Although peoples 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 maintanance of these biases.

National Institute of Health (NIH)
Eunice Kennedy Shriver National Institute of Child Health & Human Development (NICHD)
Research Project (R01)
Project #
Application #
Study Section
Cognition and Perception Study Section (CP)
Program Officer
Mann Koepke, Kathy M
Project Start
Project End
Budget Start
Budget End
Support Year
Fiscal Year
Total Cost
Indirect Cost
University of North Carolina Wilmington
Schools of Arts and Sciences
United States
Zip Code
Cohen, Dale J; Quinlan, Philip T (2016) How numbers mean: Comparing random walk models of numerical cognition varying both encoding processes and underlying quantity representations. Cogn Psychol 91:63-81
Blanc-Goldhammer, Daryn R; Cohen, Dale J (2014) Unlimited capacity parallel quantity comparison of multiple integers. J Exp Psychol Learn Mem Cogn 40:1389-403
Cohen, Dale J; Sarnecka, Barbara W (2014) Children's number-line estimation shows development of measurement skills (not number representations). Dev Psychol 50:1640-52
Cohen, Dale J; Warren, Erin; Blanc-Goldhammer, Daryn (2013) Cross-format physical similarity effects and their implications for the numerical cognition architecture. Cogn Psychol 66:355-79
Warren, Erin; Cohen, Dale J (2013) On the relativity of relative frequencies. Atten Percept Psychophys 75:614-29
Cohen, Dale J; Blanc-Goldhammer, Daryn (2011) Numerical bias in bounded and unbounded number line tasks. Psychon Bull Rev 18:331-8
Cohen, Dale J (2010) Evidence for direct retrieval of relative quantity information in a quantity judgment task: decimals, integers, and the role of physical similarity. J Exp Psychol Learn Mem Cogn 36:1389-98
Cohen, Dale J (2009) Numerical representations are neither abstract nor automatic. Behav Brain Sci 32:332-373
Cohen, Dale J (2009) Integers do not automatically activate their quantity representation. Psychon Bull Rev 16:332-6