Constructions with transparent tape are described for bisecting a segment and an angle, copying a segment, and dropping a perpendicular. A proof is included. (MNS)

Euler's discovery about the centroid of a triangle trisecting the line segment joining its circumference to its orthocenter is discussed. An activity that will help students review fundamental concepts is included. (MNS)

Examines the cause of confusion arising from ambiguity of units and semantics in length, area, and volume concept formation. Introduces the mimik, a standard area of one thousand square millimeters, and advocates its use as an interim symbol system. (JM)

Presents an Applesoft computer program to help students translate abstract sentences into concrete visible lines and thereby discover and confirm facts about slopes, intercepts, angles, and intersections. The program graphs and analyzes lines, given as equations of the form Y equals M times X plus B. (JN)

Describes an activity approach for teaching upper elementary school students the concept of angles. In the interdisciplinary activity, students practice reading and drawing angles from 0 to 360 degrees as they simulate the behaviors used to navigate a sailboat. Includes list of equipment needed and procedures used. (JN)

Lists three guidelines for the sound use of manipulatives in teaching geometry. Also describes activities that use manipulatives to teach topics in geometry and measurement and which illustrate the application of the three guidelines. (JN)

Presents activities involving the addition of antinumbers (which uses novel numerical characters); a puzzle which combines practice in working with polynomials and solving simple equations with intriguing facts about turkets; and searching for the number of different right triangles in a given square grid (which helps develop spatial…

The "Animals" program found on the Apple II and IIe system master disk can be adapted for use in the mathematics classroom. Instructions for making the necessary changes and suggestions for using it in lessons related to geometric shapes are provided. (JN)

A mathematics item on the Scholastic Aptitude Test (SAT) was found to be faulty and received wide publicity. A detailed investigation into its mathematical and psychometric properties is presented. It was found that the problem could be considered ambiguous but that almost no one noticed the ambiguity. (Author/JKS)

A previous article argued that the tradition of teaching sentential logic in geometry should be challenged and suggested that sentential logic be moved to algebra and replaced by inferential logic. Specific inferential logic topics were also suggested. This article elaborates on the inference schemes suggested and describes general proof…

Activities involving estimation of the number of objects in a configuration can motivate students to consider parametric models. (SD)

A college mathematics course designed specifically for architecture students is described. The course covers many topics and includes discussions of the role of the mathematics in diverse areas of art and science. (SD)

Symmetry properties of wallpaper patterns are analyzed. (DT)

This paper explores the role of the teacher in the orchestration of common knowledge and in the interplay between intuitive/empirical and formal aspects within the context of students learning mathematical proof using a dynamic geometry software. The case of a secondary school teacher is discussed through the analysis of her learning initiative…

This is a book about teaching maths to pupils with learning differences, not learning difficulties. Teaching and learning in schools is, and always has been, print based. Other ways of thinking--visual, kinaesthetic, practical--are discounted in the classroom. To become teachers, students must jump over a long series of hurdles, formal and…