Picturing Number in the Central Middle Ages.

Numeracy was as highly valued as literacy in the schools of Latin-speaking Europe around the year 1000, and the skills inculcated by masters, engendering specific modes of seeing and imagining, had demonstrable impact on contemporary visual culture. The trivium—grammar, rhetoric, and dialectic—continued to be taught as the foundation of learning, but the quadrivium, the four disciplines of number—arithmetic, geometry, astronomy, and music—received new emphasis. Two of the era’s greatest intellects, Gerbert of Aurillac (Pope Sylvester II; c.940–1003) and Abbo of Fleury (c.944–1004), gained renown for their mathematical prowess and charismatic teaching. They educated a generation of Europe's powerful elites—including Emperor Otto III—and a host of anonymous clerics, monks, and priests. In the closed economy of the central middle ages, these men were also the primary patrons, makers, and viewers of objects. Works of the time, like the Pericope Book of Henry II, reveal new qualities when examined through the lens of number. This project is located at the cathedral school of Reims and the monastery school of Saint-Benoît-sur-Loire (Fleury)—where Gerbert and Abbo were masters, epicenters of a pan-European network of exchange linking monastic, episcopal, and lay institutions. Numeric knowledge was drawn from late antique and early medieval tracts by such figures as Boethius, Calcidius, Macrobius, Martianus Capella, Cassiodorus, Isidore of Seville, and Bede. Manuscript copies of these works produced and used at Reims and Fleury c.1000 give evidence of active engagement with their content, visual as well as verbal. Diagrammatic images earlier devised to explicate numeric concepts were now adapted and artfully elaborated for classroom use. This is evident in important introductions to the quadrivial disciplines prepared by Abbo (Explanatio in Calculo Victorii), Abbo’s student Byrhtferth of Ramsey (Enchiridion), and Gerbert (Isagoge geometriae). Accompanying images to these tracts are witness to contemporary notions of materiality, sight, and the limits of representation. Students of arithmetic became freshly attuned to placement and order. Computistic study developed an active, agile, and "curious" eye, while the practice of geometry exercised the intellectual eye, sharpening it, according to Gerbert, "for contemplating spiritual things and truths."PHDHistory of ArtUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/116774/1/mcnameme_1.pd

Linguistic (ir-)realities. A heuristic critique of the meta-theoretical foundations of generativism.

The thesis aims to provide a heuristic critique of the meta-theoretical foundations of Chomsky's project for an explanatory linguistics. The critique is 'heuristic' in that it attempts to take the considerations adduced to indicate how those conceptual foundations are to be re-designed on lines parallel to constructivism in the philosophy of mathematics. The net result is the provision of an outline of a meta-theoretic rationale for a process orientated linguistic theory (e.g. Kempson et al.'s LDSNL framework). The thesis investigates, and is organized around, three central strands of the Chomskyan paradigm: 1) The mathematization of linguistics: the use of formal/mathematical systems as theory constitutive metaphors. 2) A scientific realist (as opposed to instrumentalist) construal of linguistic theories. 3) A conceptualist/psychologist ontology for linguistic objects with a concomitant explanation for the nature of the linguistic in terms of properties of the modularized human "mind/brain" articulated through a system of mental representations. The central conclusions drawn are: 1) There is a failure to achieve adequate warrant for a scientific realist construal of Chomskyan linguistic theories. 2) The object(s) of study that is (are) posited in the Chomskyan paradigm require a Platonist or autonomist ontological status. A corollary of this is the inability to achieve an adequate explanation for the nature of linguistic phenomena. These conclusions, together with the observation of certain conceptual tensions and antimonies in generativist thinking (e.g. the relation between types and tokens), are taken to be sufficient to prompt a re-examination of the (metaphysical realist) assumptions that underlie that thinking. The solution that is canvassed, and which promises to resolve these tensions, is by way of a linguistic version of mathematical constructivism in which the emphasis lies in linguistic phenomena being construed as primarily cognitive events in which the constructive procedures are crucially constitutive of then linguistically individuating properties

Teaching/Learning Physics: Integrating Research into Practice

The GIREP-MPTL International conference on Teaching/Learning Physics: Integrating Research into Practice [GIREP-MPTL 2014] was held from 7 to 12 July 2014 at the University of Palermo, Italy. The conference has been organised by the Groupe International de Recherche sur l’Enseignement de la Physique [GIREP] and the Multimedia in Physics Teaching and Learning [MPTL] group and it has been sponsored by the International Commission on Physics Education [ICPE] – Commission 14 of the International Union for Pure and Applied Physics [IUPAP], the European Physical Society – Physics Education Division [EPS-PED], the Latin American Physics Education Network [LAPEN] and the Società Italiana di Fisica [SIF]. The theme of the conference, Teaching/Learning Physics: Integrating Research into Practice, underlines aspects of great relevance in contemporary science education. In fact, during the last few years, evidence based Physics Education Research provided results concerning the ways and strategies to improve student conceptual understanding, interest in Physics, epistemological awareness and insights for the construction of a scientific citizenship. However, Physics teaching practice seems resistant to adopting adapting these findings to their own situation and new research based curricula find difficulty in affirming and spread, both at school and university levels. The conference offered an opportunity for in-depth discussions of this apparently wide-spread tension in order to find ways to do better. The purpose of the GIREP-MPTL 2014 was to bring together people working in physics education research and in physics education at schools from all over the world to allow them to share research results and exchange their experience. About 300 teachers, educators, and researchers, from all continents and 45 countries have attended the Conference contributing with 177 oral presentations, 15 workshops, 11 symposia, and around 60 poster presentations, together with 11 keynote addresses (general talks). After the conference, 147 papers have been submitted for the GIREP-MPTL 2014 International Conference proceedings. Each paper has been reviewed by at least two reviewers, from countries that are different to those of the authors and on the basis of criteria described on the Conference web site. Papers were subsequently revised by authors according to reviewers’ comments and the accepted papers are reported in this book, divided in 8 Sections on the basis of the keywords suggested by authors. The other book section (actually, the first one) contains the papers that six of the keynote talkers sent for publication in this Proceedings Book. We would like to thank all the authors that contributed with their papers to the realization of this book and all the referees that with their criticism helped authors to improve the quality of the papers