BibSonomy publications for /user/yish/visualizationTue Oct 13 12:59:02 CEST 2009Proceedings of the Conference of the British Society for Research into the Learning of Mathematics384-89Introducing the concept of infinite sum: Preliminary analyses of curriculum content282008Infinite application curiculum limit mathematics postviva sequences sum university visualization In this paper we report the first phase of a study that aims to analyse curriculum content, pedagogical practice and student perceptions of the complex, often counter-intuitive but significant mathematical concept of infinite sum (aka series in Calculus). Sources of student difficulty with the concept identified in previous, not very extensive, research include: certain student perceptions of infinity; limited exposure to visualisation, contextualisation and applications of infinite sums; and, teaching through reduction to an algorithmic approach. Here we report preliminary analyses regarding curriculum content and, in particular, the initial phases of a three-dimensional analysis (cognitive, epistemological, didactical) of mainstream texts used to introduce the concept to undergraduates in the UK.Tue Oct 13 12:56:16 CEST 2009Educational Studies in Mathematics3217--233Students' images and their understanding of definitions of the limit of a sequence692008Asymptotes Images Limits Sequences cognition definitions learning limit mathematics postviva sequences teaching visual visualization There are many studies on the role of images in understanding the concept of limit. However, relatively few studies have been conducted on how students’ understanding of the rigorous definition of limit is influenced by the images of limit that the students have constructed through their previous learning. This study explored how calculus students’ images of the limit of a sequence influence their understanding of definitions of the limit of a sequence. In a series of task-based interviews, students evaluated the propriety of statements describing the convergence of sequences through a specially designed hands-on activity, called the ɛ–strip activity. This paper illustrates how these students’ understanding of definitions of the limit of a sequence was influenced by their images of limits as asymptotes, cluster points, or true limit points. The implications of this study for teaching and learning the concept of limit, as well as on research in mathematics education, are also discussed.Wed Feb 04 11:31:32 CET 2009International Journal of Computers for Mathematical Learning13-31The visibility of meanings: Modelling the mathematics of banking11996banking design learning logo mathematics modelling visualization If mathematical meanings play an important role in empowering individuals in the workplace and outside, there should surely be implications for mathematical education. How, for example, can 'academic' mathematics be linked to working life? The classical (but, in our view, wrong) way of looking at the problem is that schooling is induction into decontextualised forms of mathematical knowledge which are 'applied' to a variety of settings in later life. This is the answer given by those who see mathematical modelling in school as involving the idealisation and simplification of a situation in order that it can be mathematised, and thus broken from its 'non-mathematical' referents. In this scenario, 'real-life' settings become 'motivational', and problems are surrounded by contextual clutter, to be cleared away at the earliest opportunity in order to reveal the 'real' — i.e. mathematical — structure of the problem. In theory at least, students who have mastered the mathematised relations in this way will be able to 'transfer' this knowledge by applying it to other settings.Fri Dec 12 13:13:21 CET 2008IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS853-860Software Design Patterns for Information Visualization2006Design WLEFormativeEAssessment designpatterns engineering information object-oriented patternlanguagenetwork patterns programming software visualization Despite a diversity of software architectures supporting information visualization, it is often difficult to identify, evaluate, and re-apply the design solutions implemented within such frameworks. One popular and effective approach for addressing such difficulties is to capture successful solutions in design patterns, abstract descriptions of interacting software components that can be customized to solve design problems within a particular context. Based upon a review of existing frameworks and our own experiences building visualization software, we present a series of design patterns for the domain of information visualization. We discuss the structure, context of use, and interrelations of patterns spanning data representation, graphics, and interaction. By representing design knowledge in a reusable form, these patterns can be used to facilitate software design, implementation, and evaluation, and improve developer education and communication.Sat Oct 04 02:00:10 CEST 2008The International Journal for Technology in Mathematics Education 3The Impact of the Graphical Approach on Students' Understanding of the Formal Definition of Limit.152008calculus definition graphical graphics graphs learning limit mathematics narrative understanding visual visualization The purpose of this study was to determine if the use of a graphical teaching and learning approach via the graphing calculator enhances students’ understanding of the formal definition of limit. College students in six sections of Calculus I participated by completing a test prior to the introduction of the definition, and completing a second similar test after covering this topic. Students in four sections received traditional instruction on the formal definition of limit, but in two other sections an approach utilising graphing calculators was incorporated into the instruction for one and two days, respectively. Students who received the graphical instruction for two days performed significantly better on all but one of the conceptual items on the post-test, as compared to the students who received traditional instruction and with those who received the graphical instruction for only one day. Thu Aug 21 14:41:23 CEST 2008Educational Studies in Mathematics11-32Convergence of Sequences and Series: Interactions between Visual Reasoning and the Learner572004advanced analysis beliefs convergence definitions grounded learning limit limits mathematical mathematics postviva proof real representations sequences theory thinking visualization This paper examines part of a set of students who were followed during their first-term, first-year studies in formal definition-based real analysis at a British university. It explores the approaches to problems about convergence of sequences and series made by students who have a tendency to include visual imagery in their reasoning. We explore links between the students' mathematical behavior in solving these problems and their perception of their roles as learners. We develop a theory in which the tendency to visualize, coupled with the students' view of their role, can be used to account for their mathematical behavior.Fri May 30 01:00:04 CEST 2008Representations and Mathematics Visualization. Working Group Representations and Mathematics Visualization (1998-2002), North American Chapter of the International Group for the Psychology of Mathematics Education127-142Coordinating Representations Through Programming Activities: an example using Logo2002convergence fractals ijtme2006 mythesis sequences visualization Mon Dec 03 13:17:00 CET 2007Applying UML and Patterns: An Introduction to Object-Oriented Analysis and Design and the Unified Process2002UML computer design designpatterns jime08 object oriented patterns programming science software visualization This text presents an introduction and overview of fundamental object-oriented analysis and design concepts. It shows how to investigate requirements, create solutions, and then translate designs into code. It contains a summary of UML notation and checklists of class categories.Tue May 01 13:21:14 CEST 2007Reston, VaThe Roles of Representations in School Mathematics251-268Charting a Visual Course to the Concept of Function2001algebra functions haifa-edtech interactive learning mathematics school textbook visualization Tue Sep 19 02:50:41 CEST 2006Educational Studies in Mathematics1Convergence of sequences and series: Interactions between visual reasoning and the learner's beliefs about their own role572004representation mathematical thinking beliefs definitions theory proof analysis need convergence visualization sequences advanced representations bibtex-import real grounded read This paper examines part of a set of students who were followed during their first-term, first-year studies in formal definition-based real analysis at a British university. It explores the approaches to problems about convergence of sequences and series made by students who have a tendency to include visual imagery in their reasoning. We explore links between the students’ mathematical behavior in solving these problems and their perception of their roles as learners.We develop a theory in which the tendency to visualize, coupled with the students’ view of their role, can be used to account for their mathematical behavior.