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Laurent schwartz (1915-2002) and the collective life of mathematics
Abstract
This work takes the case of laurent schwartz (1915-2002) to study the collective life of mathematics in the second half of the 20th century.Its goal is to show how collective practices have then been constitutive of mathematical work and community, as well as how they evolved over this period. through a biographical lens, by considering schwartz both as an important actor who has left numerous traces and as a simple witness, we present several tableaus of the collective. we study the encounter between schwartz and the collective life of mathematics during world war ii, in particular through his interaction with the bourbaki group. we then analyze the diffusion of the theory of distributions in mathematics and its historiography, and show schwartz?active role in these processes. a chapter devoted to the kernel theorem (théorème des noyaux) and its later written incarnations allows us to deepen our study of interactions between writing practices in mathematics and various kinds of collectives. Three forms of collective organization of the mathematical work are then investigated: the conference (through a study of the 1947 colloquium on harmonic analysis), the seminar, and, finally, the mathematical research center (taking as an example the centre de mathématiques de l'ecole polytechnique). Finally, we take on the question of schwartz's political engagement as a mathematician. we wish to show how this engagement embodies a certain conception of the mathematical community, while taking some inspiration from its particular social practices
... In the 1960s, this kind of collective organization for mathematical research quickly exploded. These collective practices gradually came to characterize the mathematical life of the period (Paumier, 2014). Affected by the Bourbaki Seminar, this collective academic activity for mathematics research quickly spread in France and soon became an important international scholarly communication activity (Remmert et al., 2016). ...
Macao, a Special Administration Region of China (Macao SAR), is unique in that its mathematics education practice and research have integrated both the eastern and western traditions. Its participation in the Programme for International Student Assessment (PISA) since 2003 inspired the research culture in mathematics education in Macao from international perspectives. In this article, we report on a survey of three kinds of research done in mathematics education in Macao: (1) research related to PISA, in particular PISA 2012 and PISA 2018; (2) research done for master’s and Ph.D. theses/dissertations in higher institutions in Macao; and (3) articles published in educational journals, particularly in mathematics education in Macao. The survey reveals emerging research cultures in mathematics education over the past decade—the interests of researchers and practitioners in topics such as comparative studies, lesson studies, mathematical problem-solving, and the use of information technology in mathematics teaching and learning. Lastly, we summarize what Macao has done well and what it needs to do better for further development of Macao’s research culture within the global trend of literacy-based mathematics education as modeled by the PISA.KeywordsResearch cultureMathematics educationMacaoPISA
Inspired by the Bourbaki Seminar, the Chinese Professor Yan’s Seminar, and the needs of domestic mathematics curriculum reformation, Beijing Mathematics Education Seminar (BMES) was founded in 1995, bringing together teachers, postgraduates, and scholars working on mathematics education. It has been recognized as a typical case of local mathematics education research culture with Chinese characteristics. Based on the core elements of cultural–historical Activity Theory, the current study, as a diachronic case study, explores the development strategies and challenges that BMES has been confronting from three aspects, that is, the subject, the object, and the instruments. Qualitative research methodology of the text analysis, informal conversations, and semi-structured interviews has been applied. The results demonstrate that the development strategies of BMES mainly include the following three points: the relay of leaders and their followers, the leading and contemporary research agenda, and inclusive and cooperative discussion format. For the current and future development, BMES is also facing a number of challenges, including the following tensions: maintaining the balance between theoretical and practical research perspectives, the orientation for the research agenda, and the relative effectiveness of “lecture” and “discussion” formats. Furthermore, the case of BMES reflects the development of Chinese mathematics education research culture in the past 25 years and to a certain extent may provide an inspiration for the construction of mathematics education research culture in other countries.KeywordsSeminarMathematics educationResearch cultureChinese characteristicsBeijingDevelopment strategy
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