An interesting class of purely pandiagonal, i.e. non-magic, whole number (integer) squares of orders (row/column dimension) of the powers of two which are related to Gray codes and square Karnaugh maps has been identified. Treated as matrices these squares possess just two non-zero eigenvalues. The construction of these squares has been automated…

A little known property of determinants is developed in a manner accessible to beginning undergraduates in linear algebra. Using the language of matrix theory, a classical result by Sylvester that describes when two polynomials have a common root is recaptured. Among results concerning the structure of polynomial roots, polynomials with pairs of…

The main purpose in this note is to provide a generalization of the concept of mean, using the algebraic structure of commutative semigroups. Also, the pedagogical aim is to discuss with undergraduate math students the idea of generalizing a concept or a structure as a typical mathematical activity.

This paper explores a geometrical way to sketch graphs of the general quadratic in two variables with Geometer's Sketchpad. To do this, a geometric procedure as described by De Temple is used, bearing in mind that this general quadratic equation (1) represents all the possible conics (conics sections), and the fact that five points (no three of…

This note presents a new proof of Gould's famous formula for the Bernoulli numbers.

The coordinates of an n-dimensional regular simplex are found. These coordinates are used to derive properties of the regular simplex that generalize their two- and three-dimensional counterparts.

Describes the current programs and future plans the Association for Science Education (ASE) in Great Britain has for helping teachers learn more about students with special educational needs in the science classroom. (WRM)

Boundary value problems (BVPs) for partial differential equations are common in mathematical physics. The differential equation is often considered in simple and symmetric regions, such as a circle, cube, cylinder, etc., with global and separable boundary conditions. In this paper and other works of the authors, a general method is used for the…

Examines the history of the "Public Understanding of Science" movement, including some of the wider debates articulated by key figures and groups in the field. Discusses the re-emergence of the issue of science communication in the 1990s as well as the development in universities of the new field of science communication. (PVD)

Offers some strategies for enabling science teachers to make better use of data-logging methods. These ideas are grounded in the belief that science teachers are expert lesson planners. Benefits gained for students using data-logging techniques are more likely to be secured through teachers re-interpreting their planning approaches in the new…

The General Secretary for the National Association for Environmental Education (NAEE) in the United Kingdom considers the place of environmental education in the curriculum. Argues that the inclusion of environmental education in the curriculum as a separate subject would add to the nightmare of the stand-alone subject curriculum. Suggests a…

Algebraic calculators with symbolic manipulation capabilities are tools in some classrooms for 14-19 year olds, and their use in learning and teaching mathematics is likely to increase over time. Explains the reports of government-initiated working groups that consider the implications of their use in academic mathematics examinations for…

Discussed is an exhaustive inquiry into the curriculum of British secondary schools. It concentrates on the four curriculum aspects of language, mathematics, science, and pupil personal and social development. (RE)

Researchers surveyed British schools in order to determine the uses of the process and content of science in other areas of the curriculum than science. In the majority of schools, however, little science was found in the curriculum outside science subjects themselves. (Author/RE)

From a safety point of view, there is a need to ensure that science teachers are appropriately qualified to teach their subject. Opportunities for accidents in school laboratories are legion and acquisition of skills and competence to obviate them is essential. (Author/RE)