References

 

Abelson, R. (1979). Differences between belief systems and knowledge systems. Cognitive Science, 3, 355-366.

 

Aguirre, J. M., Haggerty, S. M., & Linder, C. J. (1990). Student-teachers' conceptions of science, teaching and learning: a case study in preservice science education. International Journal of Science Education, 12(4), 381-390.

 

Anderson, L. W. (1987). The classroom environment study: Teaching for learning. Comparative Education Review, 31(1), 69-87.

 

Anderson, L. W., & Postlethwaite, T. N. (1989). What IEA studies say about teachers and teaching. In A. C. Purves (Ed.), International comparisons and educational reform (pp. 73-86). Alexandria, VA: Association for Supervision and Curriculum Development. (ERIC Document Reproduction Service No. ED 316 494)

 

Arsac, G., Balacheff, N., & Mante, M. (1992). Teacher's role and reproducibility of didactical situations. Educational Studies in Mathematics, 23(1), 5-29.

 

Atlantic Provinces Education Foundation. (1996). Foundations for the Atlantic Canada mathematics curriculum. Halifax: Author.

 

Ball, D. L., & McDiarmid, G. W. (1990). The subject-matter preparation of teachers. In W. R. Houston (Ed.), Handbook of research on teacher education (pp. 437-449). New York: Macmillian.

 

Barnes, D. E. (1995). Secondary mathematics teachers interactions with technology [CD-ROM]. Abstract from: ProQuest File: Dissertation Abstracts Item: 9507195

 

Battista, M. T. (1994). Teacher beliefs and the reform movement in mathematics education. Phi Delta Kappan, 75(6), 462-463, 466-468, 470.

 

Beail, N. (1985). An introduction to repertory grid technique. In N. Beail (Ed.), Repertory grid technique and personal constructs (pp. 1-24). London: Croom Helm.

 

Bennett, A., Maier, E., & Nelson, L. T. (1988). Math and the mind's eye. Portland, OR: The Mathematics Learning Centre, Portland State University.

 

Berliner, D. C. (1986). In pursuit of the expert pedagogue. Educational Researcher, 15(7), 5-13.

 

Beyerbach, B. (1988). Developing a technical vocabulary on teacher planning: Preservice teachers' concept maps. Teaching & Teacher Education, 4(4), 339-347.

 

Beynon, J. (1985). Institutional change and career histories in a comprehensive school. In S. J. Ball, & I. F. Goodson (Eds.), Teachers' lives and careers (pp. 158-179).London: Falmer.

 

Bishop, A. (1985). The social construction of meaning - a significant development for mathematics education. For the Learning of Mathematics, 5(1), 24-28.

 

Black, P., & Atkin, J. M. (1996). Changing the subject. London: Routledge.

 

Blank, R. K., & Pechman, E. M. (1995). State curriculum frameworks in mathematics and science: How are they changing across the states?. Washington, DC: Council of Chief State School Officers. (ERIC Document Reproduction Service No. ED 387 356)

 

Bober, W. C., Lee, R., Martin, J. D., O'Shea, T., Sharp, J. N., Beattie, R. H., Bilous, F., Bright, B. D., Connelly, R. D., Drost, D. R., Hope, J. A., Lesage, J. W., & Tossell, S. (1988). Journeys in math 9. Toronto: Ginn.

 

Bogdan, R. C., & Biklen, S. K. (1992). Qualitative research for education: An introduction to theory and methods (2nd ed.). Boston: Allyn & Bacon.

 

Brophy, J., & Good, T. L. (1986). Teacher behavior and student achievement. In M. C. Wittrock (Ed.), Handbook of research on teaching: Third edition (pp.328-375). New York: Macmillian.

 

Bromme, R., & Steinbring, H. (1994). Interactive development of subject matter in the mathematics classroom. Educational Studies in Mathematics, 27(3), 217-248.

 

Brown, C. A., & Borko, H. (1992). Becoming a mathematics teacher. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 209-239). New York: MacMillan.

 

Brown, S. I., Cooney, T. J., & Jones, D. (1990). Mathematics teacher education. In W. R. Houston (Ed.), Handbook of research on teacher education (pp. 639-656). New York: MacMillan.

 

Butt, R., Raymond, D., McCue, G., & Yamagishi, L. (1992). Collaborative autobiography and the teacher's voice. In I. F. Goodson (Ed.), Studying teachers' lives (pp. 51-98). New York: Teachers College Press.

