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Teaching and Learning Secondary School Mathematics pp 527–546Cite as

“Canada Is Better”: An Unexpected Reaction to the Order of Operations in Arithmetic

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Part of the book series: Advances in Mathematics Education ((AME))

Abstract

In Canadian schools the acronym BEDMAS is used as a mnemonic, which is supposed to assist students in remembering the order of operations: Brackets, Exponents, Division, Multiplication, Addition, and Subtraction. In the USA schools the prevailing mnemonic is PEMDAS, where P denotes parentheses, and it further assists memory with the phrase “Please Excuse My Dear Aunt Sally”. Note that while ‘parentheses’ and ‘brackets’ are synonyms, the order of division and multiplication (D and M) is reversed in PEMDAS vs. BEDMAS.

I present my extended reaction to the following claim:

According to the established order of operation in arithmetic, division should be performed before multiplication.

I was deeply surprised by this assertion, which was voiced by an experienced secondary school teacher of Mathematics. However, as a way of addressing my surprise, I presented the claim for discussion in two classes: a class of secondary mathematics teachers and in a class of prospective elementary school teachers. I share with the reader what happened in each class: surprising realizations, respectful disagreements, reliance on mnemonics, search for counterexamples, attempts to deal with disconfirming evidence, robustness of prior knowledge, and … a declaration of national pride.

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Notes

  1. 1.

    With apology to Francophone colleagues, I refer here to Anglophone Canada. However, I learned recently that in some Francophone schools PEMDAS is used.

  2. 2.

    In the UK the analogous mnemonic is BIDMAS referring to Brackets, Indices, Division, Multiplication, Addition and Subtraction (Hewitt, 2012). Google search also reveals occasional use of BOMDAS, POMDAS or PODMAS.

  3. 3.

    e.g., http://www.askamathematician.com/2011/04/q-how-do-you-calculate-6212-or-48293-whats-the-deal-with-this-orders-of-operation-business/; https://productforums.google.com/forum/#!topic/websearch/kZkTv_WTSxA; https://answers.yahoo.com/question/index?qid=20110427155042AACb7d8

  4. 4.

    Note that I do not claim that multiplication is a repeated addition, but that it can be interpreted/rewritten as such.

  5. 5.

    In fact, Bay-Williams and Martinie (2015) noted that in Kenya students are taught to carry out division before multiplication, which seemingly contradicts that ‘left-to-right’ order as related to division and multiplication.

  6. 6.

    Obviously Google is a greater authority than the teacher, especially when the teacher questions conventions.

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Authors and Affiliations

  1. Simon Fraser University, Burnaby, BC, Canada

    Rina Zazkis

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  1. Rina Zazkis
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Correspondence to Rina Zazkis .

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Editors and Affiliations

  1. Lakehead University, Thunder Bay, ON, Canada

    Ann Kajander

  2. Wilfrid Laurier University, Waterloo, ON, Canada

    Jennifer Holm

  3. College of Education, University of Saskatchewan, Saskatoon, SK, Canada

    Egan J Chernoff

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Zazkis, R. (2018). “Canada Is Better”: An Unexpected Reaction to the Order of Operations in Arithmetic. In: Kajander, A., Holm, J., Chernoff, E. (eds) Teaching and Learning Secondary School Mathematics. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-92390-1_50

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  • DOI: https://doi.org/10.1007/978-3-319-92390-1_50

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