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المحتويات / النص
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CONTENTS
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .vii
Part 1: Mathematical Reasoning: In Search of Understanding
1. Mathematical Reasoning in the Elementary Grades . . . . . . . . . . . . . . . . 1
SUSAN JO RUSSELL
TERC, Cambridge, Massachusetts
2. Developing Mathematical Reasoning in the Middle Grades:
Recognizing Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
CAROL E. MALLOY
University of North Carolina at Chapel Hill, Chapel Hill, North Carolina
3. Reasoning by Analogy: A Fundamental Process in Children’s
Mathematical Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
LYN D. ENGLISH
Queensland University of Technology, Brisbane, Queensland, Australia
4. The Nature of Mathematical Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . 37
ROBERT J. STERNBERG
Yale University, New Haven, Connecticut
Part 2: Reasoning in the Early Grades
5. Young Children’s Mathematical Reasoning:
A Psychological View. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
EILEEN P. TANG
Teachers College, Columbia University, New York, New York
HERBERT P. GINSBURG
Teachers College, Columbia University, New York, New York
6. Reasoning about Operations: Early Algebraic Thinking
in Grades K–6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
DEBORAH SCHIFTER
Education Development Center, Newton, Massachusetts
7. Teaching Fractions: Fostering Children’s Own Reasoning. . . . . . . . . . 82
CONSTANCE KAMII
University of Alabama at Birmingham, Birmingham, Alabama
MARY ANNWARRINGTON
University of Alabama at Birmingham, Birmingham, Alabama
iv CONTENTS
8. Developing Mathematical Reasoning within the
Context of Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
KAY MCCLAIN
Vanderbilt University, Nashville, Tennessee
PAUL COBB
Vanderbilt University, Nashville, Tennessee
KOENO GRAVEMEIJER
Freudenthal Institute, Utrecht University, Utrecht, Netherlands
BETH ESTES
Franklin Road Academy, Nashville, Tennessee
9. Mathematics Is for the Birds: Reasoning for a Reason . . . . . . . . . . . . 107
PHYLLISWHITIN
Dutch Fork Elementary School, Irmo, South Carolina
DAVID J. WHITIN
University of South Carolina, Columbia, South Carolina
Part 3: Reasoning in the Middle Grades
10. Mathematical Reasoning during Small-Group Problem Solving . . . . 115
ALICE F. ARTZT
Queens College of the City University of New York, Flushing, New York
SHIREL YALOZ-FEMIA
Hunter College High School, New York, New York
11. Developing Students’ Algebraic Reasoning Abilities . . . . . . . . . . . . . 127
CAROLE GREENES
Boston University, Boston, Massachusetts
CAROL FINDELL
Boston University, Boston, Massachusetts
12. Innovative Tasks to Improve Critical- and
Creative-Thinking Skills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
STEPHEN KRULIK
Temple University, Philadelphia, Pennsylvania
JESSE A. RUDNICK
Temple University, Philadelphia, Pennsylvania
13. Understanding Students’ Probabilistic Reasoning . . . . . . . . . . . . . . . 146
GRAHAM A. JONES
Illinois State University, Normal, Illinois
CAROL A. THORNTON
Illinois State University, Normal, Illinois
CYNTHIA W. LANGRALL
Illinois State University, Normal, Illinois
JAMES E. TARR
Middle Tennessee State University, Murfreesboro, Tennessee
v CONTENTS
14. Analyzing Mathematical Reasoning in Students’ Responses
across Multiple Performance Assessment Tasks . . . . . . . . . . . . . . . . . 156
DOMINIC PERESSINI
University of Colorado at Boulder, Boulder, Colorado
NORMANWEBB
University of Wisconsin—Madison, Madison, Wisconsin
Part 4: Reasoning in High School
15. Mathematical Reasoning: In the Eye of the Beholder. . . . . . . . . . . . . 175
PEGGY HOUSE
Northern Michigan University, Marquette, Michigan
16. The Language of Quantification in Mathematics Instruction. . . . . . 188
SUSANNA S. EPP
DePaul University, Chicago, Illinois
17. Mathematics Journal Articles: Anchors for the Guided
Development and Practice of Reasoning Skills . . . . . . . . . . . . . . . . . . 198
ROBERT GERVER
North Shore High School, Glen Head, Long Island, New York
18. Teaching and Assessing Statistical Reasoning . . . . . . . . . . . . . . . . . . . 207
JOAN B. GARFIELD
University of Minnesota, Minneapolis, Minnesota
IDDO GAL
University of Haifa, Haifa, Israel
Part 5: Mathematical Reasoning: Charting a Future of Success
19. Mathematical Reasoning and Educational Policy:
Moving beyond the Politics of Dead Language . . . . . . . . . . . . . . . . . . 221
WILLIAM F. TATE
University of Wisconsin—Madison, Madison, Wisconsin
HOWARD C. JOHNSON
Syracuse University, Syracuse, New York
20. Adventures in Mathematical Inquiry . . . . . . . . . . . . . . . . . . . . . . . . . . 234
GAIL BOLDT
University of Hawaii at Manoa, Honolulu, Hawaii
AARON LEVINE
Epiphany Elementary School, Honolulu, Hawaii
21. Using Short Questions to Develop and Assess Reasoning . . . . . . . . . 247
WILLIAM M. CARROLL
Saint Ignatius College Preparatory School, Chicago, Illinois
vi CONTENTS
22. Helping Elementary- and Middle-Grades Preservice Teachers
Understand and Develop Mathematical Reasoning . . . . . . . . . . . . . . 256
GEORGE W. BRIGHT
University of North Carolina at Greensboro, Greensboro, North Carolina
23. Twenty Questions about Mathematical Reasoning. . . . . . . . . . . . . . . 270
LYNN ARTHUR STEEN
Saint Olaf College, Northfield, Minnesota
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
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