Presented are the results of an investigation of stimulus integration capabilities of three- and four-year-old children in judgments of small and large numbers. There is much evidence that suggested young children have a concept of number for small numbers, but not for large ones. A concept of number was hypothesized by Piaget to rest on the…

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 book contains mathematics activities based upon the concepts of Fibonacci numbers and the Golden Ratio. The activities include higher order thinking skills, calculation practice, integration with different subject areas, mathematics history, extensions and home tasks, teaching notes, and questions for thought and comprehension. A visual map…

This book contains "math mind benders," puzzles that are worked like crossword puzzles except that each square is filled with a digit rather than a letter. Clues to the puzzles are interrelated with each other and a given story. Clear thinking and deductive reasoning must be used to find potential answers and eliminate those that fail to meet all…

Examines questions about reported findings that the natural number concept derives from a prior understanding of ordination rather than a prior understanding of cardination. (GO)

The use of the stanine scale to control some of the sources of error in converting letter grades to a numerical scale before they can be added or averaged is described. (Author/RK)

The representation of a binary number by a row of people sitting or standing by their chairs is reviewed. The representation is extended into a counting activity and then directions are given for combining the counters into an automatic "machine" which will add, subtract, multiply, and divide. (DT)

Not all of mathematics can be taught in formal textbooks. Just as an English course can be enlivened by selections from literature, a mathematics course can gain depth and interest from special readings. This volume can be read in conjunction with the SMSG First Course in Algebra or Intermediate Mathematics. It introduces the subject of number…

This supplement was written for students who are especially good in mathematics and who have a lively interest in the subject. It is suggested that the supplement be read with pencil and paper in hand. All questions should be considered and answered, if possible, when they occur. A casual reading of the supplement is, in most cases, unprofitable.…

Demonstrates the interplay of a cognitive system, the Basque numerative system, and a behavioral one, counting sheep. The significant features of the Basque numerative system are analyzed; then it is shown how use of these features facilitates the counting of sheep on open ranges by Basque sheep farmers in California. (Author/RM)

A brief biography of Pythagoras, including discussions of his contributions to philosophy and mathematics, is presented. (CR)

Compares one study in which 5-year-olds and another in which adults quantified random patterns of dots under unlimited exposure duration. Data on operating ranges and rates for subitizing and counting are included. (JMB)

There is offered in this book a year's work in numbers for those boys and girls who know one to ten thoroughly. The book is designed for the children themselves. The practical use of this text in various schools for several years gives evidence by its success that as soon as children can read they should have arithmetics in their hands. [Cover…

This textbook provides the foundation for a course in mathematics covering arithmetic, algebra, geometry, conic sections, and arithmetic of infinites. An appendix on practical gauging is included, as well as a supplement containing the history of logarithms. [This edition was corrected and improved by Samuel Clark.]