The three target articles presented in this special issue converged on an emerging theme: the importance of spatial proportional reasoning. They suggest that the ability to map between symbolic fractions (like 1/5) and nonsymbolic, spatial representations of their sizes or "magnitudes" may be especially important for building robust…

In 1225 Fibonacci visited the court of the Holy Roman Emperor, Frederick II. Because Frederick was an important patron of learning, this visit was important to Fibonacci. During the audience, Frederick's court mathematician posed three problems to test Fibonacci. The third was to find the real solution to the equation: x[superscript 3] +…

Discusses the efforts of one Japanese company that makes abaci to demonstrate that the abacus continues to be a feasible alternative as a calculator in the elementary school mathematics curriculum. Argues that the abacus improves number sense, mental computation, and mathematics achievement for students who use the abacus. (MDH)

In order to stimulate further discussion, this article addresses issues concerning calculator use in elementary school mathematics such as: Is computation still important in elementary school? How would a calculator-driven curriculum look? When is calculator use appropriate? and How should calculators be used? (Author/MKR)

The aim of this series of four articles is to look critically, and in some detail, at the primary strategy approach to written calculation, as set out on pages 5 to 16 of the "Guidance paper" "Calculation." The underlying principle of that approach is that children should use mental methods whenever they are appropriate, whereas for calculations…

In this article, the author argues that there is a big conceptual difference between number lines and number strips and that number lines should be consistently used as early as Y1. Her interest in the use of the number line as a powerful image of the real numbers, and how this is introduced in the early years, comes from her own experience as a…

Discussed is the need to rethink computation in terms of what is critical, how computation is taught, and what constitutes computation. (MNS)

The greatest benefit of including leap year in the calculation is not to increase precision, but to show students that a problem can be solved without such presumption. A birthday problem is analyzed showing that calculating a leap-year birthday probability is not a frivolous computation.

After reviewing several assumptions that support the future ubiquitousness of computers in society and in scholarly research, summarizes three interrelated frameworks for developing instructional computing. (GC)

The ubiquity of calculators led to many "computational abuses", when numbers substitute for substance. On the other hand, it resulted in decrease in number oriented dexterity of students. The latter led to a disdain for even simple calculations to work about unfamiliar mathematical problems. As a reaction to the former, the reputation of…

Describes the development of computers and calculators, noting intitial resistance to and later acceptance of calculators in the classroom. Advocates teaching children to perform simple calculations and stresses estimation skills over speed and accuracy for doing long, complicated computations. Includes recommendations for classroom calculator use…

In a recent edition of "Mathematics Teaching" Midge Pasternack argued the case for the use of the 0-99 square with young children rather than the ubiquitous 1-100 square. In this article, the author would like to take the opportunity to mount a defence in favour of the much maligned 1-100 square. His main criticism of the 0-99 square (apart from…

This article presents the Association of Teachers of Mathematics' response to the position statement produced by the Department for Education and Skills (DfES) in May 2006, which describes their suggested approach to teaching calculations in KS2. Mathematics teachers argue that the methods being suggested are outdated and have been superseded by…

Students should be encouraged to focus on a big mathematical idea and to look for connections between problems and solution strategies. This unified view suggests that the students are developing computational fluency with fractions.

Students in the classroom should be provided with engaging activities for improving their computational fluency, making effective use of time, and as a medium of self-motivation. Games such as Contig, the 24 Game, and Number Jumbler are useful for practicing basic facts and computational fluency of mathematics.