Studies fourth grade students identified by their teachers as having 'above average ability' in mathematics who were participating in 'pull out' enrichment sessions. Indicates that these students did not show initial difficulties with turn commands previously reported in mixed populations, and they created strategies to determine the correct…

Discusses the geometric and mathematical features of the pyramids in Cairo. Describes the relationship between the great pyramid and Pi. (ASK)

Discusses the geometric features of a building called the Alhambra in a city in the southernmost region of Australia called Granada. Describes plane patterns and analyzes those patterns while focusing on the plane symmetry. (ASK)

Emphasizes how to express the breadth of mathematics itself. Addresses other missing dimensions which make mathematics attractive to a larger number of students by making it appear less isolated and more tied to thoughts and experiences that students find familiar and congenial. (ASK)

Describes ways to examine leaf structure and shape using fractal geometry. Students can test hypotheses using the leaves of replicated plants to look for non-linear trends in leaf shape along the stems of plants, across species, and under different environmental growth conditions. (SAH)

Analyzes the functions of semiotic mediation in a long-term teaching experiment, Mathematical Discussion, on the plane representations of three-dimensional space by means of perspective drawing in grade two to five classrooms. (Author/MKR)

Presents several theoretical solutions to a geometry problem involving circles and probability. Includes simulation procedures to estimate the solutions. (MKR)

Introduces The Square Thing, a lesson that engages and invites student development of problem solving and reasoning skills, understanding through connections within the content, and mathematics voice. Describes components for successful pedagogy and benefits for students experiencing this and similar mathematics pedagogies. (Author/MM)

Eight experiments examined abilities of 3- to 4-year-olds to reorient themselves and locate a hidden object in an open circular space furnished with landmark objects. Findings showed that children failed to use geometric configuration of objects to reorient themselves. Children successfully located the object in relation to a geometric…

A test item exhibits differential item functioning (DIF) if students with the same ability find it differentially difficult. When the item is administered in French and English, differences in language difficulty and meaning are the most likely explanations. However, curriculum differences may also contribute to DIF. The responses of Ontario…

Two questions are asked that concern the work of teaching high school geometry with problems and engaging students in building a reasoned conjecture: What kinds of negotiation are needed in order to engage students in such activity? How do those negotiations impact the mathematical activity in which students participate? A teacher's work is…

Some of the graphing capabilities of The Geometer's Sketchpad (GSP) in the "Technology Tips" are introduced. The new graphing features of GSP allow teachers to implement the software not only in geometry classrooms but also into their algebra, precalculus and calculus classes.

Alf Coles and Barry Orr reflect on what it looked like when Alf taught a year 7 lesson. In this article, Alf was asked by Barry (student) if he would take a lesson with the Y7 class that he had taken over from another teacher in the department in order to see what someone else might do with his lesson plans. Alf describes what some moments with…

In his famous quadrature of the parabola, Archimedes found the area of the region bounded by a parabola and a chord. His method was to fill the region with infinitely many triangles each of whose area he could calculate. In his solution, he stated, without proof, three preliminary propositions about parabolas that were known in his time, but are…

Within statistics instruction, students are often requested to sketch the curve representing a normal distribution with a given mean and standard deviation. Unfortunately, these sketches are often notoriously imprecise. Poor sketches are usually the result of missing mathematical knowledge. This paper considers relationships which exist among…