TY - GEN
T1 - Varieties of Numerical Estimation
T2 - 39th Annual Meeting of the Cognitive Science Society: Computational Foundations of Cognition, CogSci 2017
AU - Qin, Jike
AU - Kim, Dan
AU - Opfer, John
N1 - Funding Information:
We would like to thank the administrators, teachers, students, and parents in Columbus for their involvement on the project. Also, we would like to thank Ariel Lindner and Rebecca Zagorsky for help with data collection. Partial support for this project was provided by a grant from the Institute for Educational Sciences (IES R305A160295).
Publisher Copyright:
© CogSci 2017.
PY - 2017
Y1 - 2017
N2 - There is an ongoing debate over the psychophysical functions that best fit human data from numerical estimation tasks. To test whether one psychophysical function could account for data across diverse tasks, we examined 40 kindergartners, 38 first graders, 40 second graders and 40 adults' estimates using two fully crossed 2 × 2 designs, crossing symbol (symbolic, non-symbolic) and boundedness (bounded, unbounded) on free number-line tasks (Experiment 1) and crossing the same factors on anchored tasks (Experiment 2). Across all 8 tasks, 88.84% of participants provided estimates best fit by a mixed log-linear model, and the weight of the logarithmic component (λ) decreased with age. After controlling for age, the λ significantly predicted arithmetic skills, whereas parameters of other models failed to do so. Results suggest that the logarithmic-to-linear shift theory provides a unified account of numerical estimation and provides uniquely accurate predictions for mathematical proficiency.
AB - There is an ongoing debate over the psychophysical functions that best fit human data from numerical estimation tasks. To test whether one psychophysical function could account for data across diverse tasks, we examined 40 kindergartners, 38 first graders, 40 second graders and 40 adults' estimates using two fully crossed 2 × 2 designs, crossing symbol (symbolic, non-symbolic) and boundedness (bounded, unbounded) on free number-line tasks (Experiment 1) and crossing the same factors on anchored tasks (Experiment 2). Across all 8 tasks, 88.84% of participants provided estimates best fit by a mixed log-linear model, and the weight of the logarithmic component (λ) decreased with age. After controlling for age, the λ significantly predicted arithmetic skills, whereas parameters of other models failed to do so. Results suggest that the logarithmic-to-linear shift theory provides a unified account of numerical estimation and provides uniquely accurate predictions for mathematical proficiency.
KW - cognitive development
KW - number-line estimation
KW - numerical cognition
KW - psychophysical function
UR - http://www.scopus.com/inward/record.url?scp=85056214420&partnerID=8YFLogxK
M3 - Conference Proceeding
AN - SCOPUS:85056214420
T3 - CogSci 2017 - Proceedings of the 39th Annual Meeting of the Cognitive Science Society: Computational Foundations of Cognition
SP - 2943
EP - 2948
BT - CogSci 2017 - Proceedings of the 39th Annual Meeting of the Cognitive Science Society
PB - The Cognitive Science Society
Y2 - 26 July 2017 through 29 July 2017
ER -