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Author: Richard A. Lesh
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 440
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Book Description
Author: Richard A. Lesh
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 440
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Book Description
Author: David C. Geary
Publisher: Academic Press
ISBN: 0128133686
Category : Psychology
Languages : en
Pages : 362
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Book Description
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
Author: Lyn D. English
Publisher: Routledge
ISBN: 1136481559
Category : Education
Languages : en
Pages : 364
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Book Description
To define better techniques of mathematics education, this book combines a knowledge of cognitive science with mathematics curriculum theory and research. The concept of the human reasoning process has been changed fundamentally by cognitive science in the last two decades. The role of memory retrieval, domain-specific and domain-general skills, analogy, and mental models is better understood now than previously. The authors believe that cognitive science provides the most accurate account thus far of the actual processes that people use in mathematics and offers the best potential for genuine increases in efficiency. As such, they suggest that a cognitive science approach enables constructivist ideas to be analyzed and further developed in the search for greater understanding of children's mathematical learning. Not simply an application of cognitive science, however, this book provides a new perspective on mathematics education by examining the nature of mathematical concepts and processes, how and why they are taught, why certain approaches appear more effective than others, and how children might be assisted to become more mathematically powerful. The authors use recent theories of analogy and knowledge representation -- combined with research on teaching practice -- to find ways of helping children form links and correspondences between different concepts, so as to overcome problems associated with fragmented knowledge. In so doing, they have capitalized on new insights into the values and limitations of using concrete teaching aids which can be analyzed in terms of analogy theory. In addition to addressing the role of understanding, the authors have analyzed skill acquisition models in terms of their implications for the development of mathematical competence. They place strong emphasis on the development of students' mathematical reasoning and problem solving skills to promote flexible use of knowledge. The book further demonstrates how children have a number of general problem solving skills at their disposal which they can apply independently to the solution of novel problems, resulting in the enhancement of their mathematical knowledge.
Author: Lyn D. English
Publisher: Routledge
ISBN: 1136481621
Category : Education
Languages : en
Pages : 365
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Book Description
To define better techniques of mathematics education, this book combines a knowledge of cognitive science with mathematics curriculum theory and research. The concept of the human reasoning process has been changed fundamentally by cognitive science in the last two decades. The role of memory retrieval, domain-specific and domain-general skills, analogy, and mental models is better understood now than previously. The authors believe that cognitive science provides the most accurate account thus far of the actual processes that people use in mathematics and offers the best potential for genuine increases in efficiency. As such, they suggest that a cognitive science approach enables constructivist ideas to be analyzed and further developed in the search for greater understanding of children's mathematical learning. Not simply an application of cognitive science, however, this book provides a new perspective on mathematics education by examining the nature of mathematical concepts and processes, how and why they are taught, why certain approaches appear more effective than others, and how children might be assisted to become more mathematically powerful. The authors use recent theories of analogy and knowledge representation -- combined with research on teaching practice -- to find ways of helping children form links and correspondences between different concepts, so as to overcome problems associated with fragmented knowledge. In so doing, they have capitalized on new insights into the values and limitations of using concrete teaching aids which can be analyzed in terms of analogy theory. In addition to addressing the role of understanding, the authors have analyzed skill acquisition models in terms of their implications for the development of mathematical competence. They place strong emphasis on the development of students' mathematical reasoning and problem solving skills to promote flexible use of knowledge. The book further demonstrates how children have a number of general problem solving skills at their disposal which they can apply independently to the solution of novel problems, resulting in the enhancement of their mathematical knowledge.
Author: National Research Council
Publisher: National Academies Press
ISBN: 0309147433
Category : Education
Languages : en
Pages : 399
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Book Description
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.
Author: Bobby Allen
Publisher:
ISBN: 9781387971633
Category :
Languages : en
Pages : 176
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Book Description
Mathematics Quick-Looks focus on key concepts when teaching math. They help simplify students' conceptual understanding by directing students' attention to key concepts and procedures. By highlighting the key concepts in each lesson, teachers can promote students' achievement and prepare them for more difficult concepts. Math key concepts are primary skills that can be continually used to teach a variety of math concepts and processes. They provide recognizable starting points for students when learning new math concepts and processes. Math key concepts are explicitly described and modeled by the teacher. Vocabulary that is vital to the students' conceptual understanding is mastered concurrently with the related concepts and processes. The fundamental foundation of the Quick-Looks includes math concepts and processes that can be used within and across domains. Quick-Looks allow students to focus their attention on these key math concepts and processes. The skills and vocabulary are methodically taught, using unambiguous coaching methods. Conceptual understanding, procedural mastery, and vocabulary acquisition are applied seamlessly to new content. The math concepts that represent foundational understandings that can be applied across domains have been selected and planned into quick lessons. The lessons take about ten to fifteen minutes to explicitly deliver while allowing students the opportunity to critique their mathematical thinking and the thinking of others. Teachers will have eight opportunities to explicitly teach the target math skill within the context of the math concepts, affording students ample practice opportunities for mastering the concepts and processes. Teachers will communicate the skills using the selected vocabulary and require that students use the key vocabulary when expressing their thoughts. This instructional strategy positively impact students of all performance levels by focusing teaching and learning on clearly defined concepts. The strategy facilitates recall by reducing the amount of essential information and providing a universal language for communicating mathematical concepts. The use of this instructional strategy helps students to see the patterns of math in the predetermined skills as well as in more complex concepts and processes thus advocating deeper conceptual mathematical understanding.
