Describes the basic and exceptional calculation abilities of a calculating prodigy whose performances were investigated in single- and multi-digit number multiplication, numerical comparison, raising of powers, and short-term memory tasks. Shows how his highly efficient long-term memory storage and retrieval processes, knowledge of calculation…

Examines 109 children from grades 3 through 6 for computational facility and the relationship between automaticity, or efficient processing of addition facts, and success in more complex tasks. Indicates that most errors on the multidigit sums were due to fact inaccuracy, not algorithmic errors. Discusses instructional implications for students…

Examines number naming, magnitude selection, and simple arithmetic performed by adult Chinese-English bilinguals born and educated in China to investigate the effects of surface notation on basic numerical skills. Indicates that retrieval processes in the arithmetic and selection tasks were more efficient with Arabic than Mandarin stimuli.…

Reports on the performance of a demented elderly patient who, although he had impaired functions in several cognitive domains, showed exceptional calculating abilities superior to those of young adults. Addresses the problem of various mathematical dissociations at different levels. (Contains 30 references.) (Author/ASK)

Uses neuropsychological and developmental models of number, counting, and arithmetical skills as well as supporting working memory and speed of articulation systems as the theoretical framework for comparing groups of low- and average-IQ children. Indicates that low-IQ children's conceptual understanding of counting did not differ from that of…

Studies 6- to 8-year olds' responses to sliced task, standard and choices were discontinuous quantities, and non-sliced task, standard was continuous and choices were discontinuous quantities in order to discover whether children use half boundary in ratio comparisons between continuous and discontinuous quantities. Reveals that "dhalf" plays a…

Presents a study that examined the differences between mathematically disabled children and mathematically normal children in a cross-sectional perspective. Concludes that mathematically disabled children need mathematics instruction to move from a focus on computation to strategy-learning activities. Contains 44 references. (Author/ASK)

Presents a study in which participants were trained on nine single-digit multiplication problems over three sessions. Transfer of practice was tested with nine different multiplication problems in the fourth session for half the participants. Interprets problem-size, transfer, and retention effects within a network-interference model of mental…

Presents a study in which 32 Chinese-speaking adults solved single-digit multiplication problems. Chinese adults made more errors that indicated interactions between phonological codes activated at encoding and production of answers as compared to samples of English, French, and Dutch-speaking adults from other studies. Contains 26 references.…

Investigates how students familiar with exponentiation intuitively combined information about bases and exponents in expressions of the type a(carot)n to estimate the magnitude of these expressions. Qualitative and quantitative analyses conducted on the data revealed at least five different models of magnitude estimation. Contains 17 references.…

Examines the association between young children's analogical reasoning ability and their mathematical learning. Records and analyzes children's nonverbal behaviors and their private and social speech. Concludes that analogical reasoning is significantly related to mathematical learning and children's scores on the measure of mathematical learning,…

Investigates 10-year-old children's abilities to reason by analogy in solving addition and subtraction comparison problems involving unknown compare sets and unknown reference sets. Children responded in a consistent manner to the tasks involving the basic addition problems, indicating substantial relational knowledge of these but responded in an…

Exemplifies a model of a conceptual-support net in the domain of multidigit addition that provides guidance in making curricular and classroom teaching choices about what kinds of conceptual supports to provide in a particular setting. Presents summaries of several different multidigit addition solution methods that indicate how different quantity…

Explores whether 5-month-old infants (N=56) develop numerical- or location-based expectations by using a violation of expectation paradigm with possible and impossible events. Reports that infants use a more abstract representation than object location, the numerical nature of which is discussed. Contains 25 references. (Author/ASK)

Classification of arithmetic disorders is predicated on neuropsychological features and associated learning disabilities. Assesses the compatibility of these classifications on a nonreferred, population-based cohort of children (N=139) with developmental dyscalculia. Concludes that children with dyscalculia and disabilities in reading and/or…