CONTENTS Preface . Part 1: Mathematical Reasoning: In Search of Understanding 1. Mathematical Reasoning in the Elementary Grades SUSAN JOR i rcEpK G Ca = a 1a gE VVA iassabcen usettof s Developing Mathematical Reasoning in the Middle Grades: Recognizing Diversity Cal E.M [ niver Reasoning by Analogy: A Fundamental Process in Children’s Mathematical Learning Lyn D. I Queensland river The Nature of Mathematical Reasoning R oS Part 2: Reasoning in the Early Grades 5. Young Children’s Mathematical Reasoning: A Psychological View a YrD.7 1 Reasoning about Operations: Early Algebraic Thinking in Grades K-6 DEBORAH SC! Education Deve opment ¢ enter, Newton, Massachusetts Teaching Fractions: Fostering Children’s Own Reasoning CONSTANCE K avama , al¢ RB irmisningohhaa r n, DR;i rmi1tnngaonha m, ’ Allaahbaamm a ungham, Alabama 8. Developing Mathematical Reasoning within the Context of Measurement Kay Mc Nvoeotthnoerrliaa nas] Tennessee 9. Mathematics Is for the Birds: Reasoning for a Reason P W Part 3: Reasoning in the Middle Grades 10. Mathematical Reasoning during Small-Group Problem Solving .... Developing Students’ Algebraic Reasoning Abilities ( (5 . Innovative Tasks to Improve Critical- and Creative-Thinking Skills 13. Normal, Illinois 7 1 niversity, Murfreesboro, Te nnessee 14. Analyzing Mathematical Reasoning in Students’ Responses across Multiple Performance Assessment Tasks 8| . Part 4: Reasoning in High School 15. Mathematical Reasoning: In the Eye of the Beholder PEGGY H N VOorttrhi,e rn » AiAv i gan sy UIT niJveng ersity¢ arqu tt \ lichijgoaannn The Language of Quantification in Mathematics Instruction SUSANNA S. I Mathematics Journal Articles: Anchors for the Guided Development and Practice of Reasoning Skills Rot G North Shore High School, Glen Head Teaching and Assessing Statistical Reasoning ................05. 207 JOAN B. G ota Minneapolls Part 5: Mathematical Reasoning: Charting a Future of Success 19. Mathematical Reasoninagnd Educational Policy: Moving beyond the Politics of Dead Language W BE. VViod;di sor Syracuse, New York Using Short Questions to Develop and Assess Reasoning WILLIAM M. ¢ L=LEV E Freparatory : SCH-OK 22. Helping Elementary- and Middle-Grades Preservice Teachers Understand and Develop Mathematical Reasoning GEORGE W. B , : , ‘ . : sity of North Carolina at Greensboro, Greensboro, North Carolina 23 ' J Northfield, Minnesota I a a re a acacia ye cv ache De ean wk Cand hE Int inl ec als ae 2