Teach Primary Issue 18.7

fear. What if the exercise leads to nothing interesting? Is this burdening the children with too much? The secret here is to keep the starting points small and accessible. And by working regularly in this way, children gain confidence in their creativity and, over time, build more complexity into their solutions. Without such opportunities, children will always find creating difficult. Exploring to this depth also takes time. Stopping too early in the example exercise would have blunted their curiosity and devalued their creations. I hope that by giving pupils the power to explore, it will foster a productive disposition of curious and creative learners and develop their strategic competence (Fig. 3). I don’t have the authority to decide whether their work constitutes mathematical creations. However, I will keep telling children that they are. I think these pieces of work have aesthetic and emotional value – that they are worthy mathematical pursuits and that they are original. TP An element of doubt Throughout this exercise, there was genuine uncertainty among the children about how their findings would play out. Uncertainty is one of the most powerful motivators – writers use this when they lead readers to moments of tension. The children understood that they might not reach an answer, and they also knew that I was not going to give them one. For one thing, I didn’t know what it was, but it also didn’t matter to me. This world held value in the fact that it had been created by them. In navigating its paths, they were emotionally reacting with frustration, triumph and sometimes with surprise. If I had said at the end, “This is the answer!”, it would have been akin to me scrawling all over their artwork. Of course, the tension of uncertainty can also be felt by the teacher, and sometimes that can reach Cultivating a culture of creativity Changes in attitudes and actions won’t happen in a single lesson, but, rather over time. If you want to start this journey with the children in your class, here are some things to be mindful of along the way. • Use open-ended tasks and model their introduction and evolutions with ‘What if…?’ questions. There are plenty of sources for these: NRICH, ATM publications; and I share many on my website too. • When introducing open-ended tasks, keep the initial scope small. By doing this, you give the children room to expand on them through their own ‘What if…?’ questions. They might be more obvious ideas at the start, but over time their creativity will grow. • Name pathways and discoveries after the children. Empowerment like this will encourage them to value their own and others’ ideas. • Be brave and be prepared to head towards and maintain uncertainty. Rather than providing them with answers, ask them to justify their beliefs instead. • A few pathways explored deeply are more meaningful than ten explored superficially. Encourage a community that shares ideas and healthily questions each other rather than individual pursuits. • Provide them with time to explore. Their investment might lead to them choosing to carry on at break times or at home. Encourage this! It can be a great way to build in parental involvement in maths, too. • Explore maths tasks yourself in the same way to embrace and promote the culture shift. Figure 2. ‘Jessica’s simultaneous chains’ Figure 3. Intertwined strands of proficiency Jacob Merrill is a Year 4 teacher and a trustee for the Association of Teachers of Mathematics. He shares open-ended tasks on his website. islesofwhatif.com Adaptive reasoning Strategic competence Conceptual understanding Productive disposition Procedural fluency 50 | www.teachwire.net