Using Mobile Learning to Support Students' Understanding in Geometry: A Design-Based Research Study

Introduction Educators and governments have advocated for the use of digital technologies in classroom instruction (Bereiter & Scardamlia, 2006; Common Core State Standards Initiative, 2010). Digital technologies can be used to support mathematics teaching and learning. For example, technology offers the opportunity for students to actively participate and reorganize the way they see mathematical concepts (Stohl-Lee, Hollenbrands, & Holt-Wilson, 2010) and various mathematical representations can reveal different methods to solve problems (Heid, 2005). With technological attributes, such as the graphical capabilities, technology enhanced environments were identified for facilitating the construction of geometric understanding (Clements & Battista, 1989). In mathematics, angles are particularly difficult concepts for students to grasp and students often develop many misconceptions and difficulties (Clements & Battista, 1989; Mitchelmore, 2002). A review of the literature reveals two strategies that appear to have been successful in supporting students with angle concepts, these are the use of Dynamic Geometry Environments (DGE; e.g., Vitale, Swart, & Black, 2014) and real-world connections (e.g., Gainsburg, 2008). DGEs provide the students with figures (e.g., lines, points, circles) and basic tools to create composite figures. Various dynamic transformations can also be performed, with the ability to trace the path of the movements for later visual inspection. Empirical evidence shows that DGEs support learning about angle as they: expand the repertoire of representations available, beyond those provided in textbooks; are a cognitive technology (Pea, 1987) acting as an external aid to amplify students' cognitive capacities during thinking, learning, and problem solving (Lajoie & Azevedo, 2006); and provide students with a way to access the underpinning mathematical features in geometry. There have been a number of studies to determine the affordance of teaching angle concepts with real-world connections. Researchers have used real-world objects; for example, Mitchelmore and White (2000) used adjustable models of wheels, doors, and scissors. Real-life physical situations have also been used; for instance, Fyhn (2007) used a climbing project for the students to study angles made by body formations during climbing activities. Mobile learning can provide a way of bringing these two strategies (DGE and real-world connections) together. The study of students learning angles through the use of DGE has not yet been examined. Digital technologies are constantly evolving and becoming more personalized. The use of mobile technologies is becoming ubiquitous throughout today's society. These digital technologies are also seeping into educational establishments. Mobile learning offers new affordances to teaching and learning, such as learning that is contextualized, personalized, and unrestricted by temporal and spatial constraints (Crompton, 2013), which can provide a way for students to learn about angle concepts in a more comprehensible form. There are two research questions that guided this study: * Are there additions to the indicators for the van Hiele levels of geometric thinking when the students are involved in mobile learning activities? * How can mobile learning be used to facilitate students' understanding of angle and angle measure? Design-based research (DBR) was chosen as a method to enable the researchers to answer these two questions from the development of a local instruction theory. A local instruction theory is composed of two parts, the first part is a contribution to the theory of students learning about angle to specifically understand what additional indicator behaviours students' exhibit when they are involved in mobile learning activities. The second part is that a mobile learning curriculum is developed for teaching angle based on the theory presented. …