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…

A team of teachers from the same New York City public school met to discuss and compare the Common Core State Standards for Mathematics (CCSSM) to their current math curriculum. The group consisted of four kindergarten teachers, a representative from the first-grade teaching team, and the school's math coach. During the first meeting, the…

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…

Use of the commutativity, addition-subtraction complement, and N+1 progression principles was studied by interviewing 54 capable pupils in grades 1-3. Commutativity was used extensively at each grade, while the addition-subtraction principle to solve subtraction varied across grades, and the N+1 pattern was seldom used. (MNS)

Drill activities for addition, subtraction, multiplication, and division that are derived from the history of mathematics are suggested. (MK)

This is a preliminary report on research into computational errors made by six- and seven-year-olds. (Author/MK)

The grade placement of topics in addition and subtraction was compared across the five countries through analysis of textbooks. "Remarkable" uniformity in grade placement was noted for Japan, China, the Soviet Union, and Taiwan, but the United States differed substantially. (MNS)

Reported is a teacher's efforts to introduce mental methods in arithmetic to seven-year-olds over a four-week period. (PK)

Reviewed is research regarding multidigit addition and subtraction which may be used to question the organization and placement of topics in curriculum materials. Discussed are issues surrounding multidigit addition and subtraction, and the linguistic and cultural disadvantages in constructing units of 10 experienced by children in the United…

This document is part 2 of the workbook for kindergarten pupils in the Comprehensive Instructional Management System, a unified mathematics curriculum for kindergarten through grade 7. Each objective is developed by a variety of strategies, with mastery of objectives diagnosed through a testing component. The activities in the student workbook are…

This paper describes the research program of the Mathematics Work Group of the Wisconsin Research and Development Center for Individualized Schooling. The major interest is in the development of children's abilities to solve verbal addition and subtraction problems and particularly in the processes and strategies used by children. Three factors…

The term Chisanbop is the trademark for the finger calculation method originally developed by a Korean, Sung Jin Pai. It was refined and simplified by his son, Hang Young Pai, who introduced the technique to the United States in 1976. This annotated bibliography has been organized in five categories. Readings in the first category, Historical…

The study investigated children's ability to write number sentences for simple addition and subtraction word problems. The results suggest that open number sentences may provide mathematical symbolism that allows young children to build on informal strategies for presenting and solving simple word problems. (Author/PK)

Describes a study designed to investigate the relationship between students' learning of the standard double-digit addition algorithm and basic fact mastery or numeration concepts. Results suggest basic fact mastery and knowledge of numeration concepts may not be as necessary as previously assumed to learning multidigit addition. (PK)

Presents a method of teaching two-column addition which the authors argue is based on Piaget's theory and fosters the children's own natural thinking. The method does not use objects such as straws bundled or base-ten blocks. (PK)