What is a Game for Geometry Teaching: Creative, Embodied and Im- mersive Aspects Morten Misfeldt and Lisa Gjedde Aalborg University Copenhagen, Department of Learning and philosophy, Copenhagen, Denmark misfeldt@learning.aau.dk lg@learning.aau.dk Abstract: Game based Learning (GBL) has been promoted as a way to enhance science, technology, engineering and mathe- matics education, in several aspects. In this paper we aim at conceptualizing the creative, embodied and immersive poten- tials in the context of teaching geometry in primary school. We review two cases where the concept of “game” is related to the development of pupils’ creativity and innovation skills. One intervention is inviting pupils to become designers at a “game factory”, by using the digital mathematics tool GeoGebra. The second intervention uses mobile technology to have students participate in a collaborative game requiring them to take part in an embodied activity outside the classroom. In the paper we develop a model that view game based creative learning in as a combination of constructive, immersive, and reflective aspects. We do that by considering different meanings of the word “game” in a mathematics education context. That is game as a medium, game as a framing of educational processes, and games as an object. Considering games as media highlights the similarities with texts and any other means of delivering content. We can ask what message a specific game conveys, and discuss how well suited the game is compared to other mediations of the same content. Games can be described a as “se- miotic domains” that allow players to interact with knowledge and make sense of the world (Gee, 2003). Games can act as a framing used to govern and plan educational processes, either as direct motivational driver, aiming at engaging more stu- dents in certain planned activities (Hamari, Koivisto, & Sarsa, 2014), or as an established form of process control in which complex situations can be played out. In a game the player act according to rules and the process has a natural direction towards finishing or advancing in the game. Furthermore games can frame educational processes by challenge the learners perspective through narratives and role-playing (Shaffer, 2006). Pupils creative design competencies and motivation to cre- ate and develop games have been documented as unusually relevant and high (Kafai, 1995; Tekinbas, Gresalfi, Peppler, & Santo, 2014). Mathematical thinking s can be used to think game scenarios through, to govern the competitive aspects of a game and ensure that the gameplay is fair and balanced in terms of the involved struggle. Game literacy, both in terms of playing, producing and discussing games, does thus relate to mathematical literacy and knowledge. Keywords: serious games, embodiment, epistemic games 1. Introduction: Game oriented learning and STEM The use of educational games is a promising path to enhance science, technology, engineering and mathematics (STEM) teaching. It is argued that such games can motivate, engage, provide students with relevant educational experiences more in sync with the competences needed in society and allow for better learning process. How- ever many of the educational products that builds on game mechanics are often criticized for being mere edu- tainment in the sense that they combine an entertaining gameplay with simple root learning tasks providing classical curricular content. Hence the relation between games and STEM education is richer than providing a competition and narrative around drill and practice activities or immersing students into role playing activities. The main problem that we address in this paper is how we should understand the many possible relations be- tween games and STEM education. We challenge the naïve idea that games is a (perhaps very good) substitute for genuine teaching, and we use two cases of game related activities in the area of geometry to develop a conceptualization of the ways that games relate to STEM education, with a special focus on embodiment and innovation. Hence we will attempt to approach game based learning in a much broader fashion than games as instrumental learning machines. Simultaneously we aim at focusing on specific aspects of learning (creativity and embodiment) and specific topics (geometry), in order to develop a situated understanding of what game oriented learning can be. After a brief state of the art on games, mathematics, embodiment, and creativity, we present two cases of geometry teaching where the relation between embodiment, creativity and immersion are different. Following this case description we develop and discuss a model for game oriented STEM learning dis- tinguishing the various roles of game as medium, framing, and object. 2. Games, mathematics and creativity Computer related activities that enhance collaboration and learning are often referred to as computer sup- ported collaborative learning activities (Koschmann 1996). In this tradition Shaffer (2006) has developed the 378