Virtual Or Physical: In-Service And Pre-Service Teacher’s Beliefs And Preferences On Manipulatives

Turkish Online Journal of Distance Education-TOJDE October 2012 ISSN 1302-6488 Volume: 13 Number: 4 Article 11 VIRTUAL OR PHYSICAL: In-service and Pre-Service Teacher’s Beliefs and Preferences on Manipulatives Assist. Prof. Dr. Yasar AKKAN Department of Mathematical Engineering Gümüshane University, TURKEY ABSTRACT Although the use of physical manipulatives, which have been emphasized to use in preschool education program and primary and secondary mathematics curriculum, in classroom environments is old, it is very new to use virtual manipulatives in classroom environments. The selection, preparation, and the integration to learning environments of both types of manipulatives are the most basic duties of teachers. However, the experiences, of using the physical and virtual manipulatives in course environments, of teachers and pre-service teachers are influenced by beliefs about the nature, teaching and learning of mathematics. The aim of this study is to determine and compare the beliefs of teachers and pre-service teachers in different branches for the use of virtual and physical manipulatives in mathematics education. For this purpose, 148 teachers, in the provinces of Trabzon, Kars and Gümüşhane, and 228 pre-service teachers, in the Education Faculties of Karadeniz Technical University and Kafkas University, have been applied two types of scales and interviews have been conducted with 40 teachers and pre-service teachers selected from that sample. Frequencies, percentages and arithmetic averages have been used to analyze the data. As a result, the majority of teachers and pre-service teachers have been identified to carry positive beliefs for the use of virtual and physical manipulatives in mathematics education and they have expressed that they desire to use both types of manipulatives more in the future. Keywords: Mathematics education, belief, virtual and physical manipulatives, teachers and pre-service teachers. INTRODUCTION Manipulatives are defined as "objects that appeal to several senses and that can be touched, m oved about, rearranged, and otherw ise handled by children " (Kennedy, 1986; p. 6). Stein & Bovalino (2001) has said that manipulative are one of the ways to make mathematics learning more expressive for students. Moyer (2001) has pointed out that manipulatives are materials constructed to symbolize explicitly and concretely abstract mathematical ideas. Similarly, Gagnon & Maccini (2001) identified manipulative as objects that students physically handle to symbolize mathematical concepts and relationships. Thus, Moyer (2001) and Moyer & Jones (2004) have underlined that both virtual and physical manipulatives support the understanding of the learners. 167 The researches by Marzano (1998) and Sowell (1989) have supported that Physical Manipulative (PMs) are basic tool for mathematical teaching. McNeil & Jarvin (2007) have identified that PMs are tangible objects which students use to discover mathematical concepts via visual and tactile senses of them. NTCM (2000) has declared that PMs which include an echelon of items such as tangrams, number cubes, 3-D models, and etc. are objects to be processed and arranged by students and teachers that are used to convey intangible ideas or notions by modeling or representing their ideas perceptibly. Clement (1999) have discussed that PMs are helpful for students to construct, reinforce and connect several representations of mathematical ideas that are meaningful for the learner, encourage control and elasticity to the learner. In addition, PMs include mathematical tools, designed especially for this aim, such as objects and pictures, which embody abstract mathematical concepts, and real life objects (Van de Walle, 2007). However, these manipulatives are adopted as objects that can be touched and moved about (Hacıömeroğlu & Apaydın, 2009). PMs are objects that help in understanding the mathematical conceptions more explicitly and concretely (Moyer, 2001). The use of PMs helps students to understand the concepts more easily by providing the expression of the mathematical concepts concretely (Bulut, Çölekoğlu, Seçil, Yıldırım &Yıldız, 2002) and encourages students to think by themselves, and submits various opportunities to students for problem solving, and increases the self-confidence of the students, and provides them the possibility to make their own decisions. In addition, PMs provide the opportunity to students to enrich their visions together with their peers (Kamii & Lewis, 1990; Özdemir, 2008; Williams & Kamii, 1986). Recent developments for information and communication technologies submit many new opportunities that are augmenter for the comprehending levels of students in learning and teaching processes by providing the mathematical concepts to be embodied and interrogated. Especially in courses such as mathematics where abstract concepts and relationships are discussed, developing computer software referred as “Virtual Manipulatives (VMs)”, in substantiating these concepts and relationships, becomes important (Karakırık, 2008). VMs are assumed to be helpful in developing the abilities, to understand better the concepts, to make comments on concepts and to use concepts in problem solving, of the students in pre-school and primary school period when mathematical concepts are supposed to be at the level of concrete perception via embodying by modeling in computer environment (Durmuş & Karakırık, 2006). In this regard, VMs are practical materials that are offered as interactive tools that interact with in an imaginary environment and click and drag to move the materials into intended locations. Besides, VMs are frequently active visual/pictorial copies of PMs. In their study, Moyer, Bolvard & Spikell (2002, p. 373) have described that “an im aginary m anipulative is best determ ined as an interactive, W eb-based visual sym bolization of an active object that provides opportunities for building m athem atical know ledge. Now , VM s are sim ulated on tangible m anipulatives usually utilized in schools… Nevertheless, their ability to be utilized internationally- that is, to perm it the user to prosecute and control the physical actions of these objects- com pounded w ith the opportunities that they provide to ex plore and build m athem atical principles and relationships, differentiates them as VM s ”. Lots of studies have corroborated the sensed profits of VMs. Clements & McMillen (1996), Heath (2002), and Moyer & Bolvard (2002) have concluded that one of the most important profits is their availability online. 168 It has been pointed out in the study of Moyer et al (2002, p. 375) that “… accessing m any VM s on the w eb is advantageous, thereby it allow s online schools to access freely, busy teachers and students, w ho have lim ited tim e to use these sites during class, to reach them perm anently” . Moreover, VMs are skillful in doing things that are almost impossible with PMs, pencil and pa (...truncated)