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Noticing the Pens

“Mister, where do you get your pens?” someone asked. Later that day, another student asked the same thing.

They’ve seen me using these for some time, now. When I’m at the document camera writing guided notes, I use colors to emphasize where things come from — to show what’s being substituted where. And I use them in the table of contents to highlight when we have tests, so that they know which lessons are in scope for upcoming tests. 

So these pens were nothing new. It’s just that on this day, I was also using them as a visual aid. 

I was making a point about how long ago, zero as a number was completely foreign concept. Numbers were for counting, after all. And I grabbed a handful of my Staedtler triplus fineliner 334s (red, orange, yellow, green, light green, blue, light blue) and asked them if they could see how many pens I had. And then I asked them if they could see anything when I held nothing in my hand — so that if numbers were things you could see, then how could zero be a number? Roman numerals, after all, didn’t even have a symbol for zero — it just wasn’t a thing.

And so it is, I said, with complex numbers. How can there be complex solutions to quadratic equations that in fact do not cross the x-axis at all? Like zero (or negative numbers, or irrationals numbers), they take some getting used to.

This seemed to work, to a point. Although most of them instinctively said “Zero!” when I asked if they could see any pens in my empty hand, many of them were more interested in the pens themselves. Hence…

“Mister, where do you get your pens?”

They notice even the little things.