Today in geometry I started priming the way for trigonometry. I do that by having kids question the nature of math and what we are doing. (Long story, not worth it.) But I turned off the lights and we read this aloud:


Then I had us read aloud (switching each person reading at the end of each paragraph) and excerpt from Paul Lockhart’s Measurement:


And then… I told kids to decide at their table the answer to the following philosophical question, as best as they could.

Do you think the number “5” has physical reality, or only a mathematical reality? What about the number “5/2”? What about “pi”?

They totally got into it. When kids would say “5 chair” I would say, okay, but I’m not talking about things. This chair has physical reality, I can hold it in my hand, it is in this world… but does the number “5”?

And then they would speak again. Awesome discussions resulted… I took a vote at the end.

Most students voted 5 has physical reality, about half those students said 5/2 has physical reality. And finally, no student thought that pi has physical reality.

Fascinating. And then there were some that argued that all of them had to have physical reality, or all of them do not have physical reality. It’s an all or nothing proposition for them.

At the end, students kept talking about this on the way out of the door. And they also said “this is making me question everything.” One — after our brief discussion of whether math was invented or discovered — said she has had those exact same thoughts at night when trying to fall asleep.



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