Pre-Service Classroom Teachers Opinions on Using Different Manipulatives in Mathematics Teaching

The Journal of Instructional Technologies &Teacher Education Vol.1 No1 (2012), 68-83 Pre-Service Classroom Teachers’ Opinions on Using Different Manipulatives in Mathematics Teaching Yaşar Akkan1 Zafer Çakır2 Abstract In the study, pre-service teachers’ opinions on the usage of virtual and physical manipulatives in mathematics teaching have been designated. In this context, questionnaires and interviews have been carried out with the students from the Department of Classroom Teaching in Kafkas University. From the acquired findings, pre-service teachers generally preferred to use virtual manipulatives, but they have stated that using physical manipulatives will be advantageous for 1st and 3rd grade students. In addition, it has appeared that pre-service teachers preferred virtual manipulatives to physical manipulatives owing to the reasons such as including extra activities, providing saving of time, feedback and movement independence, presenting activeness for students and constructing the information by itself, being enjoyable, decreasing the possibility of making mistakes and ensuring exploring and interrogation. Key Words: Interactive electronic textbook, prospective mathematics teachers, blended learning model, affective learning 1. Introduction Manipulatives are defined as "objects that appeal to several senses and that can be touched, moved about, rearranged, and otherwise handled by children" (Kennedy, 1986, p. 6). These are one way of making mathematics learning more meaningful to students (Stein & Bovalino, 2001), as "they are materials designed to represent explicitly and concretely mathematical ideas that are abstract" (Moyer, 2001, p. 176). Similarly, Gagnon and Maccini (2001) described manipulatives as objects that students physically manipulate to represent mathematical concepts and relationships. Indeed, Moyer (2001) and 1 Yrd.Doç. Dr., GümüşhaneÜniversitesi, Matematik Mühendisliği, 2 Yrd.Doç. Dr., GümüşhaneÜniversitesi, Matematik Mühendisliği, . 68 JITTE, Vol.1 No.1 (2012) Pre-Service Classroom Teachers’ Opinions on Using Different Manipulatives... Moyer&Jones (2004) have emphasized the unique power of both virtual and physical manipulatives, in supporting learner understanding. Physical manipulatives are a fundamental tool for teaching mathematics that is supported by many researches (Marzano 1998; Sowell 1989). McNeil and Jarvin (2007) described physical manipulatives as concrete objects which students use to explore mathematical concepts through the students visual and tactile senses. According to NCTM (2000), physical manipulatives that include an array of items such as tangrams, numbercubes, 3-D models, etc. are objects to be handled and arranged by students and eacherst hat are used to transmit abstract ideas or concepts by modeling or representing their ideas concretely. Also, Clement (1999) argues that physical manipulatives help students in building, reinforcement and connecting various representations of mathematical ideas that are meaningful to the leaner, promote control and flexibility to the learner. Thompson and Lambdin (1994) considered concrete materials appropriate for two purposes: (1) enabling teachers and students to have discourse about something concrete—discussing how tothink about materials and the meanings of various actions with them; and (2) providing something upon which students can act. In recent years, computer technologies (Java and Flash applets) have ensured a method for creating and spreading a new type of web-based manipulatives, known as virtual manipulatives. Virtual manipulatives are hands-on materials that are presented as interactive tools that students interact with in a virtual environment and click and drag to move the materials into desired locations. Also, virtual manipulatives are often dynamic visual/pictorial replicas of physical manipulatives. Moyer, Bolyard, and Spikell (2002; p. 373) described them: “A virtual manipulative is best defined as an interactive, Web-based visua l representation of a dynamic object that present support unities for constructing mathematical knowledge. Currently, virtual manipulatives are modeled on the concrete manipulatives commonly used in schools. … However, their ability to be used interactively—that is, to allow the user to engage and control the physical actions of these objects—combined with the opportunities that they offer to discover and construct mathematical principles and relationships, distinguishes them as virtual manipulatives”. Many studies have documented the perceived benefits of virtual manipulatives. One ofthe most important of these benefits is their availability online (Clements & McMillen 1996; Heath 2002; Moyer & Bolyard 2002). Moyer et al (2002) point out that, "... the advantage of many emergent virtual manipulatives is that they are on the web, thereby allowing free access for schools that are online and constant availability for busy teachers and students who have limited time to get these sites during class" (p. 375). Furthermore, virtual manipulatives are talented of doing things that are simply not possible with physical manipulatives, pencil and paper, or other tools (Clements & McMillen 1996; Crawford & Brown 2003; Forster 2006; Clements, 2002; Reimer & Moyer 2005). Further, because virtual manipulatives provide students with instantaneous, corrective feedback, this ability makes virtual manipulatives well-suited to inquiry-based learning and problem solving (Clements & McMillen 1996; Crawford & Brown 2003; Durmus & Karakirik 2006; Reimer 69 JITTE, Vol.1 No.1 (2012) Y. Akkan, Z. Çakır & Moyer 2005; Suh & Moyer 2005; 2007). Different pedagogical benefits of virtual manipulatives have the ability to provide multiple representations of a single concept at the same time (Clements & McMillen 1996; Heath 2002; Moyer & Bolyard 2002; Suh & Moyer 2005; 2007). Reimer & Moyer (2005) contended that this ability supplies an advantage over physical manipulatives, "Unlike physical manipulatives, electronic tools use graphics, numbers, and words on the computer screen to connect the iconic with the symbolic mode" (p. 7). However, teacher perceptions of manipulative value have been reported in different educational studies. Of times, both virtual and physical manipulatives are viewed as play objects, suitable only for children and, thus, have no validity for application in higher-level mathematics (Tooke, Hyatt, Leigh, Snyder & Borda, 1992). In addition, some teachers use manipulatives as rewards for appropriate student behavior. "Teachers who view manipulatives as time wasting or secondary to the serious work of learning mathematics will inadvertently encourage their students to use these materials for play, rather than for mathematical learning or understanding" (Moyer & Jones, 2004, p. 29). One of the main objectives of new Primary School Mathematic Curriculum started to be applied in Turkey in 2005 is to enable students to explain the (...truncated)