What is it Possible to Learn? On Variation as a Necessary Condition for Learning

Author: Ulla Runesson

Year: 2007

Paper Description

The purpose of the article is to explain the theory of variation and how it can be used to understand learning. The article uses the example of a 10-year-old girl named Ellen learning about graphs to illustrate the key concepts of variation theory.

Key Takeaway 1

Learning is about discerning aspects of the world. We do this by experiencing variation and invariance. The author argues that learning is not about accumulating knowledge, but about developing the ability to discern aspects of the world. This is done by experiencing variation and invariance.

Key Takeaway 2

The more aspects of the learning situation that a student is aware of and can consider simultaneously, the more their understanding of the relationship between their actions and the graphical representation of those actions will change.

Standout Quote

“Aspects can be related in different ways, as part or whole, or as figure or ground.”


ariation theory, variation, pedagogy, mathematics, task design, technology