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A Conceptual Framework for Learning to Teach Secondary Mathematics: A Situative Perspective

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This paper offers for discussion and critique a conceptual framework that applies a situative perspective on learning to the study of learning to teach mathematics. From this perspective, such learning occurs in many different situations -- mathematics and teacher preparation courses, pre-service field experiences, and schools of employment. By participating over time in these varied contexts, mathematics teachers refine their conceptions about their craft -- the big ideas of mathematics, mathematics-specific pedagogy, and sense of self as a mathematics teacher. This framework guides a research project that traces the learning trajectories of teachers from two reform-based teacher preparation programs into their early teaching careers. We provide two examples from this research to illustrate how this framework has helped us understand the process of learning to teach.

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REFERENCES

  • Adler, J.: 2000, ‘Social practice theory and mathematics teacher education: a conversation between theory and practice’, Nordic Mathematics Education Journal (NOMAD) 8(3), 31–53.

    Google Scholar 

  • Adler, J. and Reed, Y. (eds.): 2002, Challenges of Teacher Development: An Investigation of Take-Up in South Africa, Van Schaik Publishers, Pretoria, South Africa.

    Google Scholar 

  • Alibert, D.: 1988, ‘Towards new customs in the classroom’, For the Learning of Mathematics 8(2), 31–35.

    Google Scholar 

  • Anderson, J. R., Reder, L. M. and Simon, H. A.: 1997, ‘Situative versus cognitive perspectives: Form versus substance’, Educational Researcher 26(1), 18–21.

    Article  Google Scholar 

  • Balacheff, N.: 1991, ‘Treatment of refutations: Aspects of the complexity of a constructivist approach to mathematics learning’, in E. von Glasersfeld (ed. ), Radical Constructivism in Mathematics Education, Kluwer Academic Publishers, Netherlands, pp. 89–110.

    Google Scholar 

  • Ball, D.: 1990, ‘The mathematical understandings that prospective teachers bring to teacher education’, The Elementary School Journal 90(4), 449–466.

    Article  Google Scholar 

  • Ball, D.: 1993, ‘With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics’, The Elementary School Journal 93(4), 373–397.

    Article  Google Scholar 

  • Bauersfeld, H.: 1988, ‘Interaction, construction and knowledge’, in D. Grouws and T. Cooney (eds. ), Effective Mathematics Teaching, Lawrence Erlbaum, Hillsdale, New Jersey.

    Google Scholar 

  • Behr, M., Harel, G., Post, T. and Lesh, R.: 1992, ‘Rational number, ratio, and proportion’, in D. Grouws (ed. ), Handbook of Research on Mathematics Teaching and Learning, Macmillan, New York, pp. 296–333.

    Google Scholar 

  • Boaler, J. (ed.): 2000, Multiple Perspectives on Mathematics Teaching and Learning, Elsevier Science, Stanford, CA.

    Google Scholar 

  • Boaler, J. and Greeno J. G.: 2000, ‘Identity, agency and knowing in mathematics worlds [Ch. 7]’, in J. Boaler (ed. ), Multiple Perspectives on Mathematics Teaching and Learning, Elsevier Science, Stanford, CA.

    Google Scholar 

  • Borko, H., Peressini, D., Romagnano, L., Knuth, E., Yorker, C., Wooley, C., Hovermill, J. and Masarik, K.: 2000, ‘Teacher education does matter: A situative view of learning to teach secondary mathematics’, Educational Psychologist 35, 193–206.

    Article  Google Scholar 

  • Borko, H. and Putnam, R.: 1996, ‘Learning to teach’, in D. Berliner and R. Calfee (eds. ), Handbook of Educational Psychology, MacMillan, New York, pp. 673–708.

    Google Scholar 

  • Bowers, J. S., Cobb, P. and McClain, K.: 1999, ‘The evolution of mathematical practices: A case study’, Cognition and Instruction 17, 25–64.

    Article  Google Scholar 

  • Bullough, R. V., Jr.: 1992, ‘Beginning teacher curriculum decision making, personal teaching metaphors, and teacher education’, Teaching and Teacher Education 8, 239–252.

