October 9, 2012
Please take a number
How do you teach math to someone who treats numbers as a snack?
This question was on my mind as my 15-month-old son chewed on a foam “7” in a spacious room at the Waterloo Public Library. Abe and I were one of about 20 other adult-child pairs attending a LittleCounters™ workshop run by Donna Kotsopoulos and Joanne Lee. This program is designed to help parents learn how to give their kids command over foundational numeric principles.
We were each given a bag containing toy fish, scarves, plastic bowls, cloth bags, and so on – objects much like the trip hazards scattered across my own living room. This is not a coincidence – Lee and Kostopoulos are trying to bring math into the home using items and activities that are already familiar to parents.
“People balk because they think we’re doing formal teaching,” Lee says. “It’s about integrating numbers into what you’re already doing.”
The class was a blast – 20 kids playing, singing, dancing and counting with their parents. Lee, Kotsopoulos and their team of grad students were equally charmed and charming with the kids. A fish went in a bowl. Two fish in another. Coloured scarves flew up in the air – one, then two, then three. It was fun. And it was math.
I was glad that I had had a number of conversations with Lee and Kotsopoulos before this workshop, as they take a very different tone when they are in researcher mode. Both betray a sense of urgency when they speak about math skills.
“We have to talk about numbers the way we talk about nouns,” Lee told me. “Children with a head start on math maintain that advantage throughout school.”
That head start can happen with kids at Abe’s developmental stage – 12 to 24 months. His rapidly changing brain has windows of opportunity sometimes called “sensitive learning periods” during which he is particularly receptive to acquiring certain skills. There are different periods for language, social skills, gross and fine motor skills and so on.
Many learning disorders are associated with sensitive learning periods happening too early or too late, not lasting long enough, or lasting too long.
Researchers and parents both often place great emphasis on capitalizing on linguistic critical periods, but think less about mathematics. Nobody disputes the value of literacy, but Kotsopoulos and Lee are on something of a mission to encourage parents to treat number skills – numeracy – with equivalent importance.
The material they teach is not shocking. They offer advice such as:
- Establish the basics of counting using numbers no larger than three – that’s sufficient and manageable for young toddlers.
- When counting, say each number, point at objects, and show the number with your fingers.
- Don’t just count to three and leave it at that – establish the principle of cardinality by repeating the total: “One, two, three … there are three fish in the bowl.”(Kotsopoulos has told me stories of kids who can count to a hundred, but have no idea what the numbers mean – it’s as though they’re just reciting sounds.)
- Let a child master counting up before introducing concepts like counting backwards.
The researchers also take great pains to assure parents that counting activities can be built into everyday play. The workshops are as much about putting parents at ease with numbers as they are about teaching how to teach them.
Lee and Kotsopoulos often talk about their work as laying the foundation for new generations with the math skills necessary to meet Canada’s future job market – while Canada is expected to face an overall job shortage in the years to come, skilled jobs, especially in math-intensive sectors such as science, technology and engineering, will be in the ascendant. In other words, for Abe’s generation, math could make the difference between wealth and unemployment.
I buy that argument, but here’s something else to chew on: math is also a doorway into logic, problem solving, symmetry, elegance, beauty and mystery. It feels like something we both discover and invent. It is both practical and awe-inspiring.
Full disclosure: I love math and always have. When I can’t sleep, rather than counting sheep, I soothe myself to slumber with magic squares and Fibonacci patterns. Who knows if Abe will share my fascination with mathematics when he grows up? Regardless, I have no doubt that even basic numeracy will serve him well.