Studied the influence of authentic contexts and self-made graphical representations on students' well-documented tendency to apply the linear model improperly in representing and solving nonproportional word problems. Findings for 152 Flemish 8th graders and 161 10th graders do not show the expected effects; in fact, these forms of help had…

Discusses etymologies of mathematics words as a rich resource for deepening student understanding and appreciation of mathematics, history, and language. Presents detailed examples concerning the branches of mathematics, conic sections, and words of Arabic origin. (KHR)

Discusses the parallels between Klein's position at the forefront of a movement to reform mathematics education and that of the National Council of Teachers of Mathematics' (NCTM) Standards. Draws a picture of Klein as an important historical figure who saw equal importance in studying pure mathematics, applying mathematics, and teaching…

Describes an activity in which students use data analysis and mathematical modeling to obtain insight into a geometrical question. Explores a simple case of the isoperimetric inequalities. (KHR)

Presents three fundamental ideas of calculus and explains using the coordinate plane geometrically. Uses Cabri Geometry II to show how computer geometry systems can facilitate student understanding of general conic objects and its dynamic algebraic equations. (KHR)

The production and application of images based on fractal geometry are described. Discussed are fractal language groups, fractal image coding, and fractal dialects. Implications for these applications of geometry to mathematics education are suggested. (CW)

Presented is an example of a question that can be used to investigate probability and random triangles. Included is the question, analysis, and procedure for solving the question. (KR)

Described is a geometric view of Singular Value Theorem. Included are two theorems, one which is a pure matrix version of the above and the other that leads to the orthogonal diagonalization of certain matrices, i.e., the Spectral Theorem. Also included are proofs and remarks. (KR)

Presented is a lesson in which the patterns that occur within and between sequences of polygonal numbers present an opportunity for students to analyze, represent, and generalize relationships. Materials, objectives, levels, and directions for this activity are discussed. Worksheets to accompany the activities are provided. (CW)

Responds to Crowley's and Wilson's articles on the reliability of the van Hiele Geometry Test. Discusses the issue of the difficulty of trying to maximize content validity while minimizing measurement error. (YP)

Investigates the relationship between the strategies used by preservice elementary teachers in geometric problem solving and two primary mental abilities--spatial visualization and formal reasoning. Reports that the two abilities were related to problem-solving performance, and the strategies used were related to achievement in the geometry…

Discusses teaching geometric concepts, including various shapes, patterns, and areas based on the NCTM Standards. Presented are activities for the geometric concepts. (YP)

Describes two instructional activities to develop spatial imagery and the pupil's responses to these activities. Discusses how the classroom atmosphere contributed to the success of the activities. (YP)

Discusses the calculation of pi by means of experimental methods. Polygon circle ratios, Archimedes' method, Buffon's needles, a Monte Carlo method, and prime number approaches are used. Presents three BASIC programs for the calculations. (YP)

Presents activities which use patterns on geoboards or dot paper to develop geometry and measurement concepts. Includes reproducible student worksheets. (MKR)