 

Butt, R. L., Raymond, D., & Townsend, D. (1990, April). Speculations on the nature and facilitation of teacher developments as derived from teachers' stories. Paper presented at the American Educational Research Association Conference, Boston. (ERIC Document Reproduction Service No. ED 325 450)

 

Campbell, C. E. (1985). Variables which influence student teacher behavior: Implications for teacher education. Alberta Journal of Educational Research, 31(4), 258-269.

 

Carnap, R., Heyting, A., & Von Neumann, J. (1983). Symposium on the foundations of mathematics. In P. Benacerraf, & H. Putnam (Eds.), Philosophy of mathematics (2nd ed.) (pp. 41-65). Cambridge: Cambridge University Press.

 

Carroll, L. (1954). Alice's adventures in wonderland and through the looking glass. London: J. M. Dent & Sons.

 

Center for Science, Mathematics, and Engineering Education. (1996). Mathematics and science education around the world: What can we learn?. Washington, DC: National Research Council.

 

Clandinin, J., & Connelly, F. M. (1987). Teachers' personal knowledge: What counts as 'personal' in studies of the personal. Journal of Curriculum Studies, 19(6), 487-500.

 

Clark, C. M. (1988). Teacher preparation: Contributions of research on teacher thinking. Educational Researcher, 17(2), 5-12.

 

Clarke, D. M. (1997). The changing role of the mathematics teacher. Journal for Research in Mathematics Education, 28(3), 278-308.

 

Cobb, P. (1988). The tension between theories of learning and instruction in mathematics education. Educational Psychologist, 23(2), 87-103.

 

Cobb, P., Wood, T., & Yackel, E. (1990). Classrooms as learning environments for teachers and researchers. In R. Davis, C. Maher, & N. Noddings (Eds.), Constructivist views on the teaching and learning of mathematics (pp. 125-146). Reston, VA: National Council of Teachers of Mathematics.

 

Cohen, D. K. (1990). A revolution in one classroom: The case of Mrs. Oublier. Educational Evaluation and Policy Analysis, 12(3), 311-329.

 

Cohen, P. J. (1971). Comments on the foundations of set theory. In D. S. Scott (Ed.), Axiomatic set theory: Proceedings of symposia in pure mathematics, volume XIII, part I (pp. 9-15). Providence, RI: American Mathematical Society.

 

Colgan, L. E. C., & Harrison, P. J. (1997). Achieving excellence in secondary mathematics: Scarborough review of grade 12 mathematics 1995/96 cohort: Interpretations, recommendations and a plan for action. Scarborough, ON: Scarborough Board of Education.

 

Connelly, F. M., & Clandinin, D. J. (1984). Personal practical knowledge at Bay Street School: Ritual, personal philosophy and image. In R. Halkes & J. Olson (Eds.), Teacher thinking: A new perspective on persisting problems in education (pp. 134-148). Lisse: Swets & Zeitlinger.

 

Cooney, T. J. (1985). A beginning teacher's view of problem solving. Journal of Research in Mathematics Education, 16(5), 324-336.

 

Crocker, R. K. (1983). The functional paradigms of teachers. Canadian Journal of Education, 8(4), 350-361.

 

Cronbach, L. J. (1975). Beyond the two disciplines of scientific psychology. American Psychologist, 30, 116-127.

 

Crosswhite, F. J. (1987). The second international mathematics study: A look at U.S. classrooms. In I. Wirszup & R. Streit (Eds.), Developments in school mathematics education around the world (pp. 62-82). Reston, VA: National Council of Teachers of Mathematics.

 

Davis, P. J., & Hersh, R. (1981). The mathematical experience. Boston: Birkhauser.

 

Day, R. P. (1993). Emerging and evolving themes: Three case studies of preservice mathematics teachers' beliefs. (Volumes I and II) [CD-ROM]. Abstract from: ProQuest File: Dissertation Abstracts Item: 9328330

 

Denzin, N. K. (1989). Interpretive biography. Newbury Park, CA: Sage.

 

Dewey, J. (1910). How we think. Boston: D. C. Heath.

 

Donmoyer, R. (1990). Generalizability and the single-case study. In E. W. Eisner, & A. Peshkin (Eds.), Qualitative inquiry in education: The continuing debate (pp. 175-200). New York: Teachers College Press.

 

Dorgan, K. (1994). Teachers' orientations toward teaching, learning, and mathematics: Three teachers' decisions concerning the implementation of a revised elementary mathematics curriculum [CD-ROM]. Abstract from: ProQuest File: Dissertation Abstracts Item: 9415594

 

Easterby-Smith, M. (1981). The design, analysis and interpretation of repertory grids. In Mildred L. G. Shaw (Ed.), Recent advances in personal construct technology (pp. 9-30). London: Academic Press.

