<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Paolo   Bussotti</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">DIFFERENTIAL CALCULUS: THE USE OF NEWTON’S METHODUS FLUXIONUM ET SERIERUM INFINITARUM IN AN EDUCATION CONTEXT</style></title><secondary-title><style face="normal" font="default" size="100%">Problems of Education in the 21st Century</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">fluxions</style></keyword><keyword><style  face="normal" font="default" size="100%">history of mathematics</style></keyword><keyword><style  face="normal" font="default" size="100%">mathematics education</style></keyword><keyword><style  face="normal" font="default" size="100%">maxima and minima</style></keyword><keyword><style  face="normal" font="default" size="100%">Newton</style></keyword><keyword><style  face="normal" font="default" size="100%">problem solving approach to mathematics education</style></keyword><keyword><style  face="normal" font="default" size="100%">tangents</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">June/2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://oaji.net/articles/2015/457-1438197199.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">65</style></volume><pages><style face="normal" font="default" size="100%">Discontinuous</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">What is the possible use of history of mathematics for mathematics education? History of mathematics can play an important role in a didactical context, but a general theory of its use cannot be constructed. Rather a series of cases, in which the resort to history is useful to clarify mathematical concepts and procedures, can be shown. A significant example concerns differential calculus: Newton’s Methodus fluxionum et serierum infinitarum is a possible access-key to differential calculus. For, many concepts introduced by Newton ought be useful for the pupils/students (last or last but one year at the high school and first year at the university) to reach a more intuitive, geometrical and problem-oriented approach to calculus. The motivation to consider history of mathematics as an important didactical support is that the pupils/students often learn mathematics in a too formal manner, without understanding the real reasons for the introduction of several mathematical concepts. The problem is that the potential of such support is not exploited. The educational proposal is hence to show a concrete case to highlight what the teaching of mathematics based on history means. The conclusion is that a general theory, as differential calculus, should be considered by the pupils/students as a necessity, deriving from a specification, improvement and extension of the techniques used to solve significant problems posed and developed in the course of history. In this manner, mathematics appears as a human activity comparable with other activities and not as a merely formal exercise. </style></abstract><work-type><style face="normal" font="default" size="100%">Original article</style></work-type><section><style face="normal" font="default" size="100%">39-65</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Paolo   Bussotti</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">INFINITY: AN INTERDISCIPLINARY ACCESS KEY TO PHILOSOPHICAL EDUCATION THROUGH MATHEMATICS</style></title><secondary-title><style face="normal" font="default" size="100%">Problems of Education in the 21st Century</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">history of mathematics</style></keyword><keyword><style  face="normal" font="default" size="100%">philosophical education</style></keyword><keyword><style  face="normal" font="default" size="100%">science education</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2014</style></year><pub-dates><date><style  face="normal" font="default" size="100%">July/2014</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://oaji.net/articles/2015/457-1421876334.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">60</style></volume><pages><style face="normal" font="default" size="100%">Discontinuous</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">In some previous contributions of mine written for Scientia Educologica’s journals (Bussotti 2012; Bussotti, 2013; Bussotti, 2014) I dealt with the possible use of history of mathematics and science inside mathematics and science education. There is an abundant literature on this subject and I only tried to offer some ideas on possible educative itineraries in which history of mathematics and science could play a role. I had no claim to supply elements for a general theory on the relations history of mathematics-mathematics education and history of science-science education. In this editorial, I would like to deal with a possible interdisciplinary link between philosophical education and mathematics. This link is given by the infinity. The following considerations are valid for all those countries in which some high schools exist where philosophy is taught and, in general, for every course at a philosophical faculty in which the problem of the infinity is faced. Furthermore, they can also be useful in the teaching of mathematics at the high school when the concepts of infinity and infinitesimal (typically while dealing with calculus) are introduced.</style></abstract><work-type><style face="normal" font="default" size="100%">Editorial</style></work-type><section><style face="normal" font="default" size="100%">5-9</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Paolo   Bussotti</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">HISTORY AND DIDACTICS OF MATHEMATICS: A PROBLEMATIC RELATION. SOME CONSIDERATIONS BASED ON FEDERIGO ENRIQUES’S IDEAS</style></title><secondary-title><style face="normal" font="default" size="100%">Problems of Education in the 21st Century</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">didactical-historical works</style></keyword><keyword><style  face="normal" font="default" size="100%">didactics of mathematics</style></keyword><keyword><style  face="normal" font="default" size="100%">history of mathematics</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2012</style></year><pub-dates><date><style  face="normal" font="default" size="100%">November/2012</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://oaji.net/articles/2014/457-1415392119.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">48</style></volume><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">This history of mathematics is a specific and, at the same time, wide field of research with proper methods, journals, congresses and results. However, some questions about its status are without any doubt legitimate. In particular: is the public to whom the work and the publications of the historians of mathematics are addressed, limited to the specialists in this field or is it broader? It often happens that the mathematicians engaged in the active research consider history of mathematics as a sort of curiosity, but nothing really useful for their researches. They are not interested in an inquire on the historical bases of their researches because they are concentrated in discovering new theorems and solving new problems. It difficult to valuate whether and inside which limits this way of thinking is correct. The problem is complex and cannot be dealt with in this context.
 The previous considerations on the opportune use of history of mathematics in a didactical context have, of course, no claim of being systematic. They are only ideas for a discussion that, anyway, looks urgent.</style></abstract><work-type><style face="normal" font="default" size="100%">Editorial</style></work-type><section><style face="normal" font="default" size="100%">5-9</style></section></record></records></xml>