Two sequences of activities were developed to provide instruction on the algorithms for addition and subtraction of two-digit numbers. In the integrated sequence (I) the mechanics of "carrying" and "borrowing" were treated as a single process "regrouping." In the sequential treatment (S) the addition algorithm was developed before the subtraction…

Two sequences of activities were developed to provide instruction on the algorithms for addition and subtraction of two-digit numbers. In the integrated sequence (I) the mechanics of "carrying" and "borrowing" were treated as a single process "regrouping." In the sequential treatment (S) the addition algorithm was developed before the subtraction…

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)

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

Reviews research using diagrams, number sentences, and algorithms to help students learn to add and subtract; poses questions on the relationship of instruction to children's knowledge construction; and proposes a research agenda in this area. (86 references) (MKR)

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)

Reported are the results of a study to determine if specific errors in subtraction occur when students demonstrate ability to apply selected decimal numeration system principles. A secondary purpose was to examine and compare errors made by various subsets of the sample population characterized by grade level, arithmetic achievement, mental…

This study explored the effects of visual (vertical and horizontal) and oral presentation modes upon simple mathematical computations (addition, subtraction, and multiplication). Seventy-two undergraduate education majors were employed as subjects. The placement of the process sign (left, middle, right) and whether a one or two digit number…

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)

Outlines various subtraction methods, such as the decomposition method, equal-addends method, and low-stress algorithm. Describes a subtraction method by addition of complements. Discusses the advantages and disadvantages of the method. (YP)

Research recurrently indicates that children who have difficulty with arithmetic often use systematic routines that yield wrong answers. Recent research has focused less on identifying the most common errors among groups of children and more on analyzing individual children's errors. This paper considers the source of systematic errors in…

Programing a microcomputer to solve problems in whole-number arithmetic, rather than using the built-in operations of the computer, is described. Not only useful, it also enhances important mathematical concepts and is adaptable to a range of student abilities. (MNS)

Attempted to establish the incidence of using taught algorithms versus invented methods of subtraction in (n=1,370) male secondary school students and to relate the use of invented methods to age, mathematical achievement, and lateral thinking ability. Use of invented algorithms increased with age. (23 references) (MKR)