“It doesn’t work” claimed a pupil to me in class last week. “Of course it does” I replied. “Yeah ok, I suppose it does but it’s not a proper answer” replied the pupil.

This is a discussion about solving equations where the answer was not a whole number. It really made me think. Why is it that pupils don’t accept fractions (or decimals) as a solution to an equation? It’s not that my pupils aren’t familiar with fractions and decimals.

The problem is the type of questions I ask my pupils. It is fairly typical when first learning to solve equations to have “nice” whole number solutions. Maybe non-whole number solutions should be introduced right from the start.

Then I thought about some other areas of maths. Angles, area, perimeter, volume, Pythagoras, statistics, algebra, … do I focus on “nice” solutions too often in these areas too?

The positive is that I’ve already started planning to correct this. I’m currently writing a new S1 course in which this will be a focus. I wrote calculating new angles worksheets which contain decimals and algebra as well as whole numbers. Hopefully my pupils in the future won’t be so confused or bothered by answers that are not whole numbers.

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I had a designing math tasks course in graduate school, and one of the things the professor advocated was exactly what you are describing. Give the hardest problems with the ugly answers first, to make sure students are conceptualizing things broadly.

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