This teachers manual accompanies a mathematics textbook, written in Portuguese, for third graders. It closely follows the objectives and methodology of the major curricula used throughout the schools in the United States. The 11 chapters deal with: numeration (0-999,999); addition with and without regrouping; subtraction with and without…

These military-developed curriculum materials consist of three volumes of self-paced, individualized training manuals for use by those studying to be electronic computer systems technicians. Covered in the individual volumes are the following topics: computer principles (number sytems, computer circuits, computer components, computer units,…

Problems in mathematics instruction in Thailand that are related to language include the simultaneous use of both traditional Thai numerals and Hindu-Arabic numerals, misunderstanding of mathematics problems for cultural reasons, and/or difficulty in understanding problem context. Research has shown that elementary and secondary school children…

Some diverse fields in which the effects of mental representations have been noticed are first discussed, largely through illustrations of differing problem-solving experiences. Then the LAKOS Project (Logical Analysis of Cognitive Organizational Structures) at the University of Osnabruck is described. A central concern is the specification of a…

The use of counting for subtraction was investigated. Counting for subtraction is related to counting-on for addition and to four skills: the ability to use the subtrahend cardinality to gain entry into the count sequence, the ability to use the minuend cardinality to gain entry into the count sequence, the ability to use the count sequence to…

This document focuses on research on the relation between children's use and understanding of counting as a symbol system for number and the development of number conservation concepts. An underlying assumption is that a better match between mathematics curricula and the educational needs of children will be facilitated by learning more about the…

Results of research on the acquisition of counting skills in children is presented. The material, originally published in the Soviet Journal "Questions of Psychology," was deemed an important document that should be translated and made accessible to English readers. The question of how basic, extended processes are…

This is part two of a two-part SMSG text for grade seven students whose mathematical talents are underdeveloped. The reading level of this text has been adjusted downward, chapters shortened, and additional concrete examples included. Nevertheless, the authors warn that the text may not be appropriate for the very slow non-college-bound student.…

This is part one of a two-part SMSG text for grade eight students whose mathematical talents are underdeveloped. The reading level of this text has been adjusted downward, chapters shortened, and additional concrete examples included. Nevertheless, the authors warn that the text may not be appropriate for the very slow non-college-bound student.…

Pascal's Triangle is an important numerical table; with its help, a number of computation problems may be solved. Some of these problems are examined and the question of what"solving a problem" can mean is generally considered. (Author/MK)

The cognitive determinants of number series completion performance were studied by presenting a systematic set of problems to adults and to children of high and average intelligence, grades 4 and 5. Pearson correlations between these problems and the number series on the Cognitive Abilities Test were .51, .78 and .43 for the average intelligence,…

This paper reports the formative evaluation of six curriculum units related to initial number sentence writing. These units were used for a coordinated study carried out by the Mathematics Work Group of the Wisconsin Research and Development Center for Individualized Schooling. The units were tried during the 1977-78 and 1978-79 school years at a…

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 is part one of a three-part manual for teachers using SMSG junior high school text materials. Each chapter contains an introduction and a collection of sample text questions. Each section contains a discussion related to the topic at hand and answers to all the exercises. Chapter topics include: (1) rational numbers and coordinates; (2)…

A complete set of behavioral objectives for first-year algebra taught in any of grades 8 through 12 is presented. Three to six sample test items and answers are provided for each objective. Objectives were determined by surveying the most used secondary school algebra textbooks. Fourteen major categories are included: (1) whole numbers--operations…