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...