Beyond Classical Pedagogy
Teaching Elementary School Mathematics
The emergence of the National Council of Teachers of Mathematics Standards in 1989 sparked a sea change in thinking about the nature and quality of mathematics instruction in U.S. schools. Much is known about transmission forms of mathematics teaching and the influence of this teaching on students' learning, but there is still little knowledge about the alternative forms of instruction that have evolved from the recent widespread efforts to reform mathematics education.
Beyond Classical Pedagogy: Teaching Elementary School Mathematics reports on the current state of knowledge about these new instructional practices, which differ in significant ways from the traditional pedagogy that has permeated mathematics education in the past. This book provides a research-based view of the nature of facilitative teaching in its relatively mature form, along with opposing views and critique of this form of pedagogy.
The focus is on elementary school mathematics classrooms, where the majority of the reform-based efforts have occurred, and on the micro level of teaching (classroom interaction) as a source for revealing the complexity involved in teaching, teachers' learning, and the impact of both on children's learning. The work in elementary mathematics teaching is situated in the larger context of research on teaching.
Research and insights from three disciplinary perspectives are presented: the psychological perspective centers on facilitative teaching as a process of teachers' learning; the mathematical perspective focuses on the nature of the mathematical knowledge teachers need in order to engage in this form of teaching; the sociological perspective attends to the interactive process of meaning construction as teachers and students create intellectual communities in their classrooms.
The multidisciplinary perspectives presented provide the editors with the necessary triangulation to provide confirming evidence and rich detail about the nature of facilitative teaching.
Audiences for this book include scholars in mathematics education and teacher education, teacher educators, staff developers, and classroom teachers. It is also appropriate as a text for graduate courses in mathematics education, teacher education, elementary mathematics teaching methods, and methods of research in mathematics education.
Table of Contents
Contents: Preface. Part I: Setting the Stage and Raising Issues. B.S. Nelson, J. Warfield, T. Wood, Introduction. D.L. Ball, Teaching, With Respect to Mathematics and Students. Part II: Teaching Viewed From a Psychological Perspective: Teaching as Entailing Teachers' Learning. T.P. Carpenter, E. Ansell, L. Levi, An Alternative Conception of Teaching for Understanding: Case Studies of Two First-Grade Mathematics Classes. M.L. Franke, E. Kazemi, Teaching as Learning Within a Community of Practice: Characterizing Generative Growth. M.G. Sherin, Developing a Professional Vision of Classroom Events. B. Jaworski, Commentary 1: Questions and Issues. Part III: Teaching Viewed From the Discipline of Mathematics. D. Schifter, Learning to See the Invisible: What Skills and Knowledge Are Needed to Engage With Students' Mathematical Ideas? J. Warfield, Where Mathematics Content Knowledge Matters: Learning About and Building on Children's Mathematical Thinking. M.A. Simon, Two Intertwined Bodies of Work: Conducting Research on Mathematics Teacher Development and Elaborating Theory of Mathematics Teaching/Learning. B. Jaworski, Commentary 2: Issues and Questions. Part IV: Teaching Viewed From a Social and Cultural Perspective. T. Wood, T. Turner-Vorbeck, Extending the Conception of Mathematics Teaching. B. McNeal, Making Sense of Mathematics Teaching in Real Context. B. Jaworski, Commentary 3: Questions and Issues. Part V: What Do We Know About Teaching That Supports Students' Construction of Mathematical Knowledge and What Is Still Under Debate? B.S. Nelson, Constructing Facilitative Teaching. V. Richardson, Constructivist Mathematics Instruction and Current Trends in Research on Teaching. T. Wood, B.S. Nelson, J. Warfield, Final Remarks.
"Given the intense interest in constructivism and student thinking among the mathematics education community, this timely volume makes an important contribution to the teaching of elementary school mathematics....Chapters are well organized with overviews and commentaries, making the book easy to follow. This is a rich resource for those involved in the teaching and research of elementary school mathematics. Recommended for upper-division undergraduates, graduate students, faculty, and university libraries."