Comparing datasets, that is, sets of numbers in context, is a critical skill in higher order cognition. Although much is known about how people compare single numbers, little is known about how number sets are represented and compared. We investigated how subjects compared datasets that varied in their statistical properties, including ratio of means, coefficient of variation, and number of observations, by measuring eye fixations, accuracy, and confidence when assessing differences between number sets. Results indicated that participants implicitly create and (...) compare approximate summary values that include information about mean and variance, with no evidence of explicit calculation. Accuracy and confidence increased, while the number of fixations decreased as sets became more distinct , demonstrating that the statistical properties of datasets were highly related to comparisons. The discussion includes a model proposing how reasoners summarize and compare datasets within the architecture for approximate number representation. (shrink)

We argue that number principles may be learnable instead of innate, by suggesting that children acquire probabilistically true number concepts rather than algorithms. We also suggest that non-propositional representational formats (e.g., mental models) may implicitly provide information that supports the induction of numerical principles. Given probabilistically true number concepts, the problem of the acquisition of mathematical principles is eliminated.