Kevlin Henney
Oct 31, 2015 · 1 min read

Unfortunately, the teacher was incorrect. Although well made, the points made in the article about equivalence, matrix multiplication, JavaScript’s broken model of equality, etc., turn out not to be relevant to the problem.

The concept of repeated addition yields two possibilities to the problem, both of which are correct: 5×3 can be interpreted as “3 five times”, thus making 3 the addend and 5 the upper bound for repetition (i.e., 3+3+3+3+3), or as “5 three times”, thus making 5 the addend and 3 the upper bound for repetition (i.e., 5+5+5).

There is no bias that dictates one interpretation is to be preferred or even considered correct at the expense of the other. Both interpretations are in common use, both in English and in mathematics.

The Wikipedia fragment quoted offers an illustration of multiplication but not necessarily a definition. By way of contrast, Wolfram MathWorld offers the following definition:

In simple algebra, multiplication is the process of calculating the result when a number a is taken b times. The result of a multiplication is called the product of a and b, and each of the numbers a and b is called a factor of the product a b. Multiplication is denoted a×b, a·b, (a)(b), or simply a b.

To teach that there is a single valid expansion of 5×3 is, alas, to teach a falsehood. As someone who enjoys mathematics, I hope you appreciate that in the cases where such an interpretation is made and enforced, that this is a problem of education to be fixed and, as such, not something be defended.

Kevlin Henney

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