Children's numerical competence in kindergarten is highly predictive of their acquisition of mathematics in Grade 1 and Grade 2, suggesting that experiences at home before schooling are important in understanding how numeracy develops. In this study, the mathematical skills of 146 children in Kindergarten, Grade 1, and Grade 2 were correlated with the frequency with which parents reported informal activities that have quantitative components such as board and card games, shopping, or cooking. Effect sizes were consistent with research relating home literacy experiences to children's vocabulary. The present research supports claims about the importance of home experiences in children's acquisition of mathematics.

A model of the relations among cognitive precursors, early numeracy skill, and mathematical outcomes was tested for 182 children from 4.5 to 7.5 years of age. The model integrates research from neuroimaging, clinical populations, and normal development in children and adults. It includes 3 precursor pathways: quantitative, linguistic, and spatial attention. These pathways (a) contributed independently to early numeracy skills during preschool and kindergarten and (b) related differentially to performance on a variety of mathematical outcomes 2 years later. The success of the model in accounting for performance highlights the need to understand the fundamental underlying skills that contribute to diverse forms of mathematical competence.

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Individuals who do well in mathematics and science also often have good spatial skills. However, the predictive direction of links between spatial abilities and mathematical learning has not been firmly established, especially for young children. In the present research, we addressed this issue using a sample from a longitudinal data set that spanned 4 years and which includes measures of mathematical performance and various cognitive skills, including spatial ability. Children were tested once in each of 4 years (Time 1, 2, 3, and 4). At Time 3 and 4, 101 children (in Grades 2, 3, or 4 at Time 3) completed mathematical measures including (a) a number line task (0–1000), (b) arithmetic, and (c) number system knowledge. Measures of spatial ability were collected at Time 1, 2, or 3. As expected, spatial ability was correlated with all of the mathematical measures at Time 3 and 4, and predicted growth in number line performance from Time 3 to Time 4. However, spatial ability did not predict growth in either arithmetic or in number system knowledge. Path analyses were used to test whether number line performance at Time 3 was predictive of arithmetic and number system knowledge at Time 4 or whether the reverse patterns were dominant. Contrary to the prediction that the number line is an important causal construct that facilitates learning arithmetic, no evidence was found that number line performance predicted growth in calculation more than calculation predicted number line growth. However, number system knowledge at Time 3 was predictive of number line performance at Time 4, independently of spatial ability. These results provide useful information about which aspects of growth in mathematical performance are (and are not) related to spatial ability and clarify the relations between number line performance and measures of arithmetic and number system knowledge.

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Planning and self-control were examined in relation to preschoolers' (41- to 74-months) saving behavior. Employing a marble run paradigm, 54 children participated in two trials in which they could use their marbles immediately on a less desirable run, or save for a more desirable run. Twenty-nine children received the opportunity to create a budget. On Trial 1, children in the budgeting condition saved significantly more than did children in the control condition, and their planning ability related to saving (after controlling for age and language). Those who consistently budgeted at least one marble for the more desirable run were more likely to save. Control children's performance improved across trials, with no between-condition differences on Trial 2. Self-control was not related to saving.