From Euclidean Geometry to Knots and Nets

This document is the Accepted Manuscript of an article accepted for publication in Synthese. Under embargo until 19 September 2018. The final publication is available at Springer via https://doi.org/10.1007/s11229-017-1558-x.This paper assumes the success of arguments against the view that informal mathematical proofs secure rational conviction in virtue of their relations with corresponding formal derivations. This assumption entails a need for an alternative account of the logic of informal mathematical proofs. Following examination of case studies by Manders, De Toffoli and Giardino, Leitgeb, Feferman and others, this paper proposes a framework for analysing those informal proofs that appeal to the perception or modification of diagrams or to the inspection or imaginative manipulation of mental models of mathematical phenomena. Proofs relying on diagrams can be rigorous if (a) it is easy to draw a diagram that shares or otherwise indicates the structure of the mathematical object, (b) the information thus displayed is not metrical and (c) it is possible to put the inferences into systematic mathematical relation with other mathematical inferential practices. Proofs that appeal to mental models can be rigorous if the mental models can be externalised as diagrammatic practice that satisfies these three conditions.Peer reviewe

Modeling the perceptual component of conceptual learning—A coordination perspective

Although a picture may be worth a thousand words, modeling diagrams as propositions and modeling visual processing as search through a database of verbal descriptions obscures what is problematic for the learner. Cognitive modeling of language learning and geometry has obscured the learner's problem of knowing where to look—what spaces, markings, and orientations constitute the objects of interest? Today we are launching into widespread use of multimedia instructional technology, without an adequate theory to relate perceptual processes to conceptual learning. Does this matter? In this article, I review the symbolic approach to modeling perceptual processing and show its limitations for explaining difficulties children encounter in interpreting a graphic display. I present an alternative analysis by which perceptual categorization is coupled to behavior sequences, where gesturing and emotional changes are essential for resolving impasses and breaking out of loops. I conclude by asking what kind of cognitive theory we need to exploit communication technology. Have we been correct to assume that pedagogy must be grounded in an accurate psychological model of knowledge, memory, and learning

Distributional effects and individual differences in L2 morphology learning

Second language (L2) learning outcomes may depend on the structure of the input and learners’ cognitive abilities. This study tested whether less predictable input might facilitate learning and generalization of L2 morphology while evaluating contributions of statistical learning ability, nonverbal intelligence, phonological short-term memory, and verbal working memory. Over three sessions, 54 adults were exposed to a Russian case-marking paradigm with a balanced or skewed item distribution in the input. Whereas statistical learning ability and nonverbal intelligence predicted learning of trained items, only nonverbal intelligence also predicted generalization of case-marking inflections to new vocabulary. Neither measure of temporary storage capacity predicted learning. Balanced, less predictable input was associated with higher accuracy in generalization but only in the initial test session. These results suggest that individual differences in pattern extraction play a more sustained role in L2 acquisition than instructional manipulations that vary the predictability of lexical items in the input

Jointly structuring triadic spaces of meaning and action:book sharing from 3 months on

This study explores the emergence of triadic interactions through the example of book sharing. As part of a naturalistic study, 10 infants were visited in their homes from 3-12 months. We report that (1) book sharing as a form of infant-caregiver-object interaction occurred from as early as 3 months. Using qualitative video analysis at a micro-level adapting methodologies from conversation and interaction analysis, we demonstrate that caregivers and infants practiced book sharing in a highly co-ordinated way, with caregivers carving out interaction units and shaping actions into action arcs and infants actively participating and co-ordinating their attention between mother and object from the beginning. We also (2) sketch a developmental trajectory of book sharing over the first year and show that the quality and dynamics of book sharing interactions underwent considerable change as the ecological situation was transformed in parallel with the infants' development of attention and motor skills. Social book sharing interactions reached an early peak at 6 months with the infants becoming more active in the coordination of attention between caregiver and book. From 7-9 months, the infants shifted their interest largely to solitary object exploration, in parallel with newly emerging postural and object manipulation skills, disrupting the social coordination and the cultural frame of book sharing. In the period from 9-12 months, social book interactions resurfaced, as infants began to effectively integrate object actions within the socially shared activity. In conclusion, to fully understand the development and qualities of triadic cultural activities such as book sharing, we need to look especially at the hitherto overlooked early period from 4-6 months, and investigate how shared spaces of meaning and action are structured together in and through interaction, creating the substrate for continuing cooperation and cultural learning

Digitally Yours; The Body in Contemporary Photography

This article analyses two artworks by contemporary photographers, Alexa Wright and Wendy McMurdo. It focuses in particular on the relationship between digital technologies and representation of the body, and on the changes to accepted paradigms of sexuality, identity and sensuousness caused by the computation of the art object. The article appears in ‘The Issues: In Contemporary Culture and Aesthetics’, which explores the intersecting fields of contemporary art, philosophy and practice

Why 'scaffolding' is the wrong metaphor : the cognitive usefulness of mathematical representations.

The metaphor of scaffolding has become current in discussions of the cognitive help we get from artefacts, environmental affordances and each other. Consideration of mathematical tools and representations indicates that in these cases at least (and plausibly for others), scaffolding is the wrong picture, because scaffolding in good order is immobile, temporary and crude. Mathematical representations can be manipulated, are not temporary structures to aid development, and are refined. Reflection on examples from elementary algebra indicates that Menary is on the right track with his ‘enculturation’ view of mathematical cognition. Moreover, these examples allow us to elaborate his remarks on the uniqueness of mathematical representations and their role in the emergence of new thoughts.Peer reviewe

Freeform User Interfaces for Graphical Computing

報告番号: 甲15222 ; 学位授与年月日: 2000-03-29 ; 学位の種別: 課程博士 ; 学位の種類: 博士(工学) ; 学位記番号: 博工第4717号 ; 研究科・専攻: 工学系研究科情報工学専

Digital Image Access & Retrieval

The 33th Annual Clinic on Library Applications of Data Processing, held at the University of Illinois at Urbana-Champaign in March of 1996, addressed the theme of "Digital Image Access & Retrieval." The papers from this conference cover a wide range of topics concerning digital imaging technology for visual resource collections. Papers covered three general areas: (1) systems, planning, and implementation; (2) automatic and semi-automatic indexing; and (3) preservation with the bulk of the conference focusing on indexing and retrieval.published or submitted for publicatio