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Mental representations of numerical magnitude are commonly thought to undergo discontinuous change over development in the form of a "representational shift." This idea stems from an apparent categorical shift from logarithmic to linear patterns of numerical estimation on tasks that involve translating between numerical magnitudes and spatial positions(More)
shows that 'linear' estimation patterns in published number-line data actually follow a cyclic power function, a signature of proportional reasoning (Hollands & Dyre, 2000; Spence, 1990). Opfer, Siegler and Young argue that fitting a cyclic power function to number-line data is tantamount to capitalizing on chance. We claim, in contrast, that the cyclic(More)
An essential part of understanding number words (e.g., eight) is understanding that all number words refer to the dimension of experience we call numerosity. Knowledge of this general principle may be separable from knowledge of individual number word meanings. That is, children may learn the meanings of at least a few individual number words before(More)
The present study asks when young children understand that number words quantify over sets of discrete individuals. For this study, 2- to 4-year-old children were asked to extend the number word five or six either to a cup containing discrete objects (e.g., blocks) or to a cup containing a continuous substance (e.g., water). In Experiment 1, only children(More)
A large collection of estimation phenomena (e.g. biases arising when adults or children estimate remembered locations of objects in bounded spaces; Huttenlocher, Newcombe & Sandberg, 1994) are commonly explained in terms of complex Bayesian models. We provide evidence that some of these phenomena may be modeled instead by a simpler non-Bayesian alternative.(More)
Human mathematical abilities comprise both learned, symbolic representations of number and unlearned, non-symbolic evolutionarily primitive cognitive systems for representing quantities. However, the mechanisms by which our symbolic (verbal) number system becomes integrated with the non-symbolic (non-verbal) representations of approximate magnitude(More)
Developmental change in children's number-line estimation has been thought to reveal a categorical logarithmic-to-linear shift in mental representations of number. Some have claimed that the broad and rapid change in estimation patterns that occurs with corrective feedback provides strong evidence for this shift. However, quantitative models of proportion(More)
The current study investigated the development of numerical estimation in 3-to 5-year-old children sampled monthly for six months. At each session, children completed a task that assesses verbal number knowledge (GiveN task) and a numerical estimation task that assesses approximate number knowledge (Fast Cards). Results showed that children who acquired the(More)
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