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…

When proportional information is pit against whole number numerical information, children often attend to the whole number information at the expense of proportional information (e.g., indicating 4/9 is greater than 3/5 because 4 > 3). In the current study, we presented younger (3- to 4-year-olds) and older (5- to 6-year-olds) children a task…

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…

How do people make rich inferences from such sparse data? Recent research has explored this inferential ability by investigating probabilistic reasoning in infancy. For example, 8- and 11-month-old infants can make inferences from samples to populations and vice versa (Denison & Xu, 2010a; Xu & Denison, 2009; Xu & Garcia, 2008a). 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…

Investigated whether and how children age 5 to 7 employed counting to measure and integrate the duration of two events, which were accompanied by metronome beats for half the children. The rhythm enhanced use of counting in younger children. By age 7, most counted spontaneously, using sensible counting strategies. (SKC)

Examined whether representational changes in digit memory are functions of children's expertise in mental abacus operation when abacus operators reproduced series of digits forward or backward. Found skilled operators equally facile with forward and backward reproduction, but novices slower going backward. Suggests advanced operators apply their…

Preschoolers' performance on two tasks demonstrated that, given a perceptually available set of dolls, they were able to use number words to determine the quantity of a hidden or nonexistent set of items that was in a known ratio to the available set. (MM)

Compares the Genevan and Cattell-Horn theories of intelligence and describes both similarities and differences. Describes a study investigating the relation of the Piagetian operative level to the child's ability to use crystallized solution procedures (aids) in making elementary numerical comparisons. (HOD)

Data were generally consistent with the view that preschoolers and elementary schoolers can respond to memory probes by applying arithmetical processing to running gist from recently solved problems. Discussed are two competing interpretations of the development of working memory: fuzzy-trace theory and the generic-resources hypothesis. (Author/RH)

Tested 3- to 7-year-olds' ability to calculate with whole numbers, fractions, and mixed-numbers, in a task in which an amount was displayed, then hidden. Subjects were to determine the hidden amount resulting when numbers were added or substracted. Found that, although fraction problems were more difficult than whole-number problems, competence on…

Children and adults were tested on six speeded perceptual-motor and cognitive tasks, including a (1) response time task; (2) button tapping task; (3) pegboard task; (4) coding task; (5) picture matching task; and (6) mental addition task. Age-related change in processing time on most of these tasks was described by a single exponential function.…

Examined the performance of kindergartners from middle- and low-income families on arithmetic calculations presented in a nonverbal format and in three verbal formats. Children from middle-income families performed better than those from low-income families on verbal calculation tasks but not on the nonverbal task. (BC)