PROMOTING DISTANCE MATHEMATICAL DISCOURSE: ONLINE RESOURCES FOR EFFECTIVE COMMUNICATION IN GEOMETRY

Communication in mathematics can be particularly difficult because multimodal registers are needed in order to develop mathematical ideas (usually a simultaneous use of written texts, formulas, schemas, diagrams, geometric figures, graphs, and so on is essential). Effective communication of mathematics need to switch from one register to another, from one representation to another, as much as possible. One could go as far as to say that the true mathematical competence is knowing how to use the right representation at the right time. For this reason it turns out that old style pen and paper techniques are the best suited for carrying out a mathematical discourse. Mathematicians are known to like to use blackboards, both when they work on their researches and when lecturing. From a didactic point of view, students as well can take advantage of the possibility of writing by hand on paper both when they carry out their studying and, for example, when they are under examination. This is particularly true with written exams that contain open-ended questions and ask to provide justifications for the given answers, and in case of oral exams, which are the type of exam that best allows for verifying the capacity of building a mathematical discourse. With the outbreak of the COVID-19 emergency, in spring 2020 all exams needed to be held remotely and pen and paper turned out to be not available. Some technical solutions available were in fact not usable due to the lack of technical equipment on the part of the students. E.g. to effectively use an online whiteboard you need to have a digital pen: you simply cannot write mathematics with just the mouse. By means of the WIMS (WWW Interactive Multipurpose Server) platform, that we introduced at ICERI19, it was possible to build an online work environment that made it easier for students to work in mathematics, with particular attention to the task of conducting a mathematical discourse. We will describe in detail the setup used for the geometry course for prospective primary school teachers, showing the effectiveness of WIMS: - in complementing lectures by posing engaging problems , e.g. in order to let student experiment with the graphic properties of the geometric objects being studied; - as a tool to replace the written exam, allowing for the conceiving of an open-ended questions test, with automatic verification of the answers; - as a drawing board to be used during oral exams, so to let students easily provide drawings and representation to support their discourse. Some videos of students' use of these tools are available (e.g. see https://www.youtube.com/watch?v=okq5EOKNNRc&t=42s), which also show the achievement of a good level of ICT skills.