What is variation theory?
Variation theory draws close attention to the similarities and differences between mathematical concepts. It allows children to critically evaluate what is the same and what is different by focusing on key elements.
To illustrate, I want you to think of a bee.
1. You probabaly have visualised a small yellow and black insect.
2. But this concept of a bee may be overly simplistic.
3. There are a wide variety of different types of bees so the concept of a bee can be varied. Drawing attention to "what is the same, what is different" would open the concept up to the essential features of a bee such as: insect, wings, lives in a colony.
4. Here we can draw further example to non-examples of bees - when is a bee not a bee? When it's a wasp.
This would allow children to explore the essential features of what makes a bee a bee.
How this links to mathematics.
5. Consider what makes 1/2 a half. What are the essential features that make 1/2 a 1/2?
Here we may draw children's attention towards the essential elements of what 1/2 is: 2 equal parts of a whole.
Seeing 1/2 in different orientations varies the concept.
6. Extending this further with a non-example can allow for deeper exploration of the concept.