Implicit and Explicit Knowledge of Linear and Exponential Growth in 5- and 9-Year-Olds

Abstract

The present study examined children's implicit and explicit knowledge of linear and non-linear processes. Five- and nine-year-olds (N = 60) were asked to forecast linear and exponential growth by providing the corresponding number of beads. Implicit knowledge was assessed via the magnitudes of the forecasts; explicit knowledge was investigated through children's verbal explanations of the growth process. Five year olds demonstrated a primary understanding of both linearity and nonlinearity. These concepts were more stable and more advanced in 9 year olds. Although implicit and explicit knowledge were significantly correlated, results suggested that implicit knowledge develops prior to explicit knowledge in this domain. Furthermore, knowledge of linearity emerged earlier than knowledge of nonlinearity.

ACKNOWLEDGEMENTS

Thanks are due to the Swiss National Fond, supporting this research, as well as to Karen Clements, Karlijn van Roosmalen, and Hatice Uysal for data collection and processing as well as to Claire Stevenson, who proofread this article.

Notes

¹In the following analyses, Greenhouse-Geisser instead of Wilks' Lambda will be quoted to indicate within-subjects effects, if sphericity could not be assumed.

Note. Values in parentheses indicate standard deviations. ∗p < .05, ∗∗p < .01 (Bonferroni corrected).

²The criterion in the individual analyses was raised to p > .10 in order to increase the power (see also Schlottman, 2001)