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March 2001, Volume 94, Issue 3


Tunja Sequences as Examples of Employing Students' Powers to Generalize
John Mason
Demonstrates how students' power to recognize and express patterns and generality can be exploited in a variety of different ways. In particular, patterns are used to learn to multiply expressions and factor simple quadratics.

A History of Mathematical Dialogue in Textbooks and Classrooms
Edith Mendez
An examination of textbooks and classrooms from antiquity through the nineteenth century in search of historical precedents for mathematical communication in the form of dialogue between teacher and student.

Points on the Path to Probability
James Kiernan
The "problem of points" is examined through history providing insight into the nature of mathematical discovery.

Discuss with Your Colleagues: Equiareal Polygons: A Mathematical Conversation about a New Concept
Greisy Winicki-Landman
An activity that occurred spontaneously at the end of a professional development program for secondary geometry teacher. The activity is connected with mathematical definitions and illustrates the process of gradual refinement as a way to understand and construct knowledge.

Pythagorean Triples from Harmonic Sequences
Angelo DiDomenico, Randy Tanner
A surprising connection that shows how all primitive Pythagorean triples can be generated from harmonic sequences.