John E. Opfer
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View article: Cognitive support for political partisans’ understanding of policy data
Cognitive support for political partisans’ understanding of policy data Open
Political partisanship might lead educated adults–even the highly numerate–to reason selectively about numbers that are relevant to and support their ideology (“motivated numeracy”). In this pre-registered study, we sought to examine the r…
View article: From integers to fractions: The role of analogy in transfer and long-term learning
From integers to fractions: The role of analogy in transfer and long-term learning Open
Fractions are the gatekeepers to advanced mathematics but are difficult to learn. One powerful learning mechanism is analogy, which builds fraction understanding on a pre-existing foundation of integer knowledge. Indeed, a short interventi…
View article: Number, not uncertainty, drives logarithmic compression of numerosity estimates
Number, not uncertainty, drives logarithmic compression of numerosity estimates Open
When estimating the number of dots on a number line, logarithmicity of estimates typically increases with the range of numbers tested. This effect may reflect a logarithmic encoding of numbers (Dehaene et al, 2008). An alternative hypothes…
View article: From integers to fractions: The role of analogy in developing a coherent understanding of proportional magnitude.
From integers to fractions: The role of analogy in developing a coherent understanding of proportional magnitude. Open
Children display an early sensitivity to implicit proportions (e.g., 1 of 5 apples vs. 3 of 4 apples), but have considerable difficulty in learning the explicit, symbolic proportions denoted by fractions (e.g., "1/5" vs. "3/4"). Theoretica…
View article: Dynamics Versus Development in Numerosity Estimation: A Computational Model Accurately Predicts a Developmental Reversal
Dynamics Versus Development in Numerosity Estimation: A Computational Model Accurately Predicts a Developmental Reversal Open
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 intern…
View article: Cognitive mediators of US—China differences in early symbolic arithmetic
Cognitive mediators of US—China differences in early symbolic arithmetic Open
Chinese children routinely outperform American peers in standardized tests of mathematics knowledge. To examine mediators of this effect, 95 Chinese and US 5-year-olds completed a test of overall symbolic arithmetic, an IQ subtest, and thr…
View article: Cognitive Supports for Objective Numeracy
Cognitive Supports for Objective Numeracy Open
Political ideology leads educated adults–especially the highly numerate–to selectively reason about numbers that support their beliefs (“motivated numeracy”). We investigated whether supports that help children’s quantitative reasoning (nu…
View article: Compression is evident in children’s unbounded and bounded numerical estimation: Reply to Cohen and Ray (2020).
Compression is evident in children’s unbounded and bounded numerical estimation: Reply to Cohen and Ray (2020). Open
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 condi…
View article: Linear Spatial–Numeric Associations Aid Memory for Single Numbers
Linear Spatial–Numeric Associations Aid Memory for Single Numbers Open
Memory for numbers improves with age. One source of this improvement may be learning linear spatial-numeric associations, but previous evidence for this hypothesis likely confounded memory span with quality of numerical magnitude represent…
View article: The nature of the association between number line and mathematical performance: An international twin study
The nature of the association between number line and mathematical performance: An international twin study Open
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 di…
View article: Individual differences in addition strategy choice: A psychometric evaluation.
Individual differences in addition strategy choice: A psychometric evaluation. Open
The Strategy Choice Model (SCM) is a highly influential theory of human problem-solving. One strength of this theory is the allowance for both item and person variance to contribute to problem-solving outcomes, but this central tenet of th…
View article: Nuclear IHC enumeration: A digital phantom to evaluate the performance of automated algorithms in digital pathology
Nuclear IHC enumeration: A digital phantom to evaluate the performance of automated algorithms in digital pathology Open
Automatic and accurate detection of positive and negative nuclei from images of immunostained tissue biopsies is critical to the success of digital pathology. The evaluation of most nuclei detection algorithms relies on manually generated …
View article: A Field Guide for Teaching Evolution in the Social Sciences
A Field Guide for Teaching Evolution in the Social Sciences Open
The theory of evolution by natural selection has begun to revolutionize our understanding of perception, cognition, language, social behavior, and cultural practices. Despite the centrality of evolutionary theory to the social sciences, ma…
View article: Number sense and mathematics: Which, when and how?
Number sense and mathematics: Which, when and how? Open
Individual differences in number sense correlate with mathematical ability and performance, although the presence and strength of this relationship differs across studies. Inconsistencies in the literature may stem from heterogeneity of nu…
View article: A unified framework for bounded and unbounded numerical estimation.
A unified framework for bounded and unbounded numerical estimation. Open
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., additi…
View article: Learning Linear Spatial-Numeric Associations Improves Accuracy of Memory for Numbers
Learning Linear Spatial-Numeric Associations Improves Accuracy of Memory for Numbers Open
Memory for numbers improves with age and experience. One potential source of improvement is a logarithmic-to-linear shift in children's representations of magnitude. To test this, Kindergartners and second graders estimated the location of…