Fifty Brazilian children aged seven-13 were individually given addition and subtraction exercises. Counting was the preferred procedure, with use of school-taught algorithms limited. Some children decomposed numbers into tens and units and then worked at both levels. They rarely referred to previous results when doing related exercises. (MNS)

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)

Investigates 10-year-old children's abilities to reason by analogy in solving addition and subtraction comparison problems involving unknown compare sets and unknown reference sets. Children responded in a consistent manner to the tasks involving the basic addition problems, indicating substantial relational knowledge of these but responded in an…

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)

The author attempts to obtain some new evidence on simple addition processes in adults in order to evaluate the two additon models offered by Groen and Parkman (1972); a simple counting model and a more complex retrieval model, involving direct access and counting. (Author/RK)

Work by Dutch and Belgian researchers on arithmetic problems involving addition and subtraction is reviewed, especially word problems. It is an attempt to synthesize the research on the relationship between instruction in the part-whole line diagram and the solution of problems. Both logical and psychological interpretations are discussed. (MNS)

Using error analysis and individual interviews, the problem-solving actions of first and second graders were analyzed. Shortcomings of children's knowledge and solution strategies were seen to be overcome by instruction. A control group, with usual arithmetic instruction, and an experimental group were established and the hypothesized…

Reports on two studies that use new tasks to compare English children's use of strategies that reverse the order of addends in solving addition problems. Shows that knowledge of commutativity among young children is widespread, but does not establish a direct link between this knowledge and children's choice of addition strategies. (DSK)

This book explores how primary school children with dyslexia or dyspraxia and difficulty in math can learn math and provides practical support and detailed teaching suggestions. It considers cognitive features that underlie difficulty with mathematics generally or with specific aspects of mathematics. It outlines the ways in which children usually…

The article reviews the development of mathematics error analysis as a means of diagnosing students' cognitive reasoning. Errors specific to addition, subtraction, multiplication, and division are described, and suggestions for remediation are provided. (CL)

The procedures used by first- and second-grade children in solving addition problems are investigated. The subjects were 56 pupils from a parochial school in Ithaca, New York. The data indicate that first graders add by counting, while second graders use both counting and noncounting methods. (MP)

Analyzed conceptual and linguistic complexities of matching situation word problems. Found a four-level progression in conceptualizing and solving these problems: Relational ("who had more/less" but not "how much more/less"); Language Cue (equalizing or compare language); Understand Matching Situations (difference between two…

Sixty-four adults were tested on simple addition and multiplication problems presented in Arabic digit or English number-word format. Overall, response times and error rates were much higher with the word format, but more important, presentation format interacted with arithmetic operation and problem size. (DR)