Gilbert, S. and S. Ireton. (2003). Understanding models in earth and space science. NSTA Press: Arlington, Virginia.

This book has some excellent background on models although at times it goes a bit over the top when it claims that all communication is made up of models. Several important points were made that will help in this project. A model is defined as "...a system of objects or symbols that represents some aspect of another system, called its target" (Gilbert and Ireton, 2003, p. 1).Mental models are made of symbols. Symbols can be linked together to form propositions. Models are made up of these symbols, propositions and images. Models relate to their targets through corresponding features. The authors point out that when more senses are involved, a model will contain more detail and richness. There are many different types of models. For example, when someone uses a computer model, through experience, they will build up a representation of their own mental model. When someone wants to communicate this to other people, the model has to be expressed. Examples of expressed models are novels, works or art, diagrams, mathematical equations and many others. Another important point made is that most of what we learn is not from direct experience but rather from observing the models of others (p. 9). They went on to say that propositions such as written explanations are often more difficult to understand than visual explanations and images. This is an important point to consider if designing experiences to help students learn how to use a sophisticated computer model. Models can also be concrete and abstract. A plastic model of the heart is concrete and a very helpful aid to students learning while a diagram of the heart's structure is more abstract and difficult to comprehend. The students who will be using the IGEM/ISCLT3 model will mostly be high school. A substantial percentage of high school students will still be at this concrete operational level of thinking, especially in a subject area new to them. One of the challenges of this project will be to help those students move to an abstract level where they are capable of understanding how the computer model works. An important point of confusion with many students is not understanding the limits of models. sometimes a concrete model such as a physical model or diagram can create serious misconceptions.

This project has at its centerpiece a very complex model. The entire IGEMS model is based on a mathematical foundation, a mathematical model. the mathematical model itself is made up of equations and formulas. According to the authors, computer models are "...mathematics-based constructs." (p. 14). They can be used "...to create images of phenomena, to find and test relationships in complex systems, and to test multiple hypotheses..." "...visual models of complex phenomena...tools to manipulate massive databases..." they can "..allow modeling of complex "what if" questions." (p. 14)

All models use analogy to a certain extent. An analogy is a type of proposition that relates a model to a target. This could be a powerful tool in helping students understand the IGEMS model and the concepts involved. We should try and come up with analogies for the different ideas that underly the model, and for the different concepts involved. for example, the Gaussian curve and its use to predict concentration and thus exposure.

Characteristics of all models (pp. 16-17)

Model are all

• artificial - models are "human constructs"
• utilitarian - models are created for purpose, the model might be very useful to illustrate certain things but not others
• simplified - usually much simpler than their targets
• interpreted - some models use symbols that might not be familiar to everyone
• imperfect - only a target is perfect, a model never exactly duplicates its target

The fit of a model with its target can be evaluated by (p. 17)

• "relatedness to other models" - how well does it fit in with other models
• transparency - some models are very obvious and easy to grasp, e.g. transparent, while others are opaque
• robustness - this depends on the number of assumptions the model needs to function, a robust model depends on fewer assumptions
• fertility - how much does the model explain, fertile models give rise to new ideas and understanding
• "ease of enrichment" - how difficult is it to extend the model

Never confuse a model with its target! Models always have fewer variables than their target.

A "Rich" model has many features that correspond to the target's features.

We should strive to use a variety of models to help the students to develop a rich mental model.

The students need ..."exposure to multiple models that show different characteristics of the phenomenon." (p. 20) If we only use the computer model, the students' mental models will be very limited.

The IGEMS/ISC models will be the organizing framework for all of the activities.

So we need to present the concepts involved in IGEMS/ISC models in a variety of ways. We need to make sure the teachers and students are very aware of the differences between their mental models and the computer models, and the real world. The students need to actually construct and analyze expressed models. They should be able to describe the differences and similarities between the targets, the computer model, and their own mental models. The should be able to describe how well models fit their targets. The students should also analyze the computer model and compare it to other competing models. The students should also learn how to refine their models.

Chapter 2

According to the authors, metaphors carry the least information and they are more likely to be misinterpreted than analogies or similes.

Chapter 6

Students must be able to conceptualize a model and "...form an image in their own mind." p. 89 The authors suggest beginning with a "guiding question" or "driving question."