 

Edwards, T. G. (1994). Looking for change in teaching practice in a mathematics curriculum innovation project: Three case studies [CD-ROM]. Abstract from: ProQuest File: Dissertation Abstracts Item: 9427703

 

Eilenberger, G. (1986). Freedom, science, and aesthetics. In H.-O. Peitgen, & P. H. Richter (Eds.), The beauty of fractals: Images of complex dynamical systems (pp. 175-180). Berlin: Springer-Verlag.

 

Elbaz, F. (1981). The teacher's "practical knowledge": Report of a case study, Curriculum Inquiry, 11(1), 43-71.

 

Elbaz, F. (1991). Research on teacher's knowledge: The evolution of a discourse. Journal of Curriculum Studies, 23(1), 1-19.

 

Erickson, T. (1989). Get it together: Math problems for groups, grades 4-12. Berkeley, CA: EQUALS.

 

Ernest, P. (1989a). The knowledge, beliefs and attitudes of the mathematics teacher: A model. Journal of Education for Teaching, 15(1), 13-33.

 

Ernest, P. (1989b). The impact of beliefs on the teaching of mathematics. In P. Ernest (Ed.), Mathematics teaching: The state of the art (pp.249-254). London: Falmer.

 

Ernest, P. (1991). The philosophy of mathematics education. London: Falmer.

 

Ernest, P. (1992). The nature of mathematics: Towards a social constructivist account. Science & Education, 1(1), 89-100.

 

Euclid. (1956). The thirteen books of Euclid's elements (2nd ed. rev.). New York: Dover.

 

Fennema, E., & Franke, M. L. (1992). Teachers' knowledge and its impact. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147-164). New York: Macmillan.

 

Fennema, E., & Peterson, P. L. (1986). Teacher-student interactions and sex-related differences in learning mathematics. Teaching & Teacher Education, 2(1), 19-42.

 

Ferrell, M. J. (1995). How three instructors' conceptions about mathematics and mathematics teaching relate to their instructional practices [CD-ROM]. Abstract from: ProQuest File: Dissertation Abstracts Item: 9530203

 

Fey, J. T. (1979). Mathematics teaching today: Perspectives from three national surveys. Mathematics Teacher, 72(7), 490-504.

 

Flores, A., Sowder, J. T., Philipp, R. A., & Schappelle, B. P. (1995). Orchestrating, promoting, and enhancing mathematical discourse in the middle grades: A case study. In J. T. Sowder, & B. P. Schappelle (Eds.), Providing a foundation for teaching mathematics in the middle grades (pp. 275-299). Albany, NY: SUNY Press.

 

Galbraith, P. L. (1984). Attitudes to mathematics of beginning undergraduates and prospective teachers: Some implications for education. Higher Education, 13, 675-685.

 

Grossman, P. L. (1991). What are we talking about anyway? Subject-matter knowledge of secondary English teachers. In J. Brophy (Ed.), Advances in research on teaching, Volume 2 (pp. 245-264). Greenwich, CT: JAI.

 

Grossman, P. L., & Stodolsky, S. S. (1995). Content as context: The role of school subjects in secondary school teaching. Educational Researcher, 24(8), 5-11,23.

 

Grossman, P. L., Wilson, S. M., & Shulman, L. S. (1989). Teachers of substance: Subject matter knowledge for teaching. In M. C. Reynolds (Ed.), Knowledge base for the beginning teacher (pp. 23-36). New York: Pergamon.

 

Guba, E. G., & Lincoln, Y. S. (1981). Effective evaluation. San Francisco: Jossey-Bass.

 

Hargreaves, A. (1992). Cultures of teaching: A focus for change. In A. Hargreaves, & M. G. Fullan (Eds.), Understanding teacher development (pp. 216-240). New York: Teachers College Press.

 

Hargreaves, A., Davis, J., Fullan, M., Wignall, R., Stager, M., & Macmillan, R. (Eds.). (1992). Secondary school work cultures and educational change. Toronto: Ontario Institute for Studies in Education.

 

Hargreaves, A., Wignall, R., & Macmillan, R. (1992). Background to the study. In A. Hargreaves, J. Davis, M. Fullan, R. Wignall, M. Stager, & R. Macmillan (Eds.), Secondary school work cultures and educational change (pp. 3-20). Toronto: Ontario Institute for Studies in Education.

