Last edition Elsevier 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.
Last Edition
ISBN 13: 9780128050866
Imprint: Elsevier
Language: English
Authors: David C. Geary
Pub Date: 12/2016
Pages: 360
Illus: Illustrated
Weight: 680.000 grams
Size: 152 X 229 mm
Product Type: Hardcover
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- • 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
- David C. Geary, University of Missouri, Columbia, MO, USA; Daniel B. Berch, University of Virginia, Charlottesville, VA, USA; Robert Ochsendorf, National Science Foundation, Arlington, VA USA and Kathleen Mann Koepke, National Institute of Child Health and Human Development, NIH, Rockville, MD, USA
- • Contributors • Foreword: Build It and They Will Come • Preface
- Chapter 1: Insights from Cognitive Science on Mathematical Learning
- o Abstract o On the nature of theories and models in cognitive psychology o Methodological considerations o Challenges for instruction o Conclusions and future directions
- Part I: Complex Arithmetic Processing
- Chapter 2: The Understanding of Additive and Multiplicative Arithmetic Concepts
- ? Abstract ? Introduction ? What is conceptual knowledge of arithmetic? ? The importance of conceptual knowledge ? A brief history of research on conceptual knowledge ? The importance of multiplicative concepts and the state of current research ? Additive versus multiplicative concepts ? The inversion concept ? The associativity concept ? Are additive and multiplicative concepts the same? ? Individual differences and factors in the use of conceptually-based shortcuts ? Individual differences ? Factors relating to conceptually-based shortcut use ? Conclusions and future directions
- Chapter 3: Arithmetic Word Problem Solving: The Role of Prior Knowledge
- ? Abstract ? Introduction ? The role of daily life experience in solving arithmetic word problems ? The role of stereotypic representations about problem solving in school ? The role of problem schemata stored in long-term memory ? The use of schemata versus situation-based models ? How can we help students ? Conclusions and future directions
- Chapter 4: Neurodevelopmental Disorders as Model Systems for Understanding Typical and Atypical Mathematical Development
- ? Abstract ? Introduction ? Spina bifida as a model system for understanding mathematical learning disabilities ? Longitudinal approaches to the study of mathematical development and disability ? Longitudinal studies of mathematical cognition in children with SBM and their typically developing peers ? Conclusions and future directions ? Acknowledgments
- Part II: Rational Number Processing
- Chapter 5: The Transition from Natural to Rational Number Knowledge
- ? Abstract ? The importance of rational numbers ? Rational numbers: a challenge for learners and for mathematics education ? The interference of natural number knowledge in rational number tasks ? The natural number bias ? Theoretical frameworks for studying the natural number bias ? Overview of our studies using both conceptual change theory and dual process perspective ? Conclusions and future directions
- Chapter 6: Fraction Development in Children: Importance of Building Numerical Magnitude Understanding
- ? Abstract ? Integrated theory of numerical development ? Understanding of fractions involves both conceptual and procedural knowledge ? Fraction development in early childhood ? Fraction development between third and sixth grade: findings from the delaware longitudinal study ? Helping students who struggle with fractions ? Acknowledgment
- Chapter 7: Numbers as Mathematical Models: Modeling Relations and Magnitudes with Fractions and Decimals
- ? Abstract ? Understanding rational numbers ? Prior research on magnitude assessment and misconceptions about rational numbers ? Using mathematics to model relations ? Alignments between rational numbers and quantity types ? Connections between rational numbers and other math concepts ? Conclusions and future directions
- Part III: Algebraic, Geometric, and Trigonometric Concepts
- Chapter 8: Understanding Children’s Difficulties with Mathematical Equivalence
- ? Abstract ? Introduction ? Children’s difficulties with mathematical equivalence problems ? Popular accounts of children’s mathematics learning difficulties ? The change-resistance account ? Conclusions and future directions ? Acknowledgments
- Chapter 9: Learning and Solving More Complex Problems: The Roles of Working Memory, Updating, and Prior Skills for General Mathematical Achievement and Algebra
- ? Abstract ? Introduction ? Algebra and earlier mathematics skills ? General mathematics achievement, algebra, and relations with domain-general and domain-specific influences ? The present study ? Conclusions and future directions o Chapter 10: Learning Geometry: the Development of Geometrical Concepts and the Role of Cognitive Processes ? Abstract ? Classical studies on geometry ? Core intuitive principles of geometry ? Academic achievement in geometry ? The development of geometrical knowledge ? Cognitive processes involved in geometry ? Educational implications ? Conclusions and future directions
- Chapter 11: The Unit Circle as a Grounded Conceptual Structure in Precalculus Trigonometry
- ? Abstract ? Grounded conceptual structures in mathematical cognition ? Preliminary investigations ? Preliminary study: observing use and success of the unit circle ? Study 2: comparing a unit circle lesson to a rules lesson and baseline knowledge ? Challenges in learning the unit circle ? Conclusions and future directions
- Part IV: Instructional Approaches
- Chapter 12: The Power of Comparison in Mathematics Instruction: Experimental Evidence From Classrooms
- ? Abstract ? Introduction ? Short-term, researcher-led classroom research ? Year-long study helping teachers use comparison in algebra I classrooms ? Conclusions and future directions ? Acknowledgments
- Chapter 13: Evidence for Cognitive Science Principles that Impact Learning in Mathematics
- ? Abstract ? Introduction ? Scaffolding principle ? Distributed practice effect ? Feedback principle ? Worked example principle ? Interleaving principle ? Abstract and concrete representations principles ? Error reflection principle ? Analogical comparison principle ? Conclusions and future directions ? Acknowledgments
- • Index
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