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…

Illustrations are provided which show how some algebraic manipulations done prior to doing calculations can eliminate unnecessary storage of data, reduce the total number of needed steps, and avoid overflow. (MN)

This article describes techniques which enable the user of a comparatively simple calculator to perform calculations of cube roots, nth roots, trigonometric, and inverse trigonometric functions, logarithms, and exponentials. (DT)

This book guides teachers in the appropriate use of calculators in math classrooms in grades 3-8. This resource is organized into two parts. Part One addresses the broad range of classroom teachers' questions and concerns about using calculators for teaching mathematics. Issues covered include: (1) How can calculators support helping children…

An algorithm is given for computing the cube root of any real number on a calculator. (DT)

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)

Suggestions for using handheld calculators are given. Students can invent and check their own problems. The calculator can debug problems, provide practice, aid in developing concepts of place value, decimals, order of operations, powers of a number, and evaluation of formulas. (KM)

Suggestions are given for using the calculator in junior high classrooms. Square roots, factoring, and percentages are some topics discussed. A worksheet is included. (MP)

The author redefines basic numeracy as the ability to use a four-function calculator sensibly. He then defines "sensibly" and considers the place of algorithms in the scheme of mathematical calculations. (MN)