Parity of zero

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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.


  • 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.)

"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

External links[edit]

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