BİR MATEMATİK ÖĞRETMENİNİN ÖĞRENCİ DÜŞÜNCESİ BİLGİSİ ÜZERİNE BİR İNCELEME

Özet

Bu araştırmanın amacı bir matematik öğretmeninin pedagojik alan bilgisinin öğrenci düşüncesi bilgisi bileşeninde ve öğrencilerin matematiksel düşünmelerini destekleme bağlamında incelenmesidir. Araştırmada pedagojik alan bilgisinin öğrenci düşüncesi bilgisi bileşenine odaklanılmıştır. Ayrıca Fraivillig, Murphy ve Fuson (1999) tarafından geliştirilen "Advancing Children's Thinking"-"Düşünmeyi Geliştirme Modeli"'nden yararlanılmıştır. Araştırma bir özel durum çalışması olup kapsamlı olarak yürütülen bir araştırmasının parçasıdır. Araştırmanın katılımcısı araştırmaya katılmaya gönüllü olan ve bir lisede görev yapmakta olan bir matematik öğretmenidir. Araştırmada katılımcı öğretmenin matematiksel düşünmeyi destekleme bağlamında pedagojik alan bilgisini inceleyebilmek amacıyla video kaydı yardımıyla gözlem verileri toplanmıştır. Öğretmenin yedi ders saati video kaydına alınarak fonksiyon kavramına ilişkin öğretimi gözlenmiştir. Gözlem verilerinin analizi betimsel analiz kullanılarak gerçekleştirilmiştir. Araştırmanın bulguları teorik çerçeve ile uyumlu olarak sunulmuştur. Elde edilen sonuçlar, katılımcı öğretmenin fonksiyon kavramı öğretiminde kuramsal çerçeve kapsamındaki uygun koşulları sağlamada başarılı olduğunu göstermiştir. Öğretmenin fonksiyon kavramı öğretiminde genellikle öğrenci düşüncesini merkeze alan bir yaklaşım izlediği, derslerinde öğrencilerin düşüncelerini dinlediği ve öğrencileri düşüncelerini ayrıntılı biçimde açıklamaları için teşvik ettiği belirlenmiştir. Ayrıca öğretmenin araştırmanın kuramsal çerçevesine göre öğrencilerin mevcut bilgilerini ortaya çıkarma, ön bilgi ile yeni bilgiyi ilişkilendirme ve öğrenci düşüncelerine ve sorularına değer verme alt bileşenlerinde diğer bileşenlere göre daha fazla olumlu yaklaşım sergilediği görülmüştür. Sonuçlar doğrultusunda bazı önerilere yer verilmiştir

Abstract

The purpose of this study is to examine a mathematics teacher’s pedagogical content knowledge in the context of knowledge of student thinking and supporting students’ mathematical thinking. The focus of the study is knowledge of student thinking which is one of the components of pedagogical content knowledge. Besides “Advancing Children Thinking Framework” created by Fraivillig, Murphy and Fuson (1999) was used. This study is a case study that was a part of larger research. Participant of the research was a mathematics teacher who was volunteer to participate the research and working at a high school. To examine participant’s pedagogical content knowledge in the context of mathematical thinking observation data were collected by using video record. Seven lessons of the teacher towards teaching function concept were recorded via a video camera. Descriptive analysis was used to analyze observation data. Findings were presented in parallel with the theoretical framework. The results showed that the participant was successful to provide appropriate conditions determined in the theoretical framework for teaching function concept. It was found that the teacher usually followed a student-centered approach, listened students’ thought and encouraged students to explain their thoughts in detail. It was also seen that he had more positive approach at determining students’ current knowledge, connecting prior knowledge to new knowledge and valuing students’ questions and thoughts. Suggestions are presented in accordance with the results One component of the pedagogical content knowledge is the knowledge of student thinking. Knowledge of student thinking includes to know what makes the learning of specific topics easy or difficult (Ball, Thames & Phelps, 2008; Shulman, 1986), and how students acquire the mathematics content and think about it (Ball et al., 2008; Fennema & Franke, 1992). Besides it also involves addressing students’ misconceptions and learning difficulties (An, Kulm & Wu, 2004; Fennema & Franke, 1992; Kovarik, 2008; Magnusson, Krajcik & Borko, 1999; Park & Oliver, 2008; Schoenfeld, 1998; Shulman, 1986) and noticing students’ prior knowledge (Kovarik, 2008; Magnusson et al., 1999; Schoenfeld, 1998; Shulman, 1986). It is seen in the literature that there are several studies examining mathematics in-service or pre-service teachers’ pedagogical content knowledge in the context of understanding, supporting and developing students’ mathematical thinking (Crespo, 2000; Hughes, 2006; McLeman & Cavell 2009; Philipp, 2008; Philipp, Thanheiser & Clement, 2002; Peterson, Fennema, Carpenter & Loef, 1989; Vacc & Bright, 1999). But most of them deal with pre-service teachers’ knowledge. Differently, this study is focused on the examination of a mathematics teacher’s pedagogical content knowledge in the context of the knowledge of student thinking and supporting students’ mathematical thinking. Shulman’s (1986, 1987) definition for pedagogical content knowledge was adopted and the knowledge of student thinking was considered in this study. “Advancing Children Thinking Framework” created by Fraivillig, Murphy and Fuson (1999) was also used. An interconnected framework was obtained and used for this study. Method This study is a case study that was a part of larger research. Participant of the research was a high school mathematics teacher who was volunteered for participating in the research. A nickname (Ersin) was used for the teacher. To examine Ersin’s pedagogical content knowledge in the context of mathematical thinking, observation data were collected by using video record. Seven lessons of the teacher teaching function concept were recorded via a video camera. Descriptive analysis was used to analyze the observation data. In data analysis, two researchers coded the transcribed text individually. Then, they came together and reached a consensus. So intercoder consistency was provided. Findings were presented in parallel with the theoretical framework. Findings, Discussion and Conclusion The results showed that the participant was successful in performing the pedagogical approach determined in the theoretical framework for teaching function concept. There were not any negative findings for Ersin although there were for the others in the larger study. This result also supported the idea that Ersin was successful in teaching function concept. Ersin had more positive approach in some components of the knowledge of student thinking like determining students’ current knowledge, connecting prior knowledge to new knowledge and valuing students’ questions and thoughts. This result doesn’t mean that Ersin was unsuccessful at other components. It is thought that this result may be stem from student-centred approach that Ersin followed in his class generally. He listened his students’ thought and encouraged the students to explain their thoughts in detail. He formed class discussions and managed the discussion as he planned. Thus, Ersin could handle his lessons in a way that the students are more active. When entering the concept of functions or sub-concepts, he did not give information directly and took the thoughts of students. In discussions, he took many students’ thoughts and listened to different opinions without giving a true or false feedback. He prevented the dissemination of the discussion in some directions. This approach of Ersin has also been evaluated in accordance with the Teaching Principle proposed by the NCTM (2000). Similar to the result obtained in the research, when Özaltun-Çelik and Bukova-Güzel (2016) examined the questions asked by a mathematics teacher who participated in a lesson study, they reached the results that the teacher asked questions in order to reveal the students’ preliminary knowledge, to understand their ideas and to ask them to explain their correct answers. A remarking result was about misconceptions. Although Ersin was successful at determining students’ misconceptio