Teach Primary Issue 18.7

A rtworks crafted by pupils can evoke a sense of beauty. In fact, all kinds of emotional reactions can be expressed when children bring home something they have created; it forms part of their value. Likewise, mathematics possesses its own form of beauty. But can children create this themselves? To some people, the idea of a mathematical creation alone is unimaginable – let alone a beautiful one. We can show children examples like the Fibonacci sequence in sunflowers. We can enthusiastically say, “This is maths! Isn’t it beautiful?” But is it the children’s maths? There is the sense of determination and accomplishment in finding a route to a mathematical solution, but it is still a predetermined destination. It’s harder to envisage the originality and ownership a painting can have existing in maths. A grand tour By achieving conceptual understanding, children can tour new mathematical worlds. But are they only seeing points of interest – like a slideshow? Going beyond being a maths tourist requires creating new pathways, which can seem daunting. Francis Su ( tinyurl.com/tp-Su ) , argues that you don’t need to be an advanced mathematician to imagine these. He believes that something as simple as a date can be explored mathematically through Crafting your questions By keeping the initial scope small, the children had room for their own creations. Each was named after the poser. One memorable example was ‘Jessica’s simultaneous chains’ (shown in Figure 2). Jessica asked: What if we have two circular chains? What if, in the second chain, the same number cannot be in the same position as the first chain? When she came up with this idea, I felt confident in saying that no-one else in history had contemplated it before. It was an original creation. Pupils quickly became invested in the problem, sharing new findings excitedly. We extended and explored how many simultaneous chains were possible. There was exhilaration and pride upon making discoveries. At one point, a child asked if he could use powers of ten beyond 1000. He stated that it was ‘a cheat code’ and his cheeky grin suggested that he thought his creation had an element of naughtiness. It was amusing to him – an emotion attributed to his creation. Believe it or not, maths can be beautiful, says Jacob Merrill But is it ART? Understanding of what constitutes a meaningful question occurs over time, with experience and with the right inspiration. For example, in one lesson, I presented the children with the first diagram in Figure 1, and introduced the following ‘What if…?’ questions: What if we multiply and divide by 10, 100 and 1000 to complete “There was exhilaration and pride upon making discoveries” Figure 1. Creating from a ‘What if...?’ question posing questions and creating fanciful properties. With a similar mindset, I’d like to suggest how mathematical worlds can be created that evoke emotional responses. Crafting your questions I present and alter tasks in the form of ‘What if…?’ questions. By modelling such questions to children, they begin to do the same and create their own mathematical worlds. the circular chain? What if each number along the chain has to be different? The task had multiple solutions – the second part of Figure 1 shows one example. These solutions became the subject of creations for pupils. Once they had explored the problem, they sought to imagine: What if we have five, six or seven numbers in the chain? What if we cannot use the same operation twice? What if we cannot use the inverse of an operation? T EACH PR I MARY MATHS SPEC I A L I N AS SOC I A T I ON W I TH www.teachwire.net | 49