Abstract
One of the main challenges we are facing whenever teaching Mathematics to first year Politehnica University students is how to enable them to establish a connection between abstract notions and their recognition and concrete use in specialized engineering courses or even in post graduate job problems. Such a connection is needed because the multipurpose mathematical models encountered during the first university year are more often than not general notions. Nevertheless, problems with which students are usually confronted later in their work life relate to a well delimited approach in a specific engineering field. In order to serve this purpose, our present paper relies on two key elements. The first one is the visual association between abstract elements (in our case solutions of systems of differential equations) and certain representations in a real world problem (specifically, predefined trajectories of motion). The second, equally important element, is the form in which the above mentioned link is presented. Since the use of mobile technology in higher education offers a very attractive, interactive method, we have chosen to merge the mathematical e-learning dimension with a platform game developed for Android systems (phones and tablets). Consequently, the recognition of abstract notions is encompassed in the levels of the game. The mathematics behind the game deals with systems of first order linear differential equations, their associated matrix and the corresponding eigenvalues. Nevertheless, there is also a captivating story to support the game and engage the player. The main character, RC (RealComplex) has been teleported, by a mad dentist, from his cabinet, straight into the habitat of the Bengali tiger. In fact, the mad dentist had secretly transformed his dental chair into a space traveling machine. RC must travel across grasslands, subtropical rain forests, mangroves and eventually escape to an island where the space traveling machine can be transformed into an escape plane. While the game comprises four levels, two of which are mathematical levels, evolution from one level to the next is only allowed if the previous level has been completed. Thus, no one can avoid going through a mathematical revision before reaching the island and the end of the game. Moreover, a deeper understanding of the geometric representation of complex numbers is also part of the game. In fact, trajectories corresponding to complex eigenvalues are solutions to be avoided by the player since this type of directions, if chosen, disable the character's freedom to move in the game world. |