferred from teachers’ responses are summarized in two groups: difficulties identified related with trapezoid and difficulties identified related with other quadrilaterals.

 

Key words: Pedagogical Content Knowledge, Student Knowledge, Quadrilaterals

Anahtar Kelimeler

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Ortaokul Matematik Öğretmenlerinin Dörtgenler Konusunda Pedagojik Alan Bilgilerinin Öğrenci Bilgisi Bileşeninde İncelenmesi

Öz

Pedagojik alan bilgisini farklı bileşenlerde inceleyen çalışmalarda ortak iki bileşenin varlığı dikkat
çekmektedir. Bu bileşenler; öğrenci bilgisi ve öğretim stratejileri bilgisi bileşeni olarak tanımlanmaktadır.
Öğrenci bilgisi bileşeni öğrencilerin ön bilgileri- yeni bilgileri arasında kurulan bağlantılar, konuya yönelik
öğrenci hataları ve öğrencilerin konuya özgü yaşadıkları anlama güçlükleri alt bileşenlerinden oluşmaktadır.
Araştırmanın amacı ortaokul matematik öğretmenlerinin dörtgenler konusunda pedagojik alan bilgilerinin
öğrenci bilgisi bileşeninde incelenmesidir. Nitel araştırma yöntemi, görüşme metodu kullanılmıştır. Katılımcılar,
Türkiye’de bir ilde 12 farklı ortaokulda çalışan 30 matematik öğretmenidir. İçerik analizi kullanılmıştır.
Sonuçlara göre; öğretmelerin öğrencilerin ön bilgileriyle, yeni öğrendikleri arasında bağlantı kurduklarını, bunu,
“önceden öğrenilen dörtgenler” ya da “benzer dörtgenleri ilişkilendirerek” kurdukları belirlenmiştir.
Öğretmenler dörtgenlere yönelik öğrenci hatalarını dörtgenleri tanımlama, dörtgenleri görselleştirme ve
dörtgenleri sınıflandırma- aile ilişkisi kurma hataları olmak üzere üç başlıkta gruplamışlardır. Öğrencilerin
konuya özgü yaşadıkları anlama güçlükleri ise yamuğa ilişkin anlama güçlükleri ve diğer dörtgenlere ilişkin
anlama güçlükleri olmak üzere iki grupta incelenmiştir. Farklı çalışmalarla, öğretmenlerin dörtgenler
konusundaki farklı öğrenci bilgileri ortaya çıkarılıp, bu çalışmanın sonucu zenginleştirilebilir.

