Teachers’ sound mathematical content knowledge + play

Hayes (2000) states that "to optimise the potential for the development of concepts emerging through play, teachers also need sound content knowledge of [mathematical] concepts... in order to address the 'what' in teaching" (p.99). In other words, simply allowing children to play and trusting that that mathematical concepts will arise as a result of children engaging in play is not enough. This is because it does not guarantee that children will develop coherent and systematic understandings and appreciation of these mathematical concepts. Teachers need to know mathematical concepts well in order to first, recognise mathematics learning opportunities created through children's play and second, scaffold children's mathematical knowledge construction. So, what kind of mathematical thinking can be created in play situations? Hayes (2000) suggests a few examples:

Geometric thinking – e.g. when children contemplate ideas about space, or space, and how children themselves fit into a space
Algebraic thinking – e.g. when children recognise or make patterns and discuss relationships between objects
Statistical thinking – e.g. when children sort objects into categories and discuss how many Numerical thinking – e.g. when children count objects such as the number of candles on their birthday cake
Measurement thinking – e.g. when children compare their height or size of objects

Furthermore, as teachers we should be constantly improving our own understanding of mathematical content knowledge in order to know how to further children's mathematical learning.