    Article  Google Scholar 

  • Bullough, R. V., Jr. and Gitlin, A.: 1995, Becoming a Student of Teaching: Methodologies for Exploring Self and School Context, Garland Publishing, Inc, New York.

    Google Scholar 

  • Carpenter, T. P., Fennema, E. and Romberg, T. A. (eds.): 1993, Rational Numbers: An Integration of Research, Lawrence Erlbaum Associates, Hillsdale, New Jersey.

    Google Scholar 

  • Cazden, C. B.: 1986, ‘Classroom discourse’, in M. C. Wittrock (ed. ), Handbook of Research on Teaching, 3rd ed., Macmillan, New York, pp. 432–463.

    Google Scholar 

  • Clarke. D.: 1994, ‘Ten key principles from research for the professional development of mathematics teachers’, in D. B. Aichele (ed. ), Professional Development for Teachers of Mathematics, NCTM, Reston, VA, pp. 37–48.

    Google Scholar 

  • Cobb, P.: 2000, ‘The importance of a situated view of learning to the design of research and instruction’, in J. Boaler (ed. ), Multiple Perspectives on Mathematics Teaching and Learning, Ablex Publishing, Westport, CT, pp. 45–82.

    Google Scholar 

  • Cobb, P. and Bowers, J. S.: 1999, ‘Cognitive and situated learning perspectives in theory and practice’, Educational Researcher 28(2), 4–15.

    Article  Google Scholar 

  • Cobb, P., Boufi, A., McClain, K. and Whitenack, J.: 1997, ‘Reflective discourse and collective reflection’, Journal for Research in Mathematics Education 28(3), 258–277.

    Article  Google Scholar 

  • Cobb, P., Wood, T., Yackel, E., Nicholls, J., Wheatley, G., Trigatti, B. and Perlwitz, M.: 1991, ‘Assessment of a problem-centered second-grade mathematics project’, Journal for Research in Mathematics Education 22(1), 3–29.

    Article  Google Scholar 

  • Cobb, P., Yackel, E. and Wood, T.: 1993, ‘Discourse, mathematical thinking, and classroom practice’, in E. Forman, N. Minick and C. Stone (eds.), Contexts for Learning: So-ciocultural Dynamics in Children's Development, Oxford University Press, Oxford, pp. 91–119.

    Google Scholar 

  • Confrey, J. and Doer, H.: 1996, ‘Changing the curriculum to improve student understandings of function’, in D. F. Treagust (ed. ), Improving Teaching and Learning in Science and Mathematics, Teachers College Press, New York, pp. 162–171.

    Google Scholar 

  • Cooney, T.: 1985, ‘A beginning teacher's view of problem solving’, Journal for Research in Mathematics Education 16, 324–336.

    Article  Google Scholar 

  • Davis, P.: 1986, ‘The nature of proof’, in M. Carss (ed. ), Proceedings of the Fifth International Congress on Mathematical Education, Unesco, Adelaide, South Australia, pp. 352–358.

    Google Scholar 

  • Dubinsky, E. and Harel, G.: 1992, ‘The nature of the process conception of function’, in G. Harel and E. Dubinsky (eds. ), The concept of function: Aspects of Epistemology and Pedagogy. Notes and Reports Series of the Mathematical Association of America, Vol. 25, 85–106.

  • Educational Studies in Mathematics: 2002, ‘Reflections on educational studies in mathematics: The rise of research in mathematics education’, Educational Studies in Mathematics 50, 251–257.

    Article  Google Scholar 

  • Eisenhart, M.: 1996, ‘The production of biologists at school and work: Making scientists, conservationists, or flowery boneheads’, in B. A. Levinson, D. E. Foley and D. C. Holland (eds. ), The Cultural Production of the Educated Person: Critical Ethnographies of Schooling and Local Practice, SUNY Press, Albany, New York, pp. 169–185.

    Google Scholar 

  • Ensor, P.: 2001, ‘From preservice mathematics teacher education to beginning teaching: a study in recontextualizing’, Journal for Research in Mathematics Education 32, 296–320.

    Google Scholar 

  • Even, R.: 1993, ‘Subject matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept’, Journal for Research in Mathematics Education 24, 94–116.

