Aesthetic Considerations in Mathematics

Drawing on some of the principles of humanistic mathematics first outlined by Alvin White, this paper seeks to examine the way in which value judgments are implicated in the growth of the mathematics discipline. After a short overview of some of the roles ascribed to the mathematical aesthetic historically, I turn to more contemporary positioning of the aesthetic in order to develop a framework that offers insight into the particular values, assumptions and desires that constrain what is done in mathematics, how it is done and why. My goal, at least in part, is to bring together under one umbrella some of the recent work that is being done in the cultural ethnography and cognitive history of mathematics and, in so doing, provide a stronger rationale for the importance and relevance of aesthetic considerations in the history and philosophy of mathematics. Finally, I use this framework to promote the idea of a mathematics critic, who could do for mathematics what art critics do for the arts, namely, to not only evaluate and explain art, but to work toward establishing its accessibility and credibility

Putting Math in its Place A Review of Cathy O’Neil’s Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy

With its bright yellow cover and its ominous title, this book attracts attention. The subtitle, “How big data increases inequality and threatens democracy” signals very strongly that the “math” in question in the title is primarily that which relates to the statistical and computational means of collecting, analysing and using data. For some readers, the title might be surprising, because it challenges the typical understanding of mathematics as an objective and value-neutral discipline. Worse, it claims that mathematics is significantly involved in creating inequality and compromising democracy. If it is true, then the answer to the perennial student question, “when am I ever going to use this?” has now become, “when will it use you?

Geometrical reasoning in the primary school, the case of parallel lines

During the primary school years, children are typically expected to develop ways of explaining their mathematical reasoning. This paper reports on ideas developed during an analysis of data from a project which involved young children (aged 5-7 years old) in a whole-class situation using dynamic geometry software (specifically Sketchpad). The focus is a classroom episode in which the children try to decide whether two lines that they know continue (but cannot see all of the continuation) will intersect, or not. The analysis illustrates how the children can move from an empirical, visual description of spatial relations to a more theoretical, abstract one. The arguments used by the children during the lesson transcend empirical arguments, providing evidence of how young children can be capable of engaging in aspects of deductive argumentation

Informational Regulation of Industrial Safety - An Examination of the U.S. "Local Emergency Planning Committees"

A major trend in the regulation of industrial risks to human health and the environment is the provision of relevant information to (and the empowerment of) all stakeholders and risk bearers. This paper provides a concrete look at one of the key items in implementing this "regulation by information" in the United States: the so-called LEPCs or Local Emergency Planning Committees. We summarize the literature on the subject, report on some interviews we made at selected LEPCs in the states of Vermont and Maryland, and present preliminary figures from a recent survey we just completed of more than 200 LEPCs. The ending sections also contain some international comparisons and an appraisal of the actual LEPCs. La nouvelle tendance dans les réglementations concernant les risques industriels à la santé humaine et à l'environnement est de diffuser l'information pertinente à toutes les parties prenantes. Cet article considère l'un des outils clés de cette « régulation des risques par l'information » : les comités locaux de planification d'urgence, aux Etats-Unis (désignés en anglais par le sigle LEPC). Nous dressons un bilan de la littérature sur le sujet. Nous intégrons des éléments importants résultant d'entrevues faites auprès de LEPCs sélectionnés dans les États du Vermont et du Maryland. Et nous présentons certains résultats préliminaires d'une enquête récente que nous venons de réaliser auprès de plus de 200 LEPCs. Les sections finales contiennent également plusieurs comparaisons internationales et une appréciation du fonctionnement actuel des LEPCs.Chemical plant safety, Community participation, US Emergency Planning and Community Right-To-Know Act, Clean Air Act, Local Emergency Planning Committees (LEPCs), Risk Management Program, Stakeholders involvement, Sûreté des usines chimiques, participation du public, US Emergency Planning and Community Right-To-Know Act (EPCRA), Clean Air Act, Comités locaux de planification d'urgence (LEPC), Programme de gestion de risque, Implication des parties prenantes

Surprise-driven abductions in DGEs

Abductive inferences, which are the only types of inference that produce new ideas, are important in mathematical problem solving. Such inferences, according to Peirce, arise from surprising or unexpected situations. Therefore, one way to improve student problem solving may be to provide them with environments that are designed to evoke surprise. In this paper, we examine the potential of dynamic geometry environments (DGEs) to foster surprise. We conjecture that the ease with which students can explore configurations, along with the immediate feedback, may lead them to encounter surprising situations. We analyse three different examples of student problem solving featuring surprised-provoked abduction, and identify the specific role that the DGE played

Eliciting preschoolers’ number abilities using open, multi-touch environments

Research has highlighted the potential of digital technology to support the development of children’s number sense abilities. However, the main focus of such research has been on apps affording directed interactions, where only one solution strategy is available, and it has targeted mostly cardinality. Little is known, in these terms, about task design and implementation in more open environments where several different solution strategies are available. To explore this direction, we chose to study TouchCounts, an open environment that combines multi-touch affordances with aural, visual and symbolic ones as well. Using tasks that were designed to address different number sense abilities, we experimented with 4-year-old preschoolers. In this paper we present two tasks, their expected potential with respect to strengthening number sense abilities, and analyses of data collected during the preschoolers’ interactions with TouchCounts. The analyses reveal that the children used different strategies in response to the two tasks, and that a broad range of abilities related to number sense were elicited, including both cardinality and ordinality. An important contribution of this study is also a theoretical framework capable of identifying children’s learning in a multi-touch environment

Drawing off the page: How new 3D technologies provide insight into cognitive and pedagogical assumptions about mathematics

Mathematics has a history of being a two-dimensional inscribing practice. We describe the potential evolution in doing, thinking, and learning mathematics with the emergence of a technological innovation that enables real-time 3D virtual and material interactions. Using the 3D drawing pen as a simple and recently available technology, we highlight how it helps re-think long-standing assumptions and dichotomies in mathematics education including, for example, the material distinction between diagram and manipulative, the semiotic distinction between icon and index, and the developmental progression of action-icon-symbol. We then speculate on the future possibilities of the shift in technological infrastructure that 3D pens and similar technology may give rise to