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…

Humans and other animals are able to make rough estimations of quantities using what has been termed the "approximate number system" (ANS). Much evidence suggests that sensitivity to numerosity correlates with symbolic math capacity, leading to the suggestion that the ANS may serve as a start-up tool to develop symbolic math. Many…

Considerable recent work suggests that mathematical abilities in children correlate with the ability to estimate numerosity. Does math correlate only with numerosity estimation, or also with other similar tasks? We measured discrimination thresholds of school-age (6- to 12.5-years-old) children in 3 tasks: numerosity of patterns of relatively…

Are there differential benefits of training sequential number knowledge versus spatial skills for children's numerical and spatial performance? Three- to five-year-old children (N = 84) participated in 1 session of either sequential training (e.g., what comes before and after the number 5?) or non-numerical spatial training (i.e., decomposition of…

Accurate monitoring and control are essential for effective self-regulated learning. These metacognitive abilities may be particularly important for developing math skills, such as when children are deciding whether a math task is difficult or whether they made a mistake on a particular item. The present experiments investigate children's ability…

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…

In response to claims that the quality (and in particular linearity) of children's mental representation of number acts as a constraint on number development, we carried out a longitudinal assessment of the relationships between number line estimation, counting, and mathematical abilities. Ninety-nine 5-year-olds were tested on 4 occasions at 3…

Is "two" ever a plural marker in child language? By some accounts, children bootstrap the distinction between the words "one" and "two" by observing their use with singular-plural marking ("one ball/two balls"). Others argue that the numeral "two" marks plurality before children begin using numerals to denote precise quantities. We tested the…

Matching methods such as nearest neighbor propensity score matching are increasingly popular techniques for controlling confounding in nonexperimental studies. However, simple k:1 matching methods, which select k well-matched comparison individuals for each treated individual, are sometimes criticized for being overly restrictive and discarding…

The classical twin study provides a useful resource for testing hypotheses about how the family environment influences children's development, including how genes can influence sensitivity to environmental effects. However, existing statistical models do not account for the possibility that children can inherit exposure to family environments…

What is the nature of the association between age (7-11 years) and performance on mathematical equivalence problems (e.g., 7 + 4 + 5 + 7 + _)? Many prevailing theories suggest that there should be a positive association. However, change-resistance accounts (e.g., N. M. McNeil & M. W. Alibali, 2005b) predict a U-shaped association. The purpose of…