    Article  Google Scholar 

  • Frykholm, J. A.: 1998, ‘Beyond supervision: Learning to teach mathematics in community’, Teaching and Teacher Education 14(3), 305–322.

    Article  Google Scholar 

  • Frykholm, J. A.: 1999, ‘The impact of reform: Challenges for mathematics teacher preparation’, Journal of Mathematics Teacher Education 2(1), 79–105.

    Article  Google Scholar 

  • Glickman, C. D. and Bey, T. M.: 1990, ‘Supervision’, in W. R. Houston (ed. ), Handbook of Research on Teacher Education, Macmillan, New York, pp. 549–566.

    Google Scholar 

  • Greeno, J. G.: 1997, ‘On claims that answer the wrong question’, Educational Researcher 26(1), 5–17.

    Article  Google Scholar 

  • Greeno, J. G.: 1998, ‘Where is teaching?’, Issues in Education: Contributions from Cognitive Psychology 4(1), 111–119.

    Google Scholar 

  • Greeno, J. G.: 2003, ‘Situatiave research relevant to standards for school mathematics’, in J. Kilpatrick, W. G. Martin and D. Schifter (eds. ), A Research Companion to Principles and Standards for School Mathematics, National Council of Teachers of Mathematics, Reston, Virginia, pp. 304–332.

    Google Scholar 

  • Greeno, J. G., Collins, A. M. and Resnick, L. B.: 1996, ‘Cognition and learning’, in D. Berliner and R. Calfee (ed. ), Handbook of Educational Psychology, Macmillan, New York, pp. 15–46.

    Google Scholar 

  • Greeno, J. G. and MMAP: 1998, ‘The situativity of knowing, learning, and research’, American Psychologist 53(1), 5–26.

    Article  Google Scholar 

  • Grossman, P. L., Valencia, S., Evans, K., Thompson, C., Martin, S. and Place, N.: 2000, ‘Transitions into teaching: Learning to teach writing in teacher education and beyond’, Journal of Literary Research 32, 631–662.

    Article  Google Scholar 

  • Grossman, P. L., Wilson, S. M. and Shulman, L. S.: 1989, ‘Teachers of substance: Subject matter knowledge for teaching’, in M. Reynolds (ed. ), Knowledge Base for the Beginning Teacher, Pergamon, New York, pp. 23–36.

    Google Scholar 

  • Hanna, G.: 1990, ‘Some pedagogical aspects of proof’, Interchange 21(1), 6–13.

    Article  Google Scholar 

  • Hanna, G.: 1991, ‘Mathematical proof’, in D. Tall (ed. ), Advanced Mathematical Thinking, Kluwer Academic Publishers, Netherlands, pp. 54–61.

    Google Scholar 

  • Harel, G. and Dubinsky, E.: 1993, The Concept of Function: Aspects of Epistemology and Pedagogy, Mathematical Association of America, Washington, D. C.

    Google Scholar 

  • Holland, D., Lachicotte, W., Skinner, D. and Cain, C.: 1998, Identity and Agency in Cultured Worlds, Harvard University Press, Cambridge, MA.

    Google Scholar 

  • Knowles, J. G.: 1992, ‘Models for understanding pre-service and beginning teachers' biographies: Illustrations from case studies’, in I. F. Goodson (ed. ), Studying Teachers' Lives, Teachers' College Press, New York, pp. 99–152.

    Google Scholar 

  • Knuth, E. J.: 2002, ‘Secondary school mathematics teachers' conceptions of proof’, Journal for Research in Mathematics Education 33, 379–405.

    Google Scholar 

  • Lakatos, I.: 1976, Proofs and Refutations: The Logic of Mathematical Discovery, Cambridge University Press, Cambridge, UK.

    Google Scholar 

  • Lampert. M.: 2001, Teaching Problems and the Problems of Teaching, Yale University Press, New Haven.

    Google Scholar 

  • Lampert, M.: 1990, ‘When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching’, American Educational Research Journal 27, 29–63.

    Article  Google Scholar 

  • Lampert, M.: 1985, ‘How do teachers manage to teach? Perspectives on problems in practice’, Harvard Educational Review 55, 178–194.