 

Heaton, R. M. (1992). Who is minding the mathematics content? A case study of a fifth-grade teacher. Elementary School Journal, 93(2), 153-162.

 

Hersh, R. (1979). Some proposals for revising the philosophy of mathematics. Advances in Mathematics, 31, 31-50.

 

Hewson, P. W., & Hewson, M. G. (1989). Analysis and use of a task for identifying conceptions of teaching science. Journal of Education for Teaching, 15(3), 191-209.

 

Hoyles, C. (1988). From fragmentation to synthesis: An integrated approach to research on the teaching of mathematics. In D. A. Grouws, & T. J. Cooney (Eds.), Perspectives on research on effective mathematics teaching: Volume 1 (pp. 143-168). Reston, VA: National Council of Teachers of Mathematics.

 

Hubbard, J. H. (Project Director), Smith, H. W., & Staller, J. E. (Producers). (1988). Nothing but zooms [videotape]. Ithaca, NY: Art Matrix.

 

Jackson, A. (1997). The math wars: California battles it out over mathematics education reform (Part I). Notices of the American Mathematical Society, 44(6), 695-702.

 

Kant, I. (1934). Critique of pure reason (J. M. D. Meiklejohn, Trans.). London: J. M. Dent & Sons. (Original work published 1787)

 

Kelchtermans, G., & Vandenberghe, R. (1995, August). Vulnerability and power: The political dimension in teachers' professional development. Paper presented at the 7th Bi-annual Conference of the International Study Association on Teacher Thinking, St. Catharines, Ontario.

 

Kelly, G. (1955). The psychology of personal constructs. New York: Norton.

 

Kesler, R. Jr. (1985). Teachers' instructional behavior related to their conceptions of teaching and mathematics and their level of dogmatism: Four case studies. Unpublished doctoral dissertation, University of Georgia, Athens.

 

Kieren, T. E. (1995). Creating spaces for learning fractions. In J. T. Sowder, & B. P. Schappelle (Eds.), Providing a foundation for teaching mathematics in the middle grades (pp. 31-65). Albany, NY: SUNY Press.

 

Kilbourn, B. (1992). Philosophical, subject matter and classroom understandings: A case of history teaching. In T. Russell & H. Munby (Eds.), Teachers and teaching: From classroom to reflection (71-89). London: Falmer Press.

 

Kilpatrick, J. (1992). A history of research in mathematics education. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 3-38). New York: Macmillan.

 

Kitchener, K. S. (1986). The reflective judgment model: Characteristics, evidence, and measurement. In R. A. Mines & K. S. Kitchener (Eds.), Adult cognitive development: Methods and models (pp. 76-91). New York: Praeger.

 

Kleene, Stephen Cole. (1950). Introduction to metamathematics. Princeton, NJ: Van Nostrand.

 

Kline, M. (1980). Mathematics the loss of certainty. Oxford: Oxford University Press.

 

Koehler, M. S., & Grouws, D. A. (1992). Mathematics teaching practices and their effects. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 115-126). New York: Macmillan.

 

Krulik, S., & Rudnick, J. A. (1985). Developing problem-solving skills. Mathematics Teacher, 78(9), 685-692, 696-698.

 

Lakatos, I. (1976). Proofs and refutations. Cambridge: Cambridge University Press.

 

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(1), 29-63.

 

Lapointe, A. E., Mead, N. A., & Askew, J. M. (1992). Leaning mathematics. Princeton, NJ: Educational Testing Service.

 

Lederman, N. G., & Zeidler, D. L. (1987). Science teachers' conceptions of the nature of science: Do they really influence teaching behavior? Science Education, 71(5), 721-734.

 

Leinhardt, G. (1989). Math lessons: A contrast of novice and expert competence. Journal for Research in Mathematics Education, 20(1), 52-75.

 

Lerman, S. (1983). Problem-solving or knowledge-centred: the influence of philosophy on mathematics teaching. International Journal of Mathematical Education in Science and Technology, 14(1), 59-66.

 

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.

 

Lewin, K. (1935). A dynamic theory of personality: Selected papers (Donald K. Adams & Karl E. Zener, Trans.). New York: McGraw-Hill.

 

Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic inquiry. Beverly Hills, CA: Sage.

 

Lindquist, M. M., Dossey, J. A., & Mullis I. V. S. (1995). Reaching standards: A progress report on mathematics. Princeton, NJ: Educational Testing Service. (ERIC Document Reproduction Service No. ED 390 644)

 

Lo, J.-J., & Wheatley, G. H. (1994). Learning opportunities and negotiating social norms in mathematics class discussion. Educational Studies in Mathematics, 27(2), 145-164.

