The process of transition from a novice's state to that of an expert, in the domain of decimals, is described in terms of explicit, intermediate, and transitional rules which are consistent yet erroneous. Data from students in grades 6-9 are included. (MNS)

Results obtained from 11- and 15-year-olds on tests of understanding of decimal place value and its influence on addition and subtraction skills are reported and discussed. (MNS)

Patterns in decimal expansions are investigated. (DT)

This book contains a collection of fraction lessons that support curriculum and instruction. The goals of the lessons are to give all students the chance to learn how to: (1) name fractional parts of wholes and sets; (2) represent fractional parts using the standard notation including proper fractions, improper fractions, and mixed numbers, and…

The emergence and differentiation of partitioning as a process that leads young children to construct ideas of rational numbers was traced through clinical sessions with 43 primary children as they manipulated objects. The data analysis led to a five-level theory of the partitioning process. (MNS)

A method of teaching students how to recognize when zeros are necessary and when they may be omitted is presented. (MP)

Children and adolescents tested to determine the development of the operator construct of rational numbers employed different problem-solving strategies depending on test presentation. Three major phases in the rational number construct appear to be a primitive fractional construct, a unit operator phase, and a general operator phase. (SB)

Two experiments tested claim that transparency of Korean fraction names promotes fraction concepts. Findings indicated that U.S. and Korean first- and second-graders erred similarly on a fraction-identification task, by treating fractions as whole numbers. Korean children performed at chance when whole-number representation was included but…

Described is a strategy that shows students how one mathematical concept can be connected to another. The emphasis is on both process and product and can lead to creating a learning environment where students do mathematics as mathematicians do. (KR)

Investigated was the use of cognitive conflict to probe the misconceptions held by preservice elementary teachers that in a division problem the quotient must be less than the dividend. Explains how preservice teachers' reliance on information about the domain of whole numbers and their instrumental understanding support their misconceptions.…

Analyzed were 19 preservice teachers' understanding of division in 3 contexts. The teachers' knowledge was generally fragmented, and each case of division was held as a separate bit of knowledge. (Author/YP)

A visual model of fractions, the tower of bars, is used to discover patterns. Examples include equalities, inequalities, sums of unit fractions, sums of differences, symmetry, and differences and products. Infinite sequences of numbers, infinite series, and concepts of limits can be introduced. (DC)

The concept of fractional number was studied with 10- to 12-year-old and 13- to 16-year-old students who were deaf and hard of hearing (n=21) and comparison groups of hearing students (n=26). The deaf and hard-of-hearing students achieved similarly to younger hearing students in overall performance by fraction type and problem solving strategies.…

Presents the computer microworlds developed by the Children's Construction of Rational Numbers of Arithmetic (Fractions) Project. Provides an overview of three microworlds: Toys; Sticks; and Candybars. Discusses how children are expected to use the microworlds to construct an understanding of rational numbers. (MDH)

Describes how an eight year old devised a part-whole schema during a school mathematics process involving the development of a geometric model to conceptualize fractions. Provides examples that utilize this schema in dealing with the relative size of fractions, as well as addition and subtraction, multiplication, and division of fractions.…