Cognitive Foundations For Improving Mathematical Learning

The fifth volume in the Mathematical Cognition and Learning series focuses on informal learning environments and other parental influences on numerical cognitive development and formal instructional interventions for improving mathematics learning and performance. The chapters cover the use of numerical play and games for improving foundational number knowledge as well as school math performance, the link between early math abilities and the approximate number system, and how families can help improve the early development of math skills. The book goes on to examine learning trajectories in early mathematics, the role of mathematical language in acquiring numeracy skills, evidence-based assessments of early math skills, approaches for intensifying early mathematics interventions, the use of analogies in mathematics instruction, schema-based diagrams for teaching ratios and proportions, the role of cognitive processes in treating mathematical learning difficulties, and addresses issues associated with intervention fadeout. Identifies the relative influence of school and family on math learning Discusses the efficacy of numerical play for improvement in math Features learning trajectories in math Examines the role of math language in numeracy skills Includes assessments of math skills Explores the role of cognition in treating math-based learning difficulties

This book deals addresses how the development of the human capacity for mathematical cognition occurs through educational experience. Chapters include: (1) "The Development of Math Competence in the Preschool and Early School Years: Cognitive Foundations and Instructional Strategies " (Sharon Griffin); (2) "Perspectives on Mathematics Strategy Development" (Martha Carr and Hillary Hettinger); (3) "Mathematical Problem Solving" (Richard E. Mayer); (4) "Learning Disabilities in Basic Mathematics: Deficits in Memory and Cognition" (David C. Geary and Mary K. Hoard); (5) "Relationships among Basic Computational Automaticity, Working Memory and Complex Mathematical Problem Solving: What We Know and What We Need to Know" (Loel T. Tronsky and James M. Royer); (6) "Mathematics Instruction: Cognitive, Affective and Existential Perspectives" (Allan Feldman); (7) "A Brief History of American K-12 Mathematics Education in the 20th Century" (David Klein); and (8) "Assessment in Mathematics: A Developmental Approach" (John Pegg). (Author/KHR).

Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts focuses on typical and atypical learning of complex arithmetic skills and higher-order math concepts. As part of the series Mathematical Cognition and Learning, this volume covers recent advances in the understanding of children’s developing competencies with whole-number arithmetic, fractions, and rational numbers. Each chapter covers these topics from multiple perspectives, including genetic disorders, cognition, instruction, and neural networks. Covers innovative measures and recent methodological advances in mathematical thinking and learning Contains contributions that improve instruction and education in these domains Informs policy aimed at increasing the level of mathematical proficiency in the general public

Early childhood mathematics is vitally important for young children's present and future educational success. Research demonstrates that virtually all young children have the capability to learn and become competent in mathematics. Furthermore, young children enjoy their early informal experiences with mathematics. Unfortunately, many children's potential in mathematics is not fully realized, especially those children who are economically disadvantaged. This is due, in part, to a lack of opportunities to learn mathematics in early childhood settings or through everyday experiences in the home and in their communities. Improvements in early childhood mathematics education can provide young children with the foundation for school success. Relying on a comprehensive review of the research, Mathematics Learning in Early Childhood lays out the critical areas that should be the focus of young children's early mathematics education, explores the extent to which they are currently being incorporated in early childhood settings, and identifies the changes needed to improve the quality of mathematics experiences for young children. This book serves as a call to action to improve the state of early childhood mathematics. It will be especially useful for policy makers and practitioners-those who work directly with children and their families in shaping the policies that affect the education of young children.

This book focuses on elementary and middle school children’s understanding of mathematics as well as the cognitive aspects involved in the development of mathematical knowledge, skills, and understanding. Children’s success in and understanding of mathematics stem from factors beyond the mathematics curriculum. Researchers are increasingly becoming aware of the necessity to consider a complex set of variables when accounting for large individual differences in mathematics achievement. These chapters contribute to how both researchers and educators can consider the multidimensionality of skills involved in developing mathematical knowledge in the middle school years as well as to how this knowledge can be used to enhance practices in the mathematics classroom. Topics include the cognitive and spatial skills involved in mathematics knowledge, the role of motivation in mathematics learning, the neurological processes and development of children’s mathematics skills, the development of understanding of arithmetic and fraction concepts, the factors relating to children’s word problem success, and techniques to promote mathematics understanding. This book and its companion, Mathematical Teaching and Learning, take an interdisciplinary perspective to mathematical learning and development in the elementary and middle school years. The authors and perspectives in this book draw from education, neuroscience, developmental psychology, and cognitive psychology. The book will be relevant to scholars/educators in the field of mathematics education and also those in childhood development and cognition. Each chapter also includes practical tips and implications for parents as well as for educators and researchers.

Have you ever wondered why students too often have only a rudimentary understanding of mathematics, why even rich and exciting hands-on learning does not always result in "real" learning of new concepts? The answer lies in whether students have actually learned mathematical concepts, rather than merely memorizing facts and formulas. Concept-Rich Mathematics Instruction is based on the constructivist view that concepts are not simply facts to be memorized and later recalled, but rather knowledge that learners develop through an active process of adapting to new experiences. The teacher's role is critical in this process. When teachers prompt students to reflect on their experiences and report and answer questions verbally, students must re-examine and even revise their concepts of reality. Meir Ben-Hur offers expert guidance on all aspects of Concept-Rich Mathematics Instruction, including * Identifying the core concepts of the mathematics curriculum. * Planning instructional sequences that build upon concepts that students already understand. * Designing learning experiences that provoke thoughtful discussions about new concepts and prepare students to apply these concepts on their own. * Identifying student errors, particularly those caused by preconceptions, as important sources of information and as key instructional tools. * Conducting classroom dialogues that are rich in alternative representations. * Using a variety of formative assessment methods to reveal the state of students' learning. * Incorporating problem-solving activities that provoke cognitive dissonance and enhance students' cognitive competence. Concept-Rich Mathematics Instruction is grounded in the belief that all students can learn to think mathematically and solve challenging problems. If you're looking for a powerful way to improve students' performance in mathematics and move closer to fulfilling the NCTM standards, look no further: this approach provides the building blocks for constructing a first-class mathematics program. Note: This product listing is for the reflowable (ePub) version of the book.

Foundations for the Future in Mathematics Education.

Arithmetic disability stems from deficits in neurodevelopment, with great individual differences in development or function of an individual at neuroanatomical, neuropsychological, behavioral, and interactional levels. Heterogeneous Contributions to Numerical Cognition: Learning and Education in Mathematical Cognition examines research in mathematical education methods and their neurodevelopmental basis, focusing on the underlying neurodevelopmental features that must be taken into account when teaching and learning mathematics. Cognitive domains and functions such as executive functions, memory, attention, and language contribute to numerical cognition and are essential for its proper development. These lines of research and thinking in neuroscience are discussed in this book to further the understanding of the neurodevelopmental and cognitive basis of more complex forms of mathematics – and how to best teach them. By unravelling the basic building blocks of numerical thinking and the developmental basis of human capacity for arithmetic, this book and the discussions within are important for the achievement of a comprehensive understanding of numerical cognition, its brain basis, development, breakdown in brain-injured individuals, and failures to master mathematical skills. A novel innovative reference on the emerging field of numerical cognition and neurodevelopment underlying mathematical education Includes an overview of the multiple disciplines that comprise numerical cognition written by world-leading researchers in the numerical cognition and neurodevelopment fields Features an innovative organization with each section providing a general overview, developmental research, neurocognitive mechanisms, and discussion about relevant studies