A Study of Whole Classroom Mathematical Discourse and Teacher Change

This article presents a comparison of the first 2 years of an experienced middle school mathematics teacher's efforts to change her classroom practice as a result of an intervening professional development program. The teacher's intention was for her teaching to better reflect her vision of reform-based mathematics instruction. We compared events from the 1st and 2nd year's whole class discussions within a multilevel framework that considered the flow of information and the nature of peer- and teacher-directed scaffolding. Discourse analyses of classroom videos served both as an analytic tool for our study of whole classroom interactions, as well as a resource for promoting discussion and reflection during professional development meetings. The results show that there was little change in the teacher's specific goals and beliefs in light of a self-evaluation of her Year 1 practices, but substantial changes in how she set out to enact those goals. In Year 2, the teacher maintained a central, social scaffolding role, but removed herself as the analytic center to invite greater student participation. Consequently, student-led discussion increased manifold, but lacked the mathematical precision offered previously by the teacher. The analyses lead to insights about how classroom interactions can be shaped by a teacher's beliefs and interpretations of educational reform recommendations.

[1]  Kenneth A. Ross,et al.  Doing and Proving: The Place of Algorithms and Proofs in School Mathematics , 1998 .

[2]  Kenneth R. Koedinger,et al.  Teachers' and Researchers' Beliefs about the Development of Algebraic Reasoning. , 2000 .

[3]  Miriam Gamoran Sherin,et al.  Perspective on M. Lampert’s “When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching” , 2004 .

[4]  M. Franke,et al.  Teachers' knowledge and its impact. , 1992 .

[5]  L. Resnick The 1987 Presidential Address Learning In School and Out , 1987 .

[6]  A. Su,et al.  The National Council of Teachers of Mathematics , 1932, The Mathematical Gazette.

[7]  Stephanie D. Teasley,et al.  Perspectives on socially shared cognition , 1991 .

[8]  P. Cobb,et al.  Discourse, mathematical thinking, and classroom practice. , 1993 .

[9]  T. Guskey Staff Development and the Process of Teacher Change , 1986 .

[10]  Richard S. Prawat,et al.  Teaching Mathematics for Understanding: Discussing Case Studies of Four Fifth-Grade Teachers , 1992, The Elementary School Journal.

[11]  J. Stenton,et al.  Learning how to teach. , 1973, Nursing mirror and midwives journal.

[12]  Douglas A. Grouws,et al.  Handbook of research on mathematics teaching and learning , 1992 .

[13]  Deborah Schifter,et al.  Assessing teachers' development of a constructivist view of mathematics learning☆ , 1992 .

[14]  Catherine A. Brown,et al.  Learning to Teach Hard Mathematics: Do Novice Teachers and Their Instructors Give Up Too Easily? , 1992 .

[15]  Thomas J. Cooney A Beginning Teacher's View of Problem Solving. , 1985 .

[16]  P. Cobb,et al.  Sociomathematical Norms, Argumentation, and Autonomy in Mathematics. , 1996 .

[17]  Bonnie P. Schappelle,et al.  Providing a foundation for teaching mathematics in the middle grades , 1995 .

[18]  Anne M. Raymond Inconsistency between a Beginning Elementary School Teacher's Mathematics Beliefs and Teaching Practice. , 1997 .

[19]  A. Thompson The relationship of teachers' conceptions of mathematics and mathematics teaching to instructional practice , 1984 .

[20]  Martin A. Simon Reconstructing Mathematics Pedagogy from a Constructivist Perspective. , 1995 .

[21]  Deborah Loewenberg Ball,et al.  Teacher Learning and the Mathematics Reforms: What We Think We Know and What We Need to Learn. , 1996 .

[22]  Neil Mercer,et al.  Common Knowledge: The Development of Understanding in the Classroom , 1987 .

[23]  Gary D. Fenstermacher 4: A Philosophical Consideration of Recent Research on Teacher Effectiveness , 1978 .

[24]  Dorothy Vásquez-Levy Features of practical argument engagement , 1998 .

[25]  Hilda Borko,et al.  Conceptual Knowledge Falls through the Cracks: Complexities of Learning to Teach Mathematics for Understanding. , 1993 .

[26]  Judith L. Shrum,et al.  Teacher Beliefs , 1988 .

[27]  Kenneth R. Koedinger,et al.  An Investigation of Teachers' Beliefs of Students' Algebra Development , 2000, Cognition and Instruction.

[28]  Pam Grossman,et al.  Transitions into Teaching: Learning to Teach Writing in Teacher Education and Beyond , 2000 .

[29]  Richard Lehrer,et al.  Visualizing the emergent structure of children's mathematical argument , 2001, Cogn. Sci..

[30]  K. A. Ericsson,et al.  Protocol Analysis: Verbal Reports as Data , 1984 .

[31]  Juliet A. Baxter,et al.  Dilemmas of Discourse-Oriented Teaching in One Middle School Mathematics Classroom , 1996, The Elementary School Journal.

[32]  L. S. Vygotskiĭ,et al.  Mind in society : the development of higher psychological processes , 1978 .

[33]  Giyoo Hatano,et al.  Sharing cognition through collective comprehension activity , 1991, Perspectives on socially shared cognition.

[34]  C. Hirsch Curriculum and Evaluation Standards for School Mathematics , 1988 .

[35]  Magdalene Lampert,et al.  Talking Mathematics in School: Studies of Teaching and Learning , 1998 .

[36]  Deborah Loewenberg Ball,et al.  Implementing The “Professional Standards For Teaching Mathematics”: What's All This Talk about “Discourse”? , 1991 .

[37]  A. Thompson Teachers' beliefs and conceptions: A synthesis of the research. , 1992 .

[38]  J. Bruer Schools for Thought: A Science of Learning in the Classroom , 1993 .

[39]  Emily H. van Zee,et al.  Reflective discourse: developing shared understandings in a physics classroom , 1997 .

[40]  D. Hunt Cognition and Learning , 1989 .

[41]  D. Ball With an Eye on the Mathematical Horizon: Dilemmas of Teaching Elementary School Mathematics , 1993, The Elementary School Journal.

[42]  Marlene Scardamalia,et al.  Computer-Supported Intentional Learning Environments , 1989 .

[43]  Mitchell J. Nathan,et al.  The Real Story Behind Story Problems: Effects of Representations on Quantitative Reasoning , 2004 .

[44]  Peggy S. Rittenhouse Talking Mathematics in School: The Teacher's Role in Mathematical Conversation: Stepping In and Stepping Out , 1998 .

[45]  P. Elliott Assessment Standards for School Mathematics , 1995 .

[46]  최영한,et al.  미국 NCTM의 Principles and Standards for School Mathematics에 나타난 수학과 교수,학습의 이론 , 2002 .

[47]  L. Shulman Knowledge and Teaching: Foundations of the New Reform , 1987 .

[48]  Paul Cobb,et al.  An Analysis of Development of Sociomathematical Norms in One First-Grade Classroom , 2001 .

[49]  Virginia Richardson-Koehler,et al.  Teacher change and the staff development process : a case in reading instruction , 1994 .