Abstract
Although numerical magnitude processing has been related to individual differences in arithmetic, its role in children’s multiplication performance remains largely unknown. On the other hand, studies have indicated that phonological awareness is an important correlate of individual differences in children’s multiplication performance, but the involvement of phonological memory, another important phonological processing skill, has not been studied in much detail. Furthermore, knowledge about the relative contribution of above mentioned processes to the specific arithmetic operation of multiplication in children is lacking. The present study therefore investigated for the first time the unique contributions of numerical magnitude comparison and phonological processing in explaining individual differences in 63 fourth graders’ multiplication fact ability (mean age = 9.6 years, SD = .67). The results showed that children’s multiplication fact competency correlated significantly with symbolic and nonsymbolic magnitude comparison as well as with phonological short-term memory. A hierarchical regression analysis revealed that, after controlling for intellectual ability and general reaction time, both symbolic and nonsymbolic magnitude comparison and phonological short-term memory accounted for unique variance in multiplication fact performance. The ability to compare symbolic magnitudes was found to contribute the most, indicating that the access to numerical magnitudes by means of Arabic digits is a key factor in explaining individual differences in children’s multiplication fact ability.
Highlights
Arithmetic abilities such as adding or subtracting numbers are crucial for successful participation in educational and daily life settings
To test possible differences in reaction times and/or accuracy rates depending on problem-size, paired t-tests were performed comparing small vs. large problems
A hierarchical regression analysis was performed to answer the question if numerical magnitude processing contributed to individual differences in multiplication fact retrieval and if it uniquely explained variance over and above the variance explained by phonological processing, a factor that was found in previous research to be associated with children’s multiplication fact competency [13]
Summary
Arithmetic abilities such as adding or subtracting numbers are crucial for successful participation in educational and daily life settings. The basis for arithmetic skills is laid in childhood and marked individual differences in mathematical competence are already apparent in this period of life [1]. There has been a growing interest in the cognitive factors that underlie such. Numerical Magnitudes, Phonology and Multiplication Facts individual differences. The ability to process numerical magnitudes has been found to be an important domain-specific factor in the development of mathematics, for a review see [2, 3]. Cognitive abilities such as working memory, e.g. [8, 9], have been identified as crucial domain-general factors Cognitive abilities such as working memory, e.g. [4, 5], phonological processing, e.g. [6, 7], and processing speed, e.g. [8, 9], have been identified as crucial domain-general factors
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