Functional relations are prevalent in everyday life and science. Do children have intuitive knowledge of functional relations, and can they learn these relations by active information gathering (i.e., choosing a few input values and observing the corresponding outputs)? We found that 6- to 9-year-olds can learn different families of functions (linear, Gaussian, and exponential) through both informative data provided by an experimenter and data they gather from the environment for themselves. Overall, children learn linear functions more accurately than non-linear functions. When choosing data points to learn about, some children select highly similar points that only shed light on a narrow region of a function, while others choose more variable inputs and gain a more holistic view of a function. Children who use this latter, globally informative strategy have higher learning accuracy, particularly for non-linear functions. Results suggest that children are in the process of developing effective strategies for active function learning.

Authors:

Caiqin Zhou: Brown University; Rebekah Gelpi: University of Toronto; Chris Lucas: University of Edinburgh; Daphna Buchsbaum: Brown University