This book provides descriptive cases, accompanied by analytic commentaries, of nine upper-elementary grade mathematics lessons that represent an array of sound teaching practices. The cases focus on various mathematics topics and were written from authentic lessons taught by regular classroom teachers to diverse groups of students. Each lesson contains elements of sound instructional practice as well as potential dilemmas from which both preservice and in-service teachers can benefit.
Anna O. Graeber is Associate Professor Emerita in the Department of Curriculum and Instruction at the University of Maryland, with her doctorate in mathematics education from Teachers College, Columbia University. Prior to teaching at the University of Maryland, she served in various mathematics curriculum and staff development positions at Research for Better Schools, a regional educational laboratory in Philadelphia. She is best known for her research on students' misconceptions in mathematics. Linda Valli is the inaugural Jeffrey & David Mullan Professor of Teacher Education and Professional Development in the Department of Curriculum and Instruction at the University of Maryland. Her Ph.D. is from the Department of Education Policy Studies at the University of Wisconsin, Madison, where she developed her interests in educational inequalities and critical theory. She has used cases in her own teaching and conducts research on learning to teach, professional development, culturally-responsive teaching, and education policy. Kristie Jones Newton is assistant professor in the Department of Curriculum, Instruction, and Technology in Education at Temple University whose research and teaching focuses on mathematics education. As a graduate student at the University of Maryland, she participated extensively in the development and conduct of the High-Quality Teaching study, contributed significantly to the selection and writing of the cases, piloted the cases in her undergraduate math methods class, and wrote commentaries for the Facilitator's Guide.
Preface Alternative Thematic Frameworks Introduction Part I: The Teaching of Mathematics - Lesson Cases Case 1: Promoting One of the Meanings of Multiplication: Requesting Alternate Methods in Order to Foster Understanding Case 2: Fractions, Decimals and Percents: Evoking Student Reasoning Commentary: A Teacher Educator Perspective Case 3: Getting a Sense of Grams: Building Conceptual Understanding Commentary: A Teacher Educator Perspective Case 4: Converting Among Customary Units of Measure: Attending to Students' Developmental Levels Commentary: A Teacher's Perspective Case 5: Converting Units Within a System of Measurement: Encouraging Resourcefulness Commentary: An English for Speakers of Other Languages (ESOL) Perspective Case 6: Distinguishing Between Area and Perimeter: Using Multiple Representations to Aid Discrimination Case 7: Exploring the Meanings of "Volume": Recognizing a Word's Everyday Meaning and its Mathematical Meaning Commentary: An English for Speakers of Other Languages (ESOL) Perspective Commentary: A Teacher's Perspective Case 8: The Importance of Sample Size: Posing High Level Questions to Build Understanding Commentary: A Teacher's Perspective Case 9: Continuous versus Discrete Data: Using Concept Attainment to Define Mathematical Terms Part II: Perspectives on Teaching - Commentaries Learner-Centered Psychological Principles Moral Perspectives on Teaching Perspective from the Special Education Math Literature A Principal's Perspective References List of Contributors