Exploring Effects of Multi-Touch Tabletop on Collaborative Fraction Learning and the Relationship of Learning Behavior and Interaction with Learning Achievement

Introduction Mathematics refers to acquiring the basic concepts of figures, shapes and quantity (Ministry of Education, 2008). It is suggested that mathematics is an important subject as it is extensively applied in many fields. Being able to calculate, organize and apply mathematics knowledge and skills in daily life becomes prerequisites in everyday life and workspace. Therefore, mathematics learning needs to be emphasized, promoted and reflected in the aims of national education's curriculum. General guidelines of grade 1-9 curriculum of elementary and junior high school education (Ministry of Education, 2008) set the following goals and claimed that educators must guide learners to achieve them: (1) to develop take-away mathematics skill so that learners can easily apply learned knowledge in real life situations; (2) to cultivate a positive attitude towards mathematics; (3) to teach mathematics by taking into consideration needs and development levels of learners; and (4) to ensure that learners are able to appropriately utilize technology in mathematics learning and problem-solving processes. However, realization of such ideas may encounter some obstacles which can easily be found in mathematics classrooms. For instance, according to House (2006) and Yu and Chang (2009), in most Taiwanese classrooms, mathematics classes emphasize that learners memorize formulas and calculate well in the condition of not knowing why and how. Under such circumstances, learners seldom explore meanings behind mathematical concepts and they hardly develop multiple mathematical competencies. As a result, learners fail to understand mathematics concept completely and to solve related problems. Furthermore, this issue leads to learners' negative perceptions toward necessity of mathematics skills and importance of such skills in the real life. This issue is especially relevant when learners learn some difficult mathematics concepts, e.g., fraction (Booker, 1998). House (2006) and Yu and Chang (2009) suggested that to merely memorize information is not enough. Learners have to be taught in such way so that they understand mathematics concepts well enough, acquire facts and skills in a meaningful manner and have appropriate learning experience. In this case, when learners experience real-life mathematics problems outside of school, they will be able to solve them. Research on mathematics teaching and learning suggests that representations (e.g., graphical and symbolical) are important mediums not only for communication and expression but also for learning mathematics concepts. According to related studies, some concepts can be easily remembered and comprehended if they are presented in different representations (Nakahara, 2008). If learners learn difficult mathematics concepts (e.g., fraction) and use appropriately variety of their representations, learners will understanding them much easier and deeper compared to a situation when the same concepts presented in a sole representation (Dreyfus & Eisenberg, 1996). Another way to facilitate learning of difficult concepts is to learn them collaboratively (Hwang et al., 2014; Shadiev, Hwang, Chen, & Huang, 2014b; Shadiev, Hwang, & Huang, 2015). According to related studies, learning collaboratively enables learners to achieve more than they could do alone (Argyle, 1991; Wang, 2009). One reason to explain this is that learners take advantage of one another during collaboration in terms of their resources and skills; so learners may ask for help from peers or provide necessary assistance to others (Lehtinen et al., 2001). It is suggested that collaborative learning of fraction can be better enhanced with educational computing technologies, such as tablet PC (Chen, 2011; Kong, 2011; Looi & Chen, 2010) or touch-operated tabletop (Jackson, Brummel, Pollet, & Greer, 2013; Rick, Rogers, Haig, & Yuill, 2009; Schafer et al., 2013). However, several issues still exist with respect to these studies. …