Teaching for the learning of additive part-whole relations. The power of variation and connections

The purpose of the study is to create a deeper understanding of the teaching methods that best promote children’s learning of part-whole relationships between numbers (for example, that the number 7 can be divided into 5 and 2), which in turn makes it easier for them to learn addition and subtraction. The study focuses on how mathematical ideas and principles are highlighted in teaching. The research question was: What can constitute a structural approach to teaching and learning the additive part-whole relations of numbers which promotes the learning of children and young pupils?

The analysis shows that teachers who illustrated mathematical ideas using several examples promoted children’s abilities to understand part-whole relationships in arithmetic. The examples that teachers gave were also important. Learning that highlighted the relationships between different examples, both verbally and with gestures, produced high learning outcomes. Teaching where teachers explicitly made children aware of mathematical ideas and principles also provided children with good opportunities to learn additive part-whole relationships

The study has used results from four previous empirical studies that focus on how teachers can implement part-whole activities in order to promote kindergarten children’s numeracy skills and has carried out a new analysis of these. The empirical material consists of 98 video recorded teaching sessions at a primary school in South Africa and a kindergarten in Sweden. In addition, the study uses 16 individual observations where children solve arithmetic tasks both before and after the teaching programme. The data was analysed from a variation theory perspective in order to describe differences in teaching. 

Ekdahl, A-L., Kempe, U. R., Venkat, H., Björklund, C., & Benz, C. (2019). “Teaching for the learning of additive part-whole relations. The power of variation and connections”. Akademisk avhandling. Jönköping University.