Students in grades 1, 4, 7, and 10 were tested in a two-part investigation of simple and complex mental addition (with college students as a reference point). One session involved a normal reaction time task in which children made true/false judgments about a series of addition examples. The other session involved a verbal protocol interview, the…

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)

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)

The purpose of this study was to ascertain whether children in grade 3 who differ in cognitive processing capacity add and subtract differently. The researchers drew upon information from three sources: individual results from a battery of 14 tests, an objective-referenced achievement test measuring a variety of arithmetic skills related to…

Kindergartners appeared to differ in their readiness to use a concrete counting strategy for addition. Many persisted in counting with objects. Mental counting strategies were sequenced. (MNS)

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)

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.…

Presents results from an Australian study examining whether children who use cognitive strategies in solving simple addition questions develop greater proficiency in addition than children who do not use such strategies. Describes the subjects, instruments, procedure, and instructional treatment. Concludes that the development of cognitive…

Summarized are the findings from five studies carried out in Australia in 1979-80. First was a cross-sectional survey designed to determine the memory capacity of a population of children in grades 1-3. The second study investigated performance differences on a variety of mathematically related developmental tasks for the same group. Data from…

The purpose of this study was to relate children's cognitive processing capabilities and their grade level to their performance and to the strategies they used when working addition and subtraction problems. From two sets of data which assessed memory capacity and cognitive processing capacities, six groups of children with different cognitive…

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…

Presented are four interpretive reports and a list of current publications of the Mathematics Work Group at the Wisconsin R&D Center. The first interpretive report gives a brief overview of their work. Reports two through four are concerned with individual interviews, carried out during a longitudinal study, in which primary children are asked to…

The effectiveness of the Multisensory Basic Fact Program to teach addition facts to 115 remedial groups in grades two through six in Australian schools was studied. Performance increased between pre- and posttests and was maintained on the retention test. (MNS)

This study documented the spontaneously derived strategies that children use which may play a key role in the transition from counting to recall of number facts. For these strategies, the child uses a small set of known number facts to derive the solution to unknown number facts. How training in the use of derived strategies influences the…