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…

Three methods for using four-function, counting calculators for developing understanding of the meaning of square roots and operations on whole and rational numbers are described. (MP)

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…

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)

Argues that the type of calculator that is used in mathematics instruction is very important. Suggests that four-function calculators fail to give correct values of mathematical expressions far more often than do scientific calculators. (PK)

Procedures for using a calculator to check addition and subtraction problems in bases less than 10 are described. (SD)

The place of binary arithmetic in the curriculum is discussed, then uses of binary coding for methods of automatic error correction in computers and calculators are analyzed. (DT)

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)

A method of finding large primes is described. High school students can use the test using hand calculators, or by programing a computer. (SD)

This calculator experiment for seventh-grade students on prime factorization contains objectives, difficulties, a discussion, several examples, and a worksheet. (MP)

A "neat and general" divisibility algorithm for prime numbers is presented. Five illustrative examples are included. (MNS)