A study is reported which involved elementary school teachers being exposed to a new teaching approach, practicing the approach by way of in-service opportunities, and then studying the effects on their own class. (MN)

The validity of a study reporting evidence that thinking strategies facilitate the learning of basic facts is questioned. The written report is criticized as suffering from lack of clarity. (MP)

A critique of a research article is answered, specific criticisms addressed, and the integrity of the article affirmed. (MP)

Sixteen Brazilian third graders aged 8-13 were given problems involving multidigit computation. School-taught algorithms were likely to be used in school-taught problems, with little carry-over to real problem situations, but resulted in more incorrect answers. (MNS)

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)

Three models are compared in terms of detail, scope, attention to individual differences, and how they deal with qualitative change and semantic processing. Two are information-processing models of arithmetical word problem-solving performance, and the third is a model of children's counting types and thinking strategies. (MNS)

The effects of two instructional strategies for sequencing examples and nonexamples of the concept "parallelogram" were compared for sixth graders. A rational sequence was favored over a random sequence at the formal level of concept attainment; no interaction effect was found between the strategy and students' mathematical ability. (MNS)

The authors discuss the procedure, findings, and summary of a study conducted through the use of anonymous questionnaires in an attempt to determine what actual classroom practice is in second- and fifth-grade mathematics classes. (MN)

Three important elements needed for constructing expert mathematics lessons are described: rich agendas, consistent but flexible lesson structures, and clear, understandable explanations. Each is discussed in terms of its hypothetical characteristics and then tested by comparing two novice and four expert elementary mathematics teachers. (MNS)

Examined were the effects of student cognitive entry behavior, prescribed mastery level, and information about criterion on mathematics achievement. Studied were 36 third graders assigned to four levels of being informed. Findings differed for children at low and high entry levels. (MNS)

Fifth graders performed better than third graders on discovering the function rule relating two number pairs. Task difficulty and mode of presentation (graphic or symbolic) varied by function. The children seemed ready to relinquish a hypothesis in the face of disconfirming evidence. (MNS)

Documented are major categories of errors that appear as children learn decimal fractions. Then the conceptual sources of these errors are established. Different curriculum sequences influence the probability that these classes of errors will appear. They can be used as diagnostic tools to detect children's understanding of mathematics topics.…

Investigated was how easily pupils aged 12 and 13 who were initially unaware of the invariance of an operation (with decimals) modeling a situation could be led to such awareness. Results from clinical interviews are reviewed and a protocol presented. It appeared difficult to induce conservation. (MNS)

A theory is proposed for how students develop competence with the written symbols of decimal fractions. Competence is viewed as the cumulative and sequential mastery of four separate cognitive processes. The theory was tested with small groups of students, most of whom were able to acquire the first two processes. (MNS)

Evidence suggesting that children can discriminate between enjoyment and value in their attitudes toward arithmetic is reported in relation to other research. Replication with more extensive scales and measures is urged. (MP)