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…

Over a 10-month period, normal children showed an increased reliance on memory retrieval and a decreased reliance on counting when they solved addition problems. There was an increase in speed of counting and of retrieving addition facts from long-term memory. Children with a mathematical learning disability showed no change in problem-solving…

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…

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 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…

Practice on computation is provided using new and novel situations, with discovery of number patterns a bonus of the computation. Activities with disguised addition and multiplication tables for whole numbers and integers are presented for varying levels. (MNS)

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)

Traditional methods of teaching addition include algorithms that involve right-to-left procedures. This article describes efficient procedures for left-to-right addition and subtraction involving computation and computational estimation that reflect children's natural behaviors observed during activities with unifix cubes. (MDH)

This study compared the effectiveness of teaching multidigit addition of whole numbers without regrouping prior to teaching it with regrouping to teaching multidigit addition with and without regrouping simultaneously. Pretest/posttest-delayed posttest results of second grade students (n=151) from seven randomly assigned classrooms indicated no…

Results of a comparison of 73 Anglo American and 155 Chinese American (CA) fourth through sixth graders on an intelligence test and measures of the speed and consistency of retrieval of arithmetic facts from long-term memory are consistent with the hypothesis that accessing elementary arithmetic knowledge is more completely automatized in CA…