The effect of manipulatives on mathematics achievement across different learning styles

conceptualization Reflective observation Diverging Accommodating Converging Assimilating Northerners Easterners Westerners Southerners Manipulatives Lecture and exercise Figure 1. Kolb’s learning styles (Adapted from Kolb, 1984). 2 Z. Kablan D ow nl oa de d by [ K oc ae li U ni ve rs ite si ] at 0 7: 35 1 8 A ug us t 2 01 4 dimensions, and specialises in AC (Kolb, 1984). In mathematics instruction, lectures and exercises are the most common instructional methods used by teachers. Lectures and exercises as AC Researchers indicate that in mathematics instruction, traditional methods such as lecturing are more well suited to the assimilating learning style (Gardner & Korth, 1998; Jones, Reichard, & Mokhtari, 2003; Kolb & Kolb, 2009; Sharp, Harb, & Terry, 1997). Assimilators are usually rational and they are more interested in abstract concepts rather than in people. They prefer to work individually and avoid practical activities (Bhatti & Bart, 2013; Kolb & Kolb, 2009). Some researchers have argued further that lecturing directly serves the AC learning mode, which is used by both assimilators and convergers (Healey, Kneale, & Bradbeer, 2005; Orhun, 2007; Sutliff & Baldwin, 2001; Svinicki & Dixon, 1987). Similar to assimilators, convergers rely on AC; however, rather than using RO, they prefer the AE learning mode. Therefore, while convergers do not prefer lectures for extended periods of time, they do enjoy solving problems and making decisions by identifying logical solutions to issues or problems (Bhatti & Bart, 2013; Healey et al., 2005; Jones, Reichard, & Mokhtari, 2003; Kolb & Kolb, 2009). In addition to lecturing, exercise-based teaching is a prominent teaching method that is used in mathematics classrooms; it constitutes a crucial component of the problem-solving curriculum (Dana-Picard et al., 2006). In traditional mathematics teaching settings, the teacher transmits theoretical knowledge through lectures and provides application through exercises (Abiodullah & Akbar, 2010; Shandomo & Zelkowski, 2008). Although some exercises may be concrete, especially those given to younger children, this study used exercises that are conducive to AC. The exercises used were either provided in books or written in front of students and were completed by a teacher on a blackboard. This style of exercise administration is used frequently in mathematics education (Dana-Picard et al., 2006). With the primary purpose of this approach being problem solving and practicing, exercise-based techniques used in mathematics classrooms are conducive to the AC and converging learning styles (Cox, 2013; Healey et al., 2005). Related literature has also described the teaching and learning activities that are preferred by accommodators and divergers. Manipulatives as a form of concrete experience Individuals who are inclined towards the northern learning styles, both accommodating and diverging, prefer learning through concrete experience. Individuals who prefer the accommodating learning style use concrete experience and AE as their dominant learning modes. They use their feelings in decision-making process and they prefer group work (Bhatti & Bart, 2013; Gurpinar, Bati, & Tetik, 2011; Kolb & Kolb, 2005). A common approach used that is geared towards this learning style is ‘hands-on’ learning (Coker, 2000; Davies et al., 1997; Healey et al., 2005; Holley & Jenkins, 1993; Jones et al., 2003; Kolb & Kolb, 2009; Sutliff & Baldwin, 2001). The other northern group, the divergers, who learn best through feeling and reflecting, first attempt to comprehend new information through concrete experience and then later prefer observing and reflecting on their experiences (Kolb, 1984; Kolb & Kolb, 2009). Although divergers do not prefer active learning as much as Educational Psychology 3 D ow nl oa de d by [ K oc ae li U ni ve rs ite si ] at 0 7: 35 1 8 A ug us t 2 01 4 accommodators do, it is believed that concrete, hands-on methods will provide reflective thinking opportunities for these learners. As a form of hands-on learning, manipulatives in mathematics classrooms are considered effective instructional tools. Manipulatives are physical and concrete materials such as cubes, geometry boards, pattern blocks and other everyday objects that help students explore and develop an understanding of mathematical ideas and concepts (Boggan, Harper, & Whitmire, 2010; Bouck & Flanagan, 2010; Clements & McMillen, 1996; Durmuş & Karakirik, 2006).