Fractions: what makes them difficult?

Why do children find fractions difficult?

For many children, not just children with dyscalculia or maths difficulties, fractions can be confusing or challenging. There are a couple of reasons for this,

Fractions are relational

Firstly fractions are relational. When children start learning maths, numbers represent a fixed quantity. We spend a lot of work in the early years teaching children the "fourness of four" or the "twoness of 2", so that children develop an awareness that 4 is a clearly defined value. However, with fractions, this is not the case. A quarter of a pizza is very different to a quarter of a bag of 24 sweets. Therefore, we say fractions are relational as the answer depends on the "part whole relationship".

The new Irish maths curriculum for primary schools, the 2023 curriculum, recognises the importance of this, and has as its first learning outcome that children will "develop an awareness of part-whole relationships using a variety of models (area, length and set)."

Fraction notation

Fractions can also be confusing or difficult for children when it comes to notation as they are used to bigger numbers representing larger quantities. However, with fractions, when children do not understand what the denominator is they find it challenging to understand that 8 is larger than 4 but 1/8 is smaller than 1/4.

Manipulatives and beyond

Experimenting with manipulatives is vital for children but for fractions, it is also very important to make sure that is paired with clear, direct instruction.

In a bid to make sure children understand fractions, teachers often rely on the sharing of a pizza. While this can be useful at the initial stages of learning, particularly when learning about halves and quarters, it is hugely important to move beyond the slice of pizza.

Why is it important to teach fractions?

Fractions are important not just because we encounter them in lots of places in our day to day lives, such as cooking (recipes), sharing bills, hairdressers. It is also important at primary school level for children to get a good grasp on fractions. A firm understanding of fractions is necessary for when children progress to more advanced maths concepts such as algebra. That firm foundation gives children huge confidence and conceptual awareness when it comes to more complex maths foundations.