Children's intuitive mathematics: the development of knowledge about nonlinear growth.

This study is concerned with the development of children's intuitive understanding of nonlinear processes. The ability to estimate linear and exponential growth was examined in 7-, 9-, 11-, and 13-year-old children and adults (N=160). Whereas linear growth was judged correctly at all ages, estimations of exponential growth were in line with mathematically correct values only in 13-year-olds and adults. However, 9-year-olds already judged the result of exponential growth as being significantly higher than that of linear growth, and even a remarkable proportion of 7-year-olds showed such discrimination between the two types of functions. Results point to the existence of an early intuitive knowledge about the characteristics of nonlinear growth, long before those functions are taught in school.