# Parity of zero

The **parity of zero** receives some attention in mathematics education. Although zero is even, students offer a wide variety of reasons for believing that it is even, odd, both, or neither. A few articles in the education literature present representative quotations from class discussions and interviews, which are collected here. The names given for the children are pseudonyms chosen by the researchers.

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## Quotes[edit]

- Dividing by zero...allows you to prove, mathematically, anything in the universe. You can prove that 1+1=42, and from there you can prove that J. Edgar Hoover is a space alien, that William Shakespeare came from Uzbekistan, or even that the sky is polka-dotted. (See appendix A for a proof that Winston Churchill was a carrot.)
- Charles Seife,
*Zero: The Biography of a Dangerous Idea*

- Charles Seife,

## "Using Assessment to Reshape Mathematics Teaching"[edit]

Wilcox, Sandra K (2000). *Using Assessment to Reshape Mathematics Teaching*. Lawrence Erlbaum Associates. pp. page 110. ISBN 0-8058-2962-8.

- Zero is even because if you divide it in half, both people get nothing.
- Victoria, 3rd-4th grade, U.S.

## "Primary School Children's Knowledge of Odd and Even Numbers"[edit]

Frobisher, Len (1999). "Primary School Children's Knowledge of Odd and Even Numbers". Anthony Orton (ed.) *Pattern in the Teaching and Learning of Mathematics*: page 41, London: Cassell.

- ...can't split it out, because you haven't got nowt.
- Kurt, Year 4, UK

- No one gets owt if it's shared out.
- Ben, Year 4, UK

- It is even because the 2 times table it goes 0, 2, 4, 6, 8.
- Carly, Year 5, UK

## Deborah Ball's classroom[edit]

Deborah Loewenberg Ball oversaw a number of discussions in her third-grade classroom:

Ball, Deborah Loewenberg (1999). "Crossing boundaries to examine the mathematics entailed in elementary teaching" in *Contemporary Mathematics*. *Algebra, K-Theory, Groups, and Education: On the Occasion of Hyman Bass's 65th Birthday* **243**: 15-36, American Mathematical Society. Retrieved on 2007-08-30.

- Um, first I said that um, zero was even but then I guess I revised so that zero, I think, is special because um, I— um, even numbers, like they — they make even numbers; like two, um, two makes four, and four is an even number; and four makes eight; eight is an even number; and um, like that. And, and go on like that and like one plus one and go on adding the same numbers with the same numbers. And so I, I think zero's special. -
*Benny*

Ball, Deborah Loewenberg (March 1993). "With an Eye on the Mathematical Horizon: Dilemmas of Teaching Elementary School Mathematics". *The Elementary School Journal* **93** (4): 373-397.

- I didn't think zero was even
*or*odd until yesterday and then someone said it could be even because one below zero and one above zero are both odd, and that made sense. -*Sheena* - I thought zero was an even number, but from the meeting I got sort of mixed up because I heard other ideas I agree with and now I don't know which one I should agree with. … I'm going to listen more to the discussion and find out. -
*Mei*