Six widely used US Grade 1 curricula do not adequately address the following three developmental prerequisites identified by a proposed learning trajectory for the meaningful learning of the subtraction-as-addition strategy (e.g., for 13-8 think "what + 8 = 13?"): (a) reverse operations (adding 8 is undone by subtracting 8); (b) common…

"Curriculum-Based Measurement" (CBM) is a direct method of academic assessment used to screen and evaluate students' skills and monitor their responses to academic instruction and intervention. Interventioncentral.org offers a math worksheet generator at no cost that creates randomly generated "math curriculum-based measures"…

For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards…

Exemplifies a model of a conceptual-support net in the domain of multidigit addition that provides guidance in making curricular and classroom teaching choices about what kinds of conceptual supports to provide in a particular setting. Presents summaries of several different multidigit addition solution methods that indicate how different quantity…

Using drawings of various monsters to explain and enhance the learning activities, this arithmetic/mathematics curriculum guide begins with exercises requiring basic number identification. The remainder of the guide includes over one hundred addition and subtraction activities including crossword puzzles, maps, and number matching. (SH)

Developed by the Initial Learning in Mainstreaming Project, the manual presents an instructional program to teach mainstreamed handicapped elementary school students the carrying process (regrouping) for addition. In addition to detailed teaching instructions and text of tape recordings for students, the manual includes tests, worksheets, and…

Presents a first-semester course in mathematics for 6-year-old children by formulating certain general requirements for the curriculum and the instructional methods with the aim of leading children to form their initial mathematical concepts. (ASK)

Presented is a paradigm for teaching basic and semibasic arithmetic facts to children with arithmetic difficulties, in which the student progresses from the use of concrete materials such as blocks, to the use of diagrams such as tally marks, to a reasoning process, to responding in an automatic manner. (DLS)

The document presents the final report of the Initial Learning in Mainstreaming Project, which developed and tested instructional techniques in 14 specific mathematics skill areas with 429 handicapped and normal elementary school students in Grace and Soda Springs, Idaho. Skill areas included addition facts; subtraction facts; carrying…

This paper discusses an approach to the study of algorithms which values students' construction of nonstandard algorithms but also emphasizes the essential roles of the teacher and instructional activities in supporting the development of students' numerical reasoning. Episodes are presented from a 3rd grade classroom in which a 9-week teaching…

This guide is a collection of ideas for mathematics activities which were assembled and tested by primary teachers. The activities supplement the teaching of basic numeracy and include topics such as algorithms, pyramids, magic squares, multiples, and number values. The guide is organized into four sections: (1) addition and subtraction; (2)…

In the foreword to this book, Inhelder states that its essential contribution is that "it transposed to actual reality Piaget's central epistemological thesis according to which mathematical thought is, from its most elementary manifestations, the product of the subject's activity that he characterized by the term 'reflective…

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…

Using four large existing databases on student performance in the elementary grades, this study involves a task-by-task, year-by-year cross-sectional analysis of six topics in computation. Information about what students eventually learn and when they learn it is provided by the data analysis; information about when skills are introduced and…

The National Science Foundation funded Calculators and Mathematics Project, Los Angeles (CAMP-LA) developed curriculum materials focused solely on the use of calculators. The project was developed in three stages. The first stage studied the mathematics curriculums from different states and identified topics that are not included but should be if…