Dialog from a filmed lesson that uses graphing to explain positive and negative numbers is presented. The material highlights the responses of children. The work was also presented to a class of low, mixed-ability pupils since the filming, and the work of two pupils from this group is noted. (MP)

The nature of an investigation into numbers termed Nearly Isosceles Pythagorean Triples (NIPTs) is detailed. The exploration, even though it is stated to have no practical value, is defended as helping pupils see the beauty of patterns in mathematics. Two questions regarding the pattern of generating NIPTs are noted. (MP)

This document describes how to teach a computer to add numbers using the LOGO programing language. The programing project is described in the way a student might develop it. The model of developing the program uses humans as an anthropomorphic model for the computer, and the computer as a model for people. The document has an unorthodox style, as…

This booklet is the ninth in a series of nine from the Teacher Training Institute at Hofstra University (New York) and describes the content and the approach of an institute course in which the participants use the personal computer as a personal tool within the mathematical discovery process of making conjectures, testing those conjectures, and…