Connecting Beliefs and Practices: A Fine-Grained Analysis of a College Mathematics Teacher's Collections of Beliefs and Their Relationship to His Instructional Practices

REFERENCES

• Aguirre , J. M. and Speer , N. 1999 . Examining the relationship between beliefs and goals in teacher practice . Journal for Mathematical Behavior , 18 ( 3 ) : 327 – 356 .
   Google Scholar
• Ball , D. L. 1988 . Unlearning to teach mathematics . For the Learning of Mathematics , 8 ( 1 ) : 40 – 48 .
   Google Scholar
• Ball , D. L. , Lubienski , S. and Mewborn , D. S. 2001 . “ Research on teaching mathematics: The unsolved problem of teachers' mathematical knowledge ” . In Handbook of research on teaching , Edited by: Richardson , V. 433 – 456 . Washington, DC : American Educational Research Association .
   Google Scholar
• Begle , E. G. 1979 . Critical variables in mathematics education: Findings from a survey of the empirical literature , Washington, DC : Mathematical Association of American and National Council of Teachers of Mathematics .
   Google Scholar
• Borko , H. and Putnam , R. T. 1996 . “ Learning to teach ” . In Handbook of educational psychology , Edited by: Berliner , D. C. and Calfee , R. C. 673 – 708 . New York : Macmillan Library Reference USA: Simon & Schuster Macmillan .
   Google Scholar
• Bullough , R. V. , Knowles , J. G. and Crow , N. A. 1991 . Emerging as a teacher , London : Routledge .
   Google Scholar
• Calderhead , J. 1996 . “ Teachers: Beliefs and knowledge ” . In Handbook of educational psychology , Edited by: Berliner , D. C. and Calfee , R. C. 709 – 725 . New York : Macmillan Library Reference USA: Simon & Schuster Macmillan .
   Google Scholar
• Calderhead , J. and Robson , M. 1991 . Images of teaching: Student teachers' early conceptions of classroom practice . Teaching and Teacher Education , 7 : 1 – 7 .
   Web of Science ®Google Scholar
• Carpenter , T. , Fennema , E. and Franke , M. 1996 . Cognitively guided instruction: A knowledge base for reform in primary mathematics instruction . The Elementary School Journal , 97 ( 1 ) : 3 – 20 .
   Web of Science ®Google Scholar
• Carpenter , T. , Fennema , E. , Peterson , P. , Chiang , C. and Loef , M. 1989 . Using knowledge of children's mathematics thinking in classroom teaching: An experimental study. American . Educational Research Journal , 26 ( 4 ) : 499 – 531 .
   Google Scholar
• Clark , C. M. and Peterson , P. L. 1986 . “ Teachers' thought processes ” . In Handbook of research on teaching, , 3rd ed. , Edited by: Wittrock , M. C. 255 – 296 . New York : Macmillan .
   Google Scholar
• Cobb , P. , Wood , T. and Yackel , E. 1990 . “ Classrooms as learning environments for teachers and researchers ” . In Constructivist views on the teaching and learning of mathematics, vol. 4 , Edited by: Davis , R. , Maher , C. and Noddings , N. 125 – 146 . Reston, VA : National Council of Teachers of Mathematics .
   Google Scholar
• Cohen , D. K. 1990 . A revolution in one classroom: The case of Mrs. Oublier . Educational Evaluation and Policy Analysis , 12 ( 3 ) : 327 – 345 .
   Google Scholar
• Cuban , L. 1982 . Persistent instruction: The high school classroom, 1900–1980 . Phi Delta Kappan , 64 ( 10 ) : 113 – 118 .
   Google Scholar
• Cuban , L. 1990 . Reforming again, again, and again. . Educational Researcher , 19 ( 1 ) : 3 – 13 .
   Google Scholar
• Darling-Hammond , L. 1990 . Instructional policy into practice: “The power of the bottom over the top”. . Educational Evaluation and Policy Analysis , 12 ( 3 ) : 339 – 347 .
