Teaching abstract concepts

Regardless of the disciplines we teach, we often need to help students understand difficult concepts. More often than not, these concepts are those for which there is no physical referent, or for which the physical referents are outside of, or contrary to, normal experience. We call these concepts abstract. Teaching abstract concepts can be one of the greatest challenges in the classroom because understanding abstract concepts requires a level of student thinking that goes beyond thinking about the here and now. Abstract concepts can be found in all areas of study. They include examples such as time, nation, gender, class, love and relativity.

Research has shown that one of the best ways to teach abstract concepts is to make some connection with a concrete example in the real world. In other words, provide visual illustrations and physical demonstrations of course-related material whenever possible. Students get the most out of instruction that combines visual information and verbal information. So, show pictures, sketches, schematics, plots and charts while discussing abstract concepts. Consider physical models and computer simulations of your course content whenever you can. Some of the most useful suggestions are:

• Visuals (pictures, infographics, charts, graphs);

• Models (diagrams, physical, 3-D);

• Demonstrations;

• Simulations (games, scenarios, cases);

• Analogies and metaphors;

• Threshold concepts and concept maps.

This may take some creativity, but there are many excellent examples out there. For instance, in the field of astronomy, there is a tried-and-true technique for teaching about general relativity — Einstein’s monumental work on gravity. The key concept is that what we perceive as the force of gravity actually arises from the curvature of space and time. How can you get that idea across? One method is to use a thin rubber sheet to represent space-time. Then place heavy objects — metal spheres for example — onto the sheet. The spheres cause the sheet to be stretched and curved in a way analogous to the bending of space-time around stars and planets. Such a demonstration can be a powerful way to get this complex idea across, and can be used to explain the orbital dynamics of the planets and their moons.

Another example can be taken from philosophy. Plato uses the allegory of the cave to explain the human condition, and how education can be transformative in our understanding of our existence. Plato relates the story of a group of people who have lived chained to the wall of a cave all of their lives, facing a blank wall. The people watch shadows projected on the wall from objects passing in front of a fire behind them. The shadows are the people’s reality. Plato compares the philosopher to one of these people who has escaped from the cave and comes to understand that the shadows are not reality at all. He comes to know the true nature of existence.

However, the people in the cave reject what he has to say. They do not understand what he is telling them, because they know no other experience.

Of course, all such models have their limitations. Space-time is not a two-dimensional sheet, but that does not mean the model is not useful. We must be very clear in explaining to students what aspects of the model are instructive, and which are misleading. We make these kinds of distinctions all the time. The Earth is not flat, but that has not stopped us from successfully using maps as models for centuries. We just have to be clear about the limitations of our examples. You can combine different models — with different limitations — to explain the same abstract concept.

It is important to choose models, diagrams and analogies carefully. One of the things that makes teaching abstract concepts so difficult is that we do not want to introduce new misconceptions to our students. So when designing your lessons, keep the following caveats in mind:

• Make sure that students understand the model you introduce. What is correct and what is not?

• Don’t choose physical representations that make it difficult to clearly grasp the connections between the model and the abstract concept because the model is overly complicated or is too far removed from the concept.

• Always consider “expert blindness,” the fact that connections are clear to you, but not the students.

• Avoid models/examples that explain the abstract concept in part, but lead to other serious misconceptions (the model is a “lie,” and you fail to explain this).

If you have some abstract concepts in your courses that students are struggling to grasp, remember that the Teaching Center can help; we even offer workshops on teaching abstract concepts. Call on us to help you make teaching abstract concepts an effective part of your instructional strategy.

John G. Radzilowicz is a teaching and learning consultant for the University Center for Teaching and Learning.