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Direct linkKim, Dan; Opfer, John E. – Cognitive Science, 2021
Perceptual judgments result from a dynamic process, but little is known about the dynamics of number-line estimation. A recent study proposed a computational model that combined a model of trial-to-trial changes with a model for the internal scaling of discrete numbers. Here, we tested a surprising prediction of the model--a situation in which…
Descriptors: Numbers, Computation, Children, Adults
Download full textKim, Dan; Opfer, John E. – Grantee Submission, 2021
Perceptual judgments result from a dynamic process, but little is known about the dynamics of number-line estimation. A recent study proposed a computational model that combined a model of trial-to-trial changes with a model for the internal scaling of discrete numbers. Here, we tested a surprising prediction of the model--a situation in which…
Descriptors: Numbers, Computation, Children, Adults
Kim, Dan; Opfer, John E. – Developmental Psychology, 2020
Kim and Opfer (2017) found that number-line estimates increased approximately logarithmically with number when an upper bound (e.g., 100 or 1000) was explicitly marked (bounded condition) and when no upper bound was marked (unbounded condition). Using procedural suggestions from Cohen and Ray (2020), we examined whether this logarithmicity might…
Descriptors: Computation, Cognitive Development, Numbers, Cognitive Processes
Kim, Dan; Opfer, John E. – Grantee Submission, 2020
Kim and Opfer (2017) found that number-line estimates increased approximately logarithmically with number when an upper bound (e.g., 100 or 1000) was explicitly marked (bounded condition) and when no upper bound was marked (unbounded condition). Using procedural suggestions from Cohen and Ray (2020), we examined whether this logarithmicity might…
Descriptors: Computation, Cognitive Development, Numbers, Cognitive Processes
Tosto, Maria Grazia; Garon-Carrier, Gabrielle; Gross, Susan; Petrill, Stephen A.; Malykh, Sergey; Malki, Karim; Hart, Sara A.; Thompson, Lee; Karadaghi, Rezhaw L.; Yakovlev, Nikita; Tikhomirova, Tatiana; Opfer, John E.; Mazzocco, Michèle M. M.; Dionne, Ginette; Brendgen, Mara; Vitaro, Frank; Tremblay, Richard E.; Boivin, Michel; Kovas, Yulia – British Journal of Educational Psychology, 2019
Background: The number line task assesses the ability to estimate numerical magnitudes. People vary greatly in this ability, and this variability has been previously associated with mathematical skills. However, the sources of individual differences in number line estimation and its association with mathematics are not fully understood. Aims: This…
Descriptors: Twins, Individual Differences, Computation, Mathematics Skills
Sidney, Pooja; Thompson, Clarissa G.; Opfer, John E. – Grantee Submission, 2019
Children's understanding of fractions, including their symbols, concepts, and arithmetic procedures, is an important facet of both developmental research on mathematics cognition and mathematics education. Research on infants', children's, and adults' fraction and ratio reasoning allows us to test a range of proposals about the development of…
Descriptors: Mathematics Instruction, Mathematical Concepts, Concept Formation, Fractions
Kim, Dan; Opfer, John E. – Developmental Psychology, 2017
Representations of numerical value have been assessed by using bounded (e.g., 0-1,000) and unbounded (e.g., 0-?) number-line tasks, with considerable debate regarding whether 1 or both tasks elicit unique cognitive strategies (e.g., addition or subtraction) and require unique cognitive models. To test this, we examined how well a mixed log-linear…
Descriptors: Computation, Numbers, Children, Cognitive Development
Opfer, John E.; Siegler, Robert S.; Young, Christopher J. – Developmental Science, 2011
Barth and Paladino (2011) argue that changes in numerical representations are better modeled by a power function whose exponent gradually rises to 1 than as a shift from a logarithmic to a linear representation of numerical magnitude. However, the fit of the power function to number line estimation data may simply stem from fitting noise generated…
Descriptors: Numbers, Computation, Models, Prediction
Ratcliff, Roger; Love, Jessica; Thompson, Clarissa A.; Opfer, John E. – Child Development, 2012
Children (n = 130; M[subscript age] = 8.51-15.68 years) and college-aged adults (n = 72; M[subscript age] = 20.50 years) completed numerosity discrimination and lexical decision tasks. Children produced longer response times (RTs) than adults. R. Ratcliff's (1978) diffusion model, which divides processing into components (e.g., quality of…
Descriptors: Children, Young Adults, Older Adults, Reaction Time
Opfer, John E.; Martens, Marilee A. – Developmental Science, 2012
Experience engenders learning, but not all learning involves representational change. In this paper, we provide a dramatic case study of the distinction between learning and representational change. Specifically, we examined long- and short-term changes in representations of numeric magnitudes by asking individuals with Williams syndrome (WS) and…
Descriptors: Children, Computation, Numbers, Change
Opfer, John E.; Thompson, Clarissa A.; Furlong, Ellen E. – Developmental Science, 2010
Numeric magnitudes often bias adults' spatial performance. Partly because the direction of this bias (left-to-right versus right-to-left) is culture-specific, it has been assumed that the orientation of spatial-numeric associations is a late development, tied to reading practice or schooling. Challenging this assumption, we found that preschoolers…
Descriptors: Spatial Ability, Organizations (Groups), Preschool Education, Evaluation
Siegler, Robert S.; Thompson, Clarissa A.; Opfer, John E. – Mind, Brain, and Education, 2009
The relation between short-term and long-term change (also known as learning and development) has been of great interest throughout the history of developmental psychology. Werner and Vygotsky believed that the two involved basically similar progressions of qualitatively distinct knowledge states; behaviorists such as Kendler and Kendler believed…
Descriptors: Numbers, Cognitive Structures, Developmental Psychology, Information Processing
Thompson, Clarissa A.; Opfer, John E. – Journal of Experimental Child Psychology, 2008
Studies have reported high correlations in accuracy across estimation contexts, robust transfer of estimation training to novel numerical contexts, and adults drawing mistaken analogies between numerical and fractional values. We hypothesized that these disparate findings may reflect the benefits and costs of learning linear representations of…
Descriptors: Age Differences, Costs, Correlation, Computation
Opfer, John E.; Siegler, Robert S. – Cognitive Psychology, 2007
We applied overlapping waves theory and microgenetic methods to examine how children improve their estimation proficiency, and in particular how they shift from reliance on immature to mature representations of numerical magnitude. We also tested the theoretical prediction that feedback on problems on which the discrepancy between two…
Descriptors: Children, Feedback (Response), Grade 2, Numbers
