Design and implementation of teaching activities in Discrete Mathematics: an experience in the first cycle of education.

Within the subject of discrete mathematics, some of the topics and mathematical content can be presented, with interesting results even to younger children, in the first cycle of their education. Purpose of this document is to show how we designed and implemented some teaching tasks in various schools and grades, and the results we got in terms of enhancing some aspects, such as cognitive processes involved, task design, affection of students towards mathematics, connections with the curriculum.\\ After a presentation of the current situation, in Italy and some starting points from all around the World, some survey results are shown, to better understand the point of view of the actors of this, teachers. A whole chapter is dedicated to the mathematical content that lies at the base of these topics,. A description of the research methodology and theoretical framework that were used follows; this research project uses design research, a mainly qualitative research method, to better embed the processes of task design in a more research-oriented vision, analyzing also many of the cognitive processes involved by the tasks we are designing. The teaching tasks that were used, and developed during the research, are presented, with connections between them and an effort on creating some sequences of tasks with a common learning object. After an overview of the whole project, some of the tasks, and worksheet used, are presented in more details. A chapter with the results we observed is following, trying to give some overview conclusions, still providing examples. The author believes that this is a starting point for some future education research in the field; discrete mathematics proved to be appropriate and to create and interest towards important topics of mathematics, such as some aspects of algorithms, efficiency, complexity of a problem, abstraction, error correction, which are relevant in many field of mathematics, and not only mathematics. Moreover, the kind of activity proposed raised the attention on affective issues towards mathematics. We can notice that problems posed as games, as storytelling and using manipulative objects, can enhance the conception children have of mathematics, which plays a central role in the teaching and learning of it.