Ideal World Versus Real World in Teaching

Across school subjects, educators often use “ideal world” models to explain how various concepts relate to one other — speed, distance, and time, in one familiar example. When students realize that a simplified equation or model doesn't match up to the "real world," they may question the value of learning it. Professor Catherine Elgin offers a perspective that can help teachers demonstrate how "ideal world" models advance our understanding of complex phenomena.

In a high school science class, the teacher asks students to predict the path of falling objects, using equations that assume there is no air resistance. In a college economics course, students examine market behavior assuming that buyers and sellers are always well informed and act rationally. Some students might wonder whether such unrealistic, faulty assumptions discredit predictions about falling objects and the price of a pound of butter. What is an educator to do when students become skeptical of drawing conclusions from the “ideal world,” because it doesn’t match the “real world?” How can the educator make the “ideal world” more relevant and significant for the learner?

Elgin helps to resolve this issue by clarifying why we use the “ideal world” so often in learning contexts. She argues that even though these “ideal world” models are false descriptions, strictly speaking, they do help us reach a better understanding of the phenomena they describe. For example, consider the ideal gas law, typically introduced in high school chemistry classes. The equation PV=nRT refers to the behavior of a gas whose molecules are dimensionless and spherical, not subject to friction, and not attracted or repelled by one another.

No actual gas exhibits these properties — molecules are always subject to friction and other distorting forces — but all is not lost. Even with these flaws, the equation has value for understanding the relationship among pressure, volume, and temperature. Ideal gas is a fiction, but the equation is designed to highlight subtle and obscure facts about the behavior of gases. It would be difficult to discern exactly how pressure and temperature relate in the “real world,” since other factors complicate the relationship. The simplified equation gives its user access to matters of fact that are otherwise difficult to see.

Even in the non-academic arena, we often use and learn from models that are not entirely based on truth. At a home improvement store, we might compare paint samples to choose a new color for our kitchen walls. The small rectangles of color are not exactly paint samples: they are produced using printed ink, not paint. The samples are designed to highlight the color of the paint, but not their texture, smell, acidity, or other properties. The rectangles refer to and therefore exemplify the color of the paint. By fulfilling that function, the samples give us access to information of interest.

Scientists use simplified models to make advances in theory, and economists use models to predict probable market outcomes. Though these equations may be enhanced, relative to the high school versions, they still simplify the world. This is not problematic, since it is the theories behind the laws that need to account for the facts — the idealizations, or equations, do not need to be perfect and complete to be useful. Paint samples are pretty good at illuminating the color inside paint cans, and PV=nRT is a good estimation of the status of a gas. We only need to reject a model and its predictions if the theory behind it is overthrown in light of new evidence.

It is the theories that we need to test and reassess — the equations basically come along for the ride. By giving us access to abstract and otherwise complicated relationships, “ideal world” models help students understand complex relationships, and help scientists further theorize about the way things really are.

This article is based on Catherine Elgin (2007), “Understanding and the facts,” in Philosophical Studies, 132, 1, 33-42.