Early function concepts: their development and relation to certain mathematical and logical abilities

Cognition of functions (i.e., y = f(x)) has been identified as an achievement of early childhood. To investigate the development of function concepts and their relation to mathematical and logical abilities typically acquired during the age period of 5-7 years, 72 children in this age range were tested on nonnumerical function tasks (functions as exchange of properties, functions as displacement of positions, and functions as preservation of structure), numerical tasks (number conservation and arithmetic problems), and aspects of logical reasoning (class inclusion, class vicariance, and seriation). Orderly developmental trends were found in function task performance, with younger children manifesting limited success through trial-and-error strategies and older children achieving substantial success with anticipatory strategies. Moreover, certain function abilities were associated with the numerical domain, whereas others were associated with the logical domain. The findings are consistent with the developmental model of Piaget et al. according to which cognition of functions lays the groundwork for reversible operations, but also suggest that this development occurs through parallel processes within separate conceptual domains.