# Calculus: The Playful Mathematics Revolution

My memories of elementary school mathematics are divided into two opposing camps. On the one hand there’s the lingering nightmarish image of endless rows of sums, multiplication tables and tests, and even now – twenty-two years later – the recollection fills me with dread.

But then there are the other memories: connecting dots and building with blocks, pattern-making, board games and flash card competitions. These are the moments in my mathematical education which I recall most fondly, the moments which not only added to my knowledge but increased my love of the subject itself, and therefore my desire to learn more.

For decades the standard in early mathematical learning has been worksheets and repetition, with a focus on learning basic arithmetic – addition, multiplication, etc. – before moving on to more complex ideas in secondary school. But lately there have been suggestions from a number of quarters that this regime needs to be overthrown. It’s not that algebra and calculus are too advanced for children, experts say; it’s that we don’t employ the correct methods for teaching them.

Maria Droujkova, a curriculum developer and math education consultant, says the current model of mathematical education focuses on teaching simple ideas the hard way rather than teaching complex ideas the easy way.

According to The Atlantic‘s feature on Droujkova, teaching young children basics like arithmetic from the beginning not only misses the point – instilling an idea that math is about manipulating simple numbers rather than the recognition and creation of patterns – but even worse, turns children off mathematics with never-ending exercises akin to punishment or torture. The example given is that of memorising multiplication tables, which echoes military punishments involving repetitive and often pointless tasks (e.g. digging a trench with a spoon).

Droujkova – and many other academics – suggest that the best way to teach children mathematical ideas (whether simple or complex) is through play. Play allows children to integrate understanding, connect experiences, explore possibilities and solve problems. It also lets them engage their natural curiosity and take control of their own learning. As a social activity, play provides a context in which children can share knowledge and figure out patterns together.

Even with all its social and educational benefits, it seems a stretch to declare that simply playing games is enough to teach children “advanced” mathematics. But Droujkova’s aim isn’t to have five year-olds solving complex equations: it’s to provide a broad informal foundation upon which an understanding of more difficult ideas can be built. First come the fundamentals – skills like logical thinking and pattern making – then the identification and dissection of patterns, and then, finally the grasping of more abstract ideas.

So where’s the room for the teacher in all this self-guided independent learning? According to the National Association for the Education of Young Children (NAEYC), play alone is not enough to guarantee mathematical learning – the direction of an educator is necessary for reflection and context. Teachers can enhance learning by asking provoking follow-up questions that clarify and extend understanding.

Examples of effective mathematical play:

• Building with blocks or Lego
• Origami
• Snowflake cutouts
• Computer games
• Board and card games
• Drama, music and art

Nick Nedeljkovic is a freelance writer and blogger from Sydney. With a love of learning and more degrees than he can afford, he’s a passionate advocate for education in all its forms.