Mathematics teachers' Topic-Specifi pedagogical Content knowledge in the context of teaching å 0! and a / 0

Kuram ve Uygulamada Egitim Bilimleri

Volumn 10, Issue 2, 2010, Pages 749-769

  Cankoy, Osman ^a  

^a Ataturk Teacher Training Academy   (Cyprus)

Author keywords

Mathematics Teachers; Teaching Zero; Topic Specifi Pedagogical Content Knowledge

Indexed keywords

EID: 77952226352     PISSN: 13030485     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (73)

1. Adey, P. & Shayer, M. J. (1994). Really raising standards. London: Routledge.
2. An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school mathematics teachers in China and the United States. Journal of Mathematics Teachers Education, 7, 145-172.
3. Arsham, H. (2008). Zero in four dimensions: Historical, psychological, cultural and logical. Retrieved December 17, 2008, from http://www.pantaneto.co. uk/issue5/arsham.html.
4. Ball, D. (1990). Prospective elementary and secondary teachers' understanding of division. Journal for Research in Mathematics Education, 21(2), 132-144.
5. Ball, D. L. & Bass, H. (2000). Interweaving content an pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.), Multiple perspectives on the teaching and learning of mathematics (pp.83-104). Westport, CT: Ablex.
6. Ball, D. L., Hill, H. H., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Mathematical Educator, Fall, 14-46.
7. Baturo, A. & Nason, R. (1996) Student teachers' subject matter knowledge within the domain of area measurement. Educational Studies in Mathematics, 31, 235-268.
8. Bolyard, J. J. & Packenham, P. S. (2008). A review of the literature on mathematics and science teacher quality. Peabody Journal of Education, 83, 509-535.
9. Boyer, C. B. (1968). A history of mathematics. New York: John Wiley & Sons.
10. Brickhouse, N. W. (1990). Teachers' beliefs about the nature of science and their relationship to classroom practice. Journal of Teacher Education, 41(3), 53-62.
11. Burton, M., Daane, C. T., & Giesen, J. (2008). Infusing math content into a methods course: Impacting content knowledge for teaching. Issues in the Undergraduate Mathematics Preparation of School Teachers: The Journal, 1 (Content Knowledge). Retrieved January 20, 2009, from http://www.k-12prep.math. ttu.edu.
12. Chinnappan, M. & Lawson, M. J. (2005). A framework for analysis of teachers' geometric content knowledge and geometric knowledge for teaching. Journal of Mathematics Teacher Education, 8, 197-221.
13. Clark, C. M. & Peterson, P. L. (1986). Teachers' thought processes. In M. C. Wittrock (Ed.), Handbook of research on teaching (3rd Edt., pp. 255-296). New York: Macmillan.
14. Clarke, B. (1995). Expecting the unexpected: Critical incidents in the mathematics classrooms. Unpublished doctoral dissertation, University of Wisconsin-Madison.
15. Cooney, T. & Wiegel, H. (2003). Examing the mathematics in mathematics teacher education. In A. Bishop et al. (Eds.), Second international handbook of mathematics education (pp. 795-828). Dordrecht: Kluwer Academic Publishers.
16. Çakmak M. 1999). Novice and Experienced Teachers' Strategies for Mathematics Teaching in English and Turkish Primary Classrooms. Unpublished doctoral thesis, Leicester University, England.
17. Davis, P. J. & Hersch, R. (1981). The mathematical experience. London: Penguin Books.
18. Eisenhart, M., Borko, H., Underhill, R., Brown, A., Jones, D., & Agard, P. (1993). Conceptual knowledge falls through the cracks: Complexities of learning to teach mathematics for understanding. Journal for Research in Mathematics Education, 24(1), 8-40.
19. Even, R. & Tirosh, D. (1995). Subject-matter knowledge and knowledge about the students as sources of teacher presentations of the subject-matter. Educational Studies in Mathematics, 29, 1-20.
20. Eves, H. (1983). Great moments in mathematics before 1650. Washington, DC: The Mathematical Association of America.
21. Fawns, R. & Nance, D. (1993). Teacher knowledge, education studies and advanced skills credentials. Australian Journal of Education, 37, 248-258.
