Cognitive Development 23 (2008) 237–257 Available online at www.sciencedirect.com Understanding linear and exponential growth: Searching for the roots in 6- to 9-year-olds Mirjam Ebersbach a,c,∗ , Wim Van Dooren b , Wim Van den Noortgate b , Wilma C.M. Resing a a Department of Psychology, University of Leiden, The Netherlands b Department of Educational Sciences, Catholic University of Leuven, Belgium c Martin-Luther-University Halle-Wittenberg, Department of Psychology, Section Developmental Psychology, D-06099 Halle (S.), Germany Abstract Previous studies have suggested that children as young as 9 years old have developed an understanding of non-linear growth processes prior to formal education. The present experiment aimed at investigating this competency in even younger samples (i.e., in kindergartners, first, and third graders, ages 6, 7 and 9, respectively). Children (N = 90) solved non-verbal inductive reasoning tasks by forecasting linear and exponential growth. While children of all ages forecasted linear growth adequately, exponential growth was also estimated remarkably well. Surprisingly, kindergartners and third graders showed similar high achieve- ment concerning the magnitude and curve shape of forecasts, whereas first graders performed significantly worse. We concluded that primary knowledge of both linearity and non-linearity exists even in kinder- gartners. However, children’s understanding is quite fragile, as their performance was strongly affected by task sequence: Children underestimated exponential growth when the previous task required a forecast of linear growth, and overestimated linear growth when the previous task required forecasting of exponential growth. © 2008 Elsevier Inc. All rights reserved. Keywords: Intuitive mathematics; Linear and non-linear functions; Inductive reasoning; Implicit knowledge Many processes in everyday life can be conceived of in terms of functional relations. Previous research has demonstrated that children possess an early grasp of functional relations, ranging from the understanding of causal relations in infants (e.g., Sobel & Kirkham, 2006) to school ∗ Corresponding author at: Alpen-Adria University, Department of Psychology, Section Developmental Psychology and Educational Psychology, Universit¨ atsstr. 65-67, A-9020 Klagenfurt, Austria. Tel.: +43 463 27001613/+49 345 5524353. E-mail addresses: mirjam.ebersbach@uni-klu.ac.at, mirjam.ebersbach@psych.uni-halle.de (M. Ebersbach). 0885-2014/$ – see front matter © 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.cogdev.2008.01.001