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Maths misconceptions

Maths paper

Everyone knows the feeling of struggling with a task that other people seem to breeze through. It might be programming the DVD player or even just reading maps.

Well, this is how some kids feel with maths, and their difficulties are often rooted in misunderstandings of concepts that we, as teachers, don't give a second thought to. How much could we help them make progress if we were more aware of these misconceptions, and were able to tackle them head-on? We all know, after all, that understanding our mistakes can be a powerful learning experience.

With the help of Tim Coulson, who leads the National Numeracy Strategy, we've put together a list of some of the most common, and potentially most obstructive, of these misconceptions, and suggest some approaches that might put things right.

Some children will swear blind that 3.24 is bigger than 4.6 because it's got more digits. Why? Because for the first few years of learning, they only came across whole numbers, where the 'digits' rule does work.

Another seductive 'rule' that works for whole numbers, but falls to pieces when one or both of the numbers is less than one. Remember that, instead of the word 'times' we can always substitute the word 'of.' So, 1/2 times 1/4 is the same as a half of a quarter. That immediately demolishes the expectation that the product is going to be bigger than both original numbers.


4. Common regular shapes aren't recognised for what they are unless they're upright
Teachers can, inadvertently, feed this misconception if they always draw a square, right-angled or isosceles triangle in the 'usual' position. Why not draw them occasionally upside down, facing a different direction, or just tilted over, to force pupils to look at the essential properties? And, by the way, in maths, there's no such thing as a diamond! It's either a square or a rhombus.


6. To multiply by 10, just add a zero
Not always! What about 23.7 x 10, 0.35 x 10, or 2/3 x 10? Try to spot, and unpick, the 'just add zero' rule wherever it rears its head.

7. Proportion: three red sweets and two blue
Asked what proportion of the sweets is blue, how many kids will say 2/3 rather than 2/5? Why? Because they're comparing blue to red, not blue to all the sweets. Always stress that proportion is 'part to whole'.

8. Perimeter and area confuse many kids

9. Misreading scales

Words: Steve McCormack Pictures: David Moore

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Did you know?

In 2005, 75% of pupils attained level 4 or higher at KS2 maths... More than 110,000 pupils were entered in the recent Primary Mathematics Challenge (Source Mathematical Association).