Anahtar Kelimeler

Pedagojik Alan Bilgisi, Öğrenci Bilgisi, Dörtgenler

Kaynakça

• Akkas, E., Türnüklü, E. (2014). Middle school mathematics teachers’ pedagogical content knowledge regarding teaching strategies on quadrilaterals. Educational Research and Reviews, 9(7), 183- 1
• An, S., Kulm, G., Wu, Z. (2004). The pedagogical content knowledge of middle school, mathematics teachers in China and the U. S., Journal of Mathematics Teacher Education, 7, pp. 145- 172.
• Ball, D., Thames, M., Phelps, G. (2008). Content knowledge for teaching what makes it special?,
• Journal of Teacher Education, Vol. 59, No. 5, 389- 407. Baştürk, S. (2009). Mutlak değer kavramı örneğinde öğretmen adaylarının öğrenci hatalarına yaklaşımları. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 3(1), 174-194.
• Berkün, M. (2011). İlköğretim 5 ve 7. Sınıf Öğrencilerinin Çokgenler Üzerindeki İmgeleri ve Sınıflandırma Stratejileri. Yayınlanmamış Yüksek Lisans Tezi, D.E.Ü.
• Bingölbali, E., Özmantar, M.F (2009). İlköğretimde Karşılaşılan Matematiksel Zorluklar ve Çözüm
• Önerileri, Pegem Akademi, 1. Baskı. Bukova- Güzel, E. (2010). An investigation of pre-service mathematics teachers’ pedagogical content knowledge, using solid objects, Scientific Research and Essays, 5(14), 1872-1880.
• Burger, W., Shaughnessy, J. (1986). Characterizing the van hiele levels of development in geometry,
• Journal for Research in Mathematics Education, Vol. 17, No. 1, 31- 48. De Villiers, M. (1994). The role and function of a hierarchical classification of quadrilaterals. For the learning of mathematics, 14, 11-18.
• Fennema, E. and Franke, M. (1992) Teachers’ knowledge and its impact in: D. A. Grouws (Ed)
• Handbook of Research on Mathematics Teaching and Learning (New York: Macmillan Publishing). Fichbein, E. (1993). The theory of figural concepts. Educational Studies in Mathematics , 24 ( 2), 139-1
• Fujita, T. (2012). Learners’ Level of Understanding of Inclusion Relations of Quadrilaterals and Prototype Phenomenon. The Journal of Mathematical Behavior, 31: 60-72.
• Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. New
• York: Teachers College Press. Hacıömeroğlu, G. (2009). Examining a preservice secondary teacher’s growth: implications for teaching. Journal of Theory and Practice in Education, 5(2), 261- 273.
• Heinze, A. ve Ossietzky, C. (2002). “…Because a Square is not a Rectangle” Students’ Knowledge of
• Simple Geometrical Concepts When Starting to Learn Proof. In A. Cockburn ve E. Nardi (Eds.): Proceedings of The 26th Conference of the International Group for the Psychology of Mathematics Education, V.3, 81-88. Hershkowitz, R. (1989). Visualization in geometry- two sides of the coin. Focus on Learning
• Problems in Mathematics, 11(1), 61-76. Hershkowitz, R. (1990). Psychological aspects of learning geometry. P.Nesher ve J. Kilpatrick (Eds.):
• Mathematics and Cognition, Cambridge University Press: Cambridge. Kovarik, K. (2008). Mathematics educators’ and teachers’ perceptions of pedagogical content knowledge, Dissertation at the Columbia University, 2008.
• Nakahara, T. (1995). Children’s construction process of the concepts of basic quadrilaterals in Japan.
• In A.Oliver & K. Newstead (Eds.), Proceedings of the 19th Conference of the International Group for the Psychology of Mathematics Education. 3: 27–34. Magnusson, S., Krajcik, J. and Borko, H. (1999). Nature, sources and development of pedagogical content knowledge for science teaching. In J. GessNewsome and N.G. Lederman (Eds.),
• Examining Pedagogical Content Knowledge. (95–132). Dordrecht, The Netherlands: Kluwer Academic Publishers. Monaghan, F. (2000). What Difference Does It Make? Children’s Views of the Differences Between
• Some Quadrilaterals. Educational Studies in Mathematics, 42(2),179-196. Park, S., Oliver, J. (2008) Revisiting the conceptualisation of pedagogical content knowledge (PCK):
• PCK as a conceptual tool to understand Teachers as Professionals. Research Science Education, 38,261- 284. Tall, D., and Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12( 2), 151-16.
• Türnüklü, A. (2000). Eğitim bilim araştırmalarında etkin olarak kullanılabilecek nitel bir araştırma tekniği: Görüşme. Kuram ve Uygulamada Eğitim Yönetimi,24,543-559.
• Türnüklü, E. (2014). Concept Images of Trapezoid: Some cases from Turkey. Educational Journal, 3(3), 179- 185.
• Türnüklü, E., Alaylı, F., Akkaş, E. (2013). Investigation of prospective primary mathematics teachers’ perceptions and images for quadrilaterals. Educational Sciences: Theory & Practice, 13(2), 1225-1232.
• Tsamir, P., Tirosh, D., and Levenson, E. (2008). Intuitive nonexamples: The case of triangles.
• Educational Studies in Mathematics, 69(2), 81- 95. Sarfaty, Y., and Patkin, D. (2013). The ability of second grades to identify solids in different positions and to justify their answer. Pythagoras, 34(1), 212 - 222.
• Schoenfeld, A., H. (1998) Toward a theory of teaching-in- context. Issues in Education, 4(1), 1-94.
• Shulman, L. (1986) Those who understand: knowledge growth in teaching. Educational Researcher, 15 (2), 4- 14.
• Shulman, L. (1987) Knowledge and teaching: foundations of the new reform. 57, 1- 22.
• Şimşek, H., Yıldırım, A.(2006). Nitel Araştırma Yöntemleri. Ankara: Seçkin Yayıncılık.
• Yeşildere, S., Akkoç, H. (2010). Examining pre-service mathematics teachers’ pedagogical content knowledge of number patterns with regard to topic- specific strategies. Journal of Ondokuz