22. Fennema, E., & Franke, M. L. (1992). Teacher's knowledge and its impact. In Douglas A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147-164). New York: Simon and Schuster Macmillan.
23. Fenstermacher, G. (1986). Philosophy of research on teaching: three aspects. In M. C. Wittrock (Ed.), Handbook of research on teaching (3rd Edt, pp. 37-49). New York: Macmillan.
24. Geddis, A. (1993). Transforming subject-matter knowledge: The role of pedagogical content knowledge in learning to refl ect on teaching. International Journal of Science Education, 15(6), 673-683.
25. Halpern, D. F. (1992). Enhancing thinking skills in the sciences and mathematics. London: Lawrence Erlbaum.
26. Hanushek, E. (1971). Teacher characteristics and gains in student achievement: Estimation using micro data. The American Economic Review, 61, 280-288.
27. Henry, B. (1969). Zero, the troublemaker. The Arithmetic Teacher, 16(5), 365-367
28. Hiebert, J. (1986). Conceptual and procedural knowledge: The case of mathematics. Hillsdale, NJ: Erlbaum.
29. Hill, H. C., Ball, D. L., & Schilling, S. C. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers' topic-specifi c knowledge of students. Journal for Research in Mathematics Education, 39(7), 372-400.
30. Hinton, P. R. (1996). Statistics explained. New York: Routledge.
31. Hitchinson, E. (1996). Pre-service teachers knowledge: A contrast of beliefs and knowledge of ratio and proportion. Unpublished doctoral thesis, University of Wisconsin-Madison.
32. Kaplan, R. (1999). The nothing that is: A natural history of zero. Oxford: Oxford University Press,
33. Lampert, M. (1988). The teacher's role in reinventing the meaning of mathematical knowing in the classroom. In M. J. Behr et al. (Eds.), Proceedings of the 10th Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 433-480). DeKalb, IL: Northern Illinois University
34. Lantz, C. A. & Nebenzahl, E. (1996). Behavior and interpretation of the kappa statistics: resolution of the two paradoxes. Journal of Clinical Epidemiology, 49, 431.
35. Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Erlbaum.
36. Magnusson, S., Krajcik, J., & Borko, H. (1999). Nature, sources, and development of pedagogical content knowledge for science teaching. In J. Gess-Newsome & N. Lederman (Eds.), Examining pedagogical content knowledge (pp. 95-132). Dordrecht: Kluwer.
37. Mason, J. & Spence, M. (1999). Beyond mere knowledge of mathematics: The importance of knowing-to act in the moment. Educational Studies in Mathematics, 38, 135-161.
38. Munby, H., Russel, T., & Martin, A. K. (2001). Teacher knowledge and how it develops. In V. Richardson (Ed.), Handbook of research on teaching (4th Edt., pp. 877- 904). Washington, DC: American Educational Research Association.
39. Nakiboǧlu, C. & Karakoç, Ö. (2005). The forth knowledge domain a teacher should have: The pedagogical content knowledge. Kuram ve Uygulamada Egitim Bilimleri/ Educational Sciences: Theory & Practice, 5(1), 201-206.
40. Nespor, J. (1987). The role of beliefs in the practice of teaching. Journal of Curriculum Studies, 19(4), 317-328.
41. Neubrand, J. (2006). The TIMSS 1995 and 1999 video studies: In search for appropriate units of analysis. In F. K. S. Leung, K. D. Graf, & F. J. Lopez-Real (Eds.), Mathematics education in diff erent cultural traditions: A comparative study of East Asia and the West. - The 13th ICMI Study (Vol. 9., pp. 291-318). Berlin, Heidelberg, New York: Springer.
42. Neubrand, M. (2008, March). Knowledge of teachers - knowledge of students: Conceptualizations and outcomes of a mathematics teacher education study in Germany. Paper presented at the Symposium on the Occasion of the 100th Anniversary of ICMI (Rome, March 5-8, 2008) Working Group 2: The professional formation of teachers, Carl-von-Ossietzky-University, Oldenburg, Germany.
43. Nickerson, R., Perkins, D., & Smith, E. (1985). The teaching of thinking. Hillsdale, NJ: Erlbaum.
44. Ore, O. (1988). Number theory and its history. New York: Dover Publications.
45. Pogliani, L., Randic, M., & Trinajstic, N. (1998). Much ado about nothing-an introductive inquiry about zero. International Journal of Mathematics Education, Science and Technology, 29(5), 729-744.