   Google Scholar
• Dick , B. 2000 . Grounded theory: A thumbnail sketch http://www.scu.edu.au/schools/gcm/ar/arp/grounded.html available at
   Google Scholar
• diSessa , A. , Elby , A. and Hammer , D. 2002 . “ J's epistemological stance and strategies ” . In Intentional conceptual change , Edited by: Sinatra , G. and Pintrich , P. 237 – 290 . Mahwah, NJ : Lawrence Erlbaum Associates .
   Google Scholar
• Ernest , P. 1985 . The philosophy of mathematics and mathematics education . International Journal of Mathematics Education, Science, and Technology , 16 ( 5 ) : 603 – 612 .
   Google Scholar
• Ernest , P. The impact of beliefs on the teaching of mathematics . Paper presented at the ICME VI . Budapest, Hungary.
   Google Scholar
• Ernest , P. 1989 . The knowledge, beliefs and attitudes of the mathematics teacher: A model . Journal of Education for Teaching , 15 ( 1 ) : 13 – 33 .
   Web of Science ®Google Scholar
• Fennema , E. , Carpenter , T. , Franke , M. , Levi , L. , Jacobs , V. R. and Empson , S. B. 1996 . A longitudinal study of learning to use children's thinking in mathematics Instruction . Journal for Research in Mathematics Education , 27 ( 4 ) : 403 – 434 .
   Web of Science ®Google Scholar
• Fennema , E. and Scott Nelson , B. , eds. 1997 . Mathematics teachers in transition , Mahwah, New Jersey : Lawrence Erlbaum Associates .
   Google Scholar
• Franke , M. , Carpenter , T. , Fennema , E. , Ansell , E. and Behrend , J. 1998 . Understanding teachers' self-sustaining, generative change in the context of professional development . Teaching and Teacher Education , 14 : 1 – 14 .
   Google Scholar
• Franke , M. , Carpenter , T. , Levi , L. and Fennema , E. 2001 . Capturing teachers' generative change: A follow-up study of professional development in mathematics . American Educational Research Journal. , 38 : 653 – 689 .
   Web of Science ®Google Scholar
• Franke , M. , Fennema , E. and Carpenter , T. 1997 . “ Teachers creating change: Examining evolving beliefs and classroom practice ” . In Mathematics teachers in transition , Edited by: Fennama , E. and Scott Nelson , B. 255 – 282 . Mahwah, New Jersey : Lawrence Erlbaum Associates .
   Google Scholar
• Franke , M. and Kazemi , E. 2001 . Learning to teach mathematics: Focus on student thinking . Theory into Practice , 40 ( 2 ) : 102 – 109 .
   Web of Science ®Google Scholar
• Frederiksen , J. R. , Sipusic , M. , Sherin , M. G. and Wolfe , E. 1998 . Video portfolio assessment: Creating a framework for viewing the functions of teaching. . Educational Assessment , 5 ( 4 ) : 225 – 297 .
   Google Scholar
• Fullilove , R. E. and Treisman , P. U. 1990 . Mathematics achievement among African American undergraduates at the University of California, Berkeley: An evaluation of the Mathematics Workshop Program . Journal of Negro Education , 59 ( 3 ) : 463 – 478 .
   Google Scholar
• Glaser , B. 1992 . Basics of grounded theory analysis: Emergence vs. forcing , Mill Valley, CA : Sociology Press .
   Google Scholar
• Glaser , B. and Strauss , A. 1967 . The discovery of grounded theory , Chicago : Aldine .
   Google Scholar
• Green , T. F. 1971 . The activities of teaching , New York : McGraw-Hill Book Company .
   Google Scholar
• Grossman , P. L. 1992 . Why models matter: An alternate view on professional growth in teaching . Review of Educational Research , 62 ( 2 ) : 171 – 179 .
   Web of Science ®Google Scholar
• Guskey , T. R. 1986 . Staff development and the process of teacher change . Educational Researcher , 15 ( 5 ) : 5 – 12 .
