We need to talk about numbers

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.

Share: Print

Leave Comments

Blog Posts

genetic barcodes

Barcoding life, one species ...

Sharon Oosthoek | May 2, 2016

Nobody knows for sure how many species exist. But scientists are certain we have identified only a fraction of the plants, animals and fungi on the planet — roughly 1.7 million species out of an estimated 10 to 20 million. "Most of the yet-to-be-identified species will be tinier life forms, but the numbers could even be larger," says University of Guelph biologist Paul Hebert. "That's just a best guess." Making an inventory of all life then would seem a Sisyphean task. But back in 2003, Hebert and his research team proposed a DNA tool for doing exactly that. At the same time, they made a convincing case for why we might want such an inventory: our species is accelerating the extinction rate of other species, and as Hebert puts it, "people take action when they know what is happening to life." Their argument was convincing enough to lead to the creation in 2010 of the International Barcode of Life (iBOL) project, an alliance representing 26 countries and headquartered at the University of Guelph.  Since then, affiliated researchers have collected from all over the world biological samples such as feathers, fur, blood and tiny bits of tissue. In 2015, they reached their goal inventorying half a million species. They have now set a ambitious target of identifying all species on the planet by 2040. As Hebert and his team originally envisioned, the tool the researchers are using to identify species is a short section of DNA from a standardized region of the genome, found in all living things. The sequence of the molecules that make up that chunk of DNA can be used to identify different species, in the same way a supermarket scanner uses the black stripes of the UPC barcode to identify purchases. As an added bonus, the DNA section is short enough to be sequenced quickly and cheaply, yet long enough to discriminate species. Fish out of water The tool has already been used to identify invasive species and the illegal sale of mislabelled endangered fish. While Hebert and his team are certainly on board with that, their ultimate vision has always been much loftier. "Each species is a book of life that describes how to reconstruct a robin or a blue jay or a monarch butterfly," says Hebert. "It's possible that by the end of the century, one-sixth of those books of life will not longer be with us. One of the objects of our work is to register all the species on the planet before they disappear." But this isn't just about creating an inventory. Rather it's about creating a digital Noah's ark. Along with the identifying section of DNA, the barcode project saves each species' entire genome — in other words, its complete set of DNA, representing instructions for building each species. That means the chemical pathways responsible for producing yet-to-be-discovered life-saving drugs will be preserved. "It's even possible that we might be able to reconstruct species," says Hebert. "Maybe humanity will decide it's sad living on a planet with few other species on it. It would be completely impossible to restore lost species if we don't have their DNA. "        

Creating community through cuisine

Emma Drake | April 27, 2016

Food is more than a meal; it can be intrinsic to a person’s identity. But for refugees, part of their identity is challenged when they settle in countries that don’t offer foods from home. “We share culture and richness through food,” says Valencia Gaspard, a PhD student in rural studies at the University of Guelph. “Food can be used to build communities and bring people together.” Valencia is part of a team of student studying the availability of ethnocultural foods in Toronto. They will be examining how these foods are used to manifest a culture through cuisine. “Keystone ingredients, such as camel’s milk or sesame oil have great importance to the meal,” she says. “Not being able to choose what you eat is dis-empowering.” read more »

Farmers get ahead of ...

Araina Bond | April 19, 2016

Anticipating Mother Nature has always been an important part of farming. Now farmers in Northeastern Ontario can make more informed decisions using real-time data about environmental conditions, thanks to Nipissing University researchers. The Nipissing team has created an online system called GeoVisage, which uses seven weather stations throughout Northern Ontario to collect data on microclimates. That includes air and soil temperature, relative humidity, wind speed, leaf wetness and photosynthetically active radiation — that is, sunlight plants can use for photosynthesis. read more »
quinoa plants

Quinoa puts down roots ...

Jessica Shapiro | April 14, 2016

Ancient Incas considered quinoa their most sacred food. Packed with protein, vitamins and amino acids, it gave them stamina, strength and energy needed for survival. No wonder NASA has researched growing quinoa on long journeys to outer space. Despite the seed's explosion in world popularity over the past few years, including a massive increase in demand throughout North America, almost no farmers outside the Andes Mountains in South America grow it. Issues related to quality, supply, cost and importation have encouraged scientists to experiment with cultivating the crop in Ontario. At the Trent University Sustainable Agriculture Experimental Farm, Mehdi Sharifi is working with his students to make organic quinoa production viable for Ontario farmers. read more »
Larissa Barelli waters plants

Fine tuning fungi’s ...

Sharon Oosthoek | April 8, 2016

Nobody takes revenge like Mother Nature. After all, she created entomopathogenic fungi — organisms that not only kill crop pests, but offer up nutrients in the insects' bodies to the plant. "It's a cool mechanism," says University of Brock PhD biotech student Larissa Barelli who studies evolution of these fungi. "Certain species can drill through the insect's cuticle, grow within it and eat it from the inside. They can also release toxins that kill the insect. The fungi then transfers nitrogen from the insect to the plant." read more »
More Blogs »