Jim Morey

Application of Information Visualization Techniques to the Design of a Mathematical Mindtool: A Usability Study

One of the goals of information visualization is to support human thinking through the use of external visual aids. Mathematical mindtools can act as visual cognitive aids to enhance thinking and reasoning about mathematical objects and concepts. Although some mathematical mindtools incorporate information visualization techniques, the systematic use of these techniques in the design of these tools and their effect on users’ thinking and reasoning need to be investigated. A mathematical mindtool called PARSE (Platonic-Archimedean Solids Explorer) is presented in this paper. PARSE is intended to support the exploration and learning of a subset of geometric shapes. The mathematical objects and concepts embedded in PARSE have been enhanced using information visualization techniques. A usability study of PARSE and its information visualization techniques have been conducted and reported. The study shows that information visualization techniques enhance and support learning and exploration of mathematical concepts. The findings reported in this paper suggest that mathematical mindtools provide a fertile ground for investigating different information visualization techniques and their effectiveness in supporting learning tasks.

Adjusting degree of visual complexity: an interactive approach for exploring four-dimensional polytopes

Few mathematical visualization tools support integrated, flexible interaction with complex, 4D mathematical concepts. This paper presents a solution to exploring uniform 4D polytopes through a mathematical visualization tool by introducing an approach for adjusting the degree of visual complexity of these complicated geometric structures. This approach introduces a number of interactive techniques: contextualizing, filtering, focus+scoping, and stacking-unstacking. Although these techniques can be effectively used in isolation, their integrated application provides highly specified and sophisticated interaction with polytopes, helping users make sense of these challenging mathematical structures. Exploring complicated structures from other domains such as chemistry and biology may benefit from this approach.

18 Visualising, interacting and experimenting with lattices using a diagrammatic representation

This chapter presents the K -lattice machine (KLM), a tool that allows users to visualise, interact, and experiment with K lattices using a diagrammatic representation. K lattices are a subset of 2D lattices that can be represented as state-transition diagrams. KLM allows users to explore the relationship between K lattices and their state-transition diagram representations to gain insight into the structure of these lattices.

Supporting Sensemaking of Complex Objects with Visualizations: Visibility and Complementarity of Interactions

Making sense of complex objects is difficult, and typically requires the use of external representations to support cognitive demands while reasoning about the objects. Visualizations are one type of external representation that can be used to support sensemaking activities. In this paper, we investigate the role of two design strategies in making the interactive features of visualizations more supportive of users’ exploratory needs when trying to make sense of complex objects. These two strategies are visibility and complementarity of interactions. We employ a theoretical framework concerned with human–information interaction and complex cognitive activities to inform, contextualize, and interpret the effects of the design strategies. The two strategies are incorporated in the design of Polyvise, a visualization tool that supports making sense of complex four-dimensional geometric objects. A mixed-methods study was conducted to evaluate the design strategies and the overall usability of Polyvise. We report the findings of the study, discuss some implications for the design of visualization tools that support sensemaking of complex objects, and propose five design guidelines. We anticipate that our results are transferrable to other contexts, and that these two design strategies can be used broadly in visualization tools intended to support activities with complex objects and information spaces.

Crystal Lattice Automata

A description of crystal lattices in terms of automata is presented. The words of a language represented by an automata are mapped to points in R2 and R3 defining lattice points and their connections. These automata descriptions of crystal lattices reveal subtle properties that are difficult to see in other descriptions. A few applications of these automata are discussed.

Interactive metamorphic visuals: exploring polyhedral relationships

The paper presents an interactive visualization tool, Archimedean Kaleidoscope (AK), aimed at supporting a learners exploration of polyhedra. AK uses metamorphosis as a technique to help support the learners mental construction of relationships among different polyhedra. AK uses the symmetric nature of the platonic solids as the foundation for exploring the way in which polyhedra are related. The high level of interactivity helps support the exploration of these relationships.

Interface development for a gaze-controlled reading support application

This paper describes development of an application to support the digital reading of academic texts by non-native speakers, in particular Emirati University students. Text interaction is unobtrusively controlled by gaze, tracked at word level, offering user-directed support and reporting data useful for reading assessment at individual and aggregate levels. After briefly outlining some specific reading difficulties we describe specific technical requirements and features, the application design process, and results from iterative evaluation of prototypes with target user representatives.

Using Indexed-Sequential Geometric Glyphs to Explore Visual Patterns

This paper presents a visualization tool called PolygonR&D for exploring visual tiling patterns. To facilitate the exploration process, PolygonR&D uses dynamically-generated, interactive geometric glyph visualizations that intermediate reasoning between the sequential textual code and the parallel visual structure of the tilings. Sequential textual code generates indexed-sequential geometric glyphs. Not only does each glyph represent one procedure in the sequential code, but also a constituent element of the visual pattern. Users can reason with a sequence of glyphs to explore how tiling patterns are constructed. Alternatively, they can interact with glyphs to semantically unpack them. Glyphs also contain symbolic referents to other glyphs helping users see how all procedures work together to generate a tiling pattern. Experimenting with indexed-sequential glyphs in tools such as PolygonR&D can help us understand how to design interactive cognitive tools that support reciprocal reasoning between sentential and visual structures.

A data visualisation for horizontal eye-movements

The increasing ease with which large data sets can be collected brings a concomitant need for tools to help understand what this data indicates. For many user applications such data may be collected passively and unobtrusively in the flow of their activity, and on scales ranging from the individual to increasingly larger communities. With the advent of smart eyewear and the emerging availability of sophisticated but affordable eye-tracking devices, eye movement data becomes a source of detailed information about a users focus and indirectly about their cognition and attention. Visualising this usefully however, remains a challenge. In this paper we report a new data representation from significant data sets generated by a gaze-controlled digital reading application for second language speakers. The visualisation of this data allows rapid diagnosis of problem areas in texts, informing educators immediately of individual or wider issues. The generality of this visualisation to other applications is discussed.

Designing an Interactive Visualization to Explore Eye-movement Data

For many user applications large data sets may be collected passively and unobtrusively in the flow of their activity, and on scales ranging from the individual to increasingly larger communities. Large data sets, however, bring a concomitant need for tools to help understand what the data indicates. With the emergence of smart eyewear and the availability of sophisticated but affordable eye-tracking devices, eye movement data becomes a source of detailed information about a user’s focus and indirectly about their cognition and attention. Visualizing this usefully in terms meaningful for diagnosis however, remains a challenge. In this paper we report a new data representation from significant data sets generated by a gaze-controlled digital reading application for second language speakers. Current tools provide data sets aimed primarily towards statistical analysis of patterns: our focus is on end-user exploration of data sets in domain terms, so that practical implications can be readily identified. The visualization of horizontal eye movement data allows rapid diagnosis of problem areas in texts, informing educators immediately of individual or wider issues. The general applicability of this visualization to other applications is discussed.