Great teachers simplify before they complicate

When students encounter a difficult problem, their first instinct is often to tackle it all at once. They want to account for every variable, every possibility and every complication from the beginning. In engineering, that approach usually leads to frustration. The problem becomes so complex that it is difficult to know where to start, what matters most and whether the solution makes sense.

One of the most important lessons I have learned as both an engineer and an educator is that experts approach problems differently. They simplify first.

We often assume expertise means being able to handle complexity. In reality, expertise can mean knowing how to identify the fundamental principles underneath it. Whether I am teaching engineering students, working on a real-world design challenge or reflecting on my own professional experiences, I find myself returning to the same idea: meaningful learning happens when students understand how experts think, not just what experts know. 

Applying lessons from industry in the classroom

I worked in industry for many years before returning to higher education. At Michelin’s internal design school, employees from across the company learned the fundamentals of tyre design. Some had graduated from university only months earlier, while other participants had spent decades working in manufacturing plants or testing facilities or in other technical roles.

What surprised me was how universal effective teaching proved to be. Regardless of their background or experience level, learners benefited most when complex ideas were broken into manageable pieces. Before discussing sophisticated design challenges, we started with principles. Before exploring advanced applications, we established a solid foundation. The most successful learners were rarely those who memorised the most information; they were the ones who learned how to approach unfamiliar problems systematically.

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The same lesson applies in higher education. Too often, we assume that rigour means making problems more difficult. But rigour is not the same thing as complexity. Students can spend hours wrestling with a complicated problem and learn very little if they do not understand the underlying concepts. Conversely, a simple model can reveal profound insights when students understand why it works.

In my own classes, I encourage students to start with the simplest version of a problem they can imagine. What assumptions can reasonably be made? Which variables matter most? What can be temporarily set aside? Once they have developed a meaningful result, we can gradually add complexity and refine the model.

This process mirrors how professionals work in the real world. Engineers rarely start with a perfect representation of reality. Instead, they test an initial model, learn from it and build on it. The ability to simplify a problem without losing its essential features is one of the most valuable skills students can develop.

Harnessing real-world examples

That is why I believe authentic examples are so important in teaching. When students work only with textbook problems, they sometimes assume that every challenge arrives neatly defined, with all the necessary information readily available. Real-world problems are rarely so accommodating. They involve uncertainty, incomplete information and competing priorities. Students must decide which details matter, which assumptions are reasonable and how to move forward despite ambiguity.

By introducing real-world examples, educators can help students practise these forms of judgement while still benefiting from the structure and support of the classroom. For example, I have a collection of automotive and machine components that become hands-on models in class.

Importantly, this approach is not limited to engineering. Historians, business professors, scientists, artists and healthcare educators all help students navigate complex questions. Across disciplines, experts distinguish themselves not because they know every answer but because they know how to frame a problem, identify what matters and proceed thoughtfully. Teaching should make that process visible.

Honing lectures and teaching approaches for insights

One of the most influential teachers in my own education had an extraordinary ability to reduce seemingly impossible problems to their fundamental elements. He would step back, make a few simplifying assumptions and reveal a path forward that suddenly seemed obvious. The lesson stayed with me long after I left his classroom.

Today, I try to model that same way of thinking for my students. That means continually refining my lectures, revising examples and asking myself how I can explain a concept more clearly. It means showing students not only the final answer but the reasoning behind it. And it means remembering that teaching is not simply about delivering information. Students can read information on their own.

What they need from us is insight. They need to see how experienced professionals approach uncertainty, solve problems and make decisions. They need to understand not just the theory behind the practice but the practice behind the theory.

If we want students to become better problem-solvers, we should spend less time asking them to tackle increasingly complicated problems and more time helping them think like experts. The goal of higher education is not simply to produce graduates who can apply knowledge. It is to develop graduates who can navigate complexity with confidence, judgement and clarity.

And that begins by teaching them.

Jeff Warfford is a collegiate associate professor in mechanical engineering in the College of Engineering at Virginia Tech.