Moving from rhetoric to praxis: Issues faced by teachers in having students consider multiple solutions for problems in the mathematics classroom

Despite general agreement that students should consider more than one way to solve a complex mathematics problem, this practice is rarely observed in U.S. classrooms. In this paper, we examine data that trace the year-long professional development experience of 12 veteran teachers of middle grades mathematics — experienced users of a standards-based mathematics curriculum — to unearth some issues and concerns that appeared to serve as obstacles to their use of multiple solutions in the classroom. We also identify key transformations that appear to account for the success of some teachers in embedding this practice in their instructional repertoire.

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

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

[3]  D. Ball,et al.  Beyond Being Told Not to Tell , 1999 .

[4]  Mary Kay Stein,et al.  Building Student Capacity for Mathematical Thinking and Reasoning: An Analysis of Mathematical Tasks Used in Reform Classrooms , 1996 .

[5]  Magdalene Lampert,et al.  Teaching Problems and the Problems of Teaching , 2001 .

[6]  C. Lewis.  Lesson study : a handbook of teacher-led instructional change , 2002 .

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

[8]  Edward A. Silver,et al.  Teaching and Learning Mathematical Problem Solving : Multiple Research Perspectives , 1985 .

[9]  Terry Wood,et al.  Beyond Classical Pedagogy : Teaching Elementary School Mathematics , 2001 .

[10]  J. Hiebert.  Making Sense: Teaching and Learning Mathematics with Understanding , 1997 .

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

[12]  Mary Catherine O'Connor,et al.  “Can any Fraction be Turned into a Decimal?” A Case Study of a Mathematical Group Discussion , 2002 .

[13]  M. Wittrock.  Handbook of research on teaching , 1986 .

[14]  Suzanne M. Wilson.  California Dreaming: Reforming Mathematics Education , 2002 .

[15]  Anna Sfard,et al.  Learning discourse : discursive approaches to research in mathematics education , 2002 .

[16]  Terry A. Goodman,et al.  Implementing Mathematics Reform: The Challenge Within , 2000 .

[17]  S. Feldman.  The Teaching Gap. , 2004 .

[18]  Shigeru Shimada,et al.  The Open-Ended Approach: A New Proposal for Teaching Mathematics , 1997 .

[19]  Frank K. Lester,et al.  Musings about Mathematical Problem-Solving Research: 1970-1994. , 1994 .