Cognitive Foundations for Improving Mathematical Learning

✍ Scribed by David C. Geary, Daniel B. Berch, Kathleen Mann Koepke

• Publisher: Academic Press
• Year: 2019
• Tongue: English
• Leaves: 369
• Series: Mathematical Cognition and Learning
• Category: Library

✦ Synopsis

With Cognitive Foundations for Improving Mathematical Learning,weclosea
five-volume journey through the evolution and early development of number
competencies (Volume 1); the brain and genetic foundations for these and more
complex abilities (Volume 2); the cognitive bases for the learning of evolu-
tionarily novel mathematics, from arithmetic to trigonometry (Volume 3); the
influences of language and culture on mathematical learning and cognition
(Volume 4); and now formal and informal instructional approaches for improv-
ing children’s mathematics learning (Volume 5). With this final volume, we see
clear links between topics and discoveries covered in previous volumes and the
development of intervention approaches. These include interventions focused
on the relation between our evolved number sense and children’s early math
learning; the influence of home, family, and mathematical language on early
math learning; and the integration of cognitive science approaches to mathe-
matical learning into educational interventions. These represent an exciting step
forward and a much needed conciliation between basic research in mathemati-
cal cognition and mathematics education interventions that we hope will con-
tinue well beyond the publication of this volume.

