Defines one approach to problem solving in terms of student use of algorithms to find their solutions and gives examples. Discusses how problems and algorithms relate to each other. Describes strategies for teaching problem solving using algorithms. (CW)

Describes a research project designed to monitor the transition from work based on concrete materials to the more formalized aspect of mathematics found in secondary schools. The topic of subtraction was chosen by three teachers who were involved in the investigation. (PK)

This paper discusses an approach to the study of algorithms which values students' construction of nonstandard algorithms but also emphasizes the essential roles of the teacher and instructional activities in supporting the development of students' numerical reasoning. Episodes are presented from a 3rd grade classroom in which a 9-week teaching…

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)

Some insights are provided into techniques for removing the mystery of how calculators evaluate functions. (Author/MK)

It is suggested that the reasons for teaching the standard written algorithms for calculations are not out of date.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)

Describes how open-ended writing prompts provide a window into student understanding and mathematical thinking. (YDS)

This article develops an algorithm to find all solutions to the problem, making all sums of a hexagram's nine lines the same. It shows how to exploit the geometric structure of the hexagram and its group of automorphisms. (YP)

Discusses how to express an n factorial as a product of powers of primes. Provides two examples and answers. Presents four related suggestions. (YP)

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)

Three different methods of teaching fraction computation were compared using community college student scores on measures of fraction computation, fraction understanding, and attitude towards mathematics. One method used conventional algorithms; the second, a control for the effect of using a calculator, used conventional algorithms and…

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…

The author argues that children not only can but should create their own computational algorithms and that the teacher's role is "merely" to help. How children in grades K-3 add and subtract is the focus of this article. Grouping, directionality, and exchange are highlighted. (MNS)