Guarino Guarini C.R., (1624-1683) is now recognised as one of the great architects of the High Baroque. Author of imposing works on natural philosophy, mathematics and astronomy, plus a posthumous architectural 'trattato', the nature of his thought and its relation to his architecture is still unresolved. My enquiry is to investigate this legacy under the themes of geometry and light. In the 12th century Robert Grosseteste proposed that light was the substantial form of all things, and both he and his followers united spiritual and corporeal light through geometry, thus founding a lightmetaphysic, which flourished in Dante, and was augmented by the Platonism of the Florentine School. In the 16th century, printing had strengthened the spread of these doctrines. With the sixteenth-century recovery of Greek geometry 'Perspectiva', i.e. optics, was recognised as the eighth Liberal Art, and among the schoolmen, light was treated in the First Day of the Hexaemeron. Francesco Maurolyco (1494-1577) is the first modern scientist of light, and with the Galilean observations, optics moved to the forefront of European debate, as Johannes Kepler founded the theories of the lens and illumination, still inside the metaphysical tradition. Meanwhile the Neoplatonism of Francesco Patrizi da Cherso (1529-1597), undermined the philosophy of both light and ancient cosmology, a rupture of the great significance. My enquiry, guided by Guarini's references, starts with Patrizi, and examines the traditional formulations of Fortunio Liceti, Marin Cureau de la Chambre and Ismael Boulliau/Bullialdus. The new 'mechanisme' of Paris is represented by the Minim Father Marin Mersenne who depended on his friends Descartes and Hobbes. The light-encylopaedia and geometry of Father Athanasius Kircher S.J. is a vital component, complemented by the remarkable mathematical imagery of Mario Bettini S.J., a key authority for Guarini. On this foundation, Guarini's mathematics and complex light-theory is studied, and his overall philosophy is related to the symbolism of his Royal Chapel of the Holy Shroud, Turin, as an achievement of Baroque architecture, paradoxically in the context of the seventeenth-century scientific crisis.

This research study investigated how professional mathematicians understand and operate with highly-abstract, advanced mathematical concepts in their own work. In particular, this study examined how professional mathematicians operated with mathematical concepts at different levels of understanding. Moreover, this study aimed to capture what factors influence professional mathematicians' level of understanding for particular mathematical concepts. To frame these research goals, three theoretical levels of understanding were proposed, process-level, pseudo-object-level, object-level, leveraging two ways that Piaget (1964) described what it meant to know or understand a mathematical concept. Specifically, he described understanding an object as being able to "act on it," and also as being able to "understand the process of this transformation" (p. 176). Process-level understanding corresponds to only understanding the underlying processes of the concept. Pseudo-object-level understanding corresponds to only being able to act on the concept as a form of object. Object-level understanding corresponds to when an individual has both of these types of understanding. This study is most especially concerned with how professional mathematicians operate with a pseudo-object-level understanding, which is called pseudo-objectification. For this study, six professional mathematicians with research specializing in a subfield of algebra were each interviewed three times. During the first interview, the participants were given two mathematical tasks, utilizing concepts in category theory which were unfamiliar to the participants, to investigate how they operate with mathematical concepts. The second interview utilized specific journal publications from each participant to generate discussion about influences on their level of understanding for the concepts in that journal article. The third interview utilized stimulated recall to triangulate and support the findings from the first two interviews. The findings and analysis revealed that professional mathematicians do engage in pseudo-objectification with mathematical concepts. This demonstrates that pseudo-objectification can be productively leveraged by professional mathematicians. Moreover, depending on their level of understanding for a given concept, they may operate differently with the concept. For example, when participants utilized pseudo-objects, they tended to rely on figurative material, such as commutative diagrams, to operate on the concepts. Regarding influences on understanding, various factors were shown to influence professional mathematicians' level of understanding for the concepts they use in their own work. These included factors pertaining to the mathematical concept itself, as well as other sociocultural or personal factors. / Doctor of Philosophy / In this research study, I investigated how professional mathematicians utilize advanced mathematical concepts in their own work. Specifically, I examined how professional mathematicians utilize mathematical concepts that they do not fully understand. I also examined what factors might influence a professional mathematician to fully understand or choose not to fully understand a mathematical concept they are using. To address these goals, six research-active mathematicians were each interviewed three times. In these interviews, the mathematicians engaged with mathematical concepts that were unfamiliar to them, as well as concepts from one of their own personal research journal publications. The findings demonstrated that professional mathematicians sometimes utilize mathematical concepts in different ways depending on how well they understand the concepts. Moreover, even if mathematicians do not have a full understanding of the concepts they are using, they can still sometimes productively leverage this amount of understanding to successfully reach their goals. I also demonstrate that various factors can and do influence how well a professional mathematician understands a given mathematical concept. Such influences could include the purpose of use for the concept, or what a mathematician's research community values.

