The ultimate goal of this project is to provide a novel model of the cognitive and neural basis of numerical cognition, and to use this knowledge to guide the development of new training methods that could improve mathematical abilities in children. The project is a collaboration among investigators at the University of Rochester, Johns Hopkins University, and Cold Spring Harbor Laboratories. Recent research suggests that acuity of numerosity judgments is predictive of success in formal mathematics education, and that similar cognitive processes can be trained by specific kinds of domain-general experience. The core idea is that the firing of neurons encodes a probability distribution, thereby representing simultaneously the most probable sample from the distribution and the variance (i.e., confidence) of the estimate.
This project will develop and test a formal Bayesian model that has the unique feature of naturally accounting for a number of metacognitive factors, a critical but undertested factor in the acquisition of expertise. The primary advantages of this Bayesian approach are its ability to provide a natural description of: 1) how the confidence of a learner relates to the precision of their number knowledge; 2) how a learner can combine information from multiple sources of information about number; 3) how intuitive preferences (also known as prior belief) predict learners' errors; and 4) how improvements in probabilistic inference may benefit the precision of the number sense.
