Children's knowledge of arithmetic principles is a key aspect of early mathematics knowledge. Knowledge of arithmetic principles predicts how children approach solving arithmetic problems and the likelihood of their success. Prior work has begun to address how children might learn arithmetic principles in a classroom setting. Understanding of…

The present study evaluated 626 5-7-year-old children in the UK, China, Russia, and Kyrgyzstan on a cognitive test battery measuring: (1) general skills; (2) non-symbolic number sense; (3) symbolic number understanding; (4) simple arithmetic--operating with numbers; and (5) familiarity with numbers. Although most inter-population differences were…

The purpose of the study was to determine whether individual differences in at-risk 4th graders' language comprehension, nonverbal reasoning, concept formation, working memory, and use of decimal labels (i.e., place value, point, incorrect place value, incorrect fraction, or whole number) are related to their decimal magnitude understanding.…

Dot enumeration (DE) and number comparison (NC) abilities are considered markers of core number competence. Differences in DE/NC reaction time (RT) signatures are thought to distinguish between typical and atypical number development. Whether a child's DE and NC signatures change or remain stable over time, relative to other developmental…

The arithmetical performance of typically achieving 5- to 7-year-olds (N=29) was measured at four 6-month intervals. The same seven tasks were used at each time point: exact calculation, story problems, approximate arithmetic, place value, calculation principles, forced retrieval, and written problems. Although group analysis showed mostly linear…

As indicated by the distance effect and the spatial-numerical association of response codes (SNARC) effect, natural numbers are mentally represented on a number line. Purportedly, this number line underlies children's number sense, which supports the acquisition of more advanced mathematical competencies. In 3 studies with a total of 429 fifth and…

This study investigated "individual differences" in different aspects of early number concepts in preschoolers. Eighty 4-year-olds from Oxford nursery classes took part. They were tested on accuracy of counting sets of objects; the cardinal word principle; the order irrelevance principle; and predicting the results of repeated addition…

The study examined basic counting competencies, difficulties, skill progressions, and variation among 36 moderately retarded and 64 mildly retarded students (ages 5-14). Quantitative and qualitative analyses indicated deficiencies in basic counting competencies and systematic oral- and object-counting errors. Striking individual differences in…