Visualisation and Communication in Mathematics

Communication in mathematics is necessary at several levels: popularisation, teaching and research. Even a small drawing is useful in every case: to set a problem, to understand it, to find a method to tackle it and to illustrate it. An appealing aesthetic can also draw the attention on the subject.

Visualization in Biology

This chapter deals with what are commonly called seaweed, but are more correctly termed algae, that is, photosynthetic organisms that live in aquatic environments. Algae are visually beautiful and therefore a good subject for a biology teacher looking to explore the intersection of art and science with students. These connections run deep into knowledge production because drawing is fundamental not only to communicating information about organisms but also to investigating their characteristics. Observation and comparison are key tools in learning about the living world, and drawing is essential to these processes. Also discussed here will be the importance of relating texts, photographs, specimens, and drawings in assisting students to learn about algae. In addition, online sources for these tools will be explored.

The Difference between Evaluating and Understanding Students' Visual Representations of Scientists and Engineers

This chapter is a discussion of multiple tools for analyzing children's representations of scientists and engineers. Draw-A-Scientist and Draw-An-Engineer protocols have been utilized by science education researchers to investigate learners' perceptions of scientists and engineers. The chapter discusses the methods for analyzing students' perceptions of scientists and engineers how aspects of analysis lead to deeper understanding of the visual data. The discussion presented here is framed in the context in which refined protocols and rubrics are tools that uncover ranges of conceptions, and sometimes visual data are best examined by simple evaluation methods and sometimes by a qualitative rubric. The overarching question of this section is how can researchers use analysis of visual data to further what they already know about conceptions of scientists and engineers.

Better Visualization through Better Vision

Traditionally, the subject of “scientific visualization” focuses on the creation of novel or innovative graphical representations: essentially, new types of images to perceive. A truly complete approach to scientific visualization should include not only the perceived object, but also the abilities of the perceiver. Human “visual common sense” is a product of evolution, suited to the survival of the species; but it has severe and recurring limitations for the purposes of scientific understanding and education. People cannot readily understand phenomena that are too fast, slow, or complex for their visual systems to take in; they cannot see wavelengths outside visual spectrum; they have difficulty understanding three-dimensional (or, even worse, four-dimensional) objects. This chapter explores a variety of ideas and design themes for approaching scientific visualization by enhancing the powers of human vision.

Integrative Visual Projects for Cognitive Learning

This chapter comprises integrative studies on selected processes, events, and related technologies associated with several science categories. Learning projects are designed around themes drawn from events existing in everyday life, yet they familiarize the readers with complex disciplines and their applications. Complexity of apparently simple topics is presented in projects about familiar objects or actions. They are aimed at broadening the readers' general knowledge and experience rather than the technical or professional training. Topics and projects present nature- and science-related themes in terms of concept visualization including selected subjects pertaining to the basic sciences such physics, chemistry, biology, geography, or biology-inspired computing and modeling. The reader is encouraged to approach learning holistically and present concepts by creating technology based projects about visual presentation of information.

Metaphors for Dance and Programming

This chapter offers visual explanation on how to code using dance as a metaphor. This approach provides an overview of programming with ready to follow codes. It explores the implementation of restrictions and conditions in programming as compared to those ruling various dances. For those willing to learn or grasp the idea of coding for learning or acquiring better communication with co-workers, several programming languages are used to solve a similar task. Thus, similar codes are written in various languages while being related to the same topic. They delineate various dances and their rules, so the reader can compare and contrast the underlying principles for various environments. Then, exploration of invisible patterns created by movement of feet and aesthetics behind resulting patterns are presented, to highlight the dynamics behind the images generated by music, and subsequently the resulting movements of dancers according to various rules behind choreographies. The idea of randomness in coding, as compared to improvisation in dance is also investigated, when the dancers feel the music to create their own solutions to shape, space, and time, rather then following and obeying already designed rules.

Collage Strategy

In this chapter the author analyzes and defines collage in some of its many forms and media. He introduces three terms (the gap, the seam, and contested space) necessary to characterize the unique aesthetics of collage. Via a review of specific artists and art historical movements he creates taxonomy that typifies three distinctive collage strategies. He extends this review into other media including artists' books, cinematic film, and digital media. In the second part of the chapter he describes the work of three artists (including the author) and their relevance to this theory of collage and scientific visualization. Following that, he reviews the use of digital software and the pedagogical implications of collage.

Science and Art

The fourth dimension is a complex concept that deals with abstract reasoning, our sense of perception, and our imagination. Mathematics posits that a four-dimensional space is a geometric space with four dimensions. For many the fourth dimension is the element of time added to the three parameters of length, height and depth. How does a geometer incorporates time in the description of a structure, or a visual artist integrates time in a two dimensional flat surface image, when they both rely on well-defined principles that are a tangible descriptive of our reality? This chapter gives a brief overview of the different schools of thought in the Humanities and in Science, offers a possible definition of this elusive element needed to anchor the fourth dimension in our larger abstract reasoning consensus, and focuses on the specific of Mathematics and visual imaging to illustrate the particular benefit of collaborating on a simple, usable descriptive to create a sound outcome.

Exploring Perception, Cognition, and Neural Pathways of Stereo Vision and the Split–Brain Human Computer Interface

This chapter examines research from psychology of perception and cognition as well as select developments in the visual arts that inspired the design of the split-brain user interface developed for the interactive documentary Anita und Clarence in der Hölle: An Opera for Split-Brains in Modular Parts (Garvey, 2002). This experimental interface aims at ‘enhanced' interaction while creating a new aesthetic experience. This emergent aesthetic might also be described as induced artificial cognitive dissonance and recalls select innovations in the rise of modernism notably the experiments of the Surrealists. The split-brain interface project offers a model for further investigations of human perception, neural processing and cognition through experimentation with the basic principles of stereo and binocular vision. It is conceivable that such an interface could be a design strategy for augmented or virtual reality or even wearable computing. The chapter concludes with a short discussion of potential avenues for further experimentation and development.

Teaching and Learning Science as a Visual Experience

This chapter brings about concepts about implementing a framework for teaching and learning across the disciplines by introducing topics and activities pertaining to science, computing, and graphic arts as a unified cognitive and visual learning experience. First, theoretical framework is presented, to support designing integrative projects for cognitive learning. This part provides basic information about brain and mind, feelings and emotions, cognitive thinking, intelligence and cognitive styles, along with some basics about technologies used for studying cognitive activity. Then follows short introduction to ways to communicate knowledge, visual thinking, visual literacy, and knowledge visualization concepts and methods. Next, concerns about science education draw attention to a need of including into curriculum new developments in science and information about currently emerging disciplines. The goal is to enhance technological literacy of students, activate their interest, motivation, abstract thinking, and elicit a wish to achieve their aims.