This is unit twelve of a fifteen-unit SMSG secondary school text for high school students. The text is devoted almost entirely to mathematical concepts which all citizens should know in order to function satisfactorily in our society. Chapter topics include rigid motions and coordinates, squares and rectangles, and square roots and real numbers.…

Outlined are the minimum requirements for a quinmester course of introduction to high school geometry. After a description of the course content and overall goals, further details are presented in nine sections. Each section gives performance objectives, textbook references, content (including lists of vocabulary and associated properties), and…

Mathematical theorems about the properties of ellipsoids are developed. Included are Poisson's theorem concerning the magnetization of a homogeneous body of ellipsoidal shape, the polarization of a dielectric, the transport of heat or electricity through an ellipsoid, and other problems. (BB)

A sequential but non-axiomatic high school geometry course which includes Euclidean, transformation, and analytic geometry and vectors and matrices, and emphasizes the invariance property of transformations, is outlined. Sample problems, solutions, and comments are included. (MN)

Finding areas on square grid and on isometric grid geoboards is explained, then the Pythagorean Theorem is investigated when regular n-gons and when similar figures are erected on the sides of a right triangle. (DT)

For students having had instruction in plane affine geometry and two-dimensional vector spaces. The author describes how the metric concepts of distance and orthogonality can be introduced to secondary school students by the use of conics. (JG)

Five solutions to the problems of constructing an equilateral triangle within any triangle and having the vertices on the sides of the given triangle are presented and a generalization is made. (CT)

A question posed by Euler is considered: How can polyhedra be classified so that the results is in some way analogous to the simple classification of polygons according to the number of their sides? (MK)

Worksheets and instructions are given for this activity whose objective is to develop the relationship between the lengths of the sides of a triangle and its classification by angle. (MP)

Presents a qualitative and global method of graphing functions that involves transformations of the graph of a known function in the cartesian coordinate system referred to as graphic operators. Explains how the method has been taught to students and some comments about the results obtained. (MDH)

For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards…

I report on the findings from research and literature on (a) use of symbols in mathematics, (b) algebraic/trigonometric expressions, (c) solving equations, and (d) functions and calculus. From these, some insights and implications for teaching and learning are derived.

This study investigated the relationship between 3 ability-based cognitive styles (verbal deductive, spatial imagery, and object imagery) and performance on geometry problems that provided different types of clues. The purpose was to determine whether students with a specific cognitive style outperformed other students, when the geometry problems…

What aspects of spatial relations influence speakers' choice of locative? This article presents a study of static spatial descriptions from 24 languages. The study reveals two kinds of spatial terms evident cross-linguistically: specific spatial terms and general spatial terms (GSTs). Whereas specific spatial terms--including English…

Using the film "Journey to the Centre of a Triangle" with a group of 15-year-old pupils, the author describes how they had done some work on constructions such as angle bisector and perpendicular bisector. The pupils were given A3 papers, rulers, compasses and pencils and they were asked to recreate their favourite scence from the film. The film…