    Google Scholar 

  • Lampert. M. and Blunk, M. L.: 1998, Talking Mathematics in School: Studies of Teaching and Learning, Cambridge University Press, Cambridge, UK.

    Google Scholar 

  • Lave, J.: 1988, Cognition in Practice, Cambridge University Press, Cambridge, UK.

    Google Scholar 

  • Lave, J. and Wenger, E.: 1991, Situated Learning: Legitimate Peripheral Participation, Cambridge University Press, Cambridge, UK.

    Google Scholar 

  • Leinhardt, G., Zaslavsky, O. and Stein, M. K.: 1990, ‘Functions, graphs, and graphing: Tasks, learning, and teaching’, Review of Educational Research 60(1), 1–64.

    Article  Google Scholar 

  • Lo, J. J., Wheatley, G. H. and Smith, A. C.: 1994, ‘The participation, beliefs, and development of arithmetic meaning of a third-grade student in mathematics class discussions’, Journal for Research in Mathematics Education 25(1), 30–49.

    Article  Google Scholar 

  • Lloyd, G. and Wilson, M.: 1998, ‘Supporting innovation: The impact of a teacher's conceptions of functions on his implementation of a reform curriculum’, Journal for Research in Mathematics Education 29(3), 248–274.

    Article  Google Scholar 

  • Luttrell, W.: 1996, ‘Becoming somebody in and against school: Toward a psychocultural theory of gender and self-making’, in B. A. Levinson, D. E. Foley and D. C. Holland (eds. ), The Cultural Production of the Educated Person: Critical Ethnographies of Schooling and Local Practice, SUNY Press, Albany, New York, pp. 93–117.

    Google Scholar 

  • Maher, C. and Martino, A.: 1996, ‘The development of the idea of mathematical proof: A 5-year case study’, Journal for Research in Mathematics Education 27(2), 194–214.

    Article  Google Scholar 

  • Martin, W. G. and Harel, G.: 1989, ‘Proof frames of preservice elementary teachers’, Journal for Research in Mathematics Education 20(1), 41–51.

    Article  Google Scholar 

  • McLaughlin, M. and Talbert, J. E.: 1993, Contexts That Matter for Teaching and Learning: Strategic Opportunities for Meeting the Nation's Educational Goals, Stanford University, Center for Research on the Context of Secondary School Teaching, Stanford, CA.

    Google Scholar 

  • Mehan, H.: 1979, Learning Lessons, Harvard University Press, Cambridge.

    Google Scholar 

  • National Council of Teachers of Mathematics: 1989, Curriculum and Evaluation Standards for School Mathematics, Author, Reston, VA.

    Google Scholar 

  • National Council of Teachers of Mathematics: 1991, Professional Standards for Teaching Mathematics, Author, Reston, VA.

    Google Scholar 

  • National Council of Teachers of Mathematics: 1995, Assessment Standards for School Mathematics, Author, Reston, VA.

    Google Scholar 

  • National Council of Teachers of Mathematics: 2000, Principles and Standards for School Mathematics, Author, Reston, VA.

    Google Scholar 

  • Nespor, J.: 1994, Knowledge in Motion, The Falmer Press, Bristol, PA.

    Google Scholar 

  • Peressini, D., Borko, H., Romagnano, L., Yorker, C., Wooley, C., Hovermill, J. and Mas-arik, K.: 2001, ‘The transition from student teacher to first-year teacher: A situative view of learning to teach secondary mathematics’, Paper presented at the Annual Meeting of the American Educational Research Association, Seattle.

  • Peressini, D. and Knuth, E.: 1998, ‘Why are you talking when you could be listening? The role of discourse in the professional development of mathematics teachers’, Teaching and Teacher Education 14(1), 107–125.

    Article  Google Scholar 

  • Pimm, D.: 1987, Speaking Mathematically, Routledge Press, London.

    Google Scholar 

  • Putnam, R. and Borko, H.: 2000, ‘What do new views of knowledge and thinking have to say about research on teacher learning?’, Educational Researcher 29(1), 4–15.