Author: National Research Council
Publisher: National Academies Press
ISBN: 0309131987
Category : Education
Languages : en
Pages : 53
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Book Description
Results 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.
Author: Edd Bobby Allen
Publisher:
ISBN: 9781387936670
Category :
Languages : en
Pages : 0
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Book Description
Mathematics Quick-Looks focus on key concepts when teaching math. They help simplify students' conceptual understanding by directing students' attention to key concepts and procedures. By highlighting the key concepts in each lesson, teachers can promote students' achievement and prepare them for more difficult concepts. Math key concepts are primary skills that can be continually used to teach a variety of math concepts and processes. They provide recognizable starting points for students when learning new math concepts and processes. Math key concepts are explicitly described and modeled by the teacher. Vocabulary that is vital to the students' conceptual understanding is mastered concurrently with the related concepts and processes. The fundamental foundation of the Quick-Looks includes math concepts and processes that can be used within and across domains. Quick-Looks allow students to focus their attention on these key math concepts and processes. The skills and vocabulary are methodically taught, using unambiguous coaching methods. Conceptual understanding, procedural mastery, and vocabulary acquisition are applied seamlessly to new content. The math concepts that represent foundational understandings that can be applied across domains have been selected and planned into quick lessons. The lessons take about ten to fifteen minutes to explicitly deliver while allowing students the opportunity to critique their mathematical thinking and the thinking of others. Teachers will have eight opportunities to explicitly teach the target math skill within the context of the math concepts, affording students ample practice opportunities for mastering the concepts and processes. Teachers will communicate the skills using the selected vocabulary and require that students use the key vocabulary when expressing their thoughts. This instructional strategy positively impacts students of all performance levels by focusing teaching and learning on clearly defined concepts. The strategy facilitates recall by reducing the amount of essential information and providing a universal language for communicating mathematical concepts. The use of this instructional strategy helps students to see the patterns of math in the predetermined skills as well as in more complex concepts and processes thus advocating deeper conceptual mathematical understanding.
Author: Mario Graziano
Publisher: Springer
ISBN: 3319967975
Category : Science
Languages : en
Pages : 151
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Book Description
This book presents a philosophical interpretation to numerical cognition based on dual process theories and heuristics. It shows how investigations in cognitive science can shed light on issues traditionally raised by philosophers of mathematics. The analysis will also help readers to better understand the relationship between current neuroscientific research and the philosophical reflection on mathematics. The author seeks to explain the acquisition of mathematical concepts. To accomplish this, he needs to answer two questions. How can the concepts of approximate numerosity become an object of thought that is so accessible to our consciousness? How are these concepts refined and specified in such a way as to become numbers? Unfortunately, there is currently no model that can truly demonstrate the role of language in the development of numerical skills starting from approximate pre-verbal skills. However, the author details a solution to this problem: dual process theories. It is an approach widely used by theorists focusing on reasoning, decision making, social cognition, and consciousness. Here, he applies this approach to the studies on mathematical knowledge. He details the results brought about by psychological and neuroscientific studies conducted on numerical cognition by key neuroscientists. In the process, he develops the foundations of a new, potential philosophical explanation on mathematical knowledge.
Author: A. Treffers
Publisher: Springer Science & Business Media
ISBN: 9400937075
Category : Education
Languages : en
Pages : 360
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Book Description
In Dutch "WISKOBAS" stands for a particular kind of mathematics in the elementary school (ages 6-12). In tum Wiskobas was one of the depart ments in the IOWO, the Institute for the Development of Mathematics Education. This institute was concerned with the development of material for mathematics education as well as the related research on the possibility of change from the then existing arithmetic instruction to the future mathematics education. The present publication Three Dimensions has three aims: to give a picture of the goals Wiskobas set for future mathematics education, at the same time to show how such goals can be described, and to show the theoretical framework of the Wiskobas curriculum. The problem at hand is not at all simple. What is more, Wiskobas' ideas about mathematics education cannot literally be translated into strings of words. So how can we face the accusation that our objectives are unattain able and the goal itself irrational? In order to avoid this vagueness as much as possible and for the sake of clarity, this book makes continuous use of illustrations of mathematics education. In these examples both the subject-matter and the methods of description of the goals are illustrated as explicitly as possible, while at the same time creating the opportunity to read between the lines. The reader is urged to follow carefully the mathe matical material at the start of each chapter. This advice applies both to the more general education oriented, and to the more mathematical! didactical reader.
