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- Robert S. Siegler, John Opfer
- Psychological science
- 2003

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… (More)

- John Opfer, Robert S. Siegler
- 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 representations is… (More)

- John Opfer
- Cognition
- 2002

To reason competently about novel entities, people must discover whether the entity is alive and/or sentient. Exactly how people make this discovery is unknown, although past researchers have proposed that young children--unlike adults--rely chiefly on whether the object can move itself. This study examined the effect of goal-directed versus aimless… (More)

- Clarissa Thompson, John Opfer
- 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 numerical… (More)

- John Opfer, Clarissa Thompson, Ellen Furlong
- 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 expected… (More)

- John Opfer, Clarissa Thompson
- Child development
- 2008

Spontaneous transfer of learning is often difficult to elicit. This finding may be widespread partly because pretests proactively interfere with transfer. To test this hypothesis, 7-year-olds' transfer was examined across 2 numerical tasks (number line estimation and categorization) in which similar representational changes have been observed. As predicted,… (More)

- Clarissa Thompson, John Opfer
- Child development
- 2010

How does understanding the decimal system change with age and experience? Second, third, sixth graders, and adults (Experiment 1: N = 96, mean ages = 7.9, 9.23, 12.06, and 19.96 years, respectively) made number line estimates across 3 scales (0-1,000, 0-10,000, and 0-100,000). Generation of linear estimates increased with age but decreased with numerical… (More)

- John Opfer, Jeffrey M Devries
- Cognition
- 2008

Development of estimation has been ascribed to two sources: (1) a change from logarithmic to linear representations of number and (2) development of general mathematical skills. To test the representational change hypothesis, we gave children and adults a task in which an automatic, linear representation is less adaptive than the logarithmic representation:… (More)

- John Opfer, Robert S. Siegler, Christopher Young
- 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 by… (More)

- Megan J. Bulloch, John Opfer
- Developmental science
- 2009

Development of reasoning is often depicted as involving increasing use of relational similarities and decreasing use of perceptual similarities ('the perceptual-to-relational shift'). We argue that this shift is a special case of a broader developmental trend: increasing sensitivity to the predictive accuracy of different similarity types. To test this… (More)