ABSTRACT
Rational numbers are presented by three different notations: fractions (1/4), decimal numbers (0.25), and percentages (25%). The understanding of these numbers is essential for more advanced mathematical achievement. Unfortunately, many students do not reach a sufficient level of understanding of these numbers. For instance, among a large sample of college students in the United States, only 33% correctly identified the largest of four fractions (Stigler, Givvin & Thompson, 2010). One of the main reasons for this is that children are facing a real conceptual shift, and the mistakes can be explained by the fact that students tend to view fractions and decimals as whole numbers and to apply to them the rules previously used on natural numbers. This is called the natural number bias (Ni & Zhou, 2005, Siegler & Lortie-Forgues, 2017). These learning difficulties are observed with decimal numbers (Desmet, Grégoire & Mussolin, 2010) and with fractions (Siegler, Thompson & Schneider, 2011), especially in children with math learning difficulties (e.g., Jordan et al., 2017).
Some intervention programmes have been shown to be effective in supporting the learning of decimal numbers (Durkin & Rittle-Johnson, 2012) and of fractions (e.g., Fuchs, Schumacher, Long et al., 2013, Krowka & Fuchs, 2017, Hamden & Gunderson, 2017).
Based on this research work, the last two sections of this chapter provide, first, clear guidelines about how to assess children’s understanding of rational numbers and operating on them and second, very concrete instructions and exercises to help children who are struggling with rational numbers.
