Proof in dynamic geometry contexts

Proof lies at the heart of mathematics yet we know from research in mathematics education that proof is an elusive concept for many mathematics students. The question that this paper raises is whether the introduction of dynamic geometry software will improve the situation – or whether it make the transition from informal to formal proof in mathematics even harder. Through discussion of research into innovative teaching approaches with computers the paper examines whether such approaches can assist pupils in developing a conceptual framework for proof, and in appropriating proof as a means to illuminate geometrical ideas

Using materials from the history of mathematics in discovery-based learning

This paper reports on attempt to integrate history of mathematics in discovery-based learning using technology. Theoretical grounding of the idea is discussed. An exploratory environment on triangle geometry is described. It is designed to support and motivate students' activities in learning through inquiry. Conjectures about properties of Lemoine point and Simson line are produced and proved by students using e-learning textbook

Empirical modelling principles to support learning in a cultural context

Much research on pedagogy stresses the need for a broad perspective on learning. Such a perspective might take account (for instance) of the experience that informs knowledge and understanding [Tur91], the situation in which the learning activity takes place [Lav88], and the influence of multiple intelligences [Gar83]. Educational technology appears to hold great promise in this connection. Computer-related technologies such as new media, the internet, virtual reality and brain-mediated communication afford access to a range of learning resources that grows ever wider in its scope and supports ever more sophisticated interactions. Whether educational technology is fulfilling its potential in broadening the horizons for learning activity is more controversial. Though some see the successful development of radically new educational resources as merely a matter of time, investment and engineering, there are also many critics of the trends in computer-based learning who see little evidence of the greater degree of human engagement to which new technologies aspire [Tal95]. This paper reviews the potential application to educational technology of principles and tools for computer-based modelling that have been developed under the auspices of the Empirical Modelling (EM) project at Warwick [EMweb]. This theme was first addressed at length in a previous paper [Bey97], and is here revisited in the light of new practical developments in EM both in respect of tools and of model-building that has been targetted at education at various levels. Our central thesis is that the problems of educational technology stem from the limitations of current conceptual frameworks and tool support for the essential cognitive model building activity, and that tackling these problems requires a radical shift in philosophical perspective on the nature and role of empirical knowledge that has significant practical implications. The paper is in two main sections. The first discusses the limitations of the classical computer science perspective where educational technology to support situated learning is concerned, and relates the learning activities that are most closely associated with a cultural context to the empiricist perspective on learning introduced in [Bey97]. The second outlines the principles of EM and describes and illustrates features of its practical application that are particularly well-suited to learning in a cultural setting

Geant4-related R&D for new particle transport methods

A R&D project has been launched in 2009 to address fundamental methods in radiation transport simulation and revisit Geant4 kernel design to cope with new experimental requirements. The project focuses on simulation at different scales in the same experimental environment: this set of problems requires new methods across the current boundaries of condensed-random-walk and discrete transport schemes. An exploration is also foreseen about exploiting and extending already existing Geant4 features to apply Monte Carlo and deterministic transport methods in the same simulation environment. An overview of this new R&D associated with Geant4 is presented, together with the first developments in progress.Comment: 4 pages, to appear in proceedings of the Nuclear Science Symposium and Medical Imaging Conference 2009, Orland

An information technology competency model and curriculum

This paper addresses the progress made by the Association for Computing Machinery (ACM) and the IEEE Computer Society (IEEE-CS) in developing a competency model and curricular guidelines for four-year degree programs in information technology. The authors are members of an international task group representative of academic institutions, industry, and professional organizations. The task group is to develop a competency model, called IT2017, for information technology education within two years based on earlier guidelines and other perspectives. This paper provides a brief background of the project, some activities undertaken, the progress made, and expectations for future developments. IT2017 seeks to produce a futuristic model of academic excellence so information technology graduates will be prepared for new technological challenges in a global economy

Interoperability in the OpenDreamKit Project: The Math-in-the-Middle Approach

OpenDreamKit --- "Open Digital Research Environment Toolkit for the Advancement of Mathematics" --- is an H2020 EU Research Infrastructure project that aims at supporting, over the period 2015--2019, the ecosystem of open-source mathematical software systems. From that, OpenDreamKit will deliver a flexible toolkit enabling research groups to set up Virtual Research Environments, customised to meet the varied needs of research projects in pure mathematics and applications. An important step in the OpenDreamKit endeavor is to foster the interoperability between a variety of systems, ranging from computer algebra systems over mathematical databases to front-ends. This is the mission of the integration work package (WP6). We report on experiments and future plans with the \emph{Math-in-the-Middle} approach. This information architecture consists in a central mathematical ontology that documents the domain and fixes a joint vocabulary, combined with specifications of the functionalities of the various systems. Interaction between systems can then be enriched by pivoting off this information architecture.Comment: 15 pages, 7 figure

Evaluating musical software using conceptual metaphors

An open challenge for interaction designers is to find ways of designing software to enhance the ability of novices to perform tasks that normally require specialized domain expertise. This challenge is particularly demanding in areas such as music analysis, where complex, abstract, domain-specific concepts and notations occur. One promising theoretical foundation for this work involves the identification of conceptual metaphors and image schemas, found by analyzing discourse. This kind of analysis has already been applied, with some success, both to musical concepts and, separately, to user interface design. The present work appears to be the first to combine these hitherto distinct bodies of research, with the aim of devising a general method for improving user interfaces for music. Some areas where this may require extensions to existing method are noted. This paper presents the results of an exploratory evaluation of Harmony Space, a tool for playing, analysing and learning about harmony. The evaluation uses conceptual metaphors and image schemas elicited from the dialogues of experienced musicians discussing the harmonic progressions in a piece of music. Examples of where the user interface supports the conceptual metaphors, and where support could be improved, are discussed. The potential use of audio output to support conceptual metaphors and image schemas is considered

Education vs. Entertainment: A Cultural History of Children's Software

Part of the Volume on the Ecology of Games: Connecting Youth, Games, and Learning This chapter draws on ethnographic material to consider the cultural politics and recent history of children's software and reflects on how this past can inform our current efforts to mobilize games for learning. The analysis uses a concept of genre as a way of making linkages across the distributed but interconnected circuit of everyday play, software content, and industry context. Organized through three genres in children's software -- academic, entertainment, and construction -- the body of the chapter describes how these genres play out within a production and advertising context, in the design of particular software titles, and at sites of play in after-school computer centers where the fieldwork was conducted