Re-thinking teachers' mathematical knowledge: A focus on thinking practices

Perspectives in Education

Volumn 22, Issue 1, 2004, Pages 65-80

  Brodie, Karin ^a,b  

^a UNIVERSITY OF THE WITWATERSRAND   (South Africa)

^b STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2942631351     PISSN: 02582236     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Review

References (55)

1. Adler J & Reed Y (eds) 2002. Challenges of teacher development: An investigation of take-up in South Africa. Pretoria: Van Schaik.
2. Ball DL 1993. With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. The Elementary School Journal, 93(4), 373-397.
3. Ball DL 1996. Teacher learning and the mathematics reforms: what we think we know and what we need to learn. Phi Delta Kappan, 77, 500-508.
4. Ball DL 1997. What do students know? Facing challenges of distance, context and desire in trying to hear children. In Biddle BJ, Good TL & Goodson IF (eds). The international handbook of teachers and teaching. Dordrecht: Kluwer.
5. Ball D L & Bass H 2000. Interweaving context and pedagogy in teaching and learning to teach: Knowing and using mathematics. In Boaler J (ed.). Multiple perspectives on teaching and learning mathematics. Westport, CT: Ablex.
6. Ball DL, Lubienski ST & Mewborn DS 2001. Research on teaching mathematics: the unsolved problem of teachers' mathematical knowledge. In Richardson V (ed.). Handbook of research on teaching (4th edition). New York: MacMillan, 433-456.
7. Ben-Zeev T 1996. When erroneous mathematical thinking is just as correct: The oxymoron of rational erros. In Sternberg RJ & Ben-Zeev T (eds). The nature of mathematical thinking. Mahwah, NJ: Lawrence Erlbaum Associates, 55-79.
8. Ben-Zeev T 1998. Rational errors and the mathematical mind. Review of General Psychology, 2(4), 366-383.
9. Bernstein B 1996. Pedagogy, symbolic control and identity: Theory, research, critique. London: Taylor and Francis.
10. Boaler J 1997. Experiencing school mathematics: Teaching styles, sex and setting. Buckingham: Open University Press.
11. Boaler J 1998. Open and closed mathematics: Student experiences and understandings. Journal for Research in Mathematics Education, 29(1), 41-62.
12. Boaler J 2001. Opening the dimensions of mathematical capability: the development of knowledge, practice, and identity in mathematics classrooms. Paper presented at the Psychology of Mathematics Education, North America, 23, Snowbird, Utah.
13. Boaler J & Greeno JG 2000. Identity, agency and knowing in mathematics worlds. In Boaler J (ed.). Multiple perspectives on mathematics teaching and learning. Westport, CT: Ablex.
14. Brodie K, Lelliott T & Davis H 2002. Developing learner-centred practices through the FDE programme. In Adler J & Reed Y (eds). Challenges of teacher development: an investigation of take-up in South Africa. Pretoria: Van Schalk.
15. Brown JS, Collins A & Duguid P 1989. Situated Cognition and the culture of teaming. Educational Researcher, 18(1), 32-42.
16. Chazan D & Ball DL 1999. Beyond being told not to tell. For the Learning of Mathematics, 19(2), 2-10.
17. Chung S & Walsh DJ 2000. Unpacking child-centredness: A history of meanings. Journal of curriculum studies, 32, 215-234.
18. Confrey J 1990. A review of research on student conceptions in mathematics, science and programming. In Cazden CB (ed.). Review of research in education, Vol. 16. Washington: American Educational Research Association, 3-56.
19. Darling J 1994. Child-centred education and its critics. London: Paul Chapman.
20. Erlwanger SH 1973. Benny's conceptions of rules and answers in IPI mathematics. Journal of Children's Mathematical Behaviour, 1(2), 7-26.
21. Goldman S V & Greeno JG 1998, Thinking practices: Images of thinking and learning in education. In Greeno J & Goldman S (eds). Thinking practices in mathematics and science learning. Mahwah, New Jersey: Lawrence Erlbauro, 1-13.
22. Greeno JG & Goldman SV (eds) 1998. Thinking practices in mathematics and science learning. Mahweh, NJ: Erlbaum.
23. Hatano G 1996. A conception of knowledge acquisition and its implications for mathematics education. In Steffe P, Nesher P, Cobb P, Goldin G & Greer B (eds). Theories of mathematical learning. New Jersey: Lawrence Erlbaum.
24. Heaton R 2000. Teuching mathematics to the new standards: Releaming the dance. New York: Teachers' College Press.
