Teaching and Learning Fraction and Rational Numbers: The Origins and Implications of Whole Number Bias

Abstract

Many researchers agree that children's difficulty with fraction and rational numbers is associated with their whole number knowledge, but they disagree on the origin of the whole number bias. This article reviews three explanations of the nature of the bias. These accounts diverge on the questions of whether or not early quantitative representation originates from a numerical-specific cognitive mechanism, and whether or not the early quantitative representation privileges discrete quantity. The review suggests that there does not yet appear to be sufficient evidence to decide among the competing accounts as to the nature of the whole number bias. Yet, in the search for the understanding, two important issues have been brought up with regard to learning and teaching fraction and rational numbers. One question is related to how learning about fraction and rational numbers may be organized in such a way to be less strained for taking advantage of the prior knowledge of whole numbers. The second issue is concerned with what causes the gap between learning number symbols and learning number concepts. These issues have been explored by drawing upon both the accounts of whole number bias and insights from developmental studies, neuropsychological studies, and teaching experiments. The present review of literature has shown that the issues of whole number bias reflect not merely a matter of interference between prior and new knowledge in children's construction of fraction concepts, but a constellation of more general questions with regard to the origin and development of numerical cognition. How the bias is conceptualized therefore has theoretical and instructional significance.