The division by zero @NCTM webinar was really cool! Thank you @Joannbarnett and @ChondaLong for putting it together!

I'll share some of my own thoughts in this thread. #NCTM100 (1/n)

I really liked the deliberate emphasis on making something that can be so abstract into something concrete and relatable. That's really important to our younger (and older!) students to be able to make sense of mathematics as not just a collection of "rules". (2/n)

Side note: I also was quite relieved when the two models of division were just called "measurement" and "sharing." I know they're formally called "partitive" and "quotative" but for the live of me I can never remember which is which! (3/n)

Regarding the idea of "18 apples ÷ 0 friends", I've usually dismissed that as "the question doesn't make sense" and left it at that. But they had a really interesting way to think about it that I had never considered before. (4/n)

The gist was "How tall are those 0 friends? What are their hair colors? You can't say anything about those 0 friends, much less how many candies they got."

That is a mind-blowingly interesting way to think of the problem. (5/n)

Jumping into "higher-math mode", your set of friends is an empty set ∅. But then, for any predicate P, any statement of the form "∀x∈∅, P(x)" is AUTOMATICALLY true — vacuously! I wonder if there's any way to dive deeper into that aspect of the problem, just for fun. (6/n)

Then, as for the "18 candies ÷ 0 candies in each bag" problem, it was really interesting that so many people had the answer of "as many as you want" — and mentioned their students often have the same thought. Our kids are astoundingly creative and insightful. (7/n)

As expected, "infinity isn't a number" was the response to that line of reasoning. I do think that's a rabbit-hole topic of its own, but it's definitely one that might be worth exploring at some point. What IS a number, anyway? (8/n)

I do have my own thoughts on the topic of division by zero and its relation to infinity (which if you look at my profile should be obvious ), but it's always great to hear the perspectives of other teachers. They lead to awesome new thoughts and questions. (9/n)

Here's a thought that I had because of this session:

What if, instead of answering whether or not infinity is a number, we asked the students:

*IS* infinity a number?
For that matter, is ½ a number? Or -2? Or 0?

I'd love to be a fly on the wall during THAT discussion! (10/n)

Anyway, thank you to the organizers for an excellent discussion. Even though division by zero is my favorite topic already, you've given me new things to think about! @NCTM #NCTM100 (11/11)