The Bondi K-calculus is a delightful method that has been used to provide rich insights into relativistic kinematics. In this paper, we will try to show how several important results of relativistic kinetics can be derived simply by using this approach. In addition, we will also indicate how the K-calculus can be used to simplify certain…

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…

Different computational tools may offer teachers and students distinct opportunities in representing, exploring and solving mathematical tasks. In this context, we illustrate that the use of dynamic software (Cabri Geometry) helped high school teachers to think of and represent a particular task dynamically. In this process, the teachers had the…

Discussed are the difficulties that entering college freshmen seem to have with mathematics, particularly with fractional forms. A success-oriented program is suggested in which all students are successful. To obtain this goal, a number of alternative routes are discussed such as presenting decimals before fractional forms and the use of the…

Presented is a historical treatment of computational devices that use counters on a checkerboard. The discussion includes works of John Napier, Walter Minto, and Nicholas Saunderson. (MP)

An algorithm for long division is presented that involves only addition and subtraction. (MP)

Use of an ancient method of mental calculation with aliquot parts is illustrated. Other tips for helping children reason are also included. (MNS)

Suggests five steps for organizing learning experiences involving computational skills for adult basic education programs: (1) meet the needs of students; (2) incorporate lessons in communication; (3) use a variety of materials; (4) begin instruction where the student's knowledge leaves off; and (5) teach by means of concrete useful examples. (MB)

Considerations of the history of similar techniques and the structure of the method itself are used to discuss this question. (MP)

A discussion is given of a method of finger reckoning in which the numbers one through ten are represented by one's fingers. (MP)

Indicates that there has been a lot of work done and that a great deal needs to be done in the future to explore the world of children's early number. Discusses the counting, the use of algorithm, practical mathematics, the use of manipulatives, individual differences and pedagogical concerns, and classroom applications. Contains 18 references.…

Explores adult adding techniques and ponders whether they have any relevance to working with primary school children. Suggests ways that can help children develop into effective adders. (ASK)

There is a little-known but very simple generalization of the standard result that for uncorrelated random variables with common mean [mu] and variance [sigma][superscript 2], the expected value of the sample variance is [sigma][superscript 2]. The generalization justifies the use of the usual standard error of the sample mean in possibly…

This article discusses the use of a problem-based instructional task in an elementary classroom. After estimating the number of blades of grass on a football field, students write letters to explain the results of their research.

During the past few years the authors have developed a new approach to the teaching of physical science, a general education course typically found in the curricula of nearly every college and university. This approach, called "Physics in Films" (Efthimiou and Llewellyn 2006 Phys. Teach. 44 28-33), uses scenes from popular films to illustrate…