“There is no right or wrong in mathematics:” a quote from a memoir by the daughter of Fischer Black, a famed US mathematician, that she remembers him saying often. What does that mean?

When we learn how numbers work, we can do so in one of several ways. The way many of us have been brought up to learn mathematics is through memorization and learning procedures, such as algorithms. One example is the long division algorithm, which is opaque to most students and is arguably one of the most difficult to learn. Teachers and parents alike can relate to frustration as students confuse which number to put above the little house, which below, and more.

Another issue with this algorithm is that the way most people learn it. The digits are independent of value. For example, when dividing 125 by 5, first you would see how many times 5 goes into 1, then 12, then… but 1 what? 12 what? If it were truly 1 or 12, wouldn’t the digits be written in different places?

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