This qualitative case study aims to address the ways that pre-service mathematics teachers (PSTs) used a rope in a daylong research meeting for cognitive development of children's understanding of counting numbers in Tanzanian elementary schools. Three university mathematics pre-service teachers volunteered participating in this study. Collective…

Recent studies have documented an evolutionarily primitive, early emerging cognitive system for the mental representation of numerical quantity (the analog magnitude system). Studies with nonhuman primates, human infants, and preschoolers have shown this system to support computations of numerical ordering, addition, and subtraction involving…

The purpose of this study was to investigate children's construction of 10s out of the 1s they have already constructed. It was found that, for many younger children, a dime was something different from 10 pennies even though they could say with confidence that a dime was worth 10 cents. As the children grew older, their performance improved.…

This experiment aimed to expand previous findings on the development of mental number representation. We tested the hypothesis that children's familiarity with numbers is directly reflected by the shape of their mental number line. This mental number line was expected to be linear as long as numbers lay within the range of numbers children were…

Based on close observations of two 4-year-old children responding to their parents' requests for quantitative comparisons, we offer a "participationist" account of the origins and development of numerical thinking, one that portrays numbers as a product rather than a pregiven object of human communication. In parallel, we propose a…

To build cognitive foundation for number, twenty-six low-performing, low-SES first graders did mathematical physical-knowledge activities, such as "bowling," during the first half of the year. As their arithmetic readiness developed, they tried more word problems and games. At the end of the year, these children did better in mental arithmetic and…

The arithmetic portion of the Developing Mathematical Processes (DMP) program, as it applies to children of ages 5 to 8, is described in some detail. The terminal objective of the number program of the primary segment of DMP is the ability of the child to correctly write, read and validate mathematical sentences of the form A = B plus or minus X.…

Six seven-year-old children were interviewed to investigate the quality of their solutions to whole-number tasks. Detailed analyses are provided of interviews with a girl who displayed an operative counting scheme (numerical extension) and a boy with a figurative counting scheme (intuitive extension). (MNS)

A nine-year-old's conception of fractions was compared with his knowledge of units. He had effective schemes for solving some partition problems but did not consistently use units of different sizes in interpreting fractions. His solutions to equivalence problems showed no coherent method of verification. (MNS)

Describes a method of teaching the order of mathematical operations based upon the psychological theory of conceptual generalization. (MDH)

Examines the concept of number sense in mathematics learning, compares this concept to that of phonological awareness in reading, and urges application of existing research to improving mathematics instruction for students with mathematical disabilities. Reviews research on building automaticity with basic facts, adjusting instruction to address…

Discusses convergence between instructional practices suggested by research on achievement motivation and practices promoted in mathematics-instruction reform literature by focusing on fourth- through sixth-grade students (N=624) and their teachers (N=24). Concludes that the instructional practices suggested in the literature of both research…

In dynamical theory, mathematical understanding is considered to be that of a person (or group) of a topic (or problem) in a situation or setting. This paper compares the interactions between the situations and the mathematical understandings of two students by comparing the growth in understanding within a Fibonacci sequence setting in which…

This is one of a series that is a collection of translations from the extensive Soviet literature of the past 25 years on research in the psychology of mathematics instruction. It also includes works on methods of teaching mathematics directly influenced by the psychological research. Selected papers and books considered to be of value to the…

Based on the cognitive psychological theories of Vygotsky and Davydov, discusses the establishment of connections between mathematical elements, and the algorithmic rules that govern them, and children's spontaneous mathematical concepts. Presents examples that establish connections involving addition and subtraction, comparing numerical…