P-adic or g-adic sets are sets of elements formed by linear combinations of powers of p, a prime number, or g, a counting number, where the coefficients are whole numbers less than p or g. Discusses exercises illustrating basic numerical operations for p-adic and g-adic sets. Provides BASIC computer programs to verify the solutions. (MDH)

Surveys the format and contents of fifteenth- and sixteenth-century arithmetic textbooks. Discusses the types of problems that were most popular in these early texts and briefly analyzes problem contents. Notes the residual educational influence of this era's arithmetical and instructional practices. (Contains 29 references.) (Author/MDH)

Developed for elementary teachers, this activity unit is designed to teach students the importance of estimation in developing quantitative thinking. Nine ways in which estimation is useful to students are listed, and five general guidelines are offered to the teacher for planning estimation activities. Specific guidelines are provided for…

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

Defines "skill-to-meaning" instruction. Describes research designed to determine the effectiveness of skill-to-meaning mathematics instruction for educable mentally handicapped children. Discusses educational implications of the study results and notes the benefits of meaning for handicapped children. (SB)

Forty first-grade teachers' pedagogical content knowledge of children's solutions of addition and subtraction word problems was investigated. Most teachers could identify many of the critical distinctions between problems, and the primary strategies used to solve them, but did not have a coherent organizational scheme. (MNS)

Investigates issues of conceptual understanding in teaching and learning mathematics provided conceptually based instruction on place value and two-digit addition and subtraction without regrouping in four first grade classrooms. Conventional textbook-based instruction was provided in two first grade classrooms. Experimental-group students scored…

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…

A traditional view of mathematics learning suggests that basic fact knowledge provides a cornerstone for success in problem solving. But possibly, for some children, automated basic fact responses may be disadvantageous for their problem solving success. The purpose of this study was to investigate the relationship between basic fact knowledge and…

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 research focused on students' learning of mathematical rules with reasoning. A small group of students (age 11-12 yrs) was observed closely by the first author as she taught them fraction rules. The area of focus was fractions and activities were designed pertaining to the four rules of fractions: addition, subtraction, multiplication, and…

This report opens by asking how operations in general, and addition and subtraction in particular, are characterized for elementary school students, and examines the "standard" instruction of these topics through secondary schooling. Some common errors and/or "sloppiness" in the typical textbook presentations are noted, and…

The object of this study was to specify the relationship between logical and numerical structures by examining the processes used by operational and preoperational children in solving simple addition and subtraction problems. (MP)

Presents a three-year longitudinal study investigating the development of children's (n=82) understanding of multidigit number concepts and operations in grades one through three by using interview processes. Provides an existence proof that children can invent strategies for adding and subtracting and illustrates both what that invention affords…

This brief report compares the lessons on addition and subtraction of signed whole numbers in three seventh-grade Japanese mathematics texts and four U.S. mathematics texts. Japanese books contained many more worked-out examples and relevant illustrations, while U.S. books had more irrelevant illustrations and unsolved problems. (SLD)