Psychological Abilities of Primary School Children in Learning Mathematics
Author: Vasiliĭ Vasilʹevich Davydov
Publisher: National Council of Teachers of English
Published: 1991
Total Pages: 408
ISBN-13:
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Helping Children Learn Mathematics
Author: National Research Council
Publisher: National Academies Press
Published: 2002-07-31
Total Pages: 53
ISBN-13: 0309131987
DOWNLOAD EBOOKResults from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society.
Cognitive Foundations for Improving Mathematical Learning
Author: David C. Geary
Publisher: Academic Press
Published: 2019-01-03
Total Pages: 380
ISBN-13: 0128159537
DOWNLOAD EBOOKThe 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
Early Childhood Mathematics Education Research
Author: Julie Sarama
Publisher: Routledge
Published: 2009-04-01
Total Pages: 424
ISBN-13: 1135592500
DOWNLOAD EBOOKThis important new book synthesizes relevant research on the learning of mathematics from birth into the primary grades from the full range of these complementary perspectives. At the core of early math experts Julie Sarama and Douglas Clements's theoretical and empirical frameworks are learning trajectories—detailed descriptions of children’s thinking as they learn to achieve specific goals in a mathematical domain, alongside a related set of instructional tasks designed to engender those mental processes and move children through a developmental progression of levels of thinking. Rooted in basic issues of thinking, learning, and teaching, this groundbreaking body of research illuminates foundational topics on the learning of mathematics with practical and theoretical implications for all ages. Those implications are especially important in addressing equity concerns, as understanding the level of thinking of the class and the individuals within it, is key in serving the needs of all children.
Early Algebraization
Author: Jinfa Cai
Publisher: Springer Science & Business Media
Published: 2011-02-24
Total Pages: 631
ISBN-13: 3642177352
DOWNLOAD EBOOKIn this volume, the authors address the development of students’ algebraic thinking in the elementary and middle school grades from curricular, cognitive, and instructional perspectives. The volume is also international in nature, thus promoting a global dialogue on the topic of early Algebraization.
Theoretical Foundations of Learning Environments
Author: David Jonassen
Publisher: Routledge
Published: 2014-04-08
Total Pages: 276
ISBN-13: 1135670129
DOWNLOAD EBOOKTheoretical Foundations of Learning Environments describes the most contemporary psychological and pedagogical theories that are foundations for the conception and design of open-ended learning environments and new applications of educational technologies. In the past decade, the cognitive revolution of the 60s and 70s has been replaced or restructured by constructivism and its associated theories, including situated, sociocultural, ecological, everyday, and distributed conceptions of cognition. These theories represent a paradigm shift for educators and instructional designers, to a view of learning as necessarily more social, conversational, and constructive than traditional transmissive views of learning. Never in the history of education have so many different theories said the same things about the nature of learning and the means for supporting it. At the same time, although there is a remarkable amount of consonance among these theories, each also provides a distinct perspective on how learning and sense making occur. This book provides students, faculty, and instructional designers with a clear, concise introduction to these theories and their implications for the design of new learning environments for schools, universities, and corporations. It is well-suited as a required or supplementary text for courses in instructional design and theory, educational psychology, learning, theory, curriculum theory and design, and related areas.
Bringing Out the Algebraic Character of Arithmetic
Author: Analúcia D. Schliemann
Publisher: Routledge
Published: 2006-08-29
Total Pages: 164
ISBN-13: 1136799621
DOWNLOAD EBOOKBringing Out the Algebraic Character of Arithmetic contributes to a growing body of research relevant to efforts to make algebra an integral part of early mathematics instruction, an area of studies that has come to be known as Early Algebra. It provides both a rationale for promoting algebraic reasoning in the elementary school curriculum and empirical data to support it. The authors regard Early Algebra not as accelerated instruction but as an approach to existing topics in the early mathematics curriculum that highlights their algebraic character. Each chapter shows young learners engaged in mathematics tasks where there has been a shift away from computations on specific amounts toward thinking about relations and functional dependencies. The authors show how young learners attempt to work with mathematical generalizations before they have learned formal algebraic notation. The book, suitable as a text in undergraduate or graduate mathematics education courses, includes downloadable resources with additional text and video footage on how students reason about addition and subtraction as functions; on how students understand multiplication when it is presented as a function; and on how children use notations in algebraic problems involving fractions. These three videopapers (written text with embedded video footage) present relevant discussions that help identify students' mathematical reasoning. The printed text in the book includes transcriptions of the video episodes in the CD-ROM. Bringing Out the Algebraic Character of Arithmetic is aimed at researchers, practitioners, curriculum developers, policy makers and graduate students across the mathematics education community who wish to understand how young learners deal with algebra before they have learned about algebraic notation.