   Google Scholar
• Kagan , D. M. 1992 . Professional growth among preservice and beginning teachers . Review of Educational Research , 62 ( 2 ) : 129 – 169 .
   Web of Science ®Google Scholar
• Kuhs , T. M. and Ball , D. 1986 . Approaches to teaching mathematics: Mapping the domains of knowledge, skills, and dispositions , East Lansing : Michigan State University, Center on Teacher Education .
   Google Scholar
• Leder , G. C. , Pehkonen , E. and Torner , G. , eds. 2002 . Beliefs: A hidden variable in mathematics education? (vol. 31) , Dordrecht/Boston/London : Kluwer Academic Publishers .
   Google Scholar
• Lerman , S. 1990 . Alternative perspectives of the nature of mathematics and their influence on the teaching of mathematics. . British Educational Research Journal , 16 ( 1 ) : 53 – 61 .
   Google Scholar
• McLeod , D. and McLeod , S. 2002 . “ Synthesis—beliefs and mathematics education: Implications for learning, teaching, and research ” . In Beliefs: A hidden variable in mathematics education?, vol. 31 , Edited by: Leder , G. C. , Pehkonen , E. and Torner , G. 115 – 126 . Dordrecht/Boston/London : Kluwer Academic Publishers .
   Google Scholar
• Nathan , M. , Knuth , E. and Elliot , R. Analytic and social scaffolding in the mathematics classroom: One teacher's changing practices . Paper presented at the annual meeting of the American Educational Research Association . 1998 , San Diego.
   Google Scholar
• NCTM . 1989 . Curriculum and evaluation standards for school mathematics , Reston, VA : The National Council of Teachers of Mathematics .
   Google Scholar
• NCTM . 1991 . Professional standards for teaching mathematics , Reston, VA : The Nation Council of Teachers of Mathematics .
   Google Scholar
• NCTM . 2000 . Principles and standards for school mathematics , Reston, VA : The National Council of Teachers of Mathematics .
   Google Scholar
• Pajares , M. F. 1992 . Teachers' beliefs and educational research: Cleaning up a messy construct . Review of Educational Research , 62 ( 3 ) : 307 – 332 .
   Web of Science ®Google Scholar
• Peterson , P. L. 1990 . Doing more in the same amount of time: Cathy Swift . Educational Evaluation and Policy Analysis , 12 ( 3 ) : 261 – 280 .
   Google Scholar
• Prawat , R. 1992 . Teachers' beliefs about teaching and learning a constructivist perspective . American Journal of Education , 100 ( 3 ) : 354 – 395 .
   Web of Science ®Google Scholar
• Richardson , V. 1996 . “ The role of attitudes and beliefs in learning to teach ” . In Handbook of educational psychology , Edited by: Berliner , D. C. and Calfee , R. C. New York : Macmillan Library Reference USA: Simon & Schuster Macmillan .
   Google Scholar
• Schifter , D. 1993 . Mathematics process as mathematics content: A course for teachers . Journal of Mathematical Behavior , 12 : 271 – 283 .
   Google Scholar
• Schifter , D. and Simon , M. A. 1992 . Assessing teachers' development of a constructivist view of mathematics learning . Teaching and Teacher Education , 8 ( 2 ) : 187 – 197 .
   Google Scholar
• Schoenfeld , A. H. 1998 . Toward a theory of teaching-in-context . Issues in Education , 4 ( 1 ) : 1 – 94 .
   Google Scholar
• Schoenfeld , A. H. 1999 . Models of the teaching process . Journal of Mathematical Behavior , 18 ( 3 ) : 243 – 261 .
   Google Scholar
• Schoenfeld , A. H. 2000 . Purposes and methods of research in mathematics education . Notices of the American Mathematical Society , 47 ( 6 ) : 641 – 649 .
   Google Scholar
• Schoenfeld , A. H. , Minstrell , J. and van Zee , E. The detailed analysis of an established teacher carrying out a non-traditional lesson . Paper presented at the annual meeting of the American Educational Research Association . April 8–12 1996 , New York.
