Variation theory

Using both positive and negative examples in teaching

Hey 👋

Welcome to May, the dawn of spring or autumn (depending on where you’re reading this). Today, we build on our topic of examples with variation theory

Big idea 🍉

Variation theory can be a potent approach to building understanding in the classroom. But many teachers have never even heard of it. Here's what variation is and how to use it:

First up, examples are powerful tools for helping students grasp abstract or technical concepts—ideas that are difficult to convey through words alone, such as proportion, power, or prefixes.

The examples we choose and the variation between them has a big impact on the precision and transferability of the resulting understanding. When we provide multiple examples that highlight critical and non-critical features, we draw attention to the defining aspects of a concept, sharpening student understanding. This is the basis of 'variation theory'.

"Learning is a function of discernment and discernment is a function of variation."

— Ference Marton

One of the key premises of variation theory is that students benefit from not only from seeing examples of a concept, but also from examples that are not the concept. These are called negative or non-examples.

Negative examples help students refine their understanding of the boundary conditions of a concept—such as how far we can change a triangle before it stops being a triangle—and guard against overgeneralisation.

For example, based on their experience, students can sometimes assume that all living things ‘move’, and develop the misconception that plants are not alive. Providing a range of examples of living and non-living things, some of which move and do not—while drawing attention to the critical features of living things—can help students develop a more accurate picture.

Note that when using negative examples, it's important to be alive to the risk of seeding misconceptions (which can happen as a result of the mere exposure effect). We can mitigate this risk by:

  • Providing positive examples before introducing negative examples.

  • Show as few negative examples as required to make the point.

  • Prioritise building understanding around critical features.

Finally, a reminder that variation is not appropriate for all concepts. It can be time consuming (for both teachers and students) and so should be deployed only where it adds value, and even then: executed efficiently.

Challenge → Do you use negative examples in your teaching? Consider a concept your students struggle with, add a few negative examples the next time you explain it, and see how it goes.

Summary

• Providing multiple examples can help build student understanding around abstract or technical concepts.

• By providing negative examples as well as positive examples, we help students refine their understanding and reduce overgeneralisation.

• It’s best to introduce positive examples before negative examples, and be sparing in our use of negative examples.

Little links 🥕

May the forth be with you.

Peps 👊

PS. A few folks have asked recently about the rationale and plan for Snacks—help me decide whether to include something on this in a future email ⤵️

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