We need to talk about numbers
October 9, 2012
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.
The whole package
Teresa Pitman | September 26, 2014If you’ve ever bought ready-to-eat sushi, you may have noticed a blob of wasabi on the tray. It’s a convenient way to add pungent flavour to your lunch, but it also serves another purpose: it protects your food from micro-organisms. As food science professor Loong-Tak Lim explains, wasabi contains allylisothiocyanate, (AITC) a natural and potent anti-microbial that kills yeast and bacteria. Of course, not every food is enhanced by the strong flavour of wasabi, so Lim has developed a packaging system that offers the same antimicrobial benefits . Lim derives his AITC from ground mustard powder, and uses a patented nanotechnological process to spin tiny fibres that encapsulate the naturally sourced agent in the packaging. “The conventional approach to adding preservatives has been to add them to the food,” says Lim's research colleague Suramya Mihindukulasuriya. “But processing the food may break down the preservative. By having the preservative in the packaging, we don’t need as high a concentration to enhance the shelf-life, safety and quality of the food.” So-called “active packaging,” responds to changes in the environment and the food itself, Lim says. In this case, the membrane responds to a certain level of moisture and releases a preservative to prevent spoiling. Other active packaging materials respond to heat and light. Mihindukulasuriya works with a preservative called hexanal, the volatile organic compound you smell when you cut grass or slice a cucumber. Hexanal helps preserve cell membranes of fruits and vegetables so they don’t become soft or soggy as they ripen. The preservative also has some anti-microbial properties, which are activated by heat and humidity. Mihindukulasuriya calls her technique of enclosing the preservative using ultra-high electrical forces “electrospinning.” Lim jokes that “we are like Spiderman, spinning tiny fibres.” And the fibres are tiny – about 400 times smaller than a human hair. When exposed to humidity or water, these fibres become permeable and release the hexanal. During her PhD studies, Mihindukulasuriya also developed an oxygen indicator that is activated by ultraviolet radiation. When there is little or no oxygen in the package, the indicator is white, but if the package is damaged or torn, allowing oxygen to enter, the indicator turns blue. This matters because oxygen causes rapid deterioration of some foods, and higher levels of oxygen encourage the growth of more micro-organisms. These foods are sealed in vacuum packs or in packages flushed with nitrogen to remove the oxygen, but if the package becomes damaged at some point, oxygen can get inside. That’s where Mihindukulasuriya’s product comes in: a label with a blue line would indicate that the package should not be purchased. What’s next in active and intelligent packaging? Mihindukulasuriya is planning to develop a compound that will detect the volatile compounds produced by food when it spoils and indicate to consumers that the food should not be eaten. The technique would supplement expiry dates, which are only estimates based on typical situations. Not only would such packaging warn people that food had spoiled, it could also reassure them when it was safe to eat – even if the expiry date had passed. “People throw away lots of food that has expired but is still perfectly good to eat,” says Lim. This article was originally published by the University of Guelph. It has been edited for brevity, clarity and style, and is republished here with permission.