Ders Araştırması Kapsamında Matematik Öğretmen Adayları Cebir Öğretiminde Sanal Manipülatifleri Nasıl Kullanmaktadır?

Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi (EFMED) Cilt 12, Sayı 1, Haziran 2018, sayfa 152-179. ISSN: 1307-6086 Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education Vol. 12, Issue 1, June 2018, pp. 152-179. ISSN: 1307-6086 Araştırma Makalesi / Research Article How do Preservice Mathematics Teachers Use Virtual Manipulatives to Teach Algebra through Lesson Study?1 Dilan TEMEL DOĞAN 2, Meriç ÖZGELDİ 3 2 Ahmet Şimşek Ortaokulu, Akdeniz, Mersin, https://orcid.org/0000-0002-1124-0806 3 Mersin Üniversitesi, Yenişehir, Mersin, https://orcid.org/0000-0002-4623-9397 Received : 28.03.2018 Accepted : 25.05.2018 Doi: 10.17522/balikesirnef.437729 Abstract – The purpose of the study was to investigate preservice mathematics teachers’ using of virtual manipulatives to teach algebra through a lesson study. 17 preservice mathematics teachers voluntarily participated in the study. Phenomenological approach has been used as a qualitative method of research. The preservice mathematics teachers created lesson plans about the middle school algebra topics using virtual manipulatives. Interviews were used as a way to collect data to gain information about their using of virtual manipulatives to teach algebra. The findings of the study showed that preservice mathematics teachers revealed positive and negative decisions about algebra teaching by using virtual manipulatives and they found the most of the virtual manipulatives effective in exploring and visualizing algebraic relations. As a result, the lesson study has played an important role in preservice teachers’ preparing a lesson plan for teaching algebra and integrating the virtual manipulatives into the stages of a lesson plan. Key words: Virtual manipulative, algebra teaching, lesson study, preservice mathematics teachers -----------Corresponding author: Meriç ÖZGELDİ, Mersin Üniversitesi Çiftlikköy Kampüsü Eğitim Fakültesi Matematik ve Fen Bilimleri Eğitimi Bölümü 33110 Yenişehir Mersin 1 Some of the results of this study were from the first author's master's thesis Summary Introduction: As students begin to work on algebra, they are faced with many difficulties since they try to manipulate their arithmetic thinking during the transition from arithmetics to algebra. The misinterpretation of the letters and symbols and difficulties in the meaning of algebra can effect their mathematical achievement (Ersoy & Erbas, 2003). Akkaya (2006) states that students consider letters as an abbreviation of concrete objects and therefore they TEMEL DOĞAN, D. & ÖZGELDİ, M. 153 have difficulties to represent different variables. Kaş (2010) examined the reasons behind these difficulties in three topics: the structure of algebra, mental development and readiness level of the students, and difficulties in the teaching of algebra. When the causes of difficulties and errors in the teaching of algebra are examined, it is generally anticipated that there are several troubles with curriculum and teachers’ content and pedagogical knowledge (e.g. Dede & Argün, 2003; Çelik & Güneş, 2013). Teachers do not have sufficient knowledge in their field or they cannot keep up with developing new approaches in teaching algebra (Baş, Çetinkaya & Erbaş, 2011). Moreover, NCTM (National Council of Teachers of Mathematics) (2000) emphasized the importance of using concrete and virtual manipulatives playing an active role in mathematics teaching. Some of the study revealed that the most important issue in manipulatives was related to their appropriate use in mathematics teaching (Çakıroğlu & Yildiz, 2007; KurtdedeFidan, 2008; Moyer, 2001). Yetkin-Özdemir (2008) stated that prospective teachers had a positive opinion on the use of manipulatives but they did not have clear ideas about exactly how mathematical concepts would be taught with these manipulatives. As a consequence, there is a need for conceptual framework to guide in-service and preservice teachers in using of manipulatives. Most of the studies on virtual manipulative have emphasized the physical characteristics of the virtual manipulatives and qualifications of the preservice teachers’ opinions and preferences (e.g., Akkan & Çakıroğlu, 2009; Durmuş & Karakırık, 2006; Yeniceri, 2013). The number of these studies is also very limited. In this context, it is thought that this study can contribute to the studies on algebra teaching with virtual manipulatives. The purpose of this study was to investigate preservice mathematics teachers’ using of virtual manipulatives to teach algebra through a lesson study. Method: Phenomenological approach has been used as a qualitative method of research. 17 preservice mathematics teachers voluntarily participated in the study. They created lesson plans about the middle school algebra topics using virtual manipulatives. Interviews were used in this study as a way to collect data to gain information about the participants’ using of virtual manipulatives to teach algebra. Moreover, lesson study approach was used throughout the process. Findings: While many preservice teachers have pointed out that algebra teaching can be more effective with virtual manipulatives, a few teacher candidates expressed that they would have difficulties with them. They expressed three views on the lesson plan: (a) algebra teaching Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi Necatibey Faculty of Education, Electronic Journal of Science and Mathematics Education Ders Araştırması Kapsamında Matematik Öğretmen Adayları ... How do Preservice Mathematics Teachers Use Virtual Manipulatives … with virtual manipulatives, (b) discovering algebraic relations with virtual manipulatives, and (c) visualizing and concrete thinking in algebra. For instance, when the findings are examined, the preservice teachers have stated that virtual manipulatives are generally effective in teaching algebra and may facilitate teaching. However, they have stated that some of the virtual manipulatives are incomplete or narrow in that all virtual manipulatives are not effective in teaching in the same way. They indicated that students would discover the relationship between different types of topics (e.g., equation system and slope). Moreover, they found virtual manipulatives effective in visualizing and concrete thinking in algebra. It is also frequently emphasized by preservice teachers that the algebra topics would be learned and reinforced in a meaningful. Discussion: It could be indicated that virtual manipulatives can be regarded as an important tool in teaching algebraic concepts. Moyer, Bolyard, and Spikell (2002) stated that virtual manipulatives provide students with the opportunity to manipulate them through different representations while discovering the meanings of mathematical concepts and constructs. Many studies in the literature support the findings of this study that virtual manipulatives facilitate the teaching of alge (...truncated)