Although people's inability to make intuitive judgments about proportions (for a review, see Rothman & Kiviniemi, 1999) has been shown to lead to poor judgments about health related issues (Kaplan, Hammel, & Schimmel, 1985), relatively little research has been directed at understanding the cognitive representation of proportions. The current proposal will fill this gap by (1) providing extensive data on the internal representation of proportions, and (2) generating models of the cognitive representation of proportions similar to the models that exist for the cognitive representation of integers. The current proposal also addresses the role of experience in the formation and maintenance of numerical biases. Learning how and why these symbols are misinterpreted will lead to techniques to reduce these biases, which in turn will lead to more effective methods of teaching mathematics. The proposed approach combines empirical research, numerical statistical procedures, exploratory analysis, and computational modeling. In particular, the proposed research will assess the distance effect for three numerical formats and three stimuli in which quantity is inherent, assess the biases associated with cross-modality matching for the six stimuli, and use numerical statistical models to estimate the parameters of the numerical biases. Once the functional form of numerical biases are identified and described, I will study the role of experience in the formation and maintenance of these biases. ? ? ?
