Many developed nations have a serious problem with a shortage in the supply of numerate graduates, fuelled by their school students' negative attitudes towards their future study of mathematics. At the same time, the smart phone and other personal sensing technological devices are becoming commonplace amongst students in schools and universities.…

This article is about the students' investigation about the relationship between the diameter of the view tubes (x) of constant lengths and the viewable vertical distance (y) on the wall while keeping the perpendicular distance from the eyeball to the wall constant. The students collected data and used and represented it in tabular and graphical…

Engineering design graphics courses taught in colleges or universities should provide and equip students preparing for employment with the basic occupational graphics skill competences required by engineering and technology disciplines. Academic institutions should introduce and include topics that cover the newer and more efficient graphics…

In this study, I examine the role of dynamic geometry software (DGS) in curricular proof tasks. I investigated seven US high school geometry textbooks that were categorised into three groups: technology-intensive, standards-based, and traditional curricula. I looked at the frequency and purpose of DGS use in these textbooks. In addition, I…

In the exciting, "out of this world" activity described here, students measure the Earth using meter sticks while measuring their shadows in two distant locations. To obtain the size of the Earth, students discover the connection between the measurements of the shadows and a model of the spherical Earth following the method developed by…

Imagine trying to paint a picture with three colors--say red, blue, and yellow--with a blue region between any red and yellow regions, a red region between any blue and yellow regions, and a yellow region between any red and blue regions, down to infinitely fine details. Regions arranged in this way satisfy what is called the Wada property. At…

This article presents some identities on the sum of the entries in the first half of a row in Pascal's triangle. The results were discovered while the author was working on a problem involving Laplace transforms, which are used in proving of the identities.

The basic Pythagorean theorem for right-angled triangles is well-known in mathematical terms as a[squared]+b[squared]+c[squared] were "a," "b," and "c" are the lengths of the sides of the triangle with "c" as the hypotenuse. When "a," "b," and "c" are all integers and obey this…

Simplicity arguments are to be found in most geometrical works, from those of Proclus in his "Commentaries on the First Book of Euclid's Elements," up to those of contemporary manuals. Our goal is to read these arguments in their historical contexts to analyze agreements, disagreements and the multiplicity of points of view. For a better…

In this note, it is shown that in a symmetric topological space, the pairs of sets separated by the topology determine the topology itself. It is then shown that when the codomain is symmetric, functions which separate only those pairs of sets that are already separated are continuous, generalizing a result found by M. Lynch.

Vieta's famous product using factors that are nested radicals is the oldest infinite product as well as the first non-iterative method for finding [pi]. In this paper a simple geometric construction intimately related to this product is described. The construction provides the same approximations to [pi] as are given by partial products from…

This is the teacher's edition of a text for the first year of a two-year high school geometry course. The course bases plane and solid geometry and trigonometry on the fact that the translations of a Euclidean space constitute a vector space which has an inner product. Volume 1 deals largely with affine geometry, and the notion of dimension is…

The author re-enacted the "Meno's" discussion between Plato and the slave about doubling the size of the square, and found that a six-year-old's answers paralleled those of the slave; neither had formal knowledge of geometry. Plato stated that learning is recollection of knowledge held before birth. (CHK)

This booklet, one of a series, has been developed for the project, A Program for Mathematically Underdeveloped Pupils. A project team, including inservice teachers, is being used to write and develop the materials for this program. The materials developed in this booklet include (1) elementary properties of the exponent, (2) properties of the…

High-ability Jamaican students in grades one, three, five, seven, and nine were asked to draw five three-dimensional objects (cuboid, pyramid, cylinder, cone, cube) from memory, and with the object visible; later they were asked to select the best sketch of each solid from among several presented. Drawings and selections were scored for…