 

MacLane, Saunders. (1986). Mathematics form and function. New York: Springer-Verlag.

 

Mathematically Correct. (1996). What is changing in math education? [On-line]. Available: http://ourworld.compuserve.com/homepages/mathman/what.html

 

Mathison, S. (1988). Why triangulate?. Educational Researcher, 17(2), 13-17.

 

McGalliard, W. A. Jr. (1983). Selected factors in the conceptual systems of geometry teachers: Four case studies (Doctoral dissertation, University of Georgia, 1982). Dissertation Abstracts International, 44, 1363A.

 

McGlamery, S. L. (1994). Teacher learning, curriculum change, and the culture of mathematics classrooms [CD-ROM]. Abstract from: ProQuest File: Dissertation Abstracts Item: 9332309

 

McKinney, K. (1986). How the experts teach: Research in brief. Washington, DC: Office of Educational Research and Improvement, U.S. Department of Education. (ERIC Document Reproduction Service No. ED 280 681)

 

McLean, L. D., Wolfe, R., & Wahlstrom, M. (1987). Learning about teaching from comparative studies: Ontario mathematics in international perspective. Toronto: Queen's Printer for Ontario.

 

McLeod, D. B., Stake, R. E., Schappelle, B. P., Mellissinos, M., & Gierl, M. J. (1996). Setting the Standards: NCTM's role in the reform of mathematics education. In S. A. Raizen , & E. D. Britton (Eds.), Bold ventures: Volume 3: Case studies of U.S. innovations in mathematics education (pp. 13-130). Dordrecht, The Netherlands: Kluwer.

 

Mead, G. H. (1934). Mind, Self and Society. Chicago: University of Chicago Press.

 

Merriam, S. B. (1988). Case study research in education: A qualitative approach. San Francisco: Jossey-Bass.

 

Miller, T. L., Duffy, S. E., & Zane, T. (1993). Improving the accuracy of self-corrected mathematics homework. Journal of Educational Research, 86(3), 184-189.

 

Miles, M. B., & Huberman, A. M. (1984a). Drawing valid meaning from qualitative data: Toward a shared craft. Educational Researcher, 13(5), 20-30.

 

Miles, M., & Huberman, A. (1984b). Qualitative data analysis: A sourcebook of new methods. Beverly Hills, CA: Sage.

 

Miwa, T. (1987). Mathematics in junior and senior high school in Japan: Present state and prospects. In I. Wirszup & R. Streit (Eds.), Developments in school mathematics education around the world (pp. 172-224). Reston, VA: National Council of Teachers of Mathematics.

 

Morine-Dershimer, G. (1991). Tracing conceptual change in preservice teachers. Teaching & Teacher Education, 9(1), 15-26.

 

Mullis, I. (1992). NAEPfacts: Trends in school and home contexts for learning. Washington, DC: National Centre for Education Statistics. (ERIC Document Reproduction Service No. ED 353 330)

 

Munby, H. (1982). The place of teachers' beliefs in research on teacher thinking and decision making, and an alternative methodology. Instructional Science, 11(3), 201-225.

 

Mura, R. (1993). Images of mathematics held by university teachers of mathematical sciences. Educational Studies in Mathematics, 25, 375-385.

 

Mura, R. (1995). Images of mathematics held by university teachers of mathematics education. Educational Studies in Mathematics, 28(4), 385-399.

 

National Council of Teachers of Mathematics [NCTM]. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.

 

National Council of Teachers of Mathematics [NCTM]. (1991). Professional standards for teaching mathematics. Reston, VA: Author.

 

National Council of Teachers of Mathematics [NCTM]. (1995). Assessment standards for school mathematics. Reston, VA: Author.

 

National Council of Teachers of Mathematics [NCTM]. (1996). Voices of change in mathematics education. Reston, VA: Author.

 

Nespor, J. (1987). The role of beliefs in the practice of teaching. Journal of Curriculum Studies, 19, 317-328.

 

Noddings, N.(1992). Professionalization and mathematics teaching. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 197-208). New York: Macmillan.

 

Novak, J. D., & Gowin, D. B. (1984). Learning how to learn. Cambridge: Cambridge University Press.

 

Nowak, R. S. (1987). Periodic pictures. Mathematics Teacher, 80(2), 126-137.