Submitted by WILLIAM VIEIRA GONCALVES null (williamvieira@unemat.br) on 2016-09-21T00:29:22Z No. of bitstreams: 1 TESE_GONCALVES_William_Vieira.pdf: 4325935 bytes, checksum: b52e7f80ac7d448c1c0d65aecda11b20 (MD5) / Approved for entry into archive by Ana Paula Grisoto (grisotoana@reitoria.unesp.br) on 2016-09-22T20:43:16Z (GMT) No. of bitstreams: 1 goncalves_wv_dr_bauru.pdf: 4325935 bytes, checksum: b52e7f80ac7d448c1c0d65aecda11b20 (MD5) / Made available in DSpace on 2016-09-22T20:43:16Z (GMT). No. of bitstreams: 1 goncalves_wv_dr_bauru.pdf: 4325935 bytes, checksum: b52e7f80ac7d448c1c0d65aecda11b20 (MD5) Previous issue date: 2016-07-01 / Este trabalho tem como principal objetivo demonstrar que o GeoGebra apresenta uma maneira diferente de produzir significados matemáticos, com isso, sugerindo sua relevância para o ensino de matemática e de se discutir sua linguagem, possibilidades e limitações. A base inicial da pesquisa foi um estudo imersivo em diferentes comunidades virtuais, literatura acadêmica correlata, cursos específicos do software, produção e análise de diferentes construções dinâmicas. Por fim, optou-se por delimitar a análise aprofundada em entrevistas semiestruturadas com sete professores de matemática, usuários experientes do software. Confrontando-se estes entrevistados com algumas limitações do software, buscou-se estudar como eles transitam entre diferentes modos de produção de significados matemáticos. Pautando-se em reconhecer os diferentes jogos de linguagem, advindos das explicações dos sujeitos da pesquisa, foram sintetizadas três adjetivações que caracterizam os diferentes modos de produção de significados matemáticos: a Matemática do Matemático (MM), a Matemática da Escola (ME) e a Matemática do GeoGebra (MG). Esta pesquisa pautou-se na técnica de investigação qualitativa livre, em função da sua tentativa de compreender mais detalhadamente os significados e características situacionais. A análise dos dados foi realizada à luz de alguns elementos da Análise Textual Discursiva segundo Moraes e Galiazzi (2007). As categorias criadas, a posteriori, foram as seguintes: Matemática do Matemático (MM); Matemática da Escola (ME); Matemática do GeoGebra (MG); Trânsito entre as matemáticas; Percepção da MG; Necessidade de compreensão da MG; aparente Compreensão da MG e aparente Incompreensão da MG. A partir da análise dos dados foi possível confirmar o uso de diferentes jogos de linguagem e, portanto, confirmar o transitar entre a MM, a ME e a MG. Ainda, percebeu-se e analisou-se diferentes formas de transitar, concluindo-se que existe um modo de transitar, comum a todos os entrevistados. Parte-se das possibilidades semióticas da MG, aproveitando-se da maleabilidade da ME, para formalizar-se significados matemáticos, legítimos a MM. Finalmente, a partir da análise aprofundada de uma entrevista, propõe-se o reconhecimento de diferentes aspectos da MG e da história do GeoGebra, como uma forma de aprender sobre como lidar com suas possibilidades e limites. / This work aims to demonstrate that GeoGebra presents has a different way of producing mathematical meanings, suggesting its relevance to mathematics teaching and to discuss its language, possibilities and limitations. Research initial framework was an immersive study in different virtual communities, academic literature, specific courses, production and analysis of different dynamic constructions. In the end, the choice was to delimitate a depth analysis on semi-structures interviews with seven math teachers, experienced software users. Confronting this respondents with some limitations of the software, we sought to study how they transit between different modes of production of mathematical meanings. Based on recognizing the different language games, arising of research subjects were synthesized three adjectives that characterize the different mathematical modes of production: Math from Mathematician (MM), Math from School (ME, in Portuguese) and Math from Geogebra (MG, in Portuguese too). This research used the free qualitative investigation for its attempt to understand with more details the meanings and situational characteristics. Data analysis was carried out with some elements of Discursive Textual Analysis from Moraes and Galiazzi (2007). The categories created, a posteriori, were: Mathematics from Mathematician (MM); Math from School (ME); and Math from Geogebra (MG); Transit between the mathematics; Perception from MG; need of comprehension from MG; apparent comprehension from MG and incomprehension from MG. Data analysis enable to confirm the use of different languages games and, thus, confirm the transition between MM, ME and MG. I still realized and analyzed different ways of transition, concluding that there is a common way to transit between all respondents. We set of semiotic possibilities from MG, taking advantage of the malleability from ME, to formalized mathematical meanings, legitimate from MM. Finally, from the depth analysis of an interview, it is proposed to recognize different aspects from MG and of the GeoGebra history, as a way to learn about how to deal with its possibilities and limits.

