<?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%">INTRODUCTION TO THE GEOMETRICAL OBJECTS AND AXIOMS: CONCEPTUAL, DIDACTICAL AND HISTORICAL CONSIDERATIONS </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%">historical elements</style></keyword><keyword><style  face="normal" font="default" size="100%">historical-methodological lessons</style></keyword><keyword><style  face="normal" font="default" size="100%">mathematics education</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2024</style></year><pub-dates><date><style  face="normal" font="default" size="100%">June/2024</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://oaji.net/articles/2023/457-1718778448.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">82</style></volume><pages><style face="normal" font="default" size="100%">Continuous</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">For a student attending the initial years of the high school, it is not easy to fully realize what a geometrical object is. While speaking, for example, of a triangle, the teacher will underline that its sides have length, but no width and no thickness. However, a pupil has never seen an object of this kind in his daily experience. For, every straight line has a width and a thickness, however minimal they may be. How can we introduce the geometrical objects and, immediately afterwards, the geometrical reasonings so that the learners can accept them not based on a sort of faith act but relying on a real understanding? The best method is to explain their conceptual genesis, also adding some historical elements. Two abstract processes can be identified: the first one gave origin to the abstract objects, the second one to the propositions (axioms) on which the relations of such objects rely. Therefore, we suggest that the teacher dedicates two lessons to introducing the genetic bases of the geometrical thought before dealing with the mathematical details. In what follows, material for the two lessons is supplied.</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><work-type><style face="normal" font="default" size="100%">Editorial</style></work-type><section><style face="normal" font="default" size="100%">320-327</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%">MATHEMATICS EDUCATION: SOME ASPECTS CONNECTED TO ITS CONTENT</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%">mathematics education</style></keyword><keyword><style  face="normal" font="default" size="100%">philosophical discussions</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">December/2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://oaji.net/articles/2017/457-1513710148.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">75</style></volume><pages><style face="normal" font="default" size="100%">Continuous</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">The literature concerning the various methods by means of which the teaching of mathematics can be developed is simply huge and is increasing more and more. Several aspects are dealt with: the use of new technologies, especially as far as new computer programs or web sources are concerned; new techniques to develop calculations; researches concerning the possible relations between the everyday life of the pupils/students and the mathematical concepts; the best way to frame a lesson (frontal lessons, interactive lessons, discussions), and so on. This literature covers the entire school-life of a young boy/girl: from the elementary school to the university. </style></abstract><issue><style face="normal" font="default" size="100%">6</style></issue><work-type><style face="normal" font="default" size="100%">Editorial</style></work-type><section><style face="normal" font="default" size="100%">503-507</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%">Luca Bussotti</style></author><author><style face="normal" font="default" size="100%">Paolo   Bussotti</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">TRENDS AND CHALLENGES OF MATHEMATICS EDUCATION IN MOZAMBIQUE (1975-2016)</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%">ethnomatematics</style></keyword><keyword><style  face="normal" font="default" size="100%">international agencies</style></keyword><keyword><style  face="normal" font="default" size="100%">mathematics education</style></keyword><keyword><style  face="normal" font="default" size="100%">Mozambique</style></keyword><keyword><style  face="normal" font="default" size="100%">school reforms</style></keyword><keyword><style  face="normal" font="default" size="100%">teaching methods</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">October/2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://oaji.net/articles/2017/457-1509895430.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">75</style></volume><pages><style face="normal" font="default" size="100%">Continuous</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">Mathematics has always been a difficult issue, especially in the African countries. Mozambique is not an exception. This country had been colonized by Portugal until 1975. When the independence was obtained, a socialist regime was adopted (1977). The learning of mathematics entered the struggle against colonial and imperialistic ideas. Its best ally was Paulus Gerdes, one of the most relevant ethnomatematicians of the world, who carried out an intense promotion of this approach to mathematics in Mozambican school system. Albeit the great international impact of Gerdes’ ideas, Mozambique never implemented his methodology. When, at the end of the 80s, the country changed from socialism to liberalism, voting a democratic Constitution in 1990, its school system was aligned to the measures of International Monetary Fund (IMF) and World Bank (WB). The most recent ones are represented by the Millennium Development Goals. Despite the various reforms of Mozambican school system, the results of Mozambican children in mathematics are among the worst in Africa. The reasons of such a failure are here explained, through a historical approach based on national documents. The most recent experiences of school reform carried out by international agencies together with national institutions are stressed. The negative results obtained by the Mozambican learners as to mathematics are due to several reasons: 1) a lack of consideration of the Mozambican cultural substrate; 2) an improper massification of the school system, where the quality of instruction has been neglected; 3) the specific choice to marginalize mathematics education.  </style></abstract><issue><style face="normal" font="default" size="100%">5</style></issue><work-type><style face="normal" font="default" size="100%">Original article</style></work-type><section><style face="normal" font="default" size="100%">434-451</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%">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%">Raffaele Pisano</style></author><author><style face="normal" font="default" size="100%">Paolo   Bussotti</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON POPULARIZATION OF SCIENTIFIC EDUCATION IN ITALY BETWEEN 12TH AND 16TH CENTURY</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%">Abacus schools</style></keyword><keyword><style  face="normal" font="default" size="100%">mathematics education</style></keyword><keyword><style  face="normal" font="default" size="100%">science &amp; society</style></keyword><keyword><style  face="normal" font="default" size="100%">scientific education</style></keyword><keyword><style  face="normal" font="default" size="100%">Tartaglia</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2013</style></year><pub-dates><date><style  face="normal" font="default" size="100%">December/2013</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://oaji.net/articles/2014/457-1420056837.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">57</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%">Mathematics education is also a social phenomenon because it is influenced both by the needs of the labour market and by the basic knowledge of mathematics necessary for every person to be able to face some operations indispensable in the social and economic daily life. Therefore the way in which mathematics education is framed changes according to modifications of the social environment and know–how. For example, until the end of the 20th century, in the Italian faculties of engineering the teaching of mathematical analysis was profound: there were two complex examinations in which the theory was as important as the ability in solving exercises. Now the situation is different. In some universities there is only a proof of mathematical analysis; in others there are two proves, but they are sixth–month and not annual proves. The theoretical requirements have been drastically reduced and the exercises themselves are often far easier than those proposed in the recent past. With some modifications, the situation is similar for the teaching of other modern mathematical disciplines: many operations needing of calculations and mathematical reasoning are developed by the computers or other intelligent machines and hence an engineer needs less theoretical mathematics than in the past. The problem has historical roots. In this research an analysis of the phenomenon of “scientific education” (teaching geometry, arithmetic, mathematics only) with respect the methods used from the late Middle Ages by “maestri d’abaco” to the Renaissance humanists, and with respect to mathematics education nowadays is discussed. Particularly the ways through which mathematical knowledge was spread in Italy between late Middle ages and early Modern age is shown. At that time, the term “scientific education” corresponded to “teaching of mathematics, physics”; hence something different from what nowadays is called science education, NoS, etc. Moreover, the relationships between mathematics education and civilization in Italy between the 12th and the 16th century is also popularized within the Abacus schools and Niccolò Tartaglia. These are significant cases because the events connected to them are strictly interrelated. The knowledge of such significant relationships between society, mathematics education, advanced mathematics and scientific knowledge can be useful for the scholars who are nowadays engaged in mathematics education research. </style></abstract><work-type><style face="normal" font="default" size="100%">Original article</style></work-type><section><style face="normal" font="default" size="100%">90-101</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%">VITTORIO CHECCUCCI AND HIS CONTRIBUTIONS TO MATHEMATICS EDUCATION: A HISTORICAL OVERVIEW</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%">experimentations in mathematics education</style></keyword><keyword><style  face="normal" font="default" size="100%">mathematics education</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2013</style></year><pub-dates><date><style  face="normal" font="default" size="100%">April/2013</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://oaji.net/articles/2014/457-1419413389.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">53</style></volume><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">This study deals with Vittorio Checcucci’s ideas and proposals as to mathematics education. The scopes of this work are twofold: 1) the first scope is historical: my aim is to reconstruct Checcucci’s thought. This is a novelty because almost no contribution dedicated to Checcucci exists. The few existing contributions are brief articles whose aim is not to provide a general picture of his ideas; 2) the second scope is connected to mathematics education in the 21st century. A series of argumentations will be proposed to prove that many Checcucci’s ideas could be fruitfully exploited nowadays. For the first time, the thought of this mathematician is exposed to non-Italian readers because his ideas are worthy to be known, rethought and discussed in an international context. </style></abstract><work-type><style face="normal" font="default" size="100%">Original article</style></work-type><section><style face="normal" font="default" size="100%">22-39</style></section></record></records></xml>