Efficient algorithms can enhance problem-solving in many cognitive domains but can be difficult to discover and use. For example, classical studies of seriation suggest that children struggle to apply algorithmic strategies in a simple sorting problem. We investigate the spontaneous discovery of algorithmic solutions across development. We gave children a variant of the sorting problem with hidden object ranks. Children sort animated bunnies into the right order, from the shortest to the tallest, when the bunnies are standing behind a wall so their heights are not visible. Children performed far above chance on this difficult sorting task, potentially because higher demands in memory and reasoning incentivized strategic behaviors. Children independently discovered at least two efficient algorithmic solutions to the sorting problem, Selection sort and Shaker sort. This result suggests that children are far more competent at sorting tasks than previous research would suggest. Additionally, older children were more efficient sorters than younger children. This suggests that competent performance on sorting tasks improves throughout development.

Children rely on their approximate number system (ANS) to guess quantities from a young age. Studies have shown that older children displayed better ANS performance. However, previous research did not provide an explanation for this ANS improvement. We show that children’s development in ANS is primarily driven by improved attentional control and awareness of peripheral information. Children guess the number of dots on a computer screen while being eye-tracked in our experiment. The behavioral and eye-tracking results provide supporting evidence for our account. Our analysis shows that children estimate better under the longer display-time condition and more visual foveation, with the effect of visual foveation mediating that of time. It also shows that older children make fewer underestimations because they are better at directing their attention and gaze toward areas of interest, and they are also more aware of dots in their peripheral vision. Our finding suggests that the development of children’s ANS is significantly impacted by the development of children’s non-numerical cognitive abilities.

Previous research has shown that our subjective sense of certainty doesn't always accurately reflect the strength of the evidence that has been presented to us. We investigate several key factors that drive children's certainty using a Boolean concept learning task. We created an idealized learning model to predict children's accuracy and certainty during the experiment, given past evidence that they have seen in the task, and we compared its predictions with our behavioral results. Our results suggest that while predictors from the idealized learning model capture children's accuracy, behavioral predictors generated by the behavioral data can better predict children's certainty. We also show that younger children's certainty can be explained by the idealized learning model, while older children's certainty is primarily predicted by how well they observed themselves doing in the experiment.