This fourth book in the Mathematics Recovery series equips teachers with detailed pedagogical knowledge and resources for teaching number to 7 to 11-year olds. Drawing on extensive programs of research, curriculum development, and teacher development, the book offers a coherent, up-to-date approach emphasizing computational fluency and the…

The authors examined the effectiveness of strategy instruction taught by general educators in mixed-ability classrooms. Specifically, the authors compared the mathematical word problem-solving performance and computational skills of students who received schema-based instruction (SBI) with students who received general strategy instruction (GSI).…

The cognitive underpinnings of arithmetic calculation in children are noted to involve working memory; however, cognitive processes related to arithmetic calculation and working memory suggest that this relationship is more complex than stated previously. The purpose of this investigation was to examine the relative contributions of processing…

The purpose of this study was to determine conditions under which young children enumerate by counting in multiples. Contrasting effects of different numerosities and perceptual arrangements are discussed in terms of contextual support for the use and development of numerical skills among young children. (Author/RWB)

Reports a study to explore student's computational performance on computer-administered testing situations while at the computer. Students from grades 3-6 (n=100) were randomly assigned to treatment order, computer assessment first or paper/pencil assessment first. Significant differences occurred in three areas: completion time, number of mental…

Examined whether representational changes in digit memory are functions of children's expertise in mental abacus operation when abacus operators reproduced series of digits forward or backward. Found skilled operators equally facile with forward and backward reproduction, but novices slower going backward. Suggests advanced operators apply their…

Tests 107 kindergarten and first grade children to study the order-irrelevance principle. Willingness to arbitrarily assign tags is a developmentally less sophisticated ability than--and hence does not necessarily imply--an ability to predict that differently ordered counts produce the same cardinal designation. (Author)

Considered was the question of whether a strategy that was widely used by young children in clinical interviews occurred in less structured situations. Findings indicated that it did not occur in the performance of a routine counting task by preschoolers. Reasons for apparent discrepancies are discussed. (CW)

Four types of computational estimation were explored in relation to other mathematical skills and sex differences with 309 eighth graders. Open-ended estimation was the most difficult, followed by estimation relative to a reference number and estimation within an order of magnitude. (MNS)

Assessment of 121 nondisabled elementary boys and 107 boys with attention-deficit hyperactivity disorder (ADHD), ages 7 through 14 years, found significantly lower problem-solving scores in specific math concepts and slower computational performance for the boys with ADHD when reading and problem structure were held constant. Instructional…

Describes a study designed to investigate the relationship between students' learning of the standard double-digit addition algorithm and basic fact mastery or numeration concepts. Results suggest basic fact mastery and knowledge of numeration concepts may not be as necessary as previously assumed to learning multidigit addition. (PK)

Reports examples of the behaviors, including kinetic and vocal, used to facilitate problem-solving based on observations of four seventh-grade students. Discusses the use of the behaviors in problem-solving teaching. (YP)

The study investigated which addition facts children and preservice teachers view as being difficult, whether it is possible to determine facts which are difficult for all children, and whether children and adults agree on which facts are difficult. Results indicated that children and adults disagree about the difficulty of facts. (PK)

Proposes a theory of cognitive processes in doing and learning place value arithmetic. Discusses a computer model that simulates the learning of multicolumn subtraction under one-on-one tutoring to measure the relative difficulty of two methods of subtraction. The model predicts that regrouping is more difficult to learn than an alternative…

This study probed children's reasoning about both correct and incorrect but plausible statements of hypothetical children concerning the concepts of subtraction, with the intention of examining misconceptions in greater depth. Eight third graders, 14 fourth graders, and 14 fifth graders were interviewed individually to assess their understanding…