Teacher Education Does Matter: A Situative View of Learning to Teach Secondary Mathematics

The visions of mathematics classrooms called for by current educational reform efforts pose great challenges for kindergarten through Grade 12 schools and teacher education programs. Although a number of colleges and universities throughout the country are making changes in their teacher education programs to reflect these reform recommendations, we have little systematic information on the nature of these programs or their impact on prospective teachers. These issues are of central concern in the study-Learning to Teach Secondary Mathematics in Two Reform-Based Teacher Education Programs-that we draw on in this article. The article focuses on 1 preservice teacher's (Ms. Savant) knowledge, beliefs, and practices related to proof, tasks, and discourse. A situative perspective on cognition and components of teachers' professional knowledge frame our research. We examined data on Ms. Savant's experiences in her teacher education program to understand the influences of teacher education on her development as a mathematics teacher. This research indicates that Ms. Savant's teacher education experiences did make a difference in her development as a teacher. Her mathematics methods course provided a large collection of tasks, engaged her and her preservice colleagues in discourse, and provided her with both formal and informal experiences with proof-all of these experiences reflecting reform-based visions of mathematics classrooms. The situative perspective on cognition directed our attention to issues of compatibility of goals and visions across the various university and kindergarten through Grade 12 classroom settings, and it helped us to understand why some aspects of reform-based pedagogy are more easily learned than others: Why some ideas and practices learned as a student in the university setting are more easily transported to the novice teacher's kindergarten through Grade 12 field setting. We conclude that compatibility of these settings on several key dimensions is essential for the settings to reinforce each other's messages, and thus work in conjunction, rather than in opposition, to prepare reform-minded teachers.

[1]  P. Scott,et al.  Constructing Scientific Knowledge in the Classroom , 1994 .

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

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

[4]  Etienne Wenger,et al.  Situated Learning: Legitimate Peripheral Participation , 1991 .

[5]  Carolyn A. Maher,et al.  THE DEVELOPMENT OF THE IDEA OF MATHEMATICAL PROOF: A 5-YEAR CASE STUDY , 1996 .

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

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

[8]  D. Kagan.  Professional Growth Among Preservice and Beginning Teachers , 1992 .

[9]  Lauren B. Resnick,et al.  Shared cognition: Thinking as social practice , 1991, Perspectives on socially shared cognition.

[10]  David Tall,et al.  Advanced Mathematical Thinking , 1994 .

[11]  Paul Cobb,et al.  Assessment of a problem-centered second-grade mathematics project. , 1991 .

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

[13]  Jane-Jane Lo,et al.  THE PARTICIPATION, BELIEFS, AND DEVELOPMENT OF ARITHMETIC MEANING OF A THIRD-GRADE STUDENT IN MATHEMATICS CLASS DISCUSSIONS , 1994 .

[14]  G. Harel,et al.  PROOF FRAMES OF PRESERVICE ELEMENTARY TEACHERS , 1989 .

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

[16]  James H. Mosenthal,et al.  Constructing New Forms of Teaching: Subject Matter Knowledge in Inservice Teacher Education , 1992 .

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

[18]  Herbert A. Simon,et al.  Situative Versus Cognitive Perspectives: Form Versus Substance , 1997 .

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

[20]  N. Minick,et al.  Contexts for Learning: Sociocultural Dynamics in Children's Development , 1993 .

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

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

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

[24]  A. Bell,et al.  A study of pupils' proof-explanations in mathematical situations , 1976 .

[25]  R. Hersh.  Some proposals for reviving the philosophy of mathematics , 1979 .

[26]  Ralph T. Putnam,et al.  Teacher Learning: Implications of New Views of Cognition , 1997 .

[27]  Sam Wineburg,et al.  Creating a Community of Learners Among High School Teachers. , 1998 .

[28]  James Hiebert,et al.  Chapter 3 Reflection and communication: Cognitive considerations in school mathematics reform , 1992 .

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

[30]  Imre Lakatos,et al.  On the Uses of Rigorous Proof. (Book Reviews: Proofs and Refutations. The Logic of Mathematical Discovery) , 1977 .

[31]  P. Healy,et al.  Learning the lessons. , 1996, Nursing standard (Royal College of Nursing (Great Britain) : 1987).

[32]  Paul R. Halmos,et al.  What Is Teaching , 1994 .

[33]  G A Miller,et al.  A MATHEMATICAL PROOF. , 1931, Science.

[34]  E. Knuth,et al.  Why are you talking when you could be listening? The role of discourse and reflection in the professional development of a secondary mathematics teacher , 1998 .

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

[36]  I. Lakatos,et al.  Proofs and Refutations: Frontmatter , 1976 .

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

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

[39]  Gila Hanna,et al.  Some pedagogical aspects of proof , 1990 .

[40]  Ralph T. Putnam,et al.  What Do New Views of Knowledge and Thinking Have to Say About Research on Teacher Learning? , 2000 .

[41]  L. Wiener,et al.  The Nature of Proof , 1992 .

[42]  Alan H. Schoenfeld,et al.  Toward a theory of teaching-in-context , 1998 .

[43]  L. Quéré.  Cognition in Practice , 1996 .

[44]  Gary Sykes,et al.  Teacher Education and the Case Idea , 1992 .

[45]  James H. Mosenthal,et al.  The Construction of New Forms of Teaching: Subject Matter Knowledge in Inservice Teacher Education. Research Report 90-8. , 1990 .

[46]  J. Greeno.  THE SITUATIVITY OF KNOWING, LEARNING, AND RESEARCH , 1998 .

[47]  J. Talbert,et al.  Contexts That Matter for Teaching and Learning: Strategic Opportunities for Meeting the Nation's Educational Goals. , 1993 .

[48]  Nicolas Balacheff.  Treatment of Refutations: Aspects of the Complexity of a Constructivist Approach to Mathematics Learning , 1991 .

[49]  Herbert A. Simon,et al.  Rejoinder: Situative versus Cognitive Perspectives: Form versus Substance , 1997 .

[50]  David Wheeler.  Aspects of mathematical proof , 1990 .

[51]  W. Carlsen.  The effects of science teacher subject-matter knowledge on teacher questioning and classroom discourse , 1987 .

[52]  Paul Cobb,et al.  The Evolution of Mathematical Practices: A Case Study , 1999 .