A training experiment with 30 mentally handicapped children tested two models of mental-arithmetic development. Children's initial responses to a mental-addition task appeared to be the product of a mechanical prescription. Errors appeared to be more errors of method than of recall. (MNS)

Discussed are the roles played by anticipation, belief, and motivation in two young children's problem-solving activity. It is argued that a solver's beliefs and motivations are intimately related, and that the discussion of the two children's behaviors may have some generality. (Author/MNS)

Dialogue from an interview with a child about division basic facts is presented. The facts are considered by groups, and specific errors are noted. Finally, remediation ideas are given. (MNS)

Thought processes involved in counting and comparing small amounts of money were studied among 34 children and adolescents with Down's syndrome or mental retardation of unknown etiology and 15 normally developing first graders. Few intergroup differences were found in children with mental retardation. As complexity of counting tasks increased,…

Reviews research that has led to new ways of understanding mathematical development in young children. Covers research on information processing theory and cognitive science. (BB)

Cardinality responses are affected by both the direction and nature of the elements in the counting sequence. Error analysis suggests six stages in the acquisition of cardinality. Although there appears to be a developmental dependency between counting and cardinality, this relationship is not significant in all cases. (RH)

The authors examined whether absolute and relative judgments about global-scale locations and distances were generated from common representations. At the end of a 10-week class on the regional geography of the United States, participants estimated the latitudes of 16 North American cities and all possible pairwise distances between them. Although…

Three factors associated with arithmetical processes (sequence skills, arithmetical strategies, and information processing capacity) were measured in individual interviews with 35 first-grade pupils, aged 7.6 to 8.6, in one Finnish school. Mathematics achievement was determined from information supplied by teachers. Attitudes were assessed twice,…

To determine how children cope with some of the demands imposed on them by arithmetic word problems, 200 sixth-graders were asked to solve prolems modeled after those used by the National Assessment of Educational Progress. A quantitative demand was imposed on the children by adding extraneous information to the problems, and a verbal demand was…

This report presents a theory of eye movement that accounts for main features of the stochastic behavior of eye-fixation durations and direction of movement of saccades in the process of solving arithmetic exercises of addition and subtraction. The best-fitting distribution of fixation durations with a relatively simple theoretical justification…

This document focuses on one child's skip counting methods. The pupil, a second grade student at Steuben School, in Kankakee, Illinois, was interviewed as she made several attempts at counting twenty-five poker chips on a circular piece of paper. The interview was part of a larger study of "Children's Conceptions of Number and Numeral,"…

Research on the structures and processes involved in simple mental arithmetic is reviewed. Results suggest that mental arithmetic is a memory retrieval phenomenon, which develops with the experiences of elementary school and can be understood in general as retrieval from organized network representations. Simple mental addition with basic facts…

Determined whether 11 third-grade children, differing in cognitive processing capacity, solve addition and subtraction word problems differently. Results, among others, show that children who differ in cognitive processing capacity also differ in strategies they use to solve the same verbal problems and differ in their success in finding correct…

The need to provide understandable problems and ways to help children understand problems are explored. An interview with a sixth grader depicts his incorrect strategies and leads to suggestions for teaching problem solving using a range of mathematical models for each operation. (MNS)

Solutions to addition and subtraction word problems were studied in a three-year longitudinal study that followed 88 children from grades one to three. They solved problems using a variety of strategies before formal instruction and used invented strategies several years after formal instruction. Four levels of problem-solving ability were found.…