Describes an activity in which students examine bicycle chain-rings, cogs, and gear ratios as a means of exploring algebraic relationships, data collection, scatter plots, and lines of best fit. (KHR)

Studied the teaching and learning of fractions in two matched groups of 10 9-10-year-olds in the Netherlands. In the experimental group, fractions were introduced using the bar and number line as mental models, while the control group used fair sharing and the circle model. The experimental group showed more proficiency in fractions after 1 year.…

Explores ways to help children make connections between whole-number multiplication and their notion of a fraction. Illustrates an approach to constructing fraction concepts that builds on children's whole-number knowledge using specially designed computer tools. (KHR)

Use of prepartitioned models is proposed to help students construct a meaningful concept of fractions. Partitioning, geometric shapes as fractional models, concepts related to successful partitioning, and other benefits from partitioning experiences are discussed. Sample activities are suggested. (CW)

Describes two activities for developing computational skills, discovering patterns, checking answers, and factoring quadratics and equivalent fractions. Provides worksheets for the activities. (YP)

Concepts of fractions from an adult perspective as well as from a child's perspective are examined. Types of students' schemes for some terms related to fractions are reported. (YP)

Discusses the generalization of the meaning of multiplication for whole numbers. Presents an example for multiplication of fractions. Provides several diagrams to help improve understanding. (YP)

Simple experiences with probability can extend third graders' understanding of the need for fractions. Three activities are given which build on language-arts experiences and incorporate concepts in multiplication, graphs, and fractions. (MNS)

Describes five types of activities that elementary school teachers can use to help students understand decimals. These activities use money calculations, base-10 blocks, meter sticks, calculators, and problem solving. Specific examples are provided. (MDM)

Discusses four historical methods by which the seats in the House of Representatives are apportioned and the ways these methods can be used to reinforce operations involving decimal fractions and different rounding procedures. (MDH)

Proposes a model for the growth of mathematical understanding based on the consideration of understanding as a whole, dynamic, leveled but nonlinear process. Illustrates the model using the concept of fractions. How to map the growth of understanding is explained in detail. (Contains 26 references.) (MKR)

A variety of suggestions for making the mathematics curriculum more meaningful and interesting to students are described. Activities that incorporate real-world situations are provided for verbal items, common and decimal fractions, estimations and rounding off numbers, large and small numbers, geometry, probability, and statistics. (KR)

Discusses the theoretical framework of realistic mathematics education. A course on fractions is analyzed in depth with the realistic theory in the background. Examines the strategies that designers of exemplary educational material use. (MDH)

Classroom practices believed to affect student motivation were assessed for 24 upper elementary school teachers during a unit on fractions. Reform-minded teachers emphasized effort, mastery, and understanding more, and those who had received training in motivation made more accurate judgments of students' motivation. (SLD)

Illustrates the addition, subtraction, and representation of fractions using an area model and a measurement model. Also demonstrates multiplication and division of fractions by employing the area model. (ASK)