Mathematical warrants, objects and actions in higher school mathematics

'Higher school mathematics' connotes typical upper secondary school and early college mathematics. The mathematics at this level is characterised by moves to (1) rigour in justification,(2) abstraction in content and (3) fluency in symbolic manipulation. This thesis investigates these three transitions - towards rigour, abstraction, and tluencyusing philosophical method: for each of the three transitions a proposition is presented and arguments are given in favour of that proposition. These arguments employ concepts and results from contemporary English language-medium philosophy and also rely crucially on classroom issues or accounts of mathematical experience both to elucidate meaning and for the domain of application. These three propositions, with their arguments, are the three sub-theses at the centre of the thesis as a whole. The first of these sub-theses (1) argues that logical deduction, quasi-empiricism and visualisation are mathematical warrants, while authoritatively based justification is essentially non-mathematical. The second sub-thesis (2) argues that the reality of mathematical entities of the sort encountered in the higher school mathematics curriculum is actual not metaphoric. The third sub-thesis (3) claims that certain 'mathematical action' can be construed as non-propositional mathematical knowledge. The application of these general propositions to mathematics in education yields the following: 'coming to know mathematics' involves:(1) using mathematical warrants for justification and self conviction; (2) ontological commitment to mathematical objects; and (3)developing a capability to execute some mathematical procedures automatically

Communities at a Crossroads. Material semiotics for online sociability in the fade of cyberculture

How to conceptualize online sociability in the 21st century? To answer this question, Communities at a Crossroads looks back at the mid-2000s. With the burst of the creative-entrepreneur alliance, the territorialization of the internet and the commercialization of interpersonal ties, that period constituted a turning point for digital communitarian cultures. Many of the techno-libertarian culture\u2019s utopias underpinning the ideas for online sociability faced systematic counter evidence. This change in paradigm has still consequences today. Avoiding both empty invocations of community and swift conclusions of doom, Annalisa Pelizza investigates the theories of actions that have underpinned the development of techno-social digital assemblages after the \u2018golden age\u2019 of online communities. Communities at a Crossroads draws upon the analysis of Ars Electronica\u2019s Digital Communities archive, which is the largest of its kind worldwide, and in doing so presents a multi-faceted picture of internet sociability between the two centuries. Privileging an anti-essentialist, performative approach over sociological understandings of online communities, Communities at a Crossroads proposes a radical epistemological turn. It argues that in order to conceptualize contemporary online sociability, we need first to abandon the techno-libertarian communalist rhetoric. Then, it is necessary to move beyond the foundational distinction between Gemeinschaft and Gesellschaft, and adopt a material semiotic approach. In the end, we might have to relinquish the effort to define online or digital communities and engage in more meaningful mapping exercises

Third International Conference on Inverse Design Concepts and Optimization in Engineering Sciences (ICIDES-3)

Papers from the Third International Conference on Inverse Design Concepts and Optimization in Engineering Sciences (ICIDES) are presented. The papers discuss current research in the general field of inverse, semi-inverse, and direct design and optimization in engineering sciences. The rapid growth of this relatively new field is due to the availability of faster and larger computing machines

Reports to the President

A compilation of annual reports for the 1985-1986 academic year, including a report from the President of the Massachusetts Institute of Technology, as well as reports from the academic and administrative units of the Institute. The reports outline the year's goals, accomplishments, honors and awards, and future plans

The role of creative art in community education : art education and art therapy

The thesis looks firstly at creativity and the creativeprocess, approaching the subject from a whole range of different viewpoints, such as the psychological, philosophical, biographical and anthropological angles. Following from this there is an exploration of the ways in which creativity way be awakened and unfolded. Special attention is given to the conditions and situations that are likely to encourage creative development and to the blocks and difficulties that inhibit its expression.Particular reference is made, on the one hand, to art education and to the art, leisure, and teaching student, and on the other hand, to art therapy and the psychiatric patient. The themes of the individual and the community are explored in a complementary way in the final two chapters. The thesis emphasizes the viewpoint of the student and the patient, but since these people do not exist in a vacuum, this involves looking also at the teacher, the therapist and society. With reference to the psychiatric field, other specific questions arise, for example: How may creative opportunities assist the healing process? What are the reciprocal influences of artand mental illness? Throughout the thesis the term 'art' is used in the visual sense, but references are made to creativity in other fields where parallel conclusions apply. The emphasis has been placed on the adult, but the subject of 'Creativity and the Teaching Student' involves some references to child art and 'Creativity and the Community' involves all ages

Astronautics and Aeronautics, 1979-1984: A chronology

This volume of the Astronautics and Aeronautics series covers 1979 through 1984. The series provides a chronological presentation of all significant events and developments in space exploration and the administration of the space program during the period covered

Reports to the President

A compilation of annual reports for the 1986-1987 academic year, including a report from the President of the Massachusetts Institute of Technology, as well as reports from the academic and administrative units of the Institute. The reports outline the year's goals, accomplishments, honors and awards, and future plans