Abstract
We present a dataset with 272,700 two-alternative forced choice responses in a simple numerical task modeled after Tenenbaum’s “number game” experiment [6]. Subjects were shown a set (e.g. {16, 12}) and asked what other numbers were likely to belong to that set (e.g. 1, 5, 2, 98). Their generalization patterns reflect both rule-like (e.g. ‘even numbers,’ ‘powers of two’) and distance-based (e.g. ‘numbers near 50’) generalization. This dataset is available for further analysis of these simple and intuitive inferences, developing of hands-on modeling instruction, and attempts to understand how probability and rules interact in human cognition.
Highlights
Numbers and related mathematical ideas form a complex set of interrelated concepts that can be used to study the origin and use of structured mental representations
To examine learning and generalization in this domain, we present an extension of the “number game” task originally developed by Tenenbaum [6]
(2) Methods Sample 606 participants were recruited via Amazon Mechanical Turk (MTurk)
Summary
Numbers and related mathematical ideas form a complex set of interrelated concepts that can be used to study the origin and use of structured mental representations. Subjects are asked to generalize from the samples and predict what other numbers (“targets”) are likely to obey the rule. Subjects might rate 12 as relatively unlikely since the observed data suggests a rule like ‘powers of two’.
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