ABSTRACT
In this chapter, the discussion focuses first on different kinds of knowledge that students need to acquire about decimals and then considers the connections between them. In some sense, decimal fractions represent a confluence of whole numbers and common fractions. Thus, many students already have acquired considerable knowledge of whole numbers and limited knowledge of common fractions by the time they encounter decimal fractions. The three kinds of knowledge identified earlier provide a framework for comparing the systems of whole numbers, common fractions, and decimal fractions. The items for knowledge of common fraction notation sound very different than the items for whole numbers or decimal fractions. It can be argued that the major task for students in acquiring meaningful knowledge of decimals is to connect written symbols and rules of decimal fractions with the quantities they represent. The cognitive analysis proposed that understanding decimals depends on making connections-connections between different number systems and between decimal symbols and appropriate quantitative referents.
