Understanding Fractions: Integrating Results from Mathematics Education, Cognitive Psychology, and Neuroscience

Many students face difficulties with fractions. Research in mathematics education and cognitive psychology aims at understanding where and why students struggle with fractions and how to make teaching of fractions more effective. Additionally, neuroscience research is beginning to explore how the human brain processes fractions. Yet, attempts to integrate research results from these disciplines are still scarce. Therefore, the aim of this chapter is to provide an integrated view on research from mathematics education, cognitive psychology, and neuroscience to better understand students’ difficulties with fraction processing and fraction learning. We evaluate the difficulties students encounter with fractions on various levels, ranging from the brain level to the classroom level. Current research suggests that the human cognitive system is in principle prepared for processing natural numbers and fractions. Although proficiency with natural numbers is fundamental to learning fractions, the transition from natural numbers to fractions requires modifications of the initial concept of numbers, and natural number processing can interfere with fraction processing. Thus, when teaching fractions, it seems important to draw on students’ fundamental abilities to process fractions, while explicating fraction properties that are conceptually different from those of natural numbers.