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TopTheoretical Framework
In the most ideal setting, information and communication technologies are treated as a tool for teaching and learning (Burnett, 2009; Papadakis, Kalogiannakis, Zaranis, 2016a; Sife, Lwoga, & Sanga, 2007). They are used as a tool for the students to become more familiar with new technology and to integrate investigation, communication and understanding across the full range of the curriculum. Particularly, in the cognitive field of mathematics an evaluation of learning outcomes regarding computer based mathematical teaching in students showed that computer-assisted learning can significantly help in developing proper mathematical skills and the cultivation of deeper conceptual thinking in comparison to the traditional mathematical teaching method (Dimakos, & Zaranis, 2010; Hardman, 2005; Keong, Horani, & Daniel 2005; Papadakis, Kalogiannakis, Zaranis, 2016b).
Various research results relate the appropriate use of computers with the ability of students to more efficiently understand the different mathematical notions (Howie, & Blignaut, 2009; Trouche, & Drijvers, 2010). Nonetheless, computer based activities should reflect the theoretical ideas behind them (Clements, & Sarama, 2004; Dissanayake, Karunananda, & Lekamge, 2007).
Following this principle, the software designed and the students’ activities developed and examined for the pur-poses of the current study were inspired by the framework of Realistic Mathematics Education (RME). RME is an active and constantly evolving theory of teaching and learning mathematics (Van den Heuvel-Panhuizen, 2001). Indicative of this, the learning and teaching trajectories with intermediate attainment targets were first conducted for the subject of mathematical calculation at the primary school level and extended to the subject of geometry (Van den Heuvel-Panhuizen, & Buys, 2008).
In the whole trajectory of the RME teaching theory, five main characteristics of understanding geometry con-cepts are involved: (a) introducing a problem using a realistic context; (b) identifying the main objects of the prob-lem; (c) using appropriate social interaction and teacher intervention to refine the models of the problem; (d) en-couraging the process of reinvention with the development of the problem; and (e) focusing on the connections and aspects of mathematics in general (Van den Heuvel-Panhuizen, 2001). These should be the main focuses of the learning and teaching procedure concerning geometry in primary school. Following the theoretical framework that blends together Realistic Mathematics Education (RME) and the use of ICT in primary school and kindergarten, we designed a new model referred to as the Primary Shape Model (PSM) which consisted of five levels.