Beginning with a simple computer program to teach a fundamental concept and building in small increments is suggested. For the topic of repeated operations, three activities, an extension, and some problems are given. (MNS)

Solutions to addition and subtraction word problems were studied in a three-year longitudinal study that followed 88 children from grades one to three. They solved problems using a variety of strategies before formal instruction and used invented strategies several years after formal instruction. Four levels of problem-solving ability were found.…

The Purposeful Algebraic Activity Project is a longitudinal study of the development of pupils' algebraic activity in the early years of their secondary schooling. Analysis of data from a spreadsheet-based teaching programme and from semi-structured interviews leads us to identify three features of the spreadsheet environment that appear to shape…

The questions addressed in this paper are: how do students interpret the non-solution problems as a mathematical practice in the classroom? What kinds of arguments do the students offer? To deal with these questions the utterances of students working in the classroom with problems in which they had to look for general relations in order to argue…

In this paper, we discuss the (potentially positive) pedagogical role of intrinsic limitations of computational descriptions for mathematical concepts, with special focus on the concept of derivative. Our claim is that, in a suitable approach, those limitations can act for the enrichment of learners' concept images. We report a case study with a…

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)