✦ Table of Contents

Cover......Page 1
Cognitive Foundations for Improving
Mathematical Learning......Page 2
Copyright......Page 5
Contributors......Page 6
Foreword: Cognitive Foundations for Improving Mathematical Learning......Page 8
Chapters That Deal With Possible Cognitive Foundations for Numeracy......Page 9
Chapter That Deals With Home and Parental Influences......Page 10
Chapters That Deal With Interventions and Their Effects......Page 11
References......Page 13
Preface......Page 16
Introduction......Page 18
Brief History of Mathematics Intervention Studies......Page 19
Design Factors......Page 20
Diminishing Intervention Impacts Across Time (Fadeout)......Page 22
Transfer......Page 24
What Are the Cognitive Foundations for Improving Mathematics Learning?......Page 25
Fluid Intelligence......Page 27
Executive Function and Working Memory......Page 28
Implications......Page 30
Domain-General Interventions......Page 31
Domain-Specific Components......Page 32
Computer-Based Training of Number Line Judgments......Page 33
Training to Enhance Subitizing Speed......Page 35
Training Finger Differentiation: Its Impact on Arithmetic Ability......Page 37
Using Electrical Brain Stimulation to Improve Numerical and Arithmetic Processing......Page 38
Parental Influences on Child Cognition and Mathematical Learning......Page 39
A Brief History of Research on Parental Influences......Page 40
Research on Children's Home Numeracy Environment......Page 41
Conclusion......Page 42
References......Page 278
Introduction......Page 54
The Uruguayan Context......Page 55
Classroom Geometric and Arithmetic Abilities......Page 59
Approximate Number Abilities......Page 60
The Present Intervention Study......Page 62
Teachers Responses to the Software......Page 63
Design of the Current Study......Page 64
Participants......Page 65
Intervention Games......Page 68
Results......Page 69
IQ and Repeater Status by SES Quintile......Page 70
Pre-Intervention Arithmetic by Grade and Repeater Status......Page 71
ANS and Arithmetic Ability......Page 73
Pre- to Postintervention Improvement......Page 74
Conclusions and Future Directions......Page 79
References......Page 82
Introduction......Page 85
Integrated Theory of Numerical Development......Page 86
Numerical Magnitude Understanding in Early Childhood......Page 91
Play and Games in Mathematics Development......Page 92
Playing Traditional Games to Promote Numerical Knowledge......Page 93
Computer and Tablet Games......Page 97
Preschool Programs Using Games and Play......Page 99
Conclusions and Future Directions......Page 100
References......Page 101
Introduction......Page 107
Training Studies Using The Number Race´´......Page 108<br>Nonsymbolic vs. Symbolic Training......Page 111<br>Brief ANS Training......Page 112<br>Long-Term ANS Training......Page 114<br>Mechanisms Behind Long-Term ANS Training Improvements......Page 115<br>Conclusions and Future Directions......Page 118<br>References......Page 119<br>Introduction......Page 123<br>Number Talk......Page 124<br>Questionnaire Studies......Page 125<br>Observational Studies in the Lab......Page 126<br>Naturalistic Home Observations......Page 127<br>Experimental Studies......Page 130<br>Experiments in the Lab......Page 131<br>Experiments in the Field......Page 132<br>Spatial Talk......Page 133<br>Summary: Math Talk......Page 135<br>Gesture: An Additional Support for Children's Math Learning......Page 136<br>Counting Gestures......Page 137<br>Cardinal Number Gestures......Page 138<br>Gesture and Arithmetic......Page 140<br>Summary: Gesture......Page 141<br>Parental Math Attitudes and Beliefs: Intergenerational Findings......Page 142<br>Intergenerational Effects of Math Anxiety......Page 143<br>Other Negative Attitudes Toward Math......Page 144<br>Conclusions and Future Directions......Page 146<br>References......Page 149<br>Introduction......Page 159<br>The Curriculum Research Framework (CRF)......Page 160<br>Category I: A Priori Foundations......Page 161<br>Phase 2. Subject Matter A Priori Foundation......Page 162<br>Phase 4. Structure According to Specific Learning Model and Learning Trajectory......Page 163<br>Phase 6. Formative Research: Small Group......Page 178<br>Phase 7. Formative Research: Single Classroom......Page 179<br>Phase 8. Formative Research: Multiple Classrooms......Page 180<br>Phase 10. Summative Research: Large Scale......Page 181<br>Conclusions and Future Directions......Page 182<br>References......Page 183<br>Connections Between Early Mathematics Development and General Language......Page 190<br>Early Connections Between Mathematics and Literacy Skills......Page 191<br>What is Content-Specific Mathematical Language?......Page 193<br>Correlational and Experimental Evidence on the Relations Between Mathematical Language and Mathematics Performance......Page 194<br>Interventions to Improve Mathematical Language......Page 197<br>Mathematical Language and Numeracy Instruction......Page 200<br>Spatial Language......Page 201<br>Developing Methods for Mathematical Language Instruction......Page 202<br>References......Page 203<br>Introduction......Page 209<br>Early Numeracy Skills are Important for Future......Page 210<br>Identifying Children at Risk for Mathematical Learning Difficulties......Page 211<br>Early Numeracy Interventions for Low-Performing Children......Page 215<br>Studies With ThinkMath Intervention Programs......Page 219<br>Conclusions and Future Directions......Page 222<br>Acknowledgments......Page 356<br>The SES-Related Gap in Children's Early Mathematical Knowledge......Page 229<br>Potential for Early Curricular Intervention to Reduce the Math Gap......Page 231<br>The Pre-K Mathematics Intervention......Page 232<br>Responsiveness of Low-Performing Children......Page 234<br>First Approach: Tutorial Interventions in Mathematics and Attention......Page 235<br>Math Screening Measure......Page 237<br>Study Design......Page 238<br>The Math Intervention: Pre-K Mathematics Tutorial......Page 239<br>The Attention Intervention......Page 240<br>Measures and Assessment Procedures......Page 241<br>Is the Tutorial-Based Math Intervention Effective?......Page 242<br>Does Attention Training Have a Facilitative Effect on Math Outcomes?......Page 243<br>Second Approach: Intensification by Providing 2 Years of Tier 1 Math Intervention......Page 244<br>Child Sample......Page 245<br>The Math Intervention: Pre-Pre-K Mathematics and Pre-K Mathematics......Page 246<br>Measures and Assessment Procedures......Page 248<br>Does This 2-Year Intervention Improve the Mathematical Knowledge of Very Low-Performing Children?......Page 249<br>Effectiveness of the First Intervention Approach......Page 250<br>Comparison of the Two Intervention Approaches for Very Low-Performing Children......Page 251<br>Conclusion 1. Most Low-Performing Children Respond to Intensified Support in Mathematics......Page 252<br>Conclusion 3. Public Preschool Programs Should Provide High-Quality, Intensive Math Support, But New Policies and Resources .........Page 253<br>References......Page 254<br>Analogy and Analogical Reasoning in Mathematics......Page 260<br>Where Does the Analogy "Numbers are Points on the Line" Come From?......Page 264<br>Tapping Into Students Understanding of the Dense Ordering of Rational Numbers......Page 265<br>Could the Number Line Support Students Understanding of Density?......Page 267<br>Does the Number Line Have an Effect on Students Reasoning About Density?......Page 268<br>Is Density More Accessible to Students in a Geometrical Rather Than in an Arithmetical Context?......Page 270<br>Using the "Numbers are Points" Analogy and theRubber Line" Bridging Analogy......Page 274
Conclusions and Future Directions......Page 277
11
The Role of Visual Representations in Mathematical Word Problems......Page 282
Students Natural Use of Visual Representations in Mathematics......Page 283
Embedding Visual Representations in Text......Page 289
Teaching Students to Create or Complete Diagrams as They Solve Problems......Page 291
Integrating Visual Representations With Text......Page 294
Schema-Based Instruction (SBI): Integrated Instruction in Word Problems and Visual Representations......Page 297
Conclusions and Future Directions......Page 302
References......Page 303
12
The Role of Cognitive Processes in Treating Mathematics Learning Difficulties......Page 308
Why Embed Cognitive Process Training within Direct Skills Intervention?......Page 310
Why Focus on Word Problems?......Page 311
Conceptual Model for Linking Language Comprehension and Our Approach to Explicit Skills Word-Problem Intervention......Page 312
Study Overview......Page 315
Preliminary Results......Page 316
Allocating Varying Forms of Explicit Skills Intervention to Subgroups of Learners With Different Cognitive Profiles......Page 319
Why Focus Specifically on Fraction Magnitude Comparisons and Word Problems?......Page 320
Why Incorporate a Self-Explaining or Word-Problem Instructional Component Into the Multicomponent Fractions Intervention?......Page 321
Does Supported Self-Explaining Compensate for Limitations in Cognitive Processes?......Page 322
Study Overview......Page 325
Results......Page 327
Summary and Future Directions......Page 329
References......Page 330
Introduction......Page 334
Patterns of Effects Across Time and Theories of Children's Mathematical Development......Page 335
Measurement-Based Explanations......Page 336
Cognitive Processing Explanations......Page 340
Implications for the Study of Children's Mathematical Development......Page 350
Targeting At-Risk Children......Page 352
Targeting Advanced Skills in Older Children......Page 353
Complementary Follow-Through Interventions......Page 354
The Possibility of Different Effects of Improving Early Math Intervention at Scale?......Page 355
References......Page 357
C......Page 360
D......Page 361
G......Page 362
L......Page 363
N......Page 364
P......Page 365
S......Page 366
W......Page 367
Z......Page 368
Back Cover......Page 369