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)

Presents research on students' use and understanding of algorithms in Poland. Concludes that there are detrimental side effects that stem from the teaching and learning of standard written algorithms. (ASK)

The author advocates the classroom consideration of new algorithms as a means of leading students to make original hypotheses. He discusses a multiplication algorithm based on the differences between squares. (SD)

The long division algorithm approached as repeated subtractions is explained. (DT)

Indicates that there has been a lot of work done and that a great deal needs to be done in the future to explore the world of children's early number. Discusses the counting, the use of algorithm, practical mathematics, the use of manipulatives, individual differences and pedagogical concerns, and classroom applications. Contains 18 references.…

Discusses the use of manipulative materials to model operations and algorithms. Indicates that they clarify the several interpretations of each operation, establish a basis for correct mathematical language, and show why algorithms work. (JN)

Reviews the historical development of subtraction algorithms used in the United States. Indicates that the algorithms used to teach subtraction have not changed much in the last 40 years, but in the late 1800s and early 1900s, different algorithms were developed that had a great impact. Contains 22 references. (DDR)

Explores written calculation methods for division used by pupils in England (n=276) and the Netherlands (n=259). Analyses informal strategies and identifies progression towards more structured procedures that result from different teaching approaches. Comparison of methods used shows greater success in the Dutch approach which is based on…

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…

Analyzes a didactical sequence for the teaching of addition and subtraction procedures and algorithms. Uses didactical procedures by children in problem solving activities in order to gain a better understanding of the interaction between numbers, numeration, and operations knowledge which are involved in the construction of addition and…

Compares methods of subtraction used by children and teachers. Suggests ways to encourage children to invent their own subtraction algorithms. (CCM)

A subtraction algorithm for numbers having several digits is described. The algorithm requires that, for digits in the same place, the smaller is always subtracted from the larger. (SD)

Speed and accuracy in adding a colunm of one addend numbers directly down a column was compared to adding by looking for combinations which add to ten. Ninety-two fourth-grade subjects learned one of these two methods for one week and then learned the other method the following week. Using timed tests after each treatment, it was found that the…

Described is a case in which a young student stumbles upon the "integer" technique for subtraction which differs from the techniques of decomposition and equal addition. (MN)

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…