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And no, you don’t need a PhD in mathematics to teach it. In a compelling YouTube presentation and interview with The Atlantic, parent, curriculum developer, and mathematics education consultant Dr Maria Droujkova makes the case for embracing natural maths.
“Mathematics can be beautiful, meaningful and fun; and mathematics can be what you make of it,” she says. The key to natural maths is to remain open – “better is different,” she insists. There are thousands of ways to cook dinner, and as many to reach mastery in maths – open maths is like a “recipe, a folk tale, or an internet meme: diverse people remix it in diverse ways”.
But isn’t calculus too complex for a five year old? After all, children in Singapore normally don’t encounter concepts such as algebra until late primary school, and differentiation and integration until secondary school.
Dr Droujkova emphasises the distinction between the complexity of an idea, versus the difficulty of doing it. Some tasks are simple, but hard – memorising multiplication tables, for example – and other activities can be complicated, but easy – think about creating LEGO structures or folding origami, for example.
She suggests focusing on what she calls “easy complexity”. “Tell stories, make art, and find analogies that make your maths friendly. Gently grow your happy familiarity with complex ideas. Make maths easy enough for open play and complex enough for advanced mastery,” she says.
Children love to play with limits and infinity – explore these ideas by making snowflakes or fractal trees. Slice some fruit to link 2D shapes to 3D solids, and to explore the concepts of differentiation and integration. For more ideas, check out Moebius Noodles, written by Yelena McManamanl, Dr Maria Droujkova and Ever Salazar, which contains a slew of fun methods to encourage your child to think more mathematically.
Other books to provide inspiration include Introductory Calculus For Infants by Omi M Inouye, which provides a gentle introduction to the subject through a delightful storybook adventure of two friends as they explore the wonders of calculus.
Or check out Calculus by and for Young People (Ages 7, Yes 7 and Up) by Donald Cohen. Cohen suggests using the classic cookie sharing problem to explore concepts such as limits, infinities and series – try dividing six cookies fairly among seven people, without cutting each cookie into sevenths. If you’re curious to know the answer, it’s here.
Don’t forget your job as a parent is less of an instructor than a cheerleader. Provide general support – “How interesting! Let’s explore more! – and don’t be afraid to admit you don’t know the answer either (say “Hmm. Shall we find out together? or “Let me investigate and get back to you.”)
Most of all, keep it light-hearted and low pressure. Have fun!