    Article  Google Scholar 

  • Richards, J.: 1991, ‘Mathematical discussions’, in E. von Glasersfeld (ed. ), Radical Constructivism in Mathematics Education, Kluwer Academic Publishers, Netherlands, pp. 13–51.

    Google Scholar 

  • Romberg, T., Carpenter, T. and Fennema, E.: 1993, ‘Toward a common research perspective’, in T. Romberg, E. Fennema and T. Carpenter (eds. ), Integrating Research on the Graphical Representation of Functions, Lawrence Erlbaum Associates, Hillsdale, New Jersey, pp. 1–9.

    Google Scholar 

  • Schoenfeld, A.: 1992, ‘Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics’, in D. A. Grouws (ed. ), Handbook of Research on Mathematics Teaching and Learning, Macmillan, New York, pp. 334–370.

    Google Scholar 

  • Schoenfeld, A.: 1994, ‘What do we know about mathematics curricula?’, Journal of Mathematical Behavior 13(1), 55–80.

    Article  Google Scholar 

  • Schoenfeld, A. H.: 1998, ‘Toward a theory of teaching-in-context’, Issues in Education: Contributions from Cognitive Psychology 4(1), 1–94.

    Google Scholar 

  • Schoenfeld, A. H.: 1999, ‘Dilemmas/decisions: Can we model teachers' on-line decision making?’, Paper presented at the Annual Meeting of the American Educational Research Association, Montreal.

  • Shulman, L. S.: 1986, ‘Those who understand: Knowledge growth in teaching’, Educational Researcher 15(2), 4–14.

    Article  Google Scholar 

  • Silver, E. and Smith, M.: 1996, ‘Building discourse communities in mathematics classrooms: A worthwhile but challenging journey’, in P. Elliott and M. Kenney (eds. ), Communication in Mathematics: K-12 and Beyond, NCTM, Reston, VA, pp. 20–28.

    Google Scholar 

  • Simon, M. and Blume, G.: 1996, ‘Justification in the mathematics classroom: A study of prospective elementary teachers’, Journal of Mathematical Behavior 15(1), 3–31.

    Article  Google Scholar 

  • Thompson, P. W.: 1991, ‘The development of the concept of speed and its relationship to concepts of rate’, in F. Harel and J. Confrey (eds. ), The Development of Multiplicative Reasoning in the Learning of Mathematics, SUNY Press, New York.

  • Thompson, P. W. and Thompson, A. G.: 1996, ‘Talking about rates conceptually, Part II: Mathematical knowledge for teaching’, Journal for Research in Mathematics Education 27(1), 2–24.

    Article  Google Scholar 

  • Voigt, J.: 1995, ‘Thematic patterns of interaction and sociomathematical norms’, in P. Cobb and H. Bauersfeld (eds. ), The Emergence of Mathematical Meaning, Lawrence Erlbaum Associates, Hillsdale, New Jersey, pp. 163–201.

    Google Scholar 

  • Wheeler, D.: 1990, ‘Aspects of mathematical proof’, Interchange 21(1), 1–5.

    Article  Google Scholar 

  • Wineburg, S. and Grossman, P.: 1998, ‘Creating a community of learners among high school teachers’, Phi Delta Kappan 79, 350–353.

    Google Scholar 

  • Yackel, E. and Cobb, P.: 1996, ‘Sociomathematical norms, argumentation and autonomy in mathematics’, Journal for Research in Mathematics Education 27(4), 458–477.

    Article  Google Scholar 

  • Zeichner, K. and Tabachnick, B.: 1981, ‘Are the effects of university teacher education washed out by school experience?’, Journal of Teacher Education 32, 7–11.

    Google Scholar 

  • Zeichner, K., Tabachnick, B. and Densmore, K.: 1987, ‘Individual, institutional, and cultural influences on the development of teachers' craft knowledge’, in J. Calderhead (ed. ), Exploring Teachers' Thinking, Cassell, London, pp. 21–59.

    Google Scholar 

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Peressini, D., Borko, H., Romagnano, L. et al. A Conceptual Framework for Learning to Teach Secondary Mathematics: A Situative Perspective. Educational Studies in Mathematics 56, 67–96 (2004). https://doi.org/10.1023/B:EDUC.0000028398.80108.87

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