Tuesday, June 19, 2007

zero the hero

‘zero the hero came to school, zero the hero, he’s so cool, zero the hero saves the space… so all the other numbers can stay in one place. Yeah….’ (Picture jazz hands here)

This year my first graders became very concerned about whether or not zero was even or odd. Everyday during calendar math this debate would come up and we couldn’t seem to get past it. They were upset that they couldn’t put 0 into one of the clear-cut categories. I truthfully didn’t know and had somehow gotten through 3 previous years of teaching the concept of even and odd without this question coming up.

Finally I decided to see where they would take this. At first I let one math team (I use teams for math workshop centers) write their reasons for why zero was even, odd, or neither. I loved their thinking, but soon realized the debate was rising to a new level. Now that they were putting real thought behind it they were getting into heated conversations with each other.
“NO Stupid! Zero is even because 1 is odd” “Zero can’t be even! Even is if the number has a partner. Zero has no partners, like you.” “you’re a zero” great.

Though it was great that they were engaged in an academic debate, we clearly needed some good debate practice and perhaps some review of how we treat one another.

So, we started by defining the concept of zero. What is it? Is it the absence of something? Is it nothing? Is it a place-holder for the tens place? Is zero actually two different concepts: one zero represents the existence of nothing; the other zero represents a place holder in base ten?

More confused than ever, we started debating our reasons for why we thought zero was even, odd, or neither. It was interesting because the children who defined zero as being nothing fell into the ‘neither’ camp, while the children who focused on its place-holder status fell into the ‘even’ camp. A few children argued odd because zero does not represent a partner-relationship.

I was fascinated by their thoughts and opinions. I realized I’d never put much thought behind it. I’d always been told zero was neither, but I had never questioned it.

So, we wrote emails to my math professors in college, my math-teacher friends, math ph d candidates, and the math specialist at my school. Everyone had a different answer. I sent groups of kids off with index cards to ask the staff at my school what they thought. They were instructed that the adult must write down their reasoning just like I had made them. The results were fascinating. Everyone in our school had different opinions and the reasons for their opinions varied as well. More interestingly, most of them were very confident in their answer. Only one administrator and one librarian asked my kids to come back and tell them what they had discovered. Everyone else gave ‘the final answer’.

Two of my little girls’ heads almost exploded. Grownups thought they were right, but they didn’t all agree. Not one right answer? Impossible. As their minds grappled with this you could see sparks flying.

In the end we never did come to a conclusive decision, partly because I couldn’t decide how to end it. Mathematicians emailed me that zero was even, yet there still seemed to be enough debate over it to make it a mystery. I also struggled with giving my children a definite answer. I was scared to break the magic the hunt for the truth created. The excitement of having an unknown concept sparked lights with my kids. How could I take that away with a text-book concrete answer?

Their teacher next year can tell them. At least, she can tell them whatever she believes the answer is. Maybe they’ll question her to tell them why.

I’d love to hear your thoughts as well. Even, odd, neither? Why?


Jenny said...

Wow! My fifth graders could have learned from your first graders. I've always assumed (and been told) that zero was neither. Now I'm going to have to ask a friend who is a college math professor. I'll probably ask lots of folks!

organized chaos said...

I'm with you. Once we got into this I was surprised there was so much debate. I'd always assumed it was neither. Let me know what your college math professor says.