Teaching an eight-year-old girl with learning difficulties a more advanced addition strategy through multicomponent self-regulation training and a self-instructional model resulted in more rapid problem solving, fewer learning errors, and the acquisition of even more advanced addition strategies. (SLD)

This paper outlines a theoretical perspective for studying student understandings of the concept of addition. The notion of operational sense is defined as a way to describe the notion of addition as a mathematical object, paving the way for an application of the theory of reification at this level. Previous frameworks relative to problem solving…

This cross-sectional study investigated the problem-solving strategies used by schooled and unschooled Nigerian children to solve simple addition and subtraction problems. The purpose of the study was to: (1) verify with Nigerian children, models of the knowledge and strategies underlying children's solutions to simple word problems; (2) test the…

This study investigates the influence of changes in the wording of simple addition and subtraction problems without affecting their semantic structure on the level of difficulty of those problems for first and second graders and on the nature of their errors. The objective is to contribute to a better understanding of the process of constructing a…

Preschoolers 4 and 5 years of age were found to use four strategies differing in temporal characteristics as they solved simple addition problems with sums of 10 or less. Three strategies had visible and/or audible aspects, and one was covert, involving retrieval from memory. The harder the problem, the more often the children used an overt…

The purpose of the study was to survey self-regulation while responding to the addition facts. First graders' performance on microcomputer practice exercises was observed and recorded. Subjects could choose an analytic mode of operation using a symbolic or a finger strategy; or, they could choose a geometric mode of operation using a pictorial or…

Two simple quantitative models were derived from a series of experiments which explored the role of information storage in working memory when performing mental arithmetic. The decay model is a tractable analysis of a complex task which assumes a decay process in working storage. Similar analyses are recommended for problem solving activities…

Second and third graders from six Dutch elementary schools (N = 168) solved two sets of almost identical addition and subtraction sums at a two-week interval. Inconsistency in strategies, which characterized half the subjects, was related to unfamiliar sums and resulted in misinterpreted errors. (TJH)

Data were collected in the problem representations and solution strategies of 30 first graders who were given a series of simple addition and subtraction word problems. The children were interviewed three times during the school year. The influence of problem structure on children's solution strategies appears more extensive and decisive than that…

Provides domino geometry problems, problems with arithmetic progressions, and magic pentagram sums. (JM)

This paper discusses an approach to the study of algorithms which values students' construction of nonstandard algorithms but also emphasizes the essential roles of the teacher and instructional activities in supporting the development of students' numerical reasoning. Episodes are presented from a 3rd grade classroom in which a 9-week teaching…

In this study retrospective verbal reports were collected in order to study cognitive processes activated when solving simple additions. The research was devoted to a revision and validation of the earlier presented process model (Svenson 1975) by using retrospective verbal reports as a complement to the response latencies analyzed earlier.…

An instrumental technique is presented to help students create a symbolic representation that may aid the process of choosing an appropriate operation to solve a problem. Current research and practice are discussed; then the part-part-whole model is presented. (MNS)

Another way to add and subtract, in which the mental regrouping strategy is applied to an original 10-structure, is presented. Pupils use a visual model, called "little person," to move from counting to visualization. Originally designed for use with pupils with learning disabilities, this method has wider applicability. (KR)

Gifted-, normal-, and math-disabled children solved addition problems. Their problem-solving strategies and solution times were recorded. The gifted group showed the most mature distribution of strategy choices, and a verbal counting rate less than 50 percent of the rate of the other groups. (BC)