Using variation theory to analyze what preschool children experience exemplified by wholes and parts as the object of learning

Preschool children's learning isthe subject of this study. Three children aged 4, 5 and 6 participated. The data consist of individual interviews with the children before and after the intervention and a videotaped intervention. Our results show that children seem to see a whole as something that is not cut into pieces, no matter what it looks like. They do not necessarily refer to the whole when they see a half, nor do they imagine the halves or quarters in a whole that is not cut into pieces. On the other hand, if they see halves they do not have any difficulty putting them together into a whole, but this happens when they can see the material in front of them. The results reveal some interesting findings, pointing at the natural flexibility small children have in discerning a half in relation to a whole instead of in relation to a representation (like a full circle). On the other hand -the children show difficulties in seeing what parts a whole can be divided into. This is the other way around, as children in higher grades with a view of the circle as the correct representation of a whole, which sometimes makes it hard to manage problem solving at higher grades where flexibility in how to understand proportions is needed.