ABSTRACT
This chapter looks at some of the reasons why fractions present such a big mathematical and psychological stumbling block. As one encounters fractions, mathematical content takes a qualitative leap in sophistication. Suddenly, meanings and models and symbols that worked when adding, subtracting, multiplying, and dividing whole numbers are not as useful. When working with whole numbers, quantities had simple labels that came about by counting or measuring: 5 candies or 7 feet. The operations of multiplication and division often produce new quantities that are relationships between two other quantities. Understanding rational numbers involves the coordination of many different but interconnected ideas and interpretations. Unfortunately, fraction instruction has traditionally focused on only one interpretation of rational numbers, that of part—whole comparisons, after which the algorithms for symbolic operation are introduced. Although many people mistakenly use the terms fractions and rational numbers synonymously, they are very different number sets.
