Learning Addition and Subtraction

There are thousands of different systems of number words; on the island of Papua New Guinea alone there are over 700 languages (Lancy, 1983; see also Ifrah 1981/1985; Menninger, 1958/1969; Zaslavsky, 1973). Many cultures, especially those surrounding and within the Pacific Ocean, even have several different number-word systems that are used for different purposes or for counting different kinds of objects. The features of a system of number words affect how easily it can be learned and used to add and subtract numbers less than 10, to add and subtract numbers between 10 and 100, and to add and subtract numbers larger than 100. This chapter will focus on some of the features that affect these different aspects of numerical learning. The concentration will be on a comparison between European systems of number words, which are irregular up to 100 (with English used as the main example), and the Asian systems that are based on Chinese, which are totally regular. Most of the points made also generalize to a wide variety of other systems of number words, and examples will be given where available. Nonlinguistic cultural supports for learning addition and subtraction, especially the different uses of fingers as countables, will also be discussed.