Discusses problems related to teaching decimals and fractions and converting between these two representations. Provides problems and activities that teachers can use in their classrooms to overcome student difficulties related to these subjects. (ASK)

Examines strategies used by preschool children to subdivide items and focuses on how counting and sharing relate to one another. Indicates that children exhibited alternative strategies--suggesting use of a recipient as a mental cycle-marker and an adjacent recipient strategy--with pauses between allocations suggesting a re-presentation of lots…

Twenty-nine students in grades four, six, and eight were asked to find solutions to fraction equivalence problems and to verify their solutions using discrete material. Discontinuities were observed between strategies students used for producing solutions and supporting knowledge grounded in physical reality. (Author/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)

The behavior of one child as she constructed knowledge about fractions over a nine-month period is presented. The intent is to explain behavioral patterns for which certain mental processes, called schemes, seem responsible. (MNS)

This report describes an investigation of how young children respond to two types of tasks: (1) finding one-half of a continuous and a discrete material; and (2) attempting to share continuous and discrete material equally between two dolls. Continuous material, such as string, paper, or liquid, is quantified by adults using measurement units. A…

This constructivist teaching experiment investigated the role of whole-number knowledge in fraction learning. Two nine-year-old students worked for one year with a computer program (Copycat) and demonstrated that the development of whole-number knowledge and rational-number knowledge is interdependent. Contains 59 references. (KMC)

Basic fraction concepts are viewed as the seedbed for many important mathematical ideas including the notions of equivalence, inverse, decimals, probability, ratio, and proportion. It is viewed that a critical component of children's mathematical knowledge necessary for success in certain fractional number contexts appears to be intellectual…

Reports on a study designed to investigate aspects of young children's knowledge of fractions and partitions of quantities. Findings suggest that although children did not have a deep understanding of the concept of one half, a significant number demonstrated a powerful systematic procedure leading to the creation of accurate equal fractional…