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)

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.…

A six-step method of teaching subtraction by renaming is presented, using money as the learning vehicle. (MP)

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…

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)

A multiplication algorithm based on a perfect square is described. (SD)

Two methods of adding columns of single digits were compared in terms of the speed and accuracy with which sums are produced. The direct method (successive addition) was found to be better than the method of looking for combinations which sum to ten. (SD)

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)

Some techniques for developing the ability to multiply and divide by powers of ten with ease and understanding are presented. (Author/MK)

Upper elementary school students created their own algorithms for finding products of whole numbers. The algorithms were similar to familiar ones for finding products involving 9 and 11. (SD)

An activity is presented which provides a novel approach to number patterns, experience in following an unusual algorithmic procedure, and practice in systematic search techniques and basic facts. (MK)

The importance of place value is discussed. Examples illustrating place value in addition and subtraction are given. (MK)

Based on Piaget's theory that children acquire number concepts by constructing them from within, the authors conclude that teaching algorithms harms mathematics learning. A better approach is allowing them to construct their own logico-mathematical knowledge and invent their own efficient procedures. (JOW)

The author describes a technique for teaching various aspects of the subtraction algorithm (e.g., regrouping, borrowing) by relating them to the use of money. (SD)

Instructional sequences are presented for teaching two-digit multiplication and division with one- and two-digit divisors using a base-oriented approach. (MN)