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 purpose of this study was to use calculator-assisted instruction to help two fifth-grade low-achievers learn number sense. The research process includes three stages: (1) pre-test interview to detect what kinds of number sense the students did not have; (2) calculator-assisted instruction to help them develop number sense; and (3) post-test…

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…

National tests, an influential assessment practice in many countries in East Asia, are often blamed as obstacles to good instructional practices. In this paper, the positive impact of assessment, national tests in particular, is discussed using the case of Singapore. The first part of the paper includes an analysis of items from the primary grade…

Ways of using the calculator as a vehicle for investigating one aspect of the square root concept are illustrated. (MK)

Discusses the changing perceptions of numeracy in a changing world, and puts forward arguments for integrating calculator use into the earliest school years. (Author/ASK)

Two traditional presentations introducing the calculus of exponential functions are first presented. Then the suggested direct presentation using calculators is described. (MNS)

Questions students raise about the meaning of zero to the zero power present an opportunity for mathematics teachers to involve students in active participation in exploring mathematical relationships. Calculators are the needed tool to make this exploration accessible to students. How they can be used is described. (MNS)

Presents an activity in which students try to find the least common multiple (LCM) for two numbers using calculators. (ASK)

Presents an activity on number concepts using a calculator. Suggests that by using a calculator, students can search for patterns and identify them more quickly. This activity helps students make mathematical connections about divisibility rules, carry out investigations, make sense of what happened, and continue their investigation by creating…

A method is described for finding those numbers which are both triangular and square (named trisqy numbers). A program for a programmable calculator is given, as well as a proof. (MNS)

A method for finding logarithms is outlined. Four-function calculators are used to simplify the computation for those who enjoy experimenting with numbers. (MNS)

A procedure for helping students to calculate logarithms with any calculator that has a square root function is outlined. (MNS)