Described are three activities and variations that can help students to understand the concept of place value. Allowing students to use concrete materials and helping them to bridge the gap between manipulatives and paper-and-pencil tasks are emphasized. (KR)

This paper is based on a long-term didactic engineering about division problems (only in a numerical setting) at primary school. Situations and students' work are analyzed by means of a double theoretical framework: the theory of situations and the theory of conceptual fields (Vergnaud 1991). The analysis focuses mainly on classroom interactions…

The Skill Acquisition Measures (SAM) were designed by the Lancaster (Pennsylvania) School District as criterion referenced tests for mathematics. This manual consists of copies of the student test forms for level 3, with additional information for the teacher's use. Each of the test items is presented with the correct answers and the criteria for…

The effects of two curricula for teaching number concepts to kindergarten children: a part-part-whole (PPW) curriculum emphasizing set-subset relationships between cardinal numbers, and a count/say/write (CSW) standard curriculum were composed. The concept of number attained by children taught with these two curricula was compared to that of…

Heavy emphasis is placed on development of understanding of arithmetic in this mathematics curriculum prepared specifically for Navajo children and intended for use in reservation schools. Materials are presented so that only when a given concept is understood are skills associated with it and a written format introduced. Learning activities…

This is the second module of 10 in the German Headstart program. Each of the 3 units in the module contains objectives, exercises, and a self-evaluation quiz. In addition, there are several supplementary exercises and self-evaluations. The objective of this module is to enable the student to deal with three situations: (1) getting to a specified…

Examines how quantification is expressed in written English. Suggests ways of defining the categories of meanings a learner might need to be able to express and the linguistic devices used to realize these meanings. Categories of quantification are included. (Author/LMO)

Presents guidelines for designing and using extensions, which are exercises that follow or extend the basic presentation of an idea, in the mathematics area of the Montessori program to give children more experience and depth as they explore key mathematical concepts. Describes extensions that address counting, sorting, and working with decimals.…

Interviews with five Shoshoni elders during a 1-year study showed that mathematics was integral to daily life and reflective of their culture. Classroom activities are described that integrate traditional Shoshoni mathematical knowledge into mathematics instruction. This knowledge may help Shoshoni students develop a deeper understanding of…

The objectives and the scope and sequence for the elementary school mathematics program of the Denver Public Schools (Colorado) are presented. The guide begins with a statement of the philosophy and general objectives of the K-12 mathematics program and a discussion of the methods of achieving those objectives. Several important ideas and concepts…

The Skill Acquisition Measures (SAM) were designed by the Lancaster (Pennsylvania) School District as criterion referenced tests for mathematics. This manual consists of copies of the student test forms for level 2, with additional information for the teacher's use. Each of the test items is presented with the correct answers and the criteria for…

THIS PROGRAM INCORPORATES THE TRAINING NEEDS OF THE SEVERELY RETARDED CHILD IN A LOGICAL, PSYCHOLOGICAL SEQUENCE TO PROVIDE THE CHILD WITH THE OPPORTUNITY TO GROW PHYSICALLY, EMOTIONALLY, INTELLECTUALLY, AND SPIRITUALLY IN ORDER THAT ADEQUATE SELF-CARE, SOCIAL ADJUSTMENT, GOOD PLANNING OF LEISURE TIME, AND SATISFYING USEFULNESS MAY BE REALIZED FOR…

The purpose of this paper is to identify how the theory and techniques of research in cognitive development can be applied to the study of learning and instruction in mathematics. Five basic research paradigms are characterized; major directions of research on number, measurement, geometry, and adolescent reasoning are identified. Most of the…

This booklet is one of a set of five booklets which comprise the basic curriculum for "Mathematics Laboratories for Disadvantaged Students," a nationally validated Title III ESEA project. This publication provides evaluation materials and student materials related to number theory. Topics included in this booklet are prime and composite…

Middle school students consolidate their understanding of integers and rational numbers, increasing their facility with fractions, decimals, and percents and encountering proportionality. This book shows how students can explore these important ideas in such diverse activities as exchanging currency and using area models to develop algorithms for…