Teaching Without Teaching

By Yong Caiwen

Once, at a parent-teacher conference, I met a pair of lovely parents who came well-prepared with a presentation of their little girl, Gigi's, mathematical prowess. They had brought along books with numbers and sums she had been practising to write. Then, Gigi was invited in to show me she could do 2+3 on her fingers and say it was 5. Gigi was enthusiastic about everything we did. She sang the loudest, watched intently at every lesson shown to her, and was always the first to volunteer for any task. Gigi's favourite activity was polishing colourful wooden puzzles and washing cloths and hanging them on a laundry line. On the shelves nearby were beautiful mathematical materials which Gigi's parents were desperate for her to use and were devastated that she repeatedly chose to polish and dust those maths materials rather than count them or use them to write 1+2=3. They felt that we should 'teach' her maths. We were somewhat perplexed, as everywhere we saw Gigi, she was doing 'maths'!

Maths education is unique when observed in the activities of young children. Firstly, because we often underestimate children's own activities as cute but pointless play. Secondly because we forget that 1+2=3 is an abstraction, an idea, and without concrete experience, 1+2=3 is memorised but means nothing to the child. Thirdly, because we seem to think maths acquisition is somehow less natural than language acquisition. Indeed, we are much more likely to grasp and develop maths skills by living and being in it, then by being taught it. Have you never met an individual who budgets, reads time and does his shopping perfectly well and stares stupefied at word problems? Gigi had absolute interest and aptitude in maths and was developing the necessary and severely underrated preparation skills for her to become the mathematician she showed so much promise of becoming. How?

Before the age of 6, children must experience the world concretely. They are collecting and organising in their minds stores of experiences with which they use to understand the world around them. Using real objects and playing concretely also helps develop desperately needed fine motor skills, which children are so lacking these days before they are being handed a pencil. Gigi was doing all that, in addition to practising and refining vital maths skills such as order, precision, understanding of size and quantity, as well as maths vocabulary.

Gigi was extremely orderly and precise in her activities. Things were returned to their places, she picked up after everyone else, straightened pencils and rulers so they were perfectly parallel or perpendicular to the edge of shelves. When she was first introduced to the concept of size, she spent large quantities of time arranging books in the basket from largest to smallest, smallest to largest. One day, someone left an empty basket out and she quickly hogged it to make a pile of rectangular books and a pile of square books.

Gigi was once shown how to cut some fruit and made sure each child had one (a very big-deal early years maths concept called one-to-one correspondence). Very soon, she began to organise and distribute large quantities of fruit according to the number of children wanting to eat them, and very bossily insisted they waited until everyone had the same quantity. This often involved her halving and quartering fruit till they were quite unrecognisable but she commanded such devotion and faith from her peers that when they were finally allotted their plate of fruit mush, all were in agreement about how fairly it was done.

As she demonstrated such interest in size, proportion and angles, we began to introduce relevant vocabulary to her, including 'large, larger, largest', 'perpendicular', 'parallel', 'half', 'quarter' and 'thirds'. Gigi was daily practising and developing her own mathematical understanding and skills to a degree beyond what an adult could 'teach' her.

It was important that Gigi was given space and time to develop and self-educate without our adult senses always looking for opportunities to 'teach' her. How rare is it to see young children choosing to independently involve themselves in deep learning? Deep learning can occur at this age only through experience with real objects and activities that look like play to us. Gigi was doing a mighty fine job of teaching herself and it was more likely that if we had interrupted her to show her what 'maths' she was doing, she would never pick to do it again. How many of us have stared at the many new pieces of technology on display these days wanting to experience it for ourselves, and quickly losing interest and put our hands in our pocket when someone comes and tries to give us a 'demo'?

All human beings old and young, have innate tendencies, given the right challenge, to problem-solve, to orientate themselves and to figure things out in the world. It is easier to preserve this natural instinct then to recover or try and 'teach' it when we have lost it. How can we do that at home?

  • Play with your child without taking over their play. Come on, you've had your turn about 30 years ago. Go find your own blocks to build skyscrapers with.

  • Enrich your child's maths vocabulary by using precise language to describe things. It's not just a ball-shape, it's a sphere! Cool words don't need to remain in the realm of adult life.

  • Be a model: possibly the hardest of all, but your young child doesn't do what you say. They love you! And they do what you do. So if you want to encourage good number writing, eg. try writing numbered shopping lists on a piece of paper instead of tapping them on your phone or plucking them out of your mind as you stroll through the aisles. Pay and count with cash instead of a card when they are around.

  • Help your child make choices and understand quantity and size, for example by letting them decide how much they want to eat. One chicken wing or two? Eat with a tablespoon or a teaspoon?

  • Give them your spare change and have them be responsible for bringing a coin to the supermarket for unlocking the trolley. With the new currency, you can now discuss how the same 'money' can have different sizes! (thus introducing value)

  • Too many 'kums' for Chinese New Year? Make the first piercing but let them peel off the rest and decide how to share out the sections!


Yong Caiwen is a qualified 3-6 AMI directress and a trained teacher of Specific Learning Difficulties (SpLD). She was educated at the National University of Singapore (NUS), the Dyslexia Association of Singapore (DAS) and the Maria Montessori Institute in London. Caiwen has been teaching for 10 years and has taught at DAS, Katong School APSN, Manchester Grammar School, Montessori Children's Houses in London, and currently at Limespring School in Finchley, also in London. She is a mother of a 2 month old Violet, and is enthusiastic about human development and parental role / involvement in education. She is a practising RIE and Montessori mum.



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