REFLECTIONS ON LEARNING MATHEMATICS IN PHYSICS PHENOMENOLOGY AND HISTORICAL CONCEPTUAL STREAMS

Although several efforts produced by new mathematical education approaches for improving education systems and teaching, yet the results are not sufficient to adsorb the totality of innovations proposed, both in the contents and management. In this sense constructive debates and new ideas were welcomed and appreciated upon new aspects of science education, side new learning and Cognitive Modelling, for our interests. A parallel effort was produced by scientist-epistemologist-historians concerning the history of science and its foundations in science education. Historical foundations represent the most important intellectual part of the science, even if sometimes they were avoided or limited to specialist disciplines such as history of mathematics, history of physics, only. Nevertheless some results, such as the operative concept of mass by Mach, rather the coherence and validity of an algebraic–geometric group in a Euclidean geometry and in non-Euclidean geometry was firstly appointed by epistemological point of view by (e.g.,) Poincaré, etc... Thus, what kind of concrete relationship between science education (mathematics and physics) and history of science (idem) one can discuss correlated with foundations of science? and above all, how this relationship can be appointed? The history and epistemology of science help to understand evolution/involution of mathematical and physical sciences in the interpretation-modelling of a phenomenon and its interpretation-didactic-modelling, and how the interpretation can change for a different use of mathematical: e.g., mathematics à la Cauchy, non-standard analysis, constructive mathematics in physics. Based on previous studies, a discussion concerning mathematics education and history of science is presented. In our paper we will focus on learning modelling to discuss its efficacy and power both from educational point of view and the need of mathematics and physics teachers education. Some case–studies on the relationship between physics and mathematics in the history are presented, as well. Particularly we focus on a possible learning modelling activity within physics phenomenology to create a resonance among the above poles and mathematical modelling cycle to argue its efficacy, power and related with historical foundations of physical, mathematical sciences.