Children learn the cardinalities of the first numbers one, two, three and four before they learn how counting tracks cardinality for all numbers. It may be that when children start to understand counting, they also discover how numbers relate to one another in a structured number system. Do children who understand that the cardinality of a set is…

Number-recognition tasks, such as the how-many task, involve set-to-word mapping, and number-creation tasks, such as the give-n task, entail word-to-set mapping. The present study involved comparing sixty 3-year-olds' performance on the two tasks with collections of one to three items over three time points about 3 weeks apart. Inconsistent with…

Magnitude information, for instance, regarding weight, distance, or velocity, is crucial for planning goal-directed interactions. Accordingly, magnitude information, including numerical magnitude, can affect actions: Responses to small numbers are faster with the left hand than the right and vice versa (hand-based SNARC effect). Previous…

During the preschool years, children are simultaneously undergoing a reshaping of their mental number line and becoming increasingly sensitive to the social norms expressed by those around them. In the current study, 4- and 5-year-old American and Israeli children were given a task in which an experimenter laid out chips with numbers (1-5),…

This study explored whether kindergarteners who had yet to learn about multi-digit numbers at school could automatically process the underlying magnitudes, i.e., place-values, represented by the digits in a multi-digit number. A place-value Stroop task showed a pair of price tags in each trial. Each price tag contained a three-digit number, of…

Young children are sensitive to both numerical and spatial magnitude cues early in development, but many questions remain about how children's attention to magnitudes relates to their early math achievement. In two studies, we tested three hypotheses related to the flexible attention to magnitudes (FAM) account, which suggests that young…

This article offers reflections on task design in the context of a Grade R (reception year) in-service numeracy project in South Africa. The research explores under what conditions, and for what learning purpose, a task designed by someone else may be recast and how varying given task specifications may support or inhibit learning, as a result of…

Do children spontaneously represent spatial-numeric features of a task, even when it does not include printed numbers (Mix et al., 2016)? Sixty first grade students completed a novel spatial estimation task by seeking and finding pages in a 100-page book without printed page numbers. Children were shown pages 1 through 6 and 100, and then were…

The move from additive to multiplicative thinking requires significant change in children's comprehension and manipulation of numerical relationships, involves various conceptual components, and can be a slow, multistage process for some. Unit arrays are a key visuospatial representation for supporting learning, but most research focuses on 2D…

Dot comparison tasks are commonly used to index an individual's Approximate Number System (ANS) acuity, but the cognitive processes involved in completing these tasks are poorly understood. Here, we investigated how factors including numerosity ratio, set size and visual cues influence task performance. Forty-four children aged 7-9 years completed…

The present study aims to examine relations between number representations and various sources of individual differences within early stages of development of number representations. The mental number line has been found to develop from a logarithmic to a more linear representation. Sources under investigation are counting skills and executive…

Do concrete learning materials promote strong learning outcomes, or do they simply make learning tasks more initially accessible? Although concrete materials may offer an intuitive foothold on a topic, research on desirable difficulties suggests that more challenging tasks facilitate greater retention and transfer. In the approach introduced here,…

The current study examined the development of two effects that have been found in single-digit multiplication errors: relatedness and distance. Typically achieving (TA) second, fourth, and sixth graders and adults, and sixth and eighth graders with a mathematics learning disability (MLD) performed a verification task. Relatedness was defined by a…

This paper reports on one phase of a long-term project investigating mathematical content knowledge of pre-service teachers. A cohort of second year PSTs conducted a diagnostic assessment and a series of associated tutoring sessions with a primary aged child. The focus here is on the PSTs' ability to make appropriate task choices following the…

In a recent study, Gevers and colleagues (2010, "Journal of Experimental Psychology: General," Vol. 139, pp. 180-190) showed that the SNARC (spatial numerical association of response codes) effect in adults results not only from spatial coding of magnitude (e.g., mental number line hypothesis) but also from verbal coding. Because children are…