“If you can count to ten you can count to infinity really”: fostering conceptual mathematical thinking in the first year of primary school

Abstract

In this paper we investigate how teachers can foster conceptual mathematical thinking in five- and six-year-old pupils in a classroom situation. In this context we define conceptual mathematical thinking as instances where pupils verbalise mathematical thinking linked to abstraction and generalisation. We focus on one case study to explore the impact of teachers’ epistemology of mathematics in introducing two sociomathematical norms in the classroom: what counts as a mathematical answer and how such an answer is incorporated in the mathematical discourse of the teacher and pupils in the classroom. We then link the introduction of these sociomathematical norms to the presence of instances of conceptual mathematical thinking as observed in the classroom. We conclude that pupils are more consistently engaged in conceptual mathematical thinking in the classrooms of teachers who view mathematics as a web of interconnected ideas, and perceive it as being about general structure and patterns.

Keywords:

• primary mathematics
• teachers’ beliefs
• sociomathematical norms

Acknowledgements

We would like to thank the Economic and Social Research Council in the UK for their financial support of the study from which this paper draws (RES-000-22-0851). We would also like to thank all the teachers and the pupils who took part in our study. They very kindly gave up valuable time during their already busy lives to make the study possible.