Jo Van Hoof

Are secondary school students still hampered by the natural number bias? A reaction time study on fraction comparison tasks

Rational numbers and particularly fractions are difficult for students. It is often claimed that the ‘natural number bias’ underlies erroneous reasoning about rational numbers. This cross-sectional study investigated the natural number bias in first and fifth year secondary school students. Relying on dual process theory assumptions that differentiate between intuitive and analytic processes, we measured accuracies and reaction times on fraction comparison tasks. Half of the items were congruent (i.e., natural number knowledge leads to correct answers), the other half were incongruent (i.e., natural number knowledge leads to incorrect answers). Against expectations, students hardly made errors on incongruent items. Longer reaction times on correctly solved incongruent than on correctly solved congruent items indicated that students were indeed hampered by their prior knowledge about natural numbers, but could suppress their intuitive answers.

Who can escape the natural number bias in rational number tasks? A study involving students and experts

Many learners have difficulties with rational number tasks because they persistently rely on their natural number knowledge, which is not always applicable. Studies show that such a natural number bias can mislead not only children but also educated adults. It is still unclear whether and under what conditions mathematical expertise enables people to be completely unaffected by such a bias on tasks in which people with less expertise are clearly biased. We compared the performance of eighth-grade students and expert mathematicians on the same set of algebraic expression problems that addressed the effect of arithmetic operations (multiplication and division). Using accuracy and response time measures, we found clear evidence for a natural number bias in students but no traces of a bias in experts. The data suggested that whereas students based their answers on their intuitions about natural numbers, expert mathematicians relied on their skilled intuitions about algebraic expressions. We conclude that it is possible for experts to be unaffected by the natural number bias on rational number tasks when they use strategies that do not involve natural numbers.

The Transition from Natural to Rational Number Knowledge

In this chapter, we elaborate on learners’ difficulties with rational numbers. We begin with the importance of robust rational number understanding for learners’ general mathematics achievement and then move to the challenges that many learners face with respect to various aspects of rational numbers. Third, we elaborate on previous research that focused on a major source of learners’ difficulty, namely the natural number bias. Fourth, we introduce two complementary theoretical perspectives that have been employed in the past decade to study the natural number bias, namely the framework theory approach to conceptual change and the dual process perspective of reasoning, and then we review some studies that we conducted from these perspectives. We close with discussion of the theoretical and educational implications of these studies and provide suggestions for further research.