Two samples of kindergarten children's representation and understanding of written number symbols were examined in two time points in one academic year. About 85% of Chinese five year olds (mean = 5 years 10 months) were able to use conventional number symbols to represent the quantity of 30 or larger. At the end of the kindergarten year, 94% of…

Problem-posing abilities of 54 third graders who displayed different patterns of achievement in number concepts and novel problem solving were investigated in this paper. The children were administered a problem-posing pretest followed by an instructional program (for half the sample) and a delayed posttest. Among the findings are the limited…

Ways in which the emerging field of cognitive science can have a major impact on practical education are demonstrated by an overview of two projects: the work on Socratic tutoring by Collins and Stevens, and the diagnosing students' misconceptions in arithmetic by Brown and Burton. These two projects are cited as examples of how the techniques of…

This study was designed (1) to investigate the relationship between physical exertion and mental performance in elementary school children and (2) to determine if male or female mental performances are more affected by physical exertion. A total of 95 second graders participated in six treatments of induced physical exertion during their regularly…

Children may perform computational operations readily when dealing with physical materials, but may have difficulty dealing with representational stimuli (pictures of objects) or symbolic stimuli. Describes and illustrates the function of mediators in moving from physical to representational or symbolic stimuli. (PR)

Discusses a class on subtraction or difference-finding, problems such as "There are eight white flowers and five red flowers, how many more white flowers are there than red flowers?" used in the teaching of Japanese first grade children. Describes three instances of introductory teaching of "difference-finding" problems in the…

The study with 989 learning-disabled students supported the cognitive-based arithmetic problem-solving model of Dinnel et al. under continuous visual stimulus conditions but suggested a more complex neuropsychological underpinning to arithmetic performance in both visual and aural stimulus conditions. (Author/DB)

Explores mathematical methods children use to find answers for themselves. Describes some methods used for multiplication and subtraction problems. (YP)

This study tested the hypothesis that children with high working memory capacities solve single-digit additions by direct retrieval of the answers from long-term memory more often than do children with low working memory capacities. Counting and reading letter span tasks were administered to groups of third-grade (mean age=107 months) and…

Error analysis performed on data sets revealed that seventh grade students used a variety of rules of operation for solving the signed-number arithmetic problems. The data sets were obtained from an experimental study in which students were randomly assigned to study either of two lessons written on a computer based education system. The two…

Two simple quantitative models were derived from a series of experiments which explored the role of information storage in working memory when performing mental arithmetic. The decay model is a tractable analysis of a complex task which assumes a decay process in working storage. Similar analyses are recommended for problem solving activities…

Results revealed that arithmetic-disabled and spelling/arithmetic-disabled children had significantly lower storage and retrieval scores on a nonverbal task but did not differ on a verbal task; reading/spelling-disabled children differed only on retrieval scores from verbal task; and the reading/spelling/arithmetic-disabled children differed only…

The relationship between arithmetical concepts and solution methods is discussed. A case study illustrates the contention that some children with relatively sophisticated concepts express those concepts with primitive methods. (MNS)

Describes a continuous sequence of development of arithmetical and ratio reasoning capacity which very few students now attain in introductory science courses. Sequence progresses from verbal interpretation of ratio of two numbers, to arithmetical reasoning involving division, coupling arithmetical reasoning to graphical representation, and to…