Existing research has revealed key factors influencing mathematical flexibility, defined as the capacity to understand, generate, and apply a variety of strategies in solving mathematical problems. However, there is currently a lack of an integrated theoretical framework to systematically consolidate various sources of individual differences in…

This book seeks to illustrate the research on mathematics competencies and disposition in China according to the conceptual development and empirical investigation perspective. Mathematics education in China has a distinguishing feature a focus of attention to mathematical competency. Paradoxically, there has not been an explicit, refined, and…

This guidance report focuses on the teaching of mathematics to pupils in Key Stages 2 and 3. It is not intended to provide a comprehensive guide to mathematics teaching. We have made recommendations where there are research findings that schools can use to make a significant difference to pupils' learning, and have focused on the questions that…

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).…

How do children learn math--and why do some children struggle with it? The answers are in "Number Sense and Number Nonsense," a straightforward, reader-friendly book for education professionals and an invaluable multidisciplinary resource for researchers. More than a first-ever research synthesis, this highly accessible book brings math…

Explores the role of spatial orientation skill in the solution of mathematics problems. Reports the role of estimating the approximate magnitude of a figure; demonstrating the flexibility to change; adding marks to show relationships; moving or assessing the size and shape of figure; and getting the correct answer. (YP)

This paper reviews the presentation of problem solving and process aspects of mathematics in curriculum documents from Australia, UK, USA and Singapore. The place of problem solving in the documents is reviewed and contrasted, and illustrative problems from teachers' support materials are used to demonstrate how problem solving is now more often…

To investigate the development of function concepts and their relation to mathematical and logical abilities typically acquired during the age period of five to seven years, children were tested on nonnumerical function tasks, numerical tasks, and aspects of logical reasoning. (PCB)

Reports results obtained when 24 14-year-old students were presented with algebra tasks by a computer-based modeling system and, four months later, comparable paper and pencil tests together with detailed interviews. Comparison of the results revealed profound misunderstandings of algebraic notation and identified classes of strategies used by…

Determined whether chemistry students (N=332) understood analog tasks that could be used for teaching the mole concept. Also identified possible difficulties that students might have in solving mole problems. Seven major conclusions are reported and discussed, including the finding that two-step problems were more difficult to solve than one-step…

Determined if providing feedback to students had any impact on the correlation between performance in physics and a test of simple, mechanistic mathematics skills. Also determined if students who drop out of the physics course demonstrated any identifiable difference in performance on tests involving a variety of reasoning and problem-solving…

This paper reviews 25 studies of intervention research in mathematics with subjects classified as mentally retarded. Research has primarily been conducted in three areas: basic skills and concepts; rule learning and problem solving; and applications, including time, money, and measurement skills. Results are discussed in relation to instructional…

Through individual interviews with remedial and precalculus university students, five characteristics of the student were identified that influence whether a diagram is used in solving a problem and whether its use is successful. The interviews also suggested a set of subskills that contribute to the overall ability to draw effective diagrams.…

Examines the students' understanding of mathematical structure and the relationship between problem solving and the identification of the structure in 13 word problems. Multidimensional scaling and hierarchical cluster analysis were used to assess how subjects organized word problems in their minds. (YP)

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…