Discriminating Non-linearity from Linearity: Its Cognitive Foundations in Five-Year-Olds

Abstract

People often have difficulties in understanding situations that involve non-linear processes. Also, the topic of non-linear functions is introduced relatively late in the curriculum. Previous research has nevertheless shown that already children aged 6 years and older are able to discriminate non-linear from linear processes. Within the present article, we examined in more detail the cognitive foundations of this ability in kindergartners. In three experiments, 5-year-olds were presented with the first steps of linear and non-linear (i.e., polynomial and exponential) growth processes and had to forecast future growth. Their forecasts indicated that they distinguished between linear and non-linear growth by taking into account (1) the initial magnitudes of the first steps of the growth processes, (2) the slopes exhibited by these first growth steps, and sometimes also (3) the constant or increasing rates of change. However 5-year-olds' performances appeared somewhat unstable across the experiments, which will be discussed in terms of strategy acquisition and task presentation. Nevertheless, children's sensitivity toward these three characteristics indicates that 5-year-olds possess the cognitive foundations that allow them in principle to develop knowledge about both linear and non-linear processes.