This paper is concerned with the role of meaning and understanding in the acquisition of computational skill in subtraction. Evidence on the syntactic nature of subtraction errors is reviewed, with common "bugs" described. Then, data collected from interviews with four children are summarized in terms of their semantics of concrete…

Types of errors made by children in addition and subtraction are presented and discussed. Suggestions are given for testing, diagnosing, and prescribing for instruction. (MNS)

An exploratory investigation of various incorrect solution procedures used by students attempting to solve a variety of forms of open sentences is reported. The study identifies specific incorrect strategies, indicates their relative frequency of occurrence, and attempts to offer some explanation for certain of the incorrect procedures used. (MK)

This study involved the extensive testing and interviewing of 102 primary grade pupils, representing a sampling from diverse school environments, to study the capabilities and difficulties evidenced by primary-grade pupils in solving open addition and subtraction sentences. Phase 1 of the study identified the specific incorrect procedures commonly…

This is a preliminary report on research into computational errors made by six- and seven-year-olds. (Author/MK)

Tests of (n=107) third through sixth graders' basic addition facts found that 34% of errors involved the addition of zero and 83% of the remaining errors involved at least one of the digits 7, 8, or 9 when the other addend was 4 or more. (20 references) (MKR)

This study compared the error patterns of third- and fourth-grade children on addition, subtraction, and multiplication exercises in horizontal and vertical formats. The research design used parallel eight-item tests for each operation; the only difference between items on parallel forms was the formal (horizontal or vertical) of the computational…

Forty-three first-grade children, who had received no formal instruction in addition and subtraction, were individually administered 20 problems that could be solved using addition or subtraction. The problems were selected to represent the following semantic types: joining, separating, part-part-whole, comparison, and equalizing. Responses were…

This paper describes the various procedures associated with the individual interviews that are part of the data gathering processes of the Coordinated Study being carried out by the Mathematics Work Group of the Wisconsin Research and Development Center for Individualized Schooling. The first major section describes the six basic verbal addition…

A newly introduced approach, rule space, can represent large numbers of erroneous rules of arithmetic operations quantitatively and can predict the likelihood of each erroneous rule. The new model challenges the credibility of the traditional right-or-wrong scoring procedure. (Author/PN)

Recent research on solving addition and subtraction word problems has resulted in the construction of theoretical models of children's problem-solving processes. Some of these models have been translated into computer programs. Characteristics and predictions of the theoretical analysis developed by Riley, Greeno, and Heller (1983) are discussed…

An overview is presented of information processing analyses of knowledge and performance in three areas of the elementary mathematics curriculum: basic addition and subtraction facts, complex procedures such as multicolumn subtraction, and the solution of word problems. Theories of the knowledge associated with "expert" performance are discussed.…