Investigating the development of prospective mathematics teachers’ pedagogical content knowledge of generalising number patterns through school practicum

Abstract

The purpose of this study is to investigate the development of three prospective elementary mathematics teachers' pedagogical content knowledge (PCK) of number patterns with its two components: (1) knowledge of students' understanding and difficulties and (2) knowledge of topic-specific strategies and representations. For our investigation, we use Radford's (ZDM Math Educ 40:83-96, 2008) framework called 'architecture of algebraic pattern generalisation' to redefine these two components of PCK in the context of patterns. A case study was conducted to explore the development of PCK through a school practicum course and to examine how observation of number pattern lessons in schools and discussions of these observation contribute to prospective teachers' PCK. Analysis of the data indicated that observations and discussions of number pattern lessons resulted in considerable change in the way prospective teachers take into account students' understanding of and difficulties with patterns, as well as in the way they use pattern-specific strategies such as algebraic pattern generalisation during their lessons.

Analysis of Pedagogical Content Knowledge Studies in the Context of Mathematics Education in Turkey: A Meta-Synthesis Study

“…Studies 8,25,28,30,31,33, and 51, which had examined the development of PCK, stated that courses whose content was designed to reinforce teacher candidates had a positive effect on their development of PCK through reinforcement. Study 9 found that classroom teachers' PCK progressively improved during their university education.…”

“…As can be seen in Table 7, the interview was the most frequently used data collection tool in the studies. The interviews were generally conducted on scenarios that reflected the way students think (1, 3, 4, 9, 10, 12, 13, 19, 20, 27, 29, 32, 38, 53), course schedule as prepared by the participants (5,6,7,8,9,21,26,28), or teaching practices of the participants (9,13,17,18,21,26,28,30,45). Another frequently preferred data collection tool by the researchers was questionnaires.…”

“…Eleven studies were designed to examine PCK development. In seven studies (8,25,28,30,31,33,51) the effect of some content-enriched undergraduate courses on PCK were analyzed. In Study 9, the PCK development of teacher candidates throughout their undergraduate education was examined.…”

7. Sınıf Öğrencilerinin Denklem ve Eşitlik Konusundaki Öğrenmelerine Öğrenci Bileşeni Açısından Bir Bakış

“…Students Knowledge; is defined as determination of pre-details, difficulties on understanding, the misconceptions and causes of misconceptions in relation with subjects that students will learn by teachers or candidate teachers Shulman (1987). The studies on Student Knowledge Components informs us on difficulties of understanding, mistakes and misconceptions, teacher's attıtudes to students about subjects, workıng on it (Grossman, 1990;Fennema and Franke, 1992;Schoenfeld, 1998;Magnusson at al., 1999;An, Kulm and Wu, 2004;Ball at al., 2008;Park and Oliver, 2008;Hacıömeroglu, 2005;Baştürk, 2009;Yeşildere and Akkoç, 2012). As in other areas of mathematics, students have difficulties in learning algebraic issues, both in domestic and foreign studies (Asquith, Stephens, Knuth and Alibali, 2007;MacGregor and Stacey, 1997;Kaya, Keşan, İzgiol and Erkuş, 2016;Livneh and Linchevski, 1999).…”

“…Öğrenci bilgisi bileşenine yönelik yapılan çalışmalar, üzerinde çalışılan konu ile ilgili olarak, öğrencilerin konuyla alakalı karşılaştıkları anlama güçlükleri, hata ve kavram yanılgıları ve öğretmenlerin öğrencilere karşı tutumlarının neler olduğu hakkında bilgiler vermektedir (An, Kulm ve Wu, 2004;Ball vd., 2008;Baştürk, 2009;Fennema ve Franke, 1992;Grossman, 1990;Hacıömeroglu, 2005;Magnusson vd., 1999;Park ve Oliver, 2008;Schoenfeld, 1998;Yeşildere ve Akkoç, 2012). Türkiye'de öğretmenlerin pedagojik alanbilgileri üzerine yapılan çalışmalar alan yazında son yıllarda yer bulmaktadır (Aksu ve Konyalıoğlu, 2015;Baştürk ve Dönmez, 2011;Eroğlu, 2012, Gökbulut, 2010Gökkurt ve Soylu, 2016, Karahasan, 2010Kutluk, 2011;Şimşek ve Boz, 2015).…”