46. Potari, D., Zachariades, T., Christou, K., Kyriazis, G., & Pitta-Padazi, D. (2007). Teachers' mathematical and pedagogical awarness in calculus teaching. Proccedings of CERME 5, Larnaca, Cyprus.
47. Quinn, J. R., Lamberg, T. D., & Perrin, J. R. (2008). Teacher perceptions of division by zero. The Clearing House, 81(3), 101-104.
48. Reys, R. E. (1974). Division and zero-An area of needed research. The Arithmetic Teacher, 21(2), 153-156
49. Rowland, T., Huckstep, P., & Th waites, A. (2004). Refl ecting on prospective elementary teachers' mathematics content knowledge. In M. J. Høines and A. B. Fugelstad, (Eds.), Proceedings of the 28th International Group for the Psychology of Mathematics Education (Vol. 4, pp. 121-128). Bergen, Norway: Bergen University College.
50. Rowland, T., Huckstep, P., & Th waites, A. (2005). Elementary teachers' mathematical subject knowledge: The knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8, 255-281.
51. Sanders S. E. & Morris H. J. (2000). Exposing student teachers' content knowledge: Empowerment or debilitation? Educational Studies, 26(4), 397-408.
52. Schoenfeld, A. (1992). Learning to think mathematically. In D. A. Grouws (Ed.), Handbook of research in mathematics teaching and learning. New York: Macmillan.
53. Seife, C. (2000). Zero: The biography of a dangerous idea. Penguin: Harmondsworth.
54. Shavelson, R. J. & Webb, N. M. (1991). Generalizability theory: A primer. Thousand Oaks, CA: Sage.
55. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15, 4-14.
56. Shulman, L. S. (1987). Knowledge and teaching: Foundation of the new reform. Harvard Educational Review, 57(1), 1-22.
57. Spence, M. (1996). Psychologizing algebra: Case studies of knowing in the moment. Unpublished doctoral dissertation, University of Wisconsin-Madison.
58. Sternberg, R. J. (1994). Answering questions and questioning answers: Guiding children to intellectual excellence. Phi Delta Kappan, 76(2), 136-138.
59. Strauss, A. & Corbin, J. (1990). Basics of qualitative research. London, UK: Sage Publications.
60. Strauss, R. P. & Sawyer, E. A. (1986). Some new evidence on teacher and student competencies. Economics of Education Review, 5, 41-48.
61. Suryanarayan, E. R. (1996). The brahmagupta polynomials. Fibonacci Quart, 34, 30-39.
62. Swartz, R. J. & Parks, S. (1994). Infusing the teaching of critical and creative thinking into elementary instruction. Pacifi c Grove, CA: Critical Th inking Press & Software.
63. Tamir, P. (1988). Subject matter and related pedagogical knowledge in teacher education. Teaching and Teacher Education, 4(2), 99-110.
64. Tishman, S., Perkins, D., & Jay, E. (1995). The thinking classroom. Boston, MA: Allyn & Bacon.
65. Tobin, K. & Fraser, B. J. (1989). Barriers to higher-level cognitive learning in high school science. Science Education, 73(6), 659-682.
66. Tsamir, P., Sheff er, R. & Tirosh, D. (2000). Intuitions and undefi ned operations: The cases of division by zero. Focus on Learning in Mathematics, 22(1), 1-16.
67. Türnüklü, E. B. (2005). The relationship between pedagogical and mathematical content knowledge of pre-service mathematics teachers. Eurasian Journal of Educational Research, 21, 234-247.
68. Veal, W. R. & MaKinster, J. (1999). Pedagogical content knowledge taxonomies. Electronic Journal of Science Education, 3(4). Retrieved April 13, 2008, from http://www.unr.edu/homepage/crowther/ejse/vealmak.html.
69. Vorob'Ev, N. N. (1961). Fibonacci numbers. New York: Blaisdell.
70. Wells, D. (1997). The penguin dictionary of curious and interesting numbers. (Rev. ed.). London: Penguin Books.
71. Wilson, S. & Floden, R. E. (2003). Creating eff ective teachers: Concise answers for hard questions. An addendum to the report "Teacher Preparation Research: Current Knowledge, Gaps, and Recommendations." Denver, CO: Education Commission of the States. (ERIC Document Reproduction Service No. ED 476366)
72. Yildirim, A. & Şimsek, H. (2008). Sosyal bilimlerde nitel arastirma yöntemleri (7. basim). Ankara: Seçkin Yayinlari.
73. Zohar, A. (2004). Higher order thinking in science classrooms: Students' learning and teachers' professional development. Dordrecht: Kluwer Academic Press.