Preparing Teachers for Handling Students’ Mathematical Communication: Gathering Knowledge and Building Tools

The main thesis of this chapter is that to prepare teachers to their new role in the reformed mathematics classroom, we must first understand better the mechanisms of the interactions supposed to take place in these classrooms. Of particular interest are the instances of students’ collective problem-solving. The student-to-student classroom interactions are highly recommended for their potential to promote learning, but at the present stage it is not clear what should be the role of the teacher in promoting the realization of this potential. How students’ interactions should be investigated, what tools could be used for this purpose and what impact the insights thus gained can have on decisions about the optimal directions in teachers’ preparation are the main focus of the discussion that follows.

[1]  Geoffrey B. Saxe,et al.  Studying mathematics learning in collective activity , 1998 .

[2]  Leone Burton,et al.  Learning Mathematics : From Hierarchies to Networks , 1999 .

[3]  P. Cobb,et al.  Cognitive and Situated Learning Perspectives in Theory and Practice , 1999 .

[4]  Sarah Michaels,et al.  Discourse, learning, and schooling: Shifting participant frameworks: orchestrating thinking practices in group discussion , 1996 .

[5]  Ference Marton,et al.  Paths of learning: the joint constitution of insights , 1999 .

[6]  Jeffrey Frykholm,et al.  The Impact of Reform: Challenges for Mathematics Teacher Preparation , 1999 .

[7]  Jeremy Kilpatrick,et al.  International handbook of mathematics education , 1997 .

[8]  G. Roland,et al.  Council of Teachers of Mathematics , 1999 .

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

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

[11]  Michael J. Reddy Metaphor and Thought: The conduit metaphor: A case of frame conflict in our language about language , 1993 .

[12]  Deborah Loewenberg Ball,et al.  Preparing Teachers to Teach Mathematics: A Comparative Perspective , 1996 .

[13]  A. Sfard On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin , 1991 .

[14]  J. P. Smith,et al.  Efficacy and Teaching Mathematics by Telling: A Challenge for Reform. , 1996 .

[15]  M. Goos,et al.  Do it this way! Metacognitive strategies in collaborative mathematical problem solving , 1996 .

[16]  Robert B. Davis,et al.  How students think: The role of representations , 1997 .

[17]  Jorg Voigt,et al.  Negotiation of mathematical meaning and learning mathematics , 1994 .

[18]  Anna Sfard,et al.  Seeing through Symbols: The Case of Equivalent Expressions. , 1999 .

[19]  Leslie P. Steffe,et al.  Theories of Mathematical Learning , 1996 .

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

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

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

[23]  Anna Sfard,et al.  Steering (Dis)Course between Metaphors and Rigor: Using Focal Analysis to Investigate an Emergence of Mathematical Objects , 2000 .

[24]  M. O’Connor Talking Mathematics in School: Language Socialization in the Mathematics Classroom: Discourse Practices and Mathematical Thinking , 1998 .

[25]  Lyn D. English,et al.  Mathematical reasoning : analogies, metaphors, and images , 1997 .