 

O'Brien, M. J. (1995). Changing a school mathematics program: A ten year study [CD-ROM]. Abstract from: ProQuest File: Dissertation Abstracts Item: 9524593

 

Ontario Association for Mathematics Education [OAME]/ Ontario Mathematics Coordinators Association [OMCA]. (1993). Focus on renewal of mathematics education. Markham, Ontario: OAME.

 

Ontario Association for Mathematics Education [OAME]/ Ontario Mathematics Coordinators Association [OMCA]. (1995). Linking assessment and instruction in mathematics: Connecting to the Ontario Provincial Standards: Transition years. Rosseau, Ontario: OAME.

 

Ontario Ministry of Education. (1985). Curriculum guideline: Mathematics: Intermediate and senior divisions. Toronto: Queen's Printer for Ontario.

 

Ontario Ministry of Education. (1991a). Mathematics grade 10 (general level): A report card for Ontario. Toronto: Queen's Printer for Ontario.

 

Ontario Ministry of Education. (1991b). Mathematics grade 12 (advanced level): A report card for Ontario. Toronto: Queen's Printer for Ontario.

 

Ontario Ministry of Education. (1992a). Mathematics grade 10 (general level): A report for educators. Toronto: Queen's Printer for Ontario.

 

Ontario Ministry of Education. (1992b). Mathematics grade 12 (advanced level): A report for educators. Toronto: Queen's Printer for Ontario.

 

Pajares, M. F. (1992). Teachers' beliefs and educational research: Cleaning up a messy construct. Review of Educational Research, 62(3), 307-332.

 

Polanyi, M. (1958). Personal knowledge. London: Routledge & Kegan Paul.

 

Paulos, J. A. (1991). Beyond numeracy: Ruminations of a numbers man. New York: Alfred A. Knopf.

 

Peitgen, H.-O., & Richter, P. H. (1986). The beauty of fractals: Images of complex dynamical systems. Berlin: Springer-Verlag.

 

Penrose, R. (1989). The emperor's new mind. London: Oxford University Press.

 

Perry, W. G. Jr. (1981). Cognitive and ethical growth: The making of meaning. In A. W. Chickering (Ed.), The modern American college (pp. 76-116). San Francisco: Jossey-Bass.

 

Philipp, R. A., Flores, A., Sowder, J. T., & Schappelle, B. P. (1994). Conceptions and practices of extraordinary mathematics teachers. Journal of Mathematical Behavior, 13(2), 155-180.

 

Philipp, R. A., Sowder, J. T., Flores, A., & Schappelle, B. P. (1995). A responsible mathematics teacher and the choices she makes: A case study. In J. T. Sowder, & B. P. Schappelle (Eds.), Providing a foundation for teaching mathematics in the middle grades (pp. 301-326). Albany, NY: State University of New York Press.

 

Plato. (1953). Meno. In B. Jowett (Trans.), The dialogues of Plato (4th ed.) (Vol. 1, pp 265-301). Oxford: Clarendon.

 

Pope, A. (1733/1846). An essay on man. Hartford: S. Andrus & Son.

 

Pope, M. L., & Scott, E. M. (1984). Teachers' epistemology and practice. In R. Halkes, & J. K. Olson (Eds.), Teacher thinking: a new perspective on persisting problems in education (pp. 112-122). Lisse: Swets & Zeitlinger.

 

Popper, K. R. (1959). The logic of scientific discovery. London: Hutchinson.

 

Prawat, R. S. (1992). Are changes in views about mathematics teaching sufficient? The case of a fifth-grade teacher. Elementary School Journal, 93(2), 195-211.

 

Putnam, R. T. (1992). Teaching the "hows" of mathematics for everyday life: A case study of a fifth-grade teacher. Elementary School Journal, 93(2), 163-177.

 

Rav, Y. (1993). Philosophical problems of mathematics in the light of evolutionary epistemology. In Sal Restivo, J. P. Van Bendegen, & R. Fisher (Eds.), Math worlds: Philosophical and social studies of mathematics and mathematics education (pp. 80-109). Albany, NY: SUNY Press.

 

Raymond, A. M. (1993). Understanding relationships between beginning elementary teachers' mathematics beliefs and teaching practices [CD-ROM]. Abstract from: ProQuest File: Dissertation Abstracts Item: 9404352

 

Raymond, A. M. (1997). Inconsistency between a beginning elementary school teacher's mathematics beliefs and teaching practice. Journal for Research in Mathematics Education, 28(5), 550-576.

 

Remillard, J. (1992). Teaching mathematics for understanding: A fifth-grade teacher's interpretation of policy. Elementary School Journal, 93(2), 179-193.

