The books in this series provide an essential ingredient in the transition from concrete mathematical experience to the symbolic reasoning used in algebra. They aim to guide the student in building and extending manipulative patterns, collecting numerical data, and analyzing the results. The main objective of the activities in this book is for the…

Any topic, math included, becomes more accessible and understandable when human stories are related about the development of the subject. Stories make subjects real and purposeful. They provide a foundation from which students can understand and appreciate mathematics rather than merely memorize a series of rote exercises. This book presents 16…

Students learned to use mathematics to understand the importance of measurement, graphing and a simplified version of conic section and parabola. Through the development of the concept of line from which curve forms were created art and mathematics became intertwined while students accomplished far greater flexibility and mastery of an artistic…

This article presents a simple procedure to generate a sequence of rational numbers converging on the square root of 2, yielding common fraction approximations that motivate and illuminate the definition of real numbers based on rationals. Examples suggest that any irrational number can be approximated as closely as desired. A bibliography is…

There are many ways to generate mathematical problems from a starting point. This author shares some thoughts that led to production of a number of them. The problems contained here range in level from Kindergarten to college. Walter starts by providing the problems so that the reader will have the opportunity to solve them without any hints.…

Can mathematics survive as a school subject for "all?" Is mathematics a subject for "general education?" Has mathematics anything to say for anybody else but a mathematician or an immediate user of mathematics by profession? Or, will mathematics become a subject for the selected few who are to lead society by this mighty tool…

The concept of pi is one of great importance to all developed civilization and one that can be explored and mastered by elementary students through an inductive and problem-solving approach. Such an approach is outlined and discussed. The approach involves the following biblical quotation: "And he made a moltin sea ten cubits from one brim to…

A classic problem involving the "misuse" of mathematical induction is presented. The error in the "proof" is then exposed. The generalization of this problem is presented as a false theorem which should serve to highlight the error. (LS)

A game based on the group of permutations on four symbols is described. The game can be used in the study of many algebraic concepts. (SD)

Elucidated is the relationship among three threads of mathematical investigations: Kirkman's schoolgirl problems, finite geometries, and Euler's n-square officer problems. (JP)