Mathematical Cognition
1st Edition
Published on 1. January 2003
273 pages
978-1-60752-796-1 (ISBN)
Description
It is always interesting to ask the question of where specific cognitive abilities come from. This question has been asked most often about language. Whereas it is apparent that many species appear to innately possess the ability to signal, and several species have developed large labeling vocabularies and the ability to string together simple requests, strong arguments have been made that the symbolic utilization of language is uniquely human (e.g., Chomsky, 1980).
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James M. Royer
Mathematical Cognition
Book
01/2003
Information Age Publishing
€70.50
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Content
- Cover
- Mathematical Cognition
- Mathematical Cognition
- Copyright Page
- List of Contributors
- Contents
- Introduction
- REFERENCES
- 1: The Development of Math Competence in the Preschool and Early School Years: Cognitive Foundations and Instructional Strategies
- ABSTRACT
- INTRODUCTION
- The Definition Paradox
- The Development Paradox
- The Instruction Paradox
- WHAT IS MATH COMPETENCE?
- HOW DOES MATH COMPETENCE DEVELOP?
- The 4-year-old Structures
- Global Quantity Schema
- Initial Counting Schema
- The 6-year-old Structure
- The 8-year-old Structure
- The 10-year-old Structure
- HOW CAN MATH COMPETENCE BE FOSTERED IN SCHOOL SETTINGS?
- Instructional Strategies to Foster the Development of Math Competence
- Program Effects
- CONCLUSION
- AUTHOR NOTE
- REFERENCES
- 2: Perspectives on Mathematics Strategy Development
- ABSTRACT
- INTRODUCTION
- The Development of Strategies
- Variability in Strategy Use
- FACTORS AFFECTING STRATEGY DEVELOPMENT
- Conceptual Knowledge
- Semantic Structure of Problem
- Working Memory
- Contextual Effects
- Fluency (Reaction Time)
- Procedural Knowledge
- THE COGNITIVE PSYCHOLOGY PERSPECTIVE
- Siegler's Overlapping Waves Theory
- THE CONSTRUCTIVIST PERSPECTIVE
- Sequencing, Cardinality, and Counting
- Steffe's Numerical Schemes
- Case's Theory of Intellectual Development
- SOCIAL CONSTRUCTIVIST AND SITUATED COGNITIVE PERSPECTIVES
- STRATEGY DEVELOPMENT IN SPECIAL POPULATIONS
- Children with Mathematics Disabilities
- Gender Differences in the Development of Mathematics Strategies
- IMPLICATIONS FOR EDUCATION
- REFERENCES
- 3: Mathematical Problem Solving
- ABSTRACT
- INTRODUCTION
- Purpose
- Definitions
- Types of Problems
- Cognitive Processes in Mathematical Problem Solving
- TRANSLATING
- What Is Translating?
- Research on Translating
- Instructional Implications of Research on Translating
- INTEGRATING
- What Is Integrating?
- Research on Integrating
- Instructional Implications of Research on Integrating
- PLANNING
- What Is Planning?
- Research on Planning
- Instructional Implications of Research on Planning
- EXECUTING
- What is Executing?
- Research on Executing
- Instructional Implications of Research on Executing
- CONCLUSION
- AUTHOR NOTE
- REFERENCES
- 4: Learning Disabilities in Basic Mathematics: Deficits in Memory and Cognition
- ABSTRACT
- INTRODUCTION
- BACKGROUND CHARACTERISTICS OF CHILDREN WITH MD
- Diagnosis
- Prevalence and Etiology
- MODELS OF MATHEMATICAL DEVELOPMENT AND DISABILITIES
- Number
- Counting
- Arithmetic
- DEFICITS IN MEMORY AND COGNITION
- SUMMARY
- AUTHOR NOTE
- REFERENCES
- 5: Relationships Among Basic Computational Automaticity, Working Memory, and Complex Mathematical Problem Solving: What We Know and What We Need to Know
- ABSTRACT
- INTRODUCTION
- WORKING MEMORY INVOLVEMENT IN SIMPLE MENTAL ARITHMETIC
- A Theoretical Model of Working Memory
- Baddeley's Model of Working Memory
- Arithmetic/Working Memory Studies Using Baddeley's Model
- Findings Using Verification Task Methodologies
- Findings Using Production Task Methodologies
- Working Memory Resource Use in Mental Arithmetic as a Function of Practice/Development
- Summary of Working Memory Involvement in Arithmetic
- THE RELATIONSHIP BETWEEN COMPUTATIONAL EFFICIENCY AND COMPLEX MATHEMATICAL PROBLEM SOLVING
- Empirical Evidence for the Relationship
- Correlation, Regression, and Structural Equation Modeling Studies
- Studies of Elementary Students
- Studies Using Older Students and Additional Predictor Variables
- Structural Equation Modeling Studies
- Evidence from Select Samples
- IMPLICATIONS FOR FUTURE RESEARCH
- Working Memory Involvement in Mental Arithmetic
- Future Research on the Arithmetic Automatization/Higher Problem Solving Relationship
- CONCLUSION
- REFERENCES
- 6: Mathematics Instruction: Cognitive, Affective and Existential Perspectives
- ABSTRACT
- INTRODUCTION
- RESEARCH-BASED INSTRUCTION
- Math Teaching in College
- Middle School Mathematics
- RESEARCH ON TEACHING IN SCHOOLS
- PERSPECTIVES ON TEACHING
- A Model of Instructional Capacity
- A View of Math Teaching from Practice
- Research on the Affective Domain
- Teaching as a Way of Being: an Existential Perspective on Teachers and Teaching
- CONCLUSION
- NOTES
- REFERENCES
- 7: A Brief History of American K-12 Mathematics Education in the 20th Century
- ABSTRACT
- INTRODUCTION
- HISTORICAL OUTLINE: 1920 TO 1980
- THE 1980S: PRELUDE TO NATIONAL STANDARDS
- THE 1989 NCTM STANDARDS
- THE NATIONAL SCIENCE FOUNDATION
- PUBLIC RESISTANCE TO THE NCTM STANDARDS
- MATHEMATICIANS, CALIFORNIA, AND THE NATION
- CONCLUDING REMARKS
- APPENDIX
- ACKNOWLEDGMENTS
- NOTES
- REFERENCES
- 8: Assessment in Mathematics: A Developmental Approach
- ABSTRACT
- INTRODUCTION
- SOME CURRENT ASSESSMENT ISSUES IN MATHEMATICS
- OUTCOMES-BASED ASSESSMENT
- Some Issues of Outcomes-based Education
- ASSESSMENT FROM A COGNITION PERSPECTIVE
- THE SOLO MODEL
- SOLO Modes and Levels
- Two Cycles of Levels Within a Model
- Process-object Encapsulation Theories and SOLO
- Applications of SOLO in Mathematics
- Fractions
- Expressing Generalization
- Implications
- APPLYING SOLO IN THE CLASSROOM
- CONCLUSION
- REFERENCES