 

Riseborough, G. F. (1985). Pupils, teachers' careers and schooling: An empirical study. In S. J. Ball, & I. F. Goodson (Eds.), Teachers' lives and careers (pp. 202-265).London: Falmer.

 

Robitaille, D. F., Taylor, A. R., & Orpwood, G. (1996). The TIMSS-Canada report: Volume 1: Grade 8. Vancouver, Canada: Department of Curriculum Studies, University of British Columbia.

 

Rogers, W. T. (1990). Non-cognitive data: A cross-national perspective. In I. Westbury & K. Travers (Eds.), Second International Mathematics Study: Studies (pp. 191-213). Urbana. IL: College of Education, University of Illinois at Urbana-Champaign. (ERIC Document Reproduction Service No. Ed 325 360)

 

Romberg, T. A. (1992a). Further thoughts on the standards: A reaction to Apple. Journal for Research in Mathematics Education, 23(5), 432-437.

 

Romberg, T. A. (1992b). Toward a world class curriculum in the United States. In I. Wirzup & R. Streit (Eds.), Developments in school mathematics education around the world: Volume three (pp. 223-235). Reston, VA: National Council of Teachers of Mathematics.

 

Romberg, T. A., & Carpenter, T. P. (1986). Research on teaching and learning mathematics: Two disciplines of scientific enquiry. In M. C. Wittrock (Ed.), Handbook of research on teaching (3rd ed.) (pp. 850-873). New York: Macmillan.

 

Rose, A. M. (1962). A systematic summary of symbolic interaction theory. In A. M. Rose (Ed.), Human behavior and social processes: An interactionist approach (pp. 3-19). Boston: Houghton Mifflin.

 

Roulet, G. (1995). Student-teachers' conceptions of mathematics: What they are and how they are formed. In M. Quigley (Ed.), Canadian Mathematics Education Study Group/ Groupe Canadian D'Etude Didactique des Mathématiques: Proceedings, 1994 Annual Meeting. (pp. 131-139). Calgary: University of Calgary.

 

Schifter, D., & Fosnot, C. (1993). Reconstructing mathematics education: Stories of teachers meeting the challenge of reform. New York: Teachers College Press.

 

Schoenfeld, A. H. (1988). When good teaching leads to bad results: The disasters of "well-taught" mathematics courses. Educational Psychologist, 23(2), 145-166.

 

Schoenfeld, A. H. (1989). Explorations of students' mathematical beliefs and behavior. Journal for Research in Mathematics Education, 20(4), 338-355.

 

Schoenfeld, A. H. (1994). A discourse on methods. Journal for Research in Mathematics Education, 25(6), 697-710.

 

Schofield, J. (1990). Increasing the generalizability of qualitative research. In E. W. Eisner, & A. Peshkin (Eds.), Qualitative inquiry in education: The continuing debate (pp. 201-232). New York: Teachers College Press.

 

Schwab, J. (1964). Structure of the disciplines: Meanings and significances. In G. W. Ford & L. Pugno (Eds.), The structure of knowledge and the curriculum (pp. 6-30). Chicago: Rand McNally.

 

Schwartz, J. L. (1989). Intellectual mirrors: A step in the direction of making schools knowledge-making places. Harvard Educational Review, 59(1), 51-61.

 

Secada, W. G., & Byrd, L. (1993). School-level reform and teaching/learning of mathematics. NCRMSE Research Review, 2(2), 5-8. (ERIC Document Reproduction Service No. ED370770)

 

Seidman, I. E. (1991). Interviewing as qualitative research. New York: Teachers College Press.

 

Shaw, M. (1990). RepGrid [computer program]. Calgary: Centre for Person-Computer Studies.

 

Shealy, B. E. (1995). Conceptualizing the development of two first-year secondary mathematics teachers' beliefs [CD-ROM]. Abstract from: ProQuest File: Dissertation Abstracts Item: 9520868

 

Shulman, L. S. (1970). Psychology and mathematics education. In E. G. Begle (Ed.), Mathematics education: The sixty-ninth yearbook of the National Society for the Study of Education: Part 1 (pp. 23-71). Chicago: University of Chicago Press.

 

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

 

Shulman, L. S. (1987a). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-22.

 

Shulman, L. S. (1987b). Assessment for teaching: An initiative for the profession. Phi Delta Kappan, 69(1), 38-44.

 

Shulman, L. S. (1988). Disciplines of inquiry in education: An overview. In R. M. Jaeger (Ed.), Complementary methods for research in education (pp. 3-17). Washington, DC: American Educational Research Association.

