Implicit comprehension of linearity, curvature, periodicity and compositionality in young children’s drawings

How sophisticated is young children’s comprehension of geometric lines and curves, and how can we probe it? Here, we assess an early, proto-mathematical understanding of curves by asking preschoolers (N=39) and first graders (N=42) to draw the prolongation of various mathematical patterns, ranging from linear to non-linear functions such as quadratics and exponentials, periodic functions, and more complex composite patterns. Our findings reveal that even at this early age, children’s drawings indicate an accurate differentiation of several functions, including linear and non-linear ones, and an understanding of linearity and curvature. Furthermore, both age groups displayed intuitions of compositionality by distinguishing, for example, sinusoid functions with an increasing amplitude from those with a decreasing or a constant one. All children had difficulties with more complex patterns, such as those involving changes in both amplitude and frequency, as in stair-like patterns. Our results highlight children’s early understanding of proto-mathematical concepts and the potential of drawing as a powerful tool to assess them in a concrete context.