This yearbook sharpens the views of mathematical reasoning and its development at all grade levels. Various perspectives about the nature of reasoning and addresses the many issues and concerns involving mathematical reasoning such as how learners reason in mathematics, how communication promotes reasoning, how teachers gather evidence of student…

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)

Properties of the harmonic number triangle are listed, and ways of generating the elements of harmonic triangles are described. (MNS)

Ways to use styrofoam egg cartons and plastic eggs to enhance mathematics instruction are detailed. These materials are viewed as inexpensive, colorful, and easy to obtain. Suggestions for using them to teach concepts related to whole numbers and fractions are provided. (MP)

Activities designed for use with middle-school students to help them discover intriguing number patterns and practice their arithmetic skills with fractions are presented. It is felt that work with repeating number patterns should be both fun and instructive for middle-school and prealgebra students at all development levels. (MP)

Student exploration at a secondary school level of fraction relationships using special graphs is described. (MP)

Two teachers each taught a 2-week fractions unit to two classes of grades 4-5 students. Each teacher taught one class using direct instruction and the other using a small-group variation of direct instruction. Regression analysis on achievement showed significant aptitude-treatment interaction (ATI) and significant teacher effects. (Author/RL)

The author promotes an earlier introduction of decimals than is currently standard practice in most elementary mathematics programs. Suggested activities and related skills are reviewed. (MP)

Data were collected from 540 fifth-grade students on problem solving, justification, and explanation of fractions. Fewer than 10% performed adequately on the explanation task. Students who received a seven-day instructional program on fractions in measurement contexts performed better than students receiving traditional part-whole instruction.…

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…

Discussed is the meaning of the word "of" as is found in mathematical expressions that involve fractional numbers. The conceptual rather than numerical distinction is stressed. Teaching techniques regarding difficulties with this concept are suggested. (CW)

The degree to which test item bias techniques can lead to interpretable results when groups are defined in terms of specified differences in the cognitive processes involved in problem-solving strategies was studied. Data from two groups of junior high school students (N=545) were used. (TJH)

Proposes using cookies (recipe included) and pizza to help Chapter I students, grades two through five, understand basic fraction concepts. (MKR)

Describes a longitudinal constructivist teaching experiment analyzing children's ways of operating while solving fraction tasks. A case study of one third grader found that the evolution of her fraction schemes was the product of her cognitive activity and her collaborative interaction with the teacher. (42 references) (Author/MKR)