This paper reports on part of a wider study on the teaching and learning of the conventions of formal algebraic notation. Through the analysis of paper tasks given to teachers I argue that not only does the inherent mathematical structure have an effect on the way in which an equation is manipulated but also the visual impact of notation itself.…

In the study, a part of longitudinal research focused on the emergence of mathematical knowledge structures in a learner's mind is presented. It concentrates on the analysis of introspective data gained from the author's study of a non-standard arithmetic structure in terms of the model of abstraction in context (Hershkowitz, Schwarz and Dreyfus).…

The first in a three-volume set, this book focuses on young children between the ages of four and eight as they construct a deeper understanding of numbers and the operations of addition and subtraction. Rather than offer unrelated activities, this book provides a concerted, unified description of development with a focus on big ideas, progressive…

Results from the third national mathematics assessment are presented. Overall, the performance of nine year olds changed little since the second assessment, while significant gains were made by 13 year olds. Data on whole numbers, fractions and decimals, other basic concepts, and problem solving are discussed. (MNS)

Current practices in teaching about distributivity of multiplication over addition and subtraction are reviewed. Then a study is described in which two inventories were administered to 83 eighth-grade students; scores were low. Suggestions for teaching distributivity are presented. (MNS)

Potential instructional uses of the computer for expanding middle school mathematics programs are described. Content areas which are represented include geometry, number theory, computation, consumer education, and probability. (Author/JN)

The material is designed for pupil practice in: (1) associating numerals with sets of objects and finding sums of two or three numbers; (2) subtracting, one- and two-digit numbers with some regrouping; (3) mental computation using the basic operations; and (4) using combinations of basic operations with whole numbers and decimals. (MP)

Suggestions are made for helping children correct and analyze their own work so they may learn from their own mistakes. (MP)

Discusses the use of pocket calculators for the computation of a line by the least-square-fitting method. The method is exemplified with a classical student experiment. (HM)

The experiments described in this article discuss the versatility of the linear variation method in quantum chemistry and the ease with which it can be used with a simple computer program. (SA)

Presents various shortcomings of applying a per-pupil cost structure for determining teaching cost. A proposed alternative approach determines the cost of providing teaching capacity separately. It is applied to a number of situations and the comparative results are presented. (JMF)

The performance of 76 students (ages 10 to 15) with learning disabilities on four tasks of arithmetic computation within each of the four basic operations was examined. Tasks varied in difficulty level and number of strokes needed to complete all items. Intercorrelations between task sets and operations were examined as was the use of…

Presents a computational framework for modeling cognitive development that provides a language paradigm with which to compare and contrast different facets of children's knowledge. Describes the generative connectionist algorithm "cascade-correlation," the successful use of the algorithm to model cognitive development in various…

Examined children's mathematical competencies between ages 7 and 9. Found no differences in developmental rate between children with math difficulties only (MD), math and reading difficulties (MD-RD), reading difficulties only (RD), and normal math/reading achievement (NA). Found that at end of Grade 3, MD group performed better than MD-RD group…

Discusses the effects technology may have on human intelligence. Topics include the use of computational devices, including calculators, in schools; the changes word processing has brought about in writing; the use of television; and the effects of weapons on children. (LRW)