Pictorial representations are often used to help children understand the situation described in a given number-sentence scheme. These static pictorial problems essentially attempt to depict a dynamic situation (e.g., one bird flies away while there are three birds still sitting on the fence). Previous research suggested that such pictorial…

Interventions to support children with mathematical learning difficulties typically address deficits in domain-specific knowledge. However, not all students benefit from these instructional programs. In this case, some authors suggest an even more intensive instructional program combined with other factors assumed to be relevant for learning.…

Whereas some evidence exists that math anxiety may interfere with math performance from the very beginning of primary school, no study to date has attempted to investigate whether math anxiety may also interfere with early math learning (i.e., the encoding of new math knowledge) and not only with recalling already mastered contents in test…

The effects of prior encodings of manipulatives (red and blue plastic chips) on children's ability to use them as representations of quantity were tested. First graders (N = 73) were assigned to four conditions in which the encoding of plastic chips was experimentally manipulated. All children then participated in an addition activity that relied…

At the start of mathematics education children are often presented with addition and subtraction problems in the form of pictures. They are asked to solve the problems by filling in corresponding number sentences. One type of problem concerns the representation of an increase or a decrease in a depicted amount. A decrease is, however, more…

The purpose of the study reported on in this paper was to design and test multimedia for deaf and hard of hearing (DHH) learners. The study focused on counting, addition and subtraction with grade one (age 7) DHH learners in Thailand. The multimedia created for the study was informed by design considerations for DHH learners of arithmetic and…

Children's (N = 275) use of retrieval, decomposition (e.g., 7 = 4+3 and thus 6+7 = 6+4+3), and counting to solve additional problems was longitudinally assessed from first grade to fourth grade, and intelligence, working memory, and in-class attentive behavior was assessed in one or several grades. The goal was to assess the relation between…

Recent studies showed that kindergarten children solve addition, subtraction, doubling and halving problems using the core system for the approximate representation of numerical magnitude. In Study 1, 34 first-grade students in their first week of schooling solved approximate arithmetic problems in a number range up to 100 regarding all four basic…

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)

Issues include consistent individual differences in children's strategy choices, interpretation of differences within a framework, and the relation of differences to standardized test performance. (RJC)

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…

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…

Subjects were 73 first-grade children who were heterogeneous ethnically and socioeconomically. The purpose was to evaluate a component-skill analysis of the child's transition from the solution procedure counting-all to the solution procedure counting-on. The results provide a strong case for the proposed componential analysis. (MP)

The focus is on the problem-solving behaviors of primary age children on one-step verbal or story problems involving addition and subtraction. When children are given a simple word problem for which they have not learned the necessary algorithms, they are often able to derive a solution on their own. This report focuses on the child-invented…

This study investigated the relationships between Piagetian logical reasoning abilities with an information processing capacity, and first-grade children's performance on verbal addition and subtraction problems. An analysis of simple arithmetic problems indicated that several reasoning abilities identified by Piaget are needed to achieve…