Introduction

This presentation is not meant as a review of the use of visualization in education. What I would like to present here is a discussion of the types of roles visualization can play in an educational setting and to draw attention to issues that must be addressed when designing such visualizations.

Visualization

In short Visualization is the graphical display of information. The purpose of this graphical display is to provide the viewer a visual means of processing the information. It is important to note that for a vizualization to be effective it must draw upon the knowledge base of the viewer. If the viewer does not posess the knowledge to understand the graphical entities and the relations between them the visualization does not achieve its goal. Visualization has many applications. For the most part they can be classified into two categories:

Data Exploration
Communicating Information

Data Exploration is the practice of using visualization techniques to find unforseen relationships between data points or sets of points in large databases. Once a relationship has been found the same visualization can be used to communicate that relation to others. Visualization techniques can also be applied to information that is already known. For a more in depth discussion of information visualization see Matt Ward-Data Visualization

Visualization in Education

Education can be viewed as the externally facilitated development of knowledge. This external influence can take many forms (a teacher, textbook, article, movie, TV show, computer program, ...). The purpose of any visualization to be used in an educational context is to facilitate the learning of some knowledge (idea, concept, fact, algorithm, relationship, ...). In order to accomplish this a visualization must make connections between knowledge the learner has and the knowledge being taught. Therefor in order to design effective visualizations it is necessary to know (or at least have a theory about) what the learner knows. This is especially important in the context of education. As will be discussed shortly the learner knowledge base for a given concept can take several forms. These different forms influence how the visualization will be interpreted and integerated into their knowledge base. Before this issue can be addressed, however, a framework is needed for discussing knowledge and how it might be represented internally.

Representation of Knowledge

James Hiebert and Thomas Carpenter in [6] present a framework for discussing the representation of mathematical concepts in the context of teaching for understanding. The concepts in there framework, however, are not specific to mathematics and can be applied to rpresentation of knowledge in general. Their framework also provides a useful means for discussing the role that external representations play in learning. The main points of their framework are:

Relationships exist between external and internal representations.
The form of external representation with which the student interacts influenes how knowledge is represented internally.
The form in which a student externally represents knowledge if influenced by their internal representation.
Internal representations of knowledge are connected to form networks of knowledge.
Networks can be hierarchical - some representations subsume others
Networks can be graphlike - nodes represent pieces of information and the arcs represent the relationships between them.
Most likely a combination of the two.
Understanding occurs when a idea is well integrated into a richly connected network

Given this framework we can now address the types of knowledge a student can have about a given concept that they are trying to learn. These type of knowledge can be broken into four categories. Each of these will be discussed below.

Fragmented & Incorrect
Fragmented & Correct
Coherent & Incorrect
Coherent & Correct

Fragmented Knowledge

Fragmented knowledge (correct or incorrect) results in domains in which the student has had little or no experience. Often the student will posess some intuition about the domain but these intuitions have not been connected. In these case nodes exist in the network but are not strongly connected to either each other or other knowledge domains in the network. The role of visualization is then to demonstrate the relations between nodes in the network. If the original concepts were incorrect the the visualization must relations between the new correct nodes and other domains within the network. Teaching a student with fragmented knowledge, although not trivial, is not a daunting task. Because there are not many connections from the incorrect nodes to the rest of the network they can be replaced/removed without significantly damaging the network. Here we should also include the case that the student has no knowledge about a domain. Here the visualization must make connections to other domains in the network.

Coherent Knowledge

In the case of coherent correct knowledge the visualization has a wealth of knowledge to draw upon. The case where the sutdent has a coherent network of incorrect knowledge is the most difficult to teach. In this case the student is said to have a misconception (see Carey[1] and diSessa[4][5]for a discussion of misconceptions in science education) of the concept. The primary problem is this case is that the student will interpret the information being taught in the context of their misconception. Here the visualization must not only make connections to other domains but also demonstrate the inconsistancies in the students misconception. This demonstration of inconsistancies is often referred as inducing disequilibrium in the misconception of the student.