Suggests that algorithms, both traditional and student-invented, are proper objects of study not only as tools for computation, but also for understanding the nature of the operations of arithmetic. (Author/NB)

The article identifies five incorrect beliefs about mathematics often held by students who have difficulty with mathematics. They include: the relative size of numbers is more important than the relationships between quantities; computation problems must be solved by using a step-by-step algorithm; mathematics problems have only one correct…

Examines 250 sixth-grade students' understanding of arithmetic average by assessing their understanding of the computational algorithm. Results indicate that the majority of the students knew the "add-them-all-up-and-divide" averaging algorithm, but only half of the students were able to correctly apply the algorithm to solve a…

Fourteen third graders were given numerical computation and division-with-remainder (DWR) problems both before and after they were taught the division algorithm in classrooms. Their solutions were examined. The results show that students' initial acquisition of the division algorithm did improve their performance in numerical division computations…

Compares the approaches to teaching division in Britain and in Holland where different emphasis is placed on the development of mental and written methods. Describes how it is common for pupils in Britain to work from an early stage with pencil and paper rather than mentally whereas early emphasis is placed on mental strategies in Holland. (ASK)

Describes the success, the methods (mental, informal written, standard algorithm) and the strategies of informal written arithmetic to be observed when 300 elementary students worked on six addition and six subtraction problems with three-digit numbers. (Author/MM)

Several subtraction algorithms are analyzed to see if they involve borrowing. The main focus is on an analysis of a procedure called the residue method. The operational arithmetic which underlies the symbolic manipulations is examined and conditions where the method does and does not use borrowing are highlighted. (MP)

A process for helping students in the elementary grades develop their own algorithms for subtraction with carrying is described. Pupils choose their own times and ways to move from manipulative materials to written notation. (MP)

Examines the philosophy behind the issue of computational fluency in "Principles and Standards." (Author)

Fourth graders' (n=117) solutions to addition problems were analyzed in terms of standard or idiosyncratic written algorithms. Students had not previously been taught pencil-and-paper algorithms. Preference for horizontal layout, working from left to right, and a wide variety of written algorithms were found. (Contains 48 references.) (Author/MKR)

Three alternative methods of finding averages of two numbers are presented. (MP)

Describes a multicultural enrichment project for 4th graders that highlights number systems and computation algorithms of various cultures. Discusses student responses and reactions. (KHR)

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…

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)

Presents number tricks appropriate for use in workshops, mathematics clubs or at other times when stressing recreational mathematics. (PK)