In science, we use common graphical representations to indicate changes in events over time, independent of domain. Are children also sensitive to abstract patterns in the ways events change over time? In a series of four experiments, we show that young children (range: 48-84 months) distinguish different function families (Exp 1). Children can also distinguish specific function types within function families (e.g., between linear and sigmoid monotonic functions; Exp 2); nonetheless, they will group different function types within a family together, rather than with functions in a different family (Exp 3). Finally, we show that children’s sensitivity to functions is abstract, allowing them to match observable causes to verbal descriptions of their effects (Exp 4). These results suggest that although some aspects of function understanding, like learning how to interpret graphs, requires formal education, the ability to identify abstract functional relationships is intuitive and early emerging.

Causal relationships can generate many different kinds of correlations among variables. However, research on children’s causal reasoning has focused almost exclusively on just one kind of regularity: the temporal covariation between candidate causes and effects, and in particular, the covariation between interventions and outcomes. Here we show that young children recognize more abstract correlations – in the ways that object properties are distributed over sets, or change over time – and constrain their causal hypotheses accordingly. Specifically, we show that children (range: 48-84 months) distinguish candidate causes based on correlations in the distribution of discrete (set size, arity, and proportion) and continuous (mean and mode) properties of sets (Experiment 1), and also within monotonic, quadratic, and periodic functions (Experiment 2). Keywords: children; causal reasoning; abstract concepts; sets; functions

Humans learn and generate languages, music, games, and seemingly limitless varieties of other structures across domains. Unlike many AI systems, we often do so from little data. How do we learn such large varieties of richly structured representations so efficiently? One possibility is that people ``learn by programming,'' synthesizing data-generating algorithms to explain what we observe. We examine the nature and origins of this learning mechanism in adults, children, and nonhuman primates (macaque monkeys), using a highly unconstrained sequence prediction task. Although adults and children quickly learn many richly structured sequences, monkeys learn only the simplest sequences (e.g. lines). We test multiple learning models, finding that adults are best explained by a ``Language of Thought''-like program-learning model and monkeys by a simpler extrapolation strategy. Children exhibit varied learning strategies but are best fit in aggregate by an intermediately expressive model. Paper available at https://sites.google.com/view/patternlearning.

Children know a lot about counting, even before they can count; for instance, even toddlers know that the counting routine involves establishing one-to-one correspondence between number words and items counted. Here we varied the size, numerosity, density, and layout of elements of sets, and asked children which set was easier to count in pair-wise comparisons across twelve trials. We also asked children themselves to count 5 to 15 items arranged in straight lines. Even children who could not count to 15 recognized that it was easier to count fewer than more dots and recognized that structured sets were easier than random arrays; however, they failed to recognize that some layouts made tracking easier than others. This suggests that children's meta-knowledge about counting precedes their ability to count for some but not all properties of sets.