Preschoolers’ different ways of structuring part‑part‑whole relations with finger patterns when solving an arithmetic task

The study investigates the strategies five to six-year-old children use when solving an arithmetic task with an unknown part. The goal is to gain a deeper understanding of how children structure the relationships between parts and the whole of the numbers (part-part-whole-relationship). The researchers are particularly interested in the different ways children structure the task and how the different methods they use are suitable for understanding and handling such tasks. The research questions are: 1) In what ways do children structure a task with an unknown part? 2) What constitutes the ability to solve the task in a structurally good way?

The results show that some of the ways in which the children structured the arithmetic task were more fruitful for future learning than others. This was especially true of the methods that made it easier for the child to experience parts and the whole of the numbers at the same time. The researchers suggest three aspects that children should master in order to structure such tasks successfully: 1) Understand what makes up the whole. 2) Understand what makes up the parts of the whole. 3) Use finger counting to show how many elements make up the whole (cardinal number). The researchers believe the results of the study can be used to explain why some children develop robust arithmetic strategies and how to support children in solving arithmetic tasks.

The data material consists of interviews with 28 Swedish children who, during their final year in kindergarten, learned structured ways of solving arithmetic tasks. In the interviews, the children were asked to solve this task: “You have three glasses, but you need to set the table for eight people. How many more glasses do you need?”.

Kullberg, A. & Björklund, C. (2020). “Preschoolers’ different ways of structuring part‑part‑whole relations with finger patterns when solving an arithmetic task”. ZDM - Mathematics Education, 52(2020):767–778.