Mathematics education uncovered and recovered

July, 2017

The root mystery

What is \(\sqrt{25}\)? You probably know but let’s see what textbooks say. One Year 7 textbook explains: Key point: The inverse of square is square root. \(3^{2}=9 \enspace \) so the square root of  \(9=\sqrt{9}=3\)   However, just next to this explanation there is a copy-and-complete exercise that reminds students that both \(4^{2}  \) and \((-4)^{2} \) […]

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Power of words

That was hard. My 12-year-old student struggled with angles. Why is one angle greater than another? How do we measure angles? When do we need to add them? She couldn’t get her head round these questions, and I couldn’t work out why. She started to get more and more confused and upset, so I gave […]

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Mastering measurements

I’ve been to an open day in a secondary school recently. To entertain curious children, the maths department prepared a series of questions for them to answer. The numerical answers obtained were then added together to get the final number which, if correct, would earn a prize. One of the questions asked how long a […]

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Restriction of thought

A few months after my daughter started secondary school, I saw her school maths workbook. The usual A4 pages were divided in half, leaving two narrow columns to write down the solutions. It was painful to see the working out of the sum of four mixed fractions laid out over seven short lines or the […]

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Times tables vs mathematics

When I first started lessons with this boy it was clear how eager he was to show his abilities. His teachers believed him to be “below average” because he struggled with memorising his times tables. Even though he could easily work out any problem that tested his very good understanding of multiplication and related patterns, […]

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