15,772 research outputs found
The Art of Teaching Mathematics
On June 10–12, 2007, Harvey Mudd College hosted A Conference on the Art of Teaching Mathematics. The conference brought together approximately thirty mathematicians from the Claremont Colleges, Denison, DePauw, Furman, Middlebury, Penn State, Swarthmore, and Vassar to explore the topic of teaching as an art. Assuming there is an element of artistic creativity in teaching mathematics, in what ways does it surface and what should we be doing to develop this creativity
When not thinking leads to being and doing: Stereotype suppression and the self
Suppressing stereotypes often results in more stereotype use, an effect attributed to heightened stereotype activation. The authors report two experiments examining the consequences of suppression on two self-relevant outcomes: the active self-concept and overt behavior. Participants who suppressed stereotypes incorporated stereotypic traits into their self-concepts and demonstrated stereotype-congruent behavior compared to those who were exposed to the same stereotypes but did not suppress them. These findings address issues emerging from current theories of suppression, priming, and the active self
The Experience of Security in Mathematics
In this paper, we report some findings from an investigation of a topic related to affect and mathematics which is not well-represented in the literature. For some mathematicians, mathematics itself is a source of security in an uncertain world, and we investigated this feeling and experience in the case of 19 adult mathematicians working in universities and schools in Greece. The focus reported here is on ways that a relationship with mathematics offers a sense of permanence and stability on the one hand, and an assurance of novelty and progress on the other
Mathematically gifted and talented learners: Theory and practice
This is an Author's Accepted Manuscript of an article published in International Journal of Mathematical Education in Science and Technology, 40(2), 213-228, 2009, copyright Taylor & Francis, available online at: http://www.tandfonline.com/10.1080/00207390802566907.There is growing recognition of the special needs of mathematically gifted learners. This article reviews policy developments and current research and theory on giftedness in mathematics. It includes a discussion of the nature of mathematical ability as well as the factors that make up giftedness in mathematics. The article is set in the context of current developments in Mathematics Education and Gifted Education in the UK and their implications for Science and Technology. It argues that early identification and appropriate provision for younger mathematically promising pupils capitalizes on an intellectual resource which could provide future mathematicans as well as specialists in Science or Technology. Drawing on a Vygotskian framework, it is suggested that the mathematically gifted require appropriate cognitive challenges as well as attitudinally and motivationally enhancing experiences. In the second half of this article we report on an initiative in which we worked with teachers to identify mathematically gifted pupils and to provide effective enrichment support for them, in a number of London Local Authorities. A number of significant issues are raised relating to the identification of mathematical talent, enrichment provision for students and teachers’ professional development
Mathematical practice, crowdsourcing, and social machines
The highest level of mathematics has traditionally been seen as a solitary
endeavour, to produce a proof for review and acceptance by research peers.
Mathematics is now at a remarkable inflexion point, with new technology
radically extending the power and limits of individuals. Crowdsourcing pulls
together diverse experts to solve problems; symbolic computation tackles huge
routine calculations; and computers check proofs too long and complicated for
humans to comprehend.
Mathematical practice is an emerging interdisciplinary field which draws on
philosophy and social science to understand how mathematics is produced. Online
mathematical activity provides a novel and rich source of data for empirical
investigation of mathematical practice - for example the community question
answering system {\it mathoverflow} contains around 40,000 mathematical
conversations, and {\it polymath} collaborations provide transcripts of the
process of discovering proofs. Our preliminary investigations have demonstrated
the importance of "soft" aspects such as analogy and creativity, alongside
deduction and proof, in the production of mathematics, and have given us new
ways to think about the roles of people and machines in creating new
mathematical knowledge. We discuss further investigation of these resources and
what it might reveal.
Crowdsourced mathematical activity is an example of a "social machine", a new
paradigm, identified by Berners-Lee, for viewing a combination of people and
computers as a single problem-solving entity, and the subject of major
international research endeavours. We outline a future research agenda for
mathematics social machines, a combination of people, computers, and
mathematical archives to create and apply mathematics, with the potential to
change the way people do mathematics, and to transform the reach, pace, and
impact of mathematics research.Comment: To appear, Springer LNCS, Proceedings of Conferences on Intelligent
Computer Mathematics, CICM 2013, July 2013 Bath, U
The Emergence of Creativity: Insights from Carnatic Raaga Improvisation and Mathematical Proof Generation
Creativity is a broad phenomenon that scholars have interpreted in a multitude of ways. We notice that a majority of the views describe creativity as something innate. This paper aims to verge from this perspective and explore creativity in terms of the constant mutual interaction of a person and their environment. Using the theoretical framework, enactivism, and the notion of emergence, we investigate the creative processes involved in musical improvisations of south Indian classical or Carnatic music and mathematical proof generation. Interview excerpts from professional Carnatic musicians and research mathematicians on their respective creative processes during musical improvisation and proof generation are analyzed. This study gives a perspective to think about creativity, with an emphasis on emergence. This paper has been partly informed by self- reflections on musical improvisations and mathematical proof generation by the first author, who is a performing Carnatic vocalist and a mathematician
Galois Got his Gun
This paper appeals to the figure of \'Evariste Galois for investigating the
gates between mathematics and their "publics." The figure of Galois draws some
lines of/within mathematics for/from the outside of mathematics and these lines
in turn sketch the silhouette of Galois as a historical figure. The present
paper especially investigates the collective categories that have been used in
various types of public discourses on Galois's work (e.g. equations, groups,
algebra, analysis, France, Germany etc.). In a way, this paper aims at shedding
light on the boundaries some individuals drew by getting Galois his gun. It is
our aim to highlight the roles of authority some individuals (such as as
Picard) took on in regard with the public figure of Galois as well as the roles
such authorities assigned to other individuals (such as the mediating role
assigned to Jordan as a mediator between Galois's "ideas" and the public). The
boundary-works involved by most public references to Galois have underlying
them a long-term tension between academic and public legitimacies in the
definition of some models for mathematical lives (or mathematics personae
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