Examines activities and children's thinking in four main areas of the Geometry Standard in the National Council of Teachers of Mathematics' (NCTM) "Principles and Standards for School Mathematics": (1) properties of shapes; (2) locations and spatial relationships; (3) transformations and symmetry; and (4) visualization. (Author)

Illustrated is the use of isometric graph paper in the discovery of nonstandard area formulas. The use of definitions, geometric construction, record keeping, and conjectures about triangles, rhombuses, hexagons, parallelograms, isosceles trapezoids, rectangles, and trapezoids are described. (YP)

Challenges abstract mathematics requirements in U.S. high schools. Refutes various philosophical and psychological assumptions underlying math instruction, particularly the correlation between simple numbers and the physical world, the math/logical thinking connection, and frequency of use arguments. Suggests that high schools require only one…

Presents an activity in which students use geometric figures, rep-tiles, to design a tile floor. Rep-tiles are geometric figures of which copies can fit together to form a larger similar figure. Includes reproducible student worksheet. (MKR)

Presents an activity, involving pentagons and using a figure manipulator such as The Geometer's Sketchpad, that requires students to reason geometrically without making unsubstantiated assumptions based on diagrams. (MKR)

Archimedes' method for estimating the value of pi is developed and compared with the Gregory-Machin infinite series method. Programs for the TI-81 calculator for finding the upper and lower bounds using the classical method and estimating pi using infinite series are provided.(Author/MKR)

Attempts to unveil negative images portrayed by Socrates in a dialog with a boy about concepts of squares; illustrates how Socrates' manner may have confused the boy; analyzes the types of questions Socrates favored; and suggests study of this dialogue in teacher preparation programs that attempt to convey more congenial mathematics teaching. (MKR)

Presents activities with 10- and 4-straw flexigons, an object created by stringing together lengths of plastic drinking straws with nylon fishing line. Discusses several geometric theorems that can be demonstrated with flexigons. (MKR)

Presents a strategy for graphing conic sections on the polar plane without using a table of values by beginning with information gained from the graphs of circular functions. (MKR)

Presents a secondary classroom investigation into mathematical modeling techniques with the graphing calculator using a match stick puzzle. Geometric models, through their corresponding area formulas, are constructed, tested, and analyzed graphically to fit specified problem conditions. (Author/MKR)

Uses probability and Pascal's triangle to analyze the game Plinko from the game show "The Price Is Right." (MKR)

Presents a solution to the problem of finding the probability that a needle would cross a crack in a tile floor when dropped. (MKR)

Discussed are two approaches to determining which regular polygons, either inscribed within or circumscribed about the unit circle, exhibit rational area or rational perimeter. One approach involves applications of abstract theory from a typical modern algebra course, whereas the other approach employs material from a traditional…

Relates, in story form, how to make geometric and algebraic concepts more accessible to children by using one-dimensional grids. (MKR)

Presents a problem and a line of reasoning inspired by working in dynamic geometry environments and allowing students to make a geometric construction on the computer and then manipulate the construction by dragging points, lines, and segments. (MKR)