Second Handbook of Research on Mathematics Teaching and Learning
Author: Frank K. Lester
Publisher: IAP
Published: 2007-02-01
Total Pages: 1380
ISBN-13: 160752709X
DOWNLOAD EBOOKThe audience remains much the same as for the 1992 Handbook, namely, mathematics education researchers and other scholars conducting work in mathematics education. This group includes college and university faculty, graduate students, investigators in research and development centers, and staff members at federal, state, and local agencies that conduct and use research within the discipline of mathematics. The intent of the authors of this volume is to provide useful perspectives as well as pertinent information for conducting investigations that are informed by previous work. The Handbook should also be a useful textbook for graduate research seminars. In addition to the audience mentioned above, the present Handbook contains chapters that should be relevant to four other groups: teacher educators, curriculum developers, state and national policy makers, and test developers and others involved with assessment. Taken as a whole, the chapters reflects the mathematics education research community's willingness to accept the challenge of helping the public understand what mathematics education research is all about and what the relevance of their research fi ndings might be for those outside their immediate community.
Algebra in the Early Grades
Author: James J. Kaput
Publisher: Routledge
Published: 2017-09-25
Total Pages: 552
ISBN-13: 1351577093
DOWNLOAD EBOOKThis volume is the first to offer a comprehensive, research-based, multi-faceted look at issues in early algebra. In recent years, the National Council for Teachers of Mathematics has recommended that algebra become a strand flowing throughout the K-12 curriculum, and the 2003 RAND Mathematics Study Panel has recommended that algebra be “the initial topical choice for focused and coordinated research and development [in K-12 mathematics].” This book provides a rationale for a stronger and more sustained approach to algebra in school, as well as concrete examples of how algebraic reasoning may be developed in the early grades. It is organized around three themes: The Nature of Early Algebra Students’ Capacity for Algebraic Thinking Issues of Implementation: Taking Early Algebra to the Classrooms. The contributors to this landmark volume have been at the forefront of an effort to integrate algebra into the existing early grades mathematics curriculum. They include scholars who have been developing the conceptual foundations for such changes as well as researchers and developers who have led empirical investigations in school settings. Algebra in the Early Grades aims to bridge the worlds of research, practice, design, and theory for educators, researchers, students, policy makers, and curriculum developers in mathematics education.
Teaching and Learning Patterns in School Mathematics
Author: Ferdinand Rivera
Publisher: Springer Science & Business Media
Published: 2014-07-08
Total Pages: 223
ISBN-13: 9400727127
DOWNLOAD EBOOKThis book synthesizes research findings on patterns in the last twenty years or so in order to argue for a theory of graded representations in pattern generalization. While research results drawn from investigations conducted with different age-level groups have sufficiently demonstrated varying shifts in structural awareness and competence, which influence the eventual shape of an intended generalization, such shifts, however, are not necessarily permanent due to other pertinent factors such as the complexity of patterning tasks. The book proposes an alternative view of pattern generalization, that is, one that is not about shifts or transition phases but graded depending on individual experiences with target patterns. The theory of graded representations involving pattern generalization offers a much more robust understanding of differences in patterning competence since it is sensitive to varying levels of entry into generalization. Empirical evidence will be provided to demonstrate this alternative view, which is drawn from the author’s longitudinal work with elementary and middle school children, including several investigations conducted with preservice elementary majors. Two chapters of the book will be devoted to extending pattern generalization activity to arithmetic and algebraic learning of concepts and processes. The concluding chapter addresses the pedagogical significance of pattern learning in the school mathematics curriculum.
