The foundations of understanding fractions and decimal numbers

Many children and adults struggle with fractions (e.g., 1/3) and decimal numbers (e.g., 2.1) in daily life. However, fractions and decimal numbers are common in the workplace and proficiency with those numbers is important for health-related and financial decisions. Furthermore, a solid understanding of fractions and decimal numbers is necessary for mathematics and other STEM-subjects.

This research project will establish how to overcome the difficulties many children and adults encounter when dealing with fractions and decimal numbers.

Fractions are often introduced into the curriculum before decimal numbers, nevertheless performance is worse with fractions. Previous research has mainly focused on fractions and highlighted several areas of difficulties. The magnitude of a fraction is less accessible, because it is not defined by the values of the component numbers, but instead by the relationship between two numbers.

Children and adults are often biased by the magnitudes of the component numbers, for example judging 3/9 to be larger than 1/3. Fraction arithmetic procedures also remain difficult for many, because not all principles that are true for whole numbers apply to fractions (e.g., multiplying by a fraction does not necessary lead to a larger number). Furthermore, when fractions and decimal numbers are introduced, children have to learn new number forms and new notations.

Which skills help children to successfully overcome those hurdles? When children enter primary school they need to shift from using mainly spoken numbers words (e.g., 'twenty-three') to being able to write down the correct multi-digit Arabic strings (e.g., '23') upon hearing spoken number words. This is called number transcoding and fundamental for mathematical development.

In a previous research project we found that children's ability in number transcoding predicted their early fraction understanding two years later. Better number transcoding ability might be beneficial when learning new notations for fractions and decimal numbers. In this research project we will assess whether transcoding skills are foundational for a solid understanding of fractions and decimal numbers.

We will do this in the context of measuring other numerical skills that have been suggested to support the development of fraction learning such as proportional reasoning and children's knowledge about the magnitude of whole numbers.

First, we will continue an ongoing longitudinal study, following children's mathematical development from Year 6 to 8, with a focus on their learning of fractions. This study will enable us to discover which skills in early mathematical development predict better later understanding of fractions. Identifying predictors, however, is only the first step.

To make further theoretical and practical contributions it is essential to identify the mechanisms by which those skills support the learning of fractions. We will establish which of these skills are causal mechanisms in two further series of studies. We will use laboratory-based studies to investigate the processing of fractions in-depth, comparing groups of children and adults with different levels of expertise in fractions.

In these studies we will measure individual differences in the proposed predictor skills and link those to task performance and strategy use. To measure strategy use we will use both explicit measures (self-report) and implicit measures (eye-movements). Finally, in training studies with both children and adults we will identify whether training those predictor skills leads to improvement in proficiency with fractions and, if so, how best to train those skills.

In addition to increasing our knowledge about the learning of fractions and decimal numbers, this research project will in the long run help children and adults who struggle with fractions and decimal numbers.