The question is raised: What comes first: rules of calculation or the meaning of concepts? The pressures on the teacher to teach and simplify knowledge to algorithms are discussed. The relation between conceptual and procedural knowledge in school mathematics and consequences for the teacher's professional knowledge are considered. (DC)

In one school, algorithmic development has been infused in the mathematics curriculum. An example of what occurs in mathematics classes since the teachers began using the computer is given, with two students' conjectures included as well as the algebraic justification. (MNS)

This manual is a dictionary of some 150 errors made by students in their work in mathematics. A precise definition and examples are given for each of these errors and these, combined with a description of common causes of the error, form a background for diagnosis of student problems with arithmetic. Teaching strategies and ideas, each linked to a…

Presented are the mathematical explanation of the algorithm for representing rational numbers in base two, paper-and-pencil methods for producing the representation, some patterns in these representations, and pseudocode for computer programs to explore these patterns. (MNS)

This book provides a comprehensive collection of 66 teaching strategies and ideas to help overcome problems with number, each linked to a specific kind of error described in the related manual. Most of these strategies are classroom-ready and easily implemented. Some are notes for the teacher to read and then plan activities accordingly, and many…

Use of the hand-dialed, transparent, nonelectronic SEE-Calculator is proposed. Pupils can dial numbers into appropriate columns, watching the gears work; place-value concepts are enhanced. Both activities and flowcharting are suggested. (MNS)

Argues that the type of calculator that is used in mathematics instruction is very important. Suggests that four-function calculators fail to give correct values of mathematical expressions far more often than do scientific calculators. (PK)

P-adic or g-adic sets are sets of elements formed by linear combinations of powers of p, a prime number, or g, a counting number, where the coefficients are whole numbers less than p or g. Discusses exercises illustrating basic numerical operations for p-adic and g-adic sets. Provides BASIC computer programs to verify the solutions. (MDH)

This two-volume teacher's guide is to be used with a second-semester, sixth-grade mathematics program. The manner of presentation and the pedagogical ideas and tools are based on the works of Georges and Frederique Papy. They are recognized as having introduced colored arrow drawings ("papygrams") and models of our numeration system (the…

This two-volume teacher's guide is to be used with a first-semester, third-grade mathematics program. The program is in large part the outgrowth of involvement with children and was influenced by information gathered in an extended pilot project conducted nationwide during 1975-79. The manner of presentation and the pedagogical ideas and tools are…

This two-volume teacher's guide is to be used with a second-semester, third-grade mathematics program. The program is in large part the outgrowth of involvement with children and was influenced by information gathered in an extended pilot project conducted nationwide during 1975-79. The manner of presentation and the pedagogical ideas and tools…