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.

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Cathy Majtenyi | October 22, 2014

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Lucid dreaming depends on ...

Trent University Staff | October 21, 2014

New research by Trent University Oshawa Anthropology professor Roger Lohmann and graduate student Shayne Dahl indicates that cultural learning shapes the kind of awareness and control people can experience while dreaming. “Scouring the ethnographic record on dreaming for hints of lucidity under Professor Lohmann’s guidance, I found something surprising: that lucid dreaming is widely thought to have serious consequences,” said Dahl, who completed his M.A. thesis, “Knowing Means Connecting with the Source of Life: Knowledge and Ethics among Blackfoot Traditionalists” at Trent in 2012. (He is now a Ph.D. candidate at the University of Toronto.) “As one of my Blackfoot informants put it, ‘You could die in your dream.’” Lohmann and Dahl’s findings were published in the 2014 collection, Lucid Dreaming: New Perspectives on Consciousness in Sleep. Lucid dreaming – waking consciousness arising during a dream – has been a hot topic of scientific research in recent years. According to Lohmann and Dahl, the common assumption that dreams are products of isolated imaginations has distorted our understanding of lucidity’s variation in form, function, and real-world outcomes. Pop culture portrayals in films such as Avatar and Inception present fantasies where lucid dreaming enables marvelous real-world powers. Many traditional and religious cultural worldviews take the relationship between waking and dream worlds as reality rather than fantasy. Lohmann’s fieldwork in Papua New Guinea among the Asabano people explored how they used dreaming as evidence for and contact with supernatural beings. “Asabano converts often told me that seeing dreams of Jesus or Heaven convinced them that what the missionary told them was true,” said Lohmann. “It struck me that they had to believe their dreams were more than figments of their own imaginations to reach that conclusion, and that I, for example, would not be convinced by the same experience because of my different cultural background.” Similarly, Dahl’s fieldwork in Alberta included encounters with Aboriginal medicine men who practiced lucid dreaming. “Shayne’s field experiences and his search of ethnographic literature brought home to us that lucid dreaming has profound potential for people who think it’s more than just a fantasy. We found that descriptions of lucid dreams are radically different in form, function, and outcome depending on the cultural assumptions of the dreamer,” said Lohmann. Their research revealed evidence that in some cultures, lucid dreaming is unknown, while in others it is a commonly taught skill. In some, lucidity is tacit rather than acknowledged, but people nevertheless believe that they actively undertake goals in their dreams. Lohmann and Dahl found that this implicitly lucid “volitional dreaming” commonly appears in ethnographic accounts of dreaming. In cultures where “generative” theory holds sway, dreaming of something is understood to cause it to happen in the waking world. This leads people to experience lucid dreams as opportunities to create or do magic. By contrast, people who believe dreams are what one sees during “soul travel” use lucid dreams as an opportunity to spiritually visit real places. “Even when we consciously disbelieve our dreams,” Dahl said, “They still affect us at a deeper, emotional level that we can’t easily control with reason.” “All of this shows that cultural dream theories are multiple, that people invoke them in complex ways, and that they are at the very core of what lucid dreaming is and what it makes possible,” said Lohmann. This story was originally published by Trent University on, July 15, 2014. Is has been edited for style, brevity and clarity and appears here with permission.

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