The Chinese tangram puzzle was known as far back as 1813. It has remained popular ever since. It consists of seven simple polygonal pieces of card which can be assembled in the form of a square. The reader is presented with some popular shape such as the man or cat above, and then asked to construct this using the tangram pieces. There are whole…

Based on close observations of two 4-year-old children responding to their parents' requests for quantitative comparisons, we offer a "participationist" account of the origins and development of numerical thinking, one that portrays numbers as a product rather than a pregiven object of human communication. In parallel, we propose a…

In this note we give closed forms for a class of logarithmic integrals in terms of Bernoulli polynomials. This provides a method for unifying a large class of definite integrals.

The concept of how the definite integral is understood by the students deeply with the help of an activity and the connection between the functions [prime]integral of 1/t is described. The definition of integral of 1/t is remembered by the students by exploring the integral systematically and by application of their knowledge of rational…

This article reports on the use of a unique number system to facilitate teachers' understanding of the concepts of place value. Teachers' mastery of base-ten may hinder their recognition of the difficulties students have with place value, so the authors created a number system that used five symbols to represent values. Using this system, teachers…

Many have argued for the importance of numeracy, yet little is known about the opportunities for numeracy available to people in their daily lives. In this study, characteristics of rational numbers in magazines written for children, teenagers, and adults were analyzed and compared. Analysis indicated that difficult mathematical concepts that…

This booklet describes basic counting principles and provides activities designed to develop basic skills in: (l) stable ordering; (2) one-to-one matching; (3) total number; (4) different objects; and (5) different order. These are extended to more advanced strategies aimed at building counting skills strong enough to provide a basis for adding,…

Presented are a series of conjectures and proofs resulting from an examination of patterns and relationships among natural numbers. (JP)

This document is intended as a resource for persons using, designing, or evaluating instructional materials in whole number subtraction. Its purpose is to provide conceptual machinery: (1) for describing/specifying subtraction tests and exercises and (2) for formulating related questions and conjectures. It is mainly a logical analysis subject to…

This is part one of a two-part SMSG mathematics text for sixth-grade students. Chapter topics include: Exponents; Multiplication of Rational Numbers; Side and Angle Relationships of Triangles; Introducing the Integers; and Coordinates. (MK)

A DESIGNED PROGRAM FOR PRESCHOOL AND KINDERGARTEN CHILDREN WHO HAVE NOT YET LEARNED TO READ AND WRITE WAS DESCRIBED. IT DEALT WITH NUMBER CONCEPTS AND NUMERALS AND USED A MULTIPLE CHOICE PICTORIAL FORMAT. IN THE TYPICAL PROGRAMED INSTRUCTION SITUATION, THE STUDENT READ A FRAME AND MADE A RESPONSE. WHEN HE MADE THE CORRECT RESPONSE, HE WAS INFORMED…

This is a supplementary manual for teachers using SMSG junior high school text materials. A chapter-by-chapter commentary on the text is given as well as answers to all the exercises. Chapter topics include: (1) sets; (2) projective geometry; (3) repeating decimals; (4) tests for divisibility; (5) finite differences; and (6) prime numbers. (MP)

This book is part 2 of a 2-part manual for teachers using SMSG text materials for grade 4. The purpose for each of 5 chapters is stated and mathematical background for the teacher is presented. Detailed lesson plans are then provided, including sequences of statements and questions, activities, and exercise sets with answers. Needed materials and…

This pamphlet consists of 17 brief chapters, each containing a discussion of a numeration system and a set of problems on the use of that system. The numeration systems used include Egyptian fractions, ordinary continued fractions and variants of that method, and systems using positive and negative bases. The book is informal and addressed to…

The sixteen chapters of this book provide the core material for the Elements of Mathematics Program, a secondary sequence developed for highly motivated students with strong verbal abilities. The sequence is based on a functional-relational approach to mathematics teaching, and emphasizes teaching by analysis of real-life situations. This text is…