By varying task conditions and constraints on subjects, this study attempted to extend and refine a developmental theory of partitioning as a foundational process undergirding children's construction of a rational number. Subjects were 31 preponderantly higher-grade pupils enrolled at an elementary school in Nova Scotia, Canada. Two tasks were…

An intensive, naturalistic study tracked one six year old's learning for six months and more. The study was inspired by the hope that with concepts of Artificial Intelligence and sufficiently detailed observation, the path of knowledge development could be described through observing significant learning experiences. Included is a reasonably…

A solid understanding of equivalent fractions is considered a steppingstone towards a better understanding of operations with fractions. In this article, 55 rural Australian students' conceptions of equivalent fractions are presented. Data collected included students' responses to a short written test and follow-up interviews with three students…

Several researchers have noted how children's whole number schemes can interfere with their efforts to learn fractions. An Australian study found that children who were successful with the solution of rational number tasks exhibited greater whole number knowledge and more flexible solution strategies. Behr and Post (1988) indicated that children…

Examines bar models as graphical representations of rational numbers and presents related real life problems. Concludes that, through pairing the fraction bars with ratio tables and other ways of teaching numbers, numeric strategies become connected with visual strategies that allow students with diverse ways of thinking to share their…

Interviews with (n=55) children and their teachers in years one, two, and three showed a closer association between knowledge of place value and levels of counting than between levels of counting and the ability to explain the counting sequence. (13 references) (MKR)

Describes the development, refinement, and validation of a framework for nurturing and assessing multidigit number sense in young children. Major constructs incorporated were counting, partitioning, grouping, and number relationships. The framework was validated through case studies of six first-grade children. (30 references) (MKR)

Proposes a framework that identifies the components of number sense and the attributes of students who possess it. Discusses various aspects of three areas where number sense plays a key role: number concepts, operations with numbers, and applications of number and operation. (MDH)

This study evaluated the generally recommended concrete-to-abstract hierarchy for presenting a new skill, with three students with learning disabilities in grades 1, 2, and 4. The three subjects enrolled in the Multidisciplinary Diagnostic and Training Program's classroom housed on the University of Florida campus in Gainesville. Following…

Describes research which compared the processing loads of mathematical representations and strategies used by (n=3) teachers and (n=29) children aged 5-8 for interpreting subtraction operations represented in numerical form. Some representations and strategies appeared to impose an extra processing load which can interfere with conceptual…

Interprets and contrasts children's mathematical interaction from the points of view of radical constructivism and of Soviet activity theory. Proposes a superseding model based on the interrelations between the basic sequence of actions and perturbation and the interaction of constructs. Supports the model by describing how children used…

Proposes a new model of children's mathematics by composing aspects of the Fraction Project and critiques presented in the same issue. Argues that computer microworlds provide children with dynamic learning environments in which they are the primary actors and teachers with a medium for interact with children's mathematics while trying to maintain…

Describes a program in second-grade Dutch mathematics classes that emphasizes mental addition and subtraction of two-digit numbers up to 100. Deals with a strategy of counting by 10s from any number. (Contains 56 references.) (RLB)