Author Pam Harris argues that teaching real math--math that is free of distortions--will reach more students more effectively and result in deeper understanding and longer retention. This book is about teaching undistorted math using the kinds of mental reasoning that mathematicians do. Memorization tricks and algorithms meant to make math…

Encourages teachers to allow opportunities for students to present alternative algorithms, whether the students invent them or learn them, then lead a discussion about the meaning of the operations with the goal of students understanding why the algorithm works. Teachers with students of similar racial and ethnic backgrounds should encourage the…

The four-color theorem stating that any map in a plane can be colored using no more than four colors represents a problem suitable for the liberal arts student. Presented is an algorithm for coloring familiar maps through the temporary removal of states bordering three or fewer states. (MDH)

This guide represents the final experimental version of a pilot project which was conducted in the United States between 1973 and 1976. The ideas and the manner of presentation are based on the works of Georges and Frederique Papy. They are recognized for having introduced colored arrow drawings ("papygrams") and models of our numeration…

This monograph is aimed at helping the reader understand the built-in logic of various calculator operating systems. It is an outgrowth of workshop contacts with in-service and pre-service teachers of mathematics and is in response to their request for a book on the subject of calculator logic systems and calculator algorithms. The mathematical…

Describes the Plane Geometry System computer software developed at the Educational Computer Systems laboratory in Sofia, Bulgaria. The system enables students to use the concept of "algorithm" to correspond to the process of "deductive proof" in the development of plane geometry. Provides an example of the software's capability…