ABSTRACT
There was a great loss to society when Christopher Zeeman (1925–2016) died. He was a pioneering mathematician famous for several texts including Catastrophe Theory (1977) and Gyroscopes and Boomerangs (1989). He also saw the value of play in learning mathematics and suggested that one of the better ways to engage children was to find something playful in it and then play! Zeeman also saw mathematics as both an art and a science, because sometimes you invent it and at others you discover it. He suggested, “you have to invent maths to get a solution to a problem but, in the process, I often discover a whole lot more which I didn’t expect” (Arnot, 2005, pp. 20–21). Haylock (2010, p. 16) also sees mathematics as a creative endeavour in which “flexibility and imaginative thinking can lead to interesting outcomes or fresh avenues to explore for the curious mind”. But such flexible, creative and investigative approaches to mathematics take time, and Askew (2012) challenges the orthodoxy of the packaging of mathematical learning into a lesson. He suggests leaving problems unresolved at the end of a lesson and returning to them the following day is beneficial for learning. We would suggest that incubation and pondering time are valuable, and these approaches, while ‘messy’ for some teachers, actually enrich the dialogue between teacher and learner, and perhaps between child and parent, as children have the opportunity to take intriguing problems home with them to share with the family. Therefore, a significant way to develop mathematical reasoning is to create time for it and thereby free the constraints that were mentioned in Chapter 2. Being playful, creative and discovering new ideas takes time, but what a significant investment.
