This is part two of a three-part School Mathematics Study Group (SMSG) textbook. This part includes the index and chapters 6 through 10: (6) Curve Sketching and Locus Problems, (7) Conic Sections, (8) The Line and the Plane in 3-Space, (9) Quadric Surfaces, and (10) Geometric Transformations. (MK)

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)

Using differentiated instruction in the classroom can be a challenge, especially when teaching mathematics. This book cuts through the difficulties with two powerful and universal strategies that teachers can use across all math content: Open Questions and Parallel Tasks. Specific strategies and examples for grades Kindergarten - 8 are organized…

Geometry is required for many secondary school students, and is often learned, taught, and assessed more in a heuristic image-based manner, than as a formal axiomatic deductive system. Students are required to prove general theorems, but diagrams are usually used. It follows that understanding how students engage in perceiving and reasoning about…

This report makes recommendations for the development of middle-school assessment in mathematics, based on a synthesis of scientific findings in cognitive psychology and mathematics education. The focus is on background research, rather than test specifications or example tasks. Readers interested in early development and pilot efforts associated…

In the study Cabri was used for teaching geometry at 4th grade. To investigate students' geometry level, a semi-experimental method was used. In the test group, geometry subjects are taught using Cabri. A multiple choice test was used to collect data as pre and post test. Answers were assigned as 1 to correct, 0 to wrong answers. Data were…