   Google Scholar
• Schoenfeld , A. H. , Smith , J. P. I. and Arcavi , A. 1993 . “ Learning ” . In Advances in instructional psychology, vol. 4 , Edited by: Glaser , R. 55 – 175 . Hillsdale, NJ : Erlbaum .
   Google Scholar
• Scott Nelson , B. 1997 . “ Learning about teacher change in the context of mathematics education reform: Where have we come from? ” . In Mathematics teachers in transition , Edited by: Fennema , E. and Scott Nelson , B. 3 – 15 . Mahwah, NJ : Lawrence Erlbaum Associates .
   Google Scholar
• Sherin , M. 1996 . The nature and dynamics of teachers' content knowledge , Berkeley, CA : University of California, Berkeley .
   Google Scholar
• Sherin , M. 2002 . When teaching becomes learning . Cognition and Instruction , 20 ( 2 ) : 119 – 150 .
   Web of Science ®Google Scholar
• Simon , M. A. 1997 . “ Developing new models of mathematics teaching: An imperative for research on mathematics teacher development ” . In Mathematics teachers in transition , Edited by: Fennema , E. and Scott Nelson , B. 55 – 86 . Mahwah, NJ : Lawrence Erlbaum Associates .
   Google Scholar
• Skott , J. 2001 . The emerging practices of a novice teacher: The roles of his school mathematics images . Journal of Mathematics Teacher Education , 4 ( 1 ) : 3 – 28 .
   Google Scholar
• Smith , J. , Speer , N. and Horvath , A. The practice of teaching collegiate mathematics: An important but missing topic of research . Paper presented at the 10th Annual Conference on Research in Undergraduate Mathematics Education . San Diego, CA.
   Google Scholar
• Speer , N. 2005 . Issues of methods and theory in the study of mathematics teachers' professed and attributed beliefs . Educational Studies in Mathematics , 58 ( 3 ) : 361 – 391 .
   Google Scholar
• Speer , N. 2001 . Connecting beliefs and teaching practices: A study of teaching assistants in collegiate reform calculus courses , Berkeley, CA : University of California, Berkeley .
   Google Scholar
• Strauss , A. and Corbin , J. 1990 . Basics of qualitative research: Grounded theory procedures and techniques , Newbury Park, CA : Sage .
   Google Scholar
• Sykes , G. 1990 . Organizing policy into practice: Reactions to the cases . Educational Evaluation and Policy Analysis , 12 ( 3 ) : 349 – 353 .
   Google Scholar
• Thompson , A. 1985 . “ Teachers' conceptions of mathematics and the teaching of problem solving ” . In Teaching and learning mathematical problem solving: Multiple research perspectives , Edited by: Silver , E. 281 – 294 . Hillsdale : Lawrence Erlbaum Associates .
   Google Scholar
• Thompson , A. 1992 . “ Teachers' beliefs and conceptions: A synthesis of the research ” . In Handbook of research on mathematics teaching and learning , Edited by: Grouws , D. 127 – 146 . New York : Macmillan .
   Google Scholar
• Treisman , P. U. 1985 . A study of the mathematics performance of black students at the University of California, Berkeley , Berkeley : University of California . Unpublished doctoral dissertation
   Google Scholar
• Treisman , U. 1992 . Studying students studying calculus: A look at the lives of minority mathematics students in college . College Mathematics Journal , 23 ( 5 ) : 362 – 372 .
   Google Scholar
• VanLehn , K. and Brown , J. S. 1982 . Competitive argumentation in computational theories of cognition , Palo Alto, CA : Xerox Cognitive and Instructional Science Series . (No. CIS-14)
   Google Scholar
• Wiemers , N. J. 1990 . Transformation and accommodation: A case study of Joe Scott . Educational Evaluation and Policy Analysis , 12 ( 3 ) : 281 – 292 .
   Google Scholar
• Wilson , S. M. 1990 . A conflict of interests: The case of Mark Black . Educational Evaluation and Policy Analysis , 12 ( 3 ) : 293 – 310 .
   Google Scholar