The investigation of how a circle and square lying in the same plane could intersect each other is an excellent example of geometric problem-solving. This paper explores three facets of the investigation: (1) finding out how many points of intersection are possible, (2) classifying the different ways of intersection, and (3) determining which ways…

Middle and High school students of the twenty-first century possess surprising powers of spatial reasoning. They are assisted by technologies not available to earlier generations. Both of these assertions are demonstrated by students who are challenged with George Polya's classic Five Planes Problem. (Contains 5 figures.)

This is one of a series of geometry modules developed for use by secondary students in a laboratory setting. This module includes: (1) Pythagorean Theorem (with review of radicals); (2) Basic Coordinate Geometry (distance and midpoint, slope, slope of parallels and perpendiculars, and equation of a line); (3) Selecting Coordinates; (4) Coordinate…

This is one of a series of geometry modules developed for use by secondary students in a laboratory setting. The purpose of this module is to teach solution of proportions, concepts and theorems of triangle similarity, solution of the Pythagorean Theorem, solution of the isosceles right triangle, and concepts involving "rep-tile" figures…

The final report of a two-year study concerned with the digital-computer processing of graphical data. Five separate investigations carried out under this study are described briefly, and a detailed bibliography, complete with abstracts, is included in which are listed the technical papers and reports published during the period of this program.…

Convex polyhedra having square or triangular faces are analyzed algebraically. (SD)

Some practical, hands-on ways in which ideas about geodesic domes can be used in secondary school mathematics are described. Instructions for constructing a one-frequency geodesic sphere are given. (MP)

The calculator is used in conjunction with the measurement of the sides of right triangles to discover the Pythagorean property. (MP)

Describes the van Hiele levels of reasoning in geometry according to responses to clinical interview tasks concerning triangles and quadrilaterals. Subjects were 13 students from grades 1 through 12 plus a university mathematics major. Students' behavior on tasks was consistent with the van Hiele original general description of the levels.…

Presents theorems about lines and lattice points, and relates these to combinatorial analysis. (RS)

A system of area measurement developed for the isometric geoboard is used to justify some relationships that are often proved using square units of area. (Author/MK)

The effects of nonexamples on the acquisition of the geometrical concept of semiregular polyhedra were examined. Results favored the treatments containing both examples and nonexamples. (TG).

Examples are given of computer activities in analytic geometry. (MK)