The duo of artefacts is a simplified model of the complex systems of various manipulatives (either tangible or virtual) that mathematics teachers and their students use in classrooms. It offers a means to study the complexity of the interweaving of the tangible and of the digital worlds in the teaching and learning processes. A duo of artefacts is…

Despite the importance of computational estimation skill for the improvement of number sense, little research exists on preservice teachers' estimation skills and their view on estimation in the US context. This study examined the computational estimation skill of 58 preservice elementary teachers (PSTs) and its relationship to their views of the…

The basis of this intervention study is a distinction between numerical calculus and relational calculus. The former refers to numerical calculations and the latter to the analysis of the quantitative relations in mathematical problems. The inverse relation between addition and subtraction is relevant to both kinds of calculus, but so far research…

Two intervention studies are described. Both were designed to study the effects of teaching children about the inverse relation between addition and subtraction. The interventions were successful with 8-year-old children in Study 1 and to a limited extent with 5-year-old children in Study 2. In Study 1 teaching children about inversion increased…

This section contains brief articles on triangular differences, when one is not equal to one, using calculators to check solutions of quadratic equations, and a county agents' problem. (MNS)

The problem of finding cube roots when limited to a calculator with only square root capability is discussed. An algorithm is demonstrated and explained which should always produce a good approximation within a few iterations. (MP)

Discusses the Tiles and Sides problem from the December 2000 issue. Indicates that this problem is accessible to students at different grade levels. Presents samples of student responses and their teachers' analysis. (KHR)

A calculator activity, described as a bingo game, emphasizes speedy calculations as well as problem solving. (JT)

Three games in which the calculator plays an important facilitating role are presented. It promotes a "guess then adjust your guess" strategy. The games are described within the context of elementary, junior high, and secondary classrooms. (MNS)

Presents the general postage-stamp problem on Diophantine equations. Discusses ways to uncover all solutions to the problem. (ASK)

Calculators can be used in primary schools in a number of situations. They are most beneficial when working with large numbers, dealing with real data that leads to complex calculations, performing repetitive calculations, developing concepts, estimating and checking, problem solving, and looking for patterns and/or relationships. But what if the…

Problems focusing on number theory that can make good use of the calculator in discovering and proving simple theorems are proposed. The focus is on the properties of subtracting the smaller of a three digit number and its mirror number from the larger in a process that leads to zero. (MP)

Examples are given of transcripts made from tape recordings of a teacher working with groups of 10-year-old children using calculators. Attention is focussed on the teacher's role in the interactions which take place. Suggestions are offered for the possibility of a structure of strategies available to a teacher. (Author/RH)

Studied for three years were eight Swedish classes with pupils aged 10-12 using calculators whenever they could be of use, along with experimental textbooks. The experimental classes were as competent as control classes in mental arithmetic and calculations with simple algorithms, and had better understanding of numbers and problem solving. (MNS)