This section is intended to provoke thought about the unifying themes that drive the Mission to Mars unit. A full description can be found in a number of publications by the American Association for the Advancement of Sciences, specifically, Project 2061 Science For All Americans.

Systems

Any collection of things that exert some influence on one another and make up a collective whole can be thought of as a system. The items can be almost anything, including objects, machines, ideas, numbers, or organisms. Looking at a collection of things as a system draws attention to the functioning of the system as well as the interaction among its parts. Thinking in terms of systems makes the implicit assumption that each part can only be fully understandable once it is related to the rest of the system.

In establishing a system Ñ whether it is the solar system, the cardiovascular system, or the ignition system of an automobile, we, as educators, must make sure to include an adequate number of constituent parts to clarify the relationships of the parts while making sense of the system. What makes sense is dependent on what the purpose of looking at the system is. For example, if we were interested in a rough explanation of the solar system, we would include the sun and the nine planets; however, a more accurate description would include the number of moons associated with each planet, the asteroid belt, and the vast amount of comets using the sun as the foci of their highly elliptical orbits. Likewise, if we are concerned with the presentation of the human cardiovascular system, a simple description of the heart, veins and arteries would suffice upon introduction, whereas a richer account might include the capillaries, the chamber system of the heart, and the oxygenating role of the lungs. Guidelines for inclusive parts would include the type of audience and level of detail needed. What would be common in either case, however, would be the benefit of viewing the individual parts in light of their role as a functioning system.

One of the well-established components of higher-order thinking is the ability to look at a whole in terms of its parts, and conversely, to think about parts in terms of how they relate to each other and to the whole. People are comfortable speaking of water systems, the interstate highway system, the solar system, the respiratory system, and so on. In general, an informal explanation of a system is a collection of things and processes that interact to perform some function. A more formal, scientific definition of a system would provide more precise attention to details concerning inputs, outputs, and their interactions among the various components. Systems are important in many aspects of the Mars mission, most obviously in designing the spaceship.

Change and Constancy

A great deal of science and mathematics (along with other domains) has to do with understanding how change happens in nature, as well as in social systems. Constancy, on the other hand, is also of intense study in science. In fact, the simplest account to be said of anything is that it does not change. Some of the greatest discoveries of science are the conservation laws in physics (such as for mass, momentum, or energy).

Descriptions, analysis, and control of change are essential components of understanding the world around us. Descriptions of change are important for predicting what will happen. The careful analysis of change is very important for understanding phenomena. The control of change is vital, for example, in the design of human technological systems. We are able to discern three general categories of patterns of change:

1. Changes that appear to be consistent trends
2. Changes that occur in regular duration or cycles (i.e., the seasons)
3. Changes that are either irregular or unpredictable (chaos)

Models

Models can be physical, mathematical, or conceptual. They are very effective tools for learning about the things they are intended to resemble. Physical models (such as model rockets) are the most obvious to children. Whether models are physical, mathematical, or conceptual, their usefulness as an instructional device lies in suggesting how things either do work or might work.

The most familiar model is the physical model. This can be an actual device or process that behaves enough like the real object being modeled that we can hope to learn something by manipulating it. For the most part, a physical model is easier to work with than what it represents because it is either smaller, less expensive, or is shorter in duration.

Conceptual models are ways in which we give unfamiliar things meaning by likening them to familiar things in the child's experience base. This is most commonly achieved through the use of metaphor or analogy. Like any model, a conceptual model may have only limited usefulness and because it is either too simple or too complex. At its worst, a conceptual model can mislead and reinforce misconceptions. When used with careful planning, a conceptual model can become a powerful teaching tool. According to researchers, the ability to recognize and use conceptual models correctly can assist students in solving novel problems.

Mathematical models are usually more abstract than physical or conceptual models. The connection of mathematics to the outside world could be made much stronger than it typically is for students if mathematics were taught as part of science, social studies, music, and other subjects, rather than just during "mathematics time." One of the major drawbacks of traditional curricula is that mathematics is treated as a separate subject before real-world problems are identified. In this manner, the related exercises have more to do with learning specific procedures than with solving interesting problems. We have attempted to integrate the mathematics throughout the unit. For example, we believe students gradually understood the usefulness of such phenomena as free fall expressed as v=gt (a mathematical model where v is speed, t is time, and g is a constant) when predicting the speed at which an object falls. In this case, the mathatical model implies that speed increases in proportion as time elapses.

Physical, conceptual, and mathematical models can be effectively used to increase students' understanding in Mission to Mars.

Scale

Most common variables that occur in natureÑ such as length, width, weight, and temperature, show a great amount of range in terms of magnitude. As students' thinking about numbers become more refined and their experiences broaden, they will encounter larger ratios and limits of these variables. While this is an adequate starting point for the idea of scale, it is incomplete and lacks depth.

The more sophisticated concept has to do with the effect of changes in scale. Specifically, the way things work may change with scale. Buildings, animals, and social structures cannot be made significntly larger without changes in their respective structures or behavior. For example, it is not possible to make a skyscraper from the same design and materials as a small office building because the skyscraper would collapse under its own weight. Properties that depend on volume (heat capacity, weight) change more readily than properties that depend on area (bone strength or surface area). This common theme explains why a substance dissolves more readily when finely ground than when lumped, why hot water cools off more slowly in a large container than in a small container, and why a large animal must have proportionally thicker legs than a smaller animal with the same shape. It is because of scale that one can understand why microorganisms can exchange substances directly through their surfaces while larger animals need more elaborate and highly evolved branched surfaces such as lungs, veins, or roots. The issue of scale is particularly important for understanding the solar system in the Mission to Mars.