 

Sikes, P. J. (1985). The life cycle of the teacher. In S. J. Ball, & I. F. Goodson (Eds.), Teachers' lives and careers (pp. 27-60).London: Falmer.

 

Simon, M. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114-145).

 

Siskin, L. S. (1991). Departments as different worlds: Subject subcultures in secondary schools. Educational Administration Quarterly, 27(2), 134-160.

 

Siskin, L. S. (1994). Realms of knowledge: Academic departments in secondary schools. Washington, DC: Falmer.

 

Spradley, J. P. (1980). Participant observation. Fort Worth, TX: Holt, Rinehart and Winston.

 

Stanic, G. M. A., & Kilpatrick, J. (1989). Historical perspectives on problem solving in the mathematics curriculum. In Randall I. Charles, & Edward A. Silver (Eds.), The teaching and assessing of mathematical problem solving (pp. 1-22). Reston, VA: National Council of Teachers of Mathematics/Lawrence Erlbaum Associates.

 

Steen, L. A. (1988). The science of patterns. Science, 240, 611-616.

 

Stein, J., et al. (Eds.). (1967). The Random House dictionary of the English language. New York: Random House.

 

Stewart, J., Davison, T. M. K., Hamilton, O. M. G., Laxton, J., Lenz, M. P. (1988). Finite mathematics. Toronto: McGraw-Hill Ryerson.

 

Stodolsky, S. S. (1993). A framework for subject matter comparisons in high school. Teaching and Teacher Education, 9, 333-346.

 

Thom, R. (1973). Modern mathematics: Does it exist? In A. G. Howson (Ed.), Developments in mathematics education: Proceedings of the second international congress on mathematical education (pp. 194-209). Cambridge: Cambridge University Press.

 

Thomas, L., & Harri-Augstein, S, (1985). Teaching and learning as the negotiation pf personal meaning. In N. Beail (Ed.), Repertory grid technique and personal constructs (pp. 256-274). London: Croom Helm.

 

Thompson, A. (1984). The relationship of teachers' conceptions of mathematics and mathematics teaching to instructional practice. Educational Studies in Mathematics, 15(2), 105-127.

 

Thompson, A. (1992). Teachers' beliefs and conceptions: A synthesis of the research. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127-146). New York: Macmillan.

 

Thompson, A. (1992, August). The public image of mathematics and mathematics education reform. Paper presented at the Seventh International Congress of Mathematics Education, Quebec City, Canada.

 

Underhill, R. G. (1988). Focus on research into practice in diagnostic and prescriptive mathematics: Mathematics teachers' beliefs: Review and reflections. Focus on Learning Problems in Mathematics, 10(3), 43-58.

 

Van Begdegem, J. P. (1993). Foundations of mathematics or mathematical practice: Is one forced to chose? In S. Restivo, J. P. Van Bendegen, & R. Fisher (Eds.), Math worlds: Philosophical and social studies of mathematics and mathematics education (pp. 21-38). Albany, NY: SUNY Press.

 

Walker, R. (1980). The conduct of educational case studies: Ethics, theory and procedures. In W. B. Dockrell & D. Hamilton (Eds.), Rethinking educational research (pp. 30-63). London: Hodder & Stoughton.

 

Weiss, I. R. (1994). A profile of science and mathematics education in the United States: 1993. Chapel Hill, NC: Horizon Research, Inc. (ERIC Document Reproduction Service No. ED 377 058)

 

Whimbey, A., & Lochhead, J. (1979). Problem solving and comprehension: A short course in analytic reasoning. Philadelphia: Franklin Institute Press.

 

Wilson, M. R. (1994). One preservice secondary teacher's understanding of function: The impact of a course integrating mathematical content and pedagogy. Journal for Research in Mathematics Education, 25(4), 346-370.

 

Wilson, S. M., & Wineburg, S. S. (1988). Peering at history through different lenses: The role of disciplinary perspectives in teaching history. Teachers College Record, 89(4), 525-539.

 

Wood, T., Cobb, P., & Yackel, E. (1991). Change in teaching mathematics: A case study. American Educational Research Journal, 28(3), 587-616.

 

Woods, D. (Ed.). (1985). PS news, 36(Jan.-Feb.). Hamilton, ON: Department of Chemical Engineering, McMaster University.

 

Yackel, E., Cobb, P., & Wood, T. (1991). Small-group interactions as a source of learning opportunities in second-grade mathematics. Journal for Research in Mathematics Education, 22(5), 390-408.

 

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