Why Do We Teach Technically “Wrong” Things?

When teaching students, especially in the early stages of their education, it’s common to simplify complex ideas or teach models that are, in some ways, technically “wrong.” (In mathematics, we might say that something isn’t “rigorous”.) This may seem counterintuitive at first—after all, shouldn’t we strive to teach the “truth” from the start? However, I think there are compelling reasons why educators rely on imperfect models and simplified concepts in their teaching.

models that are fit for purpose

One key reason is the need for developmentally appropriate models. These simplified versions of complex concepts are easier for students to grasp, especially when they are still developing their cognitive skills. While these models may not be entirely accurate, they provide a foundation that can be revised (or “broken”) later as the student advances and is ready to tackle more nuanced understandings of the world.

Examples of Simplified Models:

• Subtraction: for younger students, subtraction is about “taking away” – we start with a number of concrete objects and then we remove some of them, then ask students how many remain. It’s a bit nonsensical in that context to talk about removing 5 objects when you only have 3 to begin with, so subtraction is initially taught without introducing negative numbers. The idea that you “can’t subtract a larger number from a smaller one” is later revised when students learn about negative numbers and broader number systems.
• The Atomic Nucleus: in science, the atom is often depicted as a simple nucleus with electrons orbiting it, much like planets around the sun. This model is later revised to incorporate quantum mechanics and the probabilistic nature of each electron’s behaviour.

These models may be technically incorrect, but they serve as an essential bridge to more accurate scientific and mathematical understanding. As students mature, they can refine and update their mental models to accommodate more sophisticated ideas.

Imperfect Models Are Still Useful

For the vast majority of learners—those who won’t specialise in advanced scientific or mathematical fields—these simplified models may be all they need to navigate everyday life. I feel as though 90-95% of students won’t pursue careers that require a deep understanding of these subjects, so teaching them perfectly accurate models from the start may not always be practical.

The quote from George Box, “All models are wrong, but some are useful,” encapsulates this idea well. Box was highlighting that even though models are simplifications of reality, they can still provide valuable insights and serve practical purposes. For most people, an imperfect model offers enough accuracy and intuition to make sense of the world and solve everyday problems. Here are some well-known examples of imperfect but nonetheless useful models:

• Newtonian Physics: High school students often learn about the laws of motion and gravity using Newton’s equations. While these are technically inaccurate at relativistic speeds or quantum scales, they work fine for most real-world applications, such as predicting the motion of everyday objects.
• Resistive Fluids: In many physics problems, students are asked to ignore air resistance or friction when calculating motion. For instance, when calculating the trajectory of a projectile, the effect of air resistance is often omitted, even though it’s crucial in real-world scenarios like baseball or car racing.
• Ideal Gas Law: The equation PV = nRT is a simplified model of how gases behave. It ignores interactions between gas molecules, but it provides a useful approximation for most common situations, like understanding the behaviour of air in a balloon.
• Linear Equations in Economics: In economics, linear models are used to predict relationships between variables, even though real-world systems are often far more complex. These models are useful for basic predictions and decision-making but don’t capture the full complexity of economic interactions.

By ignoring complicating factors, students can focus on mastering the basic principles (very helpful from a cognitive load theory point of view). As their understanding deepens, they can gradually reintroduce these elements to form a more complete picture of the phenomena being studied.

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Conclusion: The Role of Simplified Models in Education

While teaching “imperfect” models might seem counterproductive at first, these simplified frameworks play a crucial role in education. They provide an initial foundation on which students can build a more accurate understanding of the world. For most people, these models are useful and practical, enabling them to make sense of the world in an accessible and manageable way.

As students grow and learn, these simplified models are revisited, challenged, and refined, just as scientific theories themselves evolve. In the end, these early approximations help make complex ideas approachable while still providing enough accuracy to be useful for most practical applications.