A subtraction algorithm that does not involve borrowing is presented and called the residue method. It has been taught in junior and senior high school classes and preservice and inservice classes for teachers. The method has helped in classes where arithmetic in other bases is presented. (MP)

Children's difficulties remembering correct algorithms for operations with fractions are traced to difficulties in the instructional sequence. Many teachers "teach mistakes" by failing to provide sufficient referents for their pupils. (MP)

Three differences between the mathematics training of students from Spanish-speaking countries and that typical for pupils in the United States are discussed. (MP)

It is suggested that the reasons for teaching the standard written algorithms for calculations are not out of date. Alternative algorithms, such as mental algorithms, calculators, and nonstandard written methods, are discussed. (MP)

Three types of arithmetic algorithms are discussed and compared. These are algorithms designed to get the right answer, computer algorithms, and algorithms designed to get the right answer and understand why. (MP)

The question is raised: What comes first: rules of calculation or the meaning of concepts? The pressures on the teacher to teach and simplify knowledge to algorithms are discussed. The relation between conceptual and procedural knowledge in school mathematics and consequences for the teacher's professional knowledge are considered. (DC)

Discusses mathematics education research on multiplication and division which implies that instruction should emphasize development of a sound conceptual basis for multiplication and division rather than memorization of tables and rules. Presents action research ideas. (10 references) (MKR)

Describes an informal research activity in which third grade students invent their own algorithms for multidigit multiplication and division. Discusses teaching implications and action research ideas. (ASK)

In a two-year study, frequencies and descriptions of systematic errors in four algorithms in arithmetic were studied in regular and special education classrooms. (Author/SD)

Students who were unsuccessful in performing long division were taught to use a successive subtractions algorithm. (SD)

The author argues that secondary-school teachers need to be more aware of the content of primary level mathematics work. Citing an algorithm, he discusses the issue of basic skills in relation to the increasing use of calculators. (SD)

This study investigated the effects of the nature of the algorithm, reinforcement, and level of problem difficulty on the ability of fourth graders to solve addition problems as measured by the number of problems correctly solved and the number of columns attempted. Subjects were selected for high scores on a test of basic addition facts; only…

The purpose of this study was to investigate the relationship between a student's confidence in his computational procedures for each of the four basic arithmetic operations and the student's achievement on computation problems. All of the students in grades 5 through 8 in one school system (a total of 6186 students) were given a questionnaire to…

Boys' and girls' achievement in arithmetic computation was compared with their feelings of self-confidence in performing computations. A total of 2654 girls and 2786 boys from grades 5 through 8 in one school system participated. Each student was given a test to assess the degree of self-confidence in methods of performing the four basic…

A previous study had confirmed that a substantial number of low achievers in grades 5 through 8 had high algorithmic confidence in each of the four arithmetic operations with whole numbers. The purpose of the present study was to follow up the results through interviewing low achievement-high confidence students in order to ascertain if they…