25. Hickey DT, Moore AL & Pelligrino JW 2001. The motivational and academic consequences of elementary mathematics environments: Do constructivist innovations and reforms make a difference? American Educational Research Journal, 38(3), 611-652.
26. Hiebert J (ed) 1986. Conceptual and procedural knowledge: the case of mathematics. Hillsdale, NJ: Lawrence Erlbaram Associates.
27. Hiebert J & Lefevre P 1986. Conceptual and procedural knowledge in mathematics: an introductory analysis. In Hieebert J (ed.). Conceptual and procedural knowledge: The case of mathematics. Hillsdale, NJ: Lawrence Erlbaum, 1-27.
28. Hiebert J & Wearne D 1986. Procedures over concepts: the acquisition of decimal number knowledge. In Hiebert J (ed.). Conceptual and procedural knowledge: The case of mathematics. Hillsdale, NJ: Lawrence Erlbaum, 199-223.
29. Kilpatrick J, Swafford J & Findell B (eds.) 2001. Adding it up: Helping children learn mathematics. Washington DC: National Academy Press.
30. Kirshner D & Whitson J (eds) 1997. Situated cognition: Social, Semiotic and Psychological perspectives. Mahwah, NJ: Lawrence Erlbaum Associates.
31. 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.
32. Lampert M 2001. Teaching problems and the problems of teaching. New Haven: Yale University Press.
33. Lave J 1988. Cognition in practice. Cambridge: Cambridge University Press.
34. Lave J 1993. Situating Learning in Communities of Practice. In Resnick LB, Levine JM & Teasley SD (eds). Perspectives on Socially Shared Cognition. Washington, DC: American Psychological Association.
35. Lave J 1996. Teaching, as learning, in practice. Mind Culture and Activity, 3(3), 149-164.
36. Lave J & Wenger E 1991. Situated learning: Legitimate peripheral participation. Cambridge: Cambridge University Press.
37. Mason J, Burton L & Stacey K 1982. Thinking mathematically. London: Addison-Wesley.
38. RAND Mathematics Study Panel 2002. Mathematical proficiency for all students: Towards a strategic research and development program in mathematics education (DRU-2773-OERI). Arlington, VA: RAND Education, Science and Technology Policy Institute.
39. Sasman M, Linchevski L, Olivier A & Liebenberg R 1998. Probing children's thinking in the process of generalisation. Paper presented at the Fourth Annual Congress of the Association for Mathematics Education of South Africa (AMES A). Pietersburg.
40. Schoenfeld AH 1988. When good teaching leads to bad results: The disasters of 'well-taught' mathematics courses. Educational Psychologist, 23(2), 145-166.
41. Schoenfeld AH 2002. Making mathematics work for all children: Issues of standards, testing, and equity. Educational Researcher, 31(1), 13-25.
42. Shulman LS 1986. Those who understand: knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
43. Shulman LS 1987. Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-22.
44. Shulman LS 2003. Personal communication.
45. Silver EA & Stein MK 1996. The Quasar project: The "revolution of the possible" in mathematics instructional reform in urban middle schools. Urban Education, 30(4), 476 - 521.
46. Skemp R 1976. Relational understanding and instrumental understanding. Mathematics Teaching, (77), 20-26.
47. Smith JP, DiSessa AA & Roschelle J 1993. Misconceptions reconceived: a constructivist analysis of knowledge in transition. The Journal of the Learning Sciences, 3(2), 115-163.
48. Stigler JW & Hiebert J 1999. The teaching gap: Best ideas from the world's teachers for improving education in the classroom. New York: Free Press.
49. Taylor N & Vinjevold P (eds) 1999. Getting learning right: Report of the President's Education Initiative Research Project. Johannesburg: Joint Education Trust.
50. Thompson AG & Thompson PW 1996. Talking about rates conceptually, part II: mathematical knowledge for teaching. Journal for Research in Mathematics Education, 27(1), 2-24.
51. Tirosh D, Even R & Robinson N 1998. Simplifying algebraic expressions: Teacher awareness and teaching approaches. Educational Studies in Mathematics, 35, 51-64.
52. Vygotsky LS 1978. Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.
53. Vygotsky LS 1986. Thought and language. Cambridge, MA: MIT Press.
54. Walkerdine V 1984. Developmental psychology and the child-centred pedagogy: The insertion of Piaget into early education. In Henriques J, Holloway W, Urwin C, Venn C & Walkerdine V (eds). Changing the subject: Social regulation and subjectivity. London: Methuen.
55. Wenger E 1998. Communities of practice: Learning, meaning and identity. Cambridge: Cambridge University Press.