Teacher's and Students' Understanding: The Role of Tools and Inscriptions in Supporting Effective Communication.

The 2 episodes featured in this issue provide a rich setting in which to investigate not only the influence but also the confluence of students' and teacher's understandings on the quality of whole class discussions. In particular, I focus on the communication between the students and myself as the teacher in the classroom. This unique perspective allows me to offer insights into the teacher's decision-making process and how those decisions influenced the opportunities for learning. As part of the analysis I consider the role of tools in both supporting and constraining communication in the classroom. The analysis therefore makes explicit the tensions in teaching by highlighting the importance of the teacher's understanding of the students' offered explanations and justifications and the mathematics that is to be taught.

[1]  Martin A. Simon,et al.  Towards a constructivist perspective: An intervention study of mathematics teacher development , 1991 .

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

[3]  Baruch B. Schwarz,et al.  The emergent perspective in rich learning environments: Some roles of tools and activities in the construction of sociomathematical norms , 1999 .

[4]  Martin A. Simon.  Focusing on learning mathematics , 1996 .

[5]  W. Dörfler.  Computer Use and Views of the Mind , 1993 .

[6]  Patrick W Thompson,et al.  The development of the concept of speed and its relationship to concepts of rate , 1994 .

[7]  Carolyn A. Maher,et al.  The Teacher as Designer, Implementer, and Evaluator of Children's Mathematical Learning Environments. , 1987 .

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

[9]  Martin A. Simon,et al.  Justification in the mathematics classroom: A study of prospective elementary teachers , 1996 .

[10]  Martin A. Simon.  Developing new models of mathematics teaching: An imperative for research on mathematics teacher development , 1997 .

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

[12]  Judith T. Sowder.  Middle Grade Teachers' Mathematical Knowledge and Its Relationship to Instruction: A Research Monograph , 1998 .

[13]  Luciano Meira,et al.  The Microevolution of Mathematical Representations in Children's Activity , 1995 .

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

[15]  Elizabeth Fennema,et al.  Using Children’s Mathematical Knowledge in Instruction , 1993 .

[16]  Paul Cobb,et al.  A method for conducting longitudinal analyses of classroom videorecordings and transcripts , 1996 .

[17]  Ann L. Brown,et al.  How people learn: Brain, mind, experience, and school. , 1999 .

[18]  L. Shulman.  Those Who Understand: Knowledge Growth in Teaching , 1986 .

[19]  T. P. Carpenter,et al.  Chapter 4 Cognitively guided instruction: Building on the knowledge of students and teachers* , 1992 .

[20]  Elizabeth Fennema,et al.  Capturing Teachers’ Generative Change: A Follow-Up Study of Professional Development in Mathematics , 2001 .

[21]  Paul M. Cobb,et al.  « Construction individuelle, acculturation mathématique et communauté scolaire » , 1994 .

[22]  Paul Cobb,et al.  Constructivist, emergent, and sociocultural perspectives in the context of developmental research , 1996 .

[23]  Paul Cobb,et al.  Symbolizing, Modeling, and Instructional Design , 2000 .

[24]  T. P. Carpenter,et al.  Cognitively Guided Instruction: A Knowledge Base for Reform in Primary Mathematics Instruction , 1996, The Elementary School Journal.

[25]  Helen M. Doerr.  An Integrated Approach to Mathematical Modeling: A Classroom Study , 1995 .

[26]  Leslie P. Steffe,et al.  Teaching experiment methodology: Underlying principles and essential elements , 2000 .

[27]  R. Linn,et al.  Qualitative methods in research on teaching , 1985 .

[28]  A. Strauss,et al.  The discovery of grounded theory: strategies for qualitative research aldine de gruyter , 1968 .

[29]  E. Glasersfeld.  Radical Constructivism: A Way of Knowing and Learning. Studies in Mathematics Education Series: 6. , 1995 .

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

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

[32]  Richard Lesh,et al.  Task-Analysis Cycles as Tools for Supporting Students’ Mathematical Development , 2003 .

[33]  R. Pea.  Practices of distributed intelligence and designs for education , 1993 .

[34]  P. Thompson,et al.  Fractions and multiplicative reasoning , 2003 .

[35]  Gaea Leinhardt,et al.  Subject-Matter Knowledge and Elementary Instruction: A Case from Functions and Graphing , 1990 .

[36]  M. Reynolds,et al.  Knowledge Base for the Beginning Teacher , 1989 .

[37]  Susan J. Lamon,et al.  Integrating research on teaching and learning mathematics , 1988 .

[38]  D. Ball.  The Mathematical Understandings That Prospective Teachers Bring to Teacher Education , 1990, The Elementary School Journal.

[39]  Anna Sfard,et al.  On Reform Movement and the Limits of Mathematical Discourse , 2000 .

[40]  D. Ball.  What Do Students Know? Facing Challenges of Distance, Context, and Desire in Trying to Hear Children , 1997 .

[41]  Luciano Meira,et al.  Making Sense of Instructional Devices: The Emergence of Transparency in Mathematical Activity. , 1998 .

[42]  Magdalene Lampert,et al.  When the Problem Is Not the Question and the Solution Is Not the Answer: Mathematical Knowing and Teaching , 1990 .

[43]  P. Grossman.  The Making of a Teacher: Teacher Knowledge and Teacher Education , 1990 .

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