John E Opfer
Biographic Data
| ID | 144990 |
|---|---|
| NAME | John E Opfer |
| GIVEN NAMES | John E |
| FAMILY NAME | Opfer |
| SIGNATURE | OPFER J E |
| AFFILIATIONS | The Ohio State University |
| ORCID | 0000-0001-8406-3196 |
| VERIFIED | Yes |
| TOTAL WORKS | 10 |
| TOTAL CITATIONS | 4 |
| AUTHOR COUNT | 10 |
| EDITOR COUNT | 0 |
| FIRST PUBLICATION YEAR | 2003 |
| LATEST PUBLICATION YEAR | 2024 |
| H-INDEX | 1 |
Varieties of Number-Line Estimation
A number-line task with a Bayesian active learning algorithm provides insights into the development of non-symbolic number estimation
From integers to fractions
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"). Theoretically, reducing the gap between representations of implicit versus explicit proportions would improve understanding of fractions, but little is known about how the representations develop and interact with one ano…
Compression is evident in children’s unbounded and bounded numerical estimation
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 come from restrictions on the response space provided. Consistent with our previous findings, logarith…
The nature of the association between number line and mathematical performance
BackgroundThe 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.AimsThis large-scale genetically sensitive study uses a twin design to estimate the magnitude of the effects of ge…
A field guide for teaching evolution in the social sciences
Number sense and mathematics
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 number sense and mathematical ability constructs. Sample characteristics may also play a role as changes in the relationship between number sense and mathematics may differ across development and cultural contexts…
A unified framework for bounded and unbounded numerical estimation
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 model accounted for 86 5- to 9-year-olds' estimates on bounded and unbounded number-line tasks and ho…
How Numbers Bias Preschoolers' Spatial Search
Numbers often bias adults' spatial performance. Because the direction of this bias (left-to-right versus right-to-left) is culture-specific, it has been assumed that spatial-numeric associations develop with reading practice or schooling. The authors tested this assumption by examining spatial-numeric associations in pre-reading preschoolers. Preschoolers were shown two boxes (sample and matching boxes) subdivided into seven verbally numbered "ro…
The Development of Numerical Estimation
We examined children's and adults' numerical estimation and the representations that gave rise to their estimates. The results were inconsistent with two prominent models of numerical representation: the logarithmic-ruler model, which proposes that people of all ages possess a single, logarithmically spaced representation of numbers, and the accumulator model, which proposes that people of all ages represent numbers as linearly increasing magnitu…
Number sense and mathematics
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 number sense and mathematical ability constructs. Sample characteristics may also play a role as changes in the relationship between number sense and mathematics may differ across development and cultural contexts…
From integers to fractions
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"). Theoretically, reducing the gap between representations of implicit versus explicit proportions would improve understanding of fractions, but little is known about how the representations develop and interact with one ano…
The nature of the association between number line and mathematical performance
BackgroundThe 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.AimsThis large-scale genetically sensitive study uses a twin design to estimate the magnitude of the effects of ge…
The Development of Numerical Estimation
We examined children's and adults' numerical estimation and the representations that gave rise to their estimates. The results were inconsistent with two prominent models of numerical representation: the logarithmic-ruler model, which proposes that people of all ages possess a single, logarithmically spaced representation of numbers, and the accumulator model, which proposes that people of all ages represent numbers as linearly increasing magnitu…
How Numbers Bias Preschoolers' Spatial Search
Numbers often bias adults' spatial performance. Because the direction of this bias (left-to-right versus right-to-left) is culture-specific, it has been assumed that spatial-numeric associations develop with reading practice or schooling. The authors tested this assumption by examining spatial-numeric associations in pre-reading preschoolers. Preschoolers were shown two boxes (sample and matching boxes) subdivided into seven verbally numbered "ro…
Number sense and mathematics
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 number sense and mathematical ability constructs. Sample characteristics may also play a role as changes in the relationship between number sense and mathematics may differ across development and cultural contexts…
A unified framework for bounded and unbounded numerical estimation
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 model accounted for 86 5- to 9-year-olds' estimates on bounded and unbounded number-line tasks and ho…
A field guide for teaching evolution in the social sciences
The nature of the association between number line and mathematical performance
BackgroundThe 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.AimsThis large-scale genetically sensitive study uses a twin design to estimate the magnitude of the effects of ge…
Compression is evident in children’s unbounded and bounded numerical estimation
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 come from restrictions on the response space provided. Consistent with our previous findings, logarith…
A number-line task with a Bayesian active learning algorithm provides insights into the development of non-symbolic number estimation
From integers to fractions
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"). Theoretically, reducing the gap between representations of implicit versus explicit proportions would improve understanding of fractions, but little is known about how the representations develop and interact with one ano…
Varieties of Number-Line Estimation
Cognitive and developmental aspects of mathematical skills (9 works) · Psychology (9 works) · Mathematics (8 works) · Mathematics Education and Teaching Techniques (6 works) · Number line (6 works) · Statistics (6 works) · Computer Science (5 works) · Arithmetic (4 works) · Cognition (4 works) · Cognitive psychology (4 works)