Why does my child have so much trouble with fractions?

Of all the areas of maths that cause problems for the young learner, fractions causes the most and I have often seen students in middle and upper secondary school still struggling to understand them. Fixing one simple misunderstanding can solve this.

When children start to learn about numbers, they do so by counting and recognizing quantities (e.g. ‘How many apples are there?’, ‘Can you count to 10?’, etc.).  Kindergartens and schools reinforce counting quantities and digits are formally introduced.. Over and over our children are told numbers tell us how many things there are. This is all important and good…. Until we start with fractions.

Fractions are a way of describing things that are less than one. The tricky part is the bottom bit of a fraction (the denominator). The denominator stops being a normal number and tells us a size instead[i]. For example the ‘4’ in ¼ tells us that the whole object (e.g. cake) should be divided into 4 equal parts (the size is 4).

When we learn, we tend to use what we know already to make sense of new things. For young children, who have been told over and over that a number is a quantity they can count, the denominator is seen in the light of what they have learnt already. This prior knowledge tells them that the denominator is a quantity because it is a number.  This leads them to all sorts of odd results. For example, ½ + ½ = 2/4 (because you can add quantities together).

If your child is struggling with fractions, sit down with them and explain how sizes work in fractions (using clothing sizes as a comparison can help). Once they understand that the denominator just describes the size, the rest becomes easy.

[i] For the purists, we know that the denominator uses quantities to describe the size and does not change from a normal number in this sense, however, for clarity in young learners it is far more important for them to understand the concept of a denominator as describing a size.