To the beginnings of the XXI century, which possible use of neurosciences results in research in Mathematics Education ?

Abstract

In the last 20 years we witnessed a development of research on "how" our brain works, how it processes the information, how it stores, how it links these, which are the areas appointed to a certain function and how these are interconnected with this each other etc. Then how it learn. Many people are interested to these results, first of all psychologists that are interested in the problems since long time, but also the neurophysiologists and the many categories of people who have intentions of speculative nature, but also with other kind of application. We can think to problems arising from situations of disability, related to brain injury to various types and more, etc ... In the study of the processes of teaching / learning the knowledge of the results of this field is central. Not only for the study of disorders in learning mathematics or in situations of physical disability but also for those situations that are labeled with the word "normal." Do so an innate mathematical knowledge exist? Is an understanding of natural language innate? What is the relationship between natural languages and mathematics? To all these questions, the neurophysiology of the brain begins to give tentative results. They, as scientific knowledge, can not be definitive , but they could immediately help us to "better" interpret the phenomena of teaching / learning of Mathematics. We present a general outline of this work: 1. A possible consolidated overview of the neuroscience research and learning of Mathematics: The Numeric Module, the approximation, the distance effect. 2. Does the numerical module explains everything? 3. The effects on teaching / learning of Numeric Module: discrete / continuous, etc.. A new classification of obstacles? 4. Plasticity and disability: an example of injured brain. 5. The mirror neurons: the laboratory, the processes of communication in teaching / learning, etc. 6. Fractions: the open problem of the day ... What we discuss, even if in a first approximation, in this work is to be a further study on some epistemological and educational issues related to neuroscience research and consolidate learning of Mathematics. Specifically we want to discuss some of the most significant results on key aspects of mathematics learning such as the Numeric Module, the approximation, the concept of fraction and rational number and the behaviour continuous / discrete significant for same didactical activity in scientific subject. With this objective in this work, we will discuss an appropriate analysis of the case study referred to a injured brain with cognitive difficulties in learning of the order relation, a reading of the processes of teaching learning activities through the workshop mirror neurons.