This publication provides research-based guidance for intensifying instruction in reading and mathematics for students with significant learning difficulties, including students with disabilities, in kindergarten through grade 12. The guide gives technical assistance providers and states information reflecting "best practices" for implementing…

A classification of the simple combinatorial configurations which correspond to various cases of distribution and ordering of objects into boxes is given (in French). Concrete descriptions, structured relations, translations, and formalizations are discussed. (MNS)

Mental skills developed through the study of mathematics are identified, and ways in which this information can shape the role of teachers of algebra are suggested. (MNS)

This monograph provides teachers with a wide range of articles on the teaching of problem solving in the mathematics classroom. The first section, on Understanding the Problem, includes articles which provide a sense of the "problem" of teaching problem solving. The second section, on Devising a Plan, provides suggested plans for…

When the words "problem" and "answers" are used in connection with computational exercises, students think they are solving problems. Distinguishing between computational forms and problems is illustrated with a variety of topics. (MNS)

Several common errors reflecting difficulties in probabilistic reasoning are identified, relating to ambiguity, previous outcomes, sampling, unusual events, and estimating. Knowledge of these mistakes and interpretations may help mathematics teachers understand the thought processes of their students. (MNS)

The mechanisms, images, and language needed for the development of rational-number ideas are briefly discussed. Such ideas are sophisticated and different from natural-numbers ideas. (MNS)

Ignored concepts of numbers, notation, and operation with rational numbers are described. It is proposed that these be taught in the time now devoted to paper-and-pencil skills made obsolete by calculators. (MNS)

Questions about teaching rational numbers are discussed, dealing with when to teach the meaning of fractions and of decimals, when and how to teach computation with fractions and with decimals, and other issues. (MNS)

Division of fractions and division of decimals, both troublesome, are discussed in relation to helping students learn well and retain what they have learned. A strong conceptual base, mastery of related concepts and skills, and meaningful development are stressed. (MNS)

Archimedes' shoemaker's knife problem is interesting in its own right and also allows the demonstration of heuristic teaching ideas and a different method of doing a routine construction. The focus in the article is on the thought processes involved and questions asked when attempting proofs with the problem. (MNS)

How writing skills are used in remedial mathematics classes to help college students attain better problem-solving achievement is described. Data affirm the value of the approach. (MNS)

Children need more than activities to help them see that the relationship expressed in a formula is true. Giving them the underlying principles will contribute to better comprehension, retention, and transfer. (MNS)

This introductory book of a two-part publication, designed as an in-service tool for teachers of grades K-9, is based on the postulate that a teacher should become a better problem solver in order to teach problem solving more effectively to students. This booklet provides an overview of problem solving as a process used daily by all individuals…

The role of computers (especially microcomputers) in the mathematics curriculum and suggestions for using them in mathematics instruction are discussed in this yearbook. The 27 articles are presented under five headings. Part 1, Issues, includes articles on comprehensive instructional computing, possible new curricula, and a syllabus for a…