Assessed the achievement in addition, subtraction, multiplication, and division of 93 fourth graders before and after they received either computer or traditional classroom drill-and-practice instruction. Students who received computer instruction showed greater increases in achievement scores in subtraction and multiplication than did students…

There is substantial empirical evidence showing the impact of the type of numbers in the solution of problems with a multiplicative structure. The theory of the intuitive models of arithmetic operations is today the most plausible theoretical account for these findings. In an attempt to contribute to a better understanding of the effects of number…

Four sequential Basic Skill Levels (levels G, H, HA, and I) of a self-paced, individualized mathematics program designed to improve the achievement of junior high school students are presented in this student workbook. Each level includes a pretest, four to seven lessons, quizzes (checkpoints) after each fourth lesson, a posttest, and a level…

This is one of a series of student booklets designed for use in a bilingual mathematics program in grades 6-8. The general format is to present each page in both Spanish and English. The mathematical topics in this booklet include factors, prime and composite numbers, divisibility, and exponents. (MK)

This guide represents the final experimental version of an extended pilot project which was conducted in the United States between 1973 and 1976. The manner of presentation and pedagogical ideas and tools are based on the works of Georges and Frederique Papy. They are recognized as having introduced colored arrow drawings ("papygrams")…

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…

Research Ideas for the Classroom is a three-volume series of research interpretations for early childhood, middle grades, and high school mathematics classrooms. Each volume looks at research from the perspective of the learner, the content, and the teacher, and chapters are co-authored by a researcher and a teacher. Chapter titles in the early…

A program for teaching "number sense" is suggested based on experiences in teaching numeracy to Papua New Guinean adults. Number sense starts out with some sort of "feel" about the size of a number and extends upwards to include any such mental arithmetical skills as can reasonably be incorporated in an appropriate program.…

Six sequential Basic Skill Levels (levels A through F) of a self-paced, individualized mathematics program designed to improve the achievement of junior high school students are presented in this student workbook. Each level includes a pretest, seven to 10 lessons, quizzes (checkpoints) after each fourth lesson, a posttest, and a level review…

Five sequential Basic Skill Levels (levels J, K, L, M, and MA) of a self-paced, individualized mathematics program designed to improve the achievement of junior high school students are presented in this student workbook. Each level includes a pretest, four to six lessons, quizzes (checkpoints) after each fourth lesson, a posttest, and a level…

This is a project in an emerging line of research investigating children's informed knowledge of mathematics questions. The purpose of this study was to analyze the ability of students who had not received multiplication or division instruction to solve multiplication and division word problems. The study consisted of videotaped interviews with 89…

One of a series of pre-apprenticeship phase 1 training modules dealing with math skills, this self-paced student module covers the multiplication and division of common fractions and whole and mixed numbers. Included in the module are the following: cover sheet listing module title, goals, and performance indicators; introduction; study…

One of a series of pre-apprenticeship phase 1 training modules dealing with math skills, this self-paced student module covers compound numbers. Included in the module are the following: cover sheet listing module title, goals, and performance indicators; introduction; study guide/check list with directions for module completion; information…

After a year of instruction, 70 kindergarten children were individually interviewed as they solved basic, multistep, and nonroutine word problems. Thirty-two used a valid strategy for all 9 problems, and 44 correctly answered 7 or more problems. Modeling provided a unifying framework for thinking about problem solving. (Author/MDH)

Discusses the two overgeneralizations "multiplications makes bigger" and "division makes smaller" in the context of solving word problems involving rational numbers less than one. Presents activities to help students make sense of multiplication and division in these situations. (MDH)