Within a professional organization for women in mathematics in the US, two mathematicians and a middle school teacher organize a program to link teachers of students at the pre-university level with professionals in the mathematical sciences in and outside of academia to promote collaborations among different communities in the mathematics education of students. This paper describes the program and its operations, some of its experiences, as well as some results from a formative evaluation conducted for the program. Some recommendations are given for potential organizers of similar programs in other countries.

Sonderausgabe des "Dresdner Universitätsjournal" von 2001

Sonderausgabe des 'Dresdner Universitätsjournal' von 2001:Zum Geleit S. 3 Vorwort S. 4 Inhaltsverzeichnis S. 5 Vom Knopf an der Turmspitze der Annenkirche: Die Geometrie des Gotthelf Fischer (1763–1832) S. 6 Frühe Lehrerbildung in Dresden: Lehrer und Eisenbahner – anfänglich stärkste Absolventengruppen S. 8 Junge Wissenschaftler auf neuen Lehrstühlen: Antimathematische Tendenzen – chancenlos unter Gustav Zeuner (1828–1907) S. 10 Von der Feinmechanik zur Mathematik: Die Verbindung von Technik, Kunst und darstellender Geometrie S. 12 Zwischen Mathematik und Physik: Der 2. Mathematische Lehrstuhl unter Aurel Voss (1845–1931) S. 14 Mathematiker als Bibliothekare: Die Katalogisierung – weiterentwickelt von Mathematikern S. 15 Gebündelte Reformbestrebungen: Neuer Aufschwung nach einem schwierigen Jahrzehnt S. 16 Neues vom Kreuzgymnasium: Einführung der Differential- und Integralrechnung in Mathematiklehrpläne S. 18 Mathematiker in der Gesellschaft ISIS: Wachsendes Interesse an mechanischen Rechengeräten S. 20 Rententafeln und Nettotarife: Zur Geschichte des Versicherungstechnischen Seminars S. 22 Dresdner als Ordinarien in Heidelberg: Erfolgreich auf dem Gebiet der kombinatorischen Topologie S. 24 Ein mitreißender Hochschullehrer: Gerhard Kowalewski (1876–1950) – Lehrer von Generationen Studierender S. 26 Frauen leben für die Mathematik: Dresdner Mathematik-Promovendinnen S. 28 Wissenschaftler und Humanist: Erich Trefftz (1888–1937) – „Motor“ der Akademischen Fliegergruppe Dresden S. 30 Mathematik und Politik: Personelle Veränderungen in der Dresdner Mathematik um 1940 S. 32 Impressum / Bildnachweis S. 34

Within a professional organization for women in mathematics in the US, two mathematicians and a middle school teacher organize a program to link teachers of students at the pre-university level with professionals in the mathematical sciences in and outside of academia to promote collaborations among different communities in the mathematics education of students. This paper describes the program and its operations, some of its experiences, as well as some results from a formative evaluation conducted for the program. Some recommendations are given for potential organizers of similar programs in other countries.