The focus is on using mathematical concepts and operations to decode holiday messages. Worksheets are provided for levels one-two, three-four, five-six, and seven-eight. (MNS)

The article discusses ways to make mathematics instruction with learning-disabled and other children more developmentally appropriate by building on children's informal understandings in active purposeful learning, using less direct instruction and paper-and-pencil work. Ideas are applied to the teaching of fractions. Instructional materials are…

This study explored first graders' fraction learning when the teacher elicited and built on children's informal knowledge of fractions during discussions of equal-sharing tasks; the study focused on key classroom interactions resulting in cognitive change. Findings suggest that thinking about fractions is influenced by the structure of the child's…

This is the teacher's manual to accompany part 2 of the workbook for grade 5 pupils in the Comprehensive Instructional Management System, a teacher-designed unified mathematics curriculum for kindergarten through grade 7. It is composed of a curriculum, a testing component, and a computer-managed reporting system. The curriculum is organized into…

Activities are presented to give students a picture of decimal concepts of tenths and hundredths. Three models (linear, regional, and value) are described, followed by four activities. (MNS)

Fourth-grade students' understanding of the order and equivalence of rational numbers was investigated in 132 interviews during an 18-week teaching experiment. Six children were instructed individually and as a group at two sites, with instruction relying heavily on manipulative aids. Strategies used to compare fractions were identified. (MNS)

Three lessons are outlined which employ "scholar dollars," pretend bills and coins of different denominations that students can make and use to help solve subtraction, division, and decimal problems. The technique clarifies difficult mathematical concepts by making them less abstract. (PP)

This article describes constructivist techniques for teaching concepts of decimals and metrics through the combination of innovative measuring tools, activities and videos in classrooms. Even though the chronological age of the students involved differed--fifth and sixth graders or pre-service teachers--it was discovered that similar activities…

Findings on ratio and on fractions from a research project on strategies and errors in secondary mathematics are discussed, with typical errors described. Pupils seemed to learn rules without understanding. (MNS)

Contrasts student achievement using commercial curricula (CC) for initial fraction learning with that of using the Rational Number Project (RNP) fraction curriculum. Indicates that students using RNP materials had statistically higher mean scores on concepts, order, transfer, and estimation. Interview data showed differences in the quality of…

This study compared effectiveness of either a concrete-representational-abstract (CRA) or a representational-abstract (RA) instructional sequence in teaching fraction concepts to 50 middle school students with mathematics disabilities. On all achievement measures, students in the CRA group had overall higher mean scores than did students in the RA…

Researchers used a fifth-grade videodisc fractions program to examine accountability in mastery learning programs. Four classes were randomly assigned to two treatments (those who were and were not aware of participation in mastery learning). Results revealed standardized mean differences for achievement favoring knowledge of being in the mastery…

Discusses research findings that relate to teaching fractions for conceptual understanding. Gives teacher/student dialogues that illustrate the thought processes of students as they form part-whole and improper fraction concepts. (MDH)

Studies the co-emergence of teaching and children's construction of specific conceptions that support the generation of improper fractions in a constructivist teaching experiment with two fourth-grade students posing and solving tasks in a computer microworld. Reports that examination of the teacher's adaptation of learning situations (tasks) and…

This publication presents teaching strategies to develop understanding of fractions as sensible numbers. Written for the mathematics teacher in grades K-5, it gives suggestions for teacher-led discussions and structured exploratory activities. The activities are conducted with manipulative materials that emphasize the important characteristics and…