Is the Role of Equations in the Doing of Word Problems in School Algebra Changing? Initial Indications From Teacher Study Groups

Cognition and Instruction

Volumn 30, Issue 1, 2012, Pages 1-38

  Chazan, Daniel ^a   Sela, Hagit ^a   Herbst, Patricio ^b  

^a UNIVERSITY OF MARYLAND   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84855930889     PISSN: 07370008     EISSN: None     Source Type: Journal    
DOI: 10.1080/07370008.2011.636593     Document Type: Article

References (78)

1. Balacheff, N. and Gaudin, N. 2010. Modeling students' conceptions: The case of function. Research in Collegiate Mathematics Education, 16: 183-211.
2. Bell, A. 1993. Some experiments in diagnostic teaching. Educational Studies in Mathematics, 24(1): 115-137.
3. Bellman, A., Bragg, S. C., Chapin, S. H., Gardella, T. J., Hall, B. C., Handlin, W. G. Sr. and Manfre, E. 1998. Algebra: Tools for a changing world, Teacher's Edition, Upper Saddle River, NJ: Prentice Hall.
4. Bicchieri, C. and Muldoon, R. 2011. "Social norms". In The Stanford encyclopedia of philosophy Edited by: Zalta, E. N. Retrieved from http://plato.stanford.edu/archives/spr2011/entries/social-norms/
5. Breslich, E. 1931. Problems in teaching secondary school mathematics, Chicago, IL: University of Chicago.
6. Brousseau, G. 1997. Theory of didactical situations in mathematics, Vol. 19, Dordrecht, DE: Kluwer.
7. Briars, D. J. and Larkin, J. H. 1984. An integrated model of skill in solving elementary word problems. Cognition and Instruction, 1(3): 245-296.
8. Carpenter, T. P., Fennema, E. and Franke, M. L. 1996. Cognitively guided instruction: A knowledge base for reform in primary mathematics instruction. The Elementary School Journal, 97(1): 3-20.
9. Carter, J., Cuevas, G., Casey, R., Day, R., Harris, B., Hayek, L. and Marks, D. 2003. Algebra 1, Columbus, OH: Glencoe/McGraw-Hill.
10. Center for Mathematics Education, Education Development Center. 2009. CME Project: Algebra I, New York, NY: Pearson.
11. Chapman, O. 2009. "Teachers' conceptions and use of mathematical contextual problems in Canada". In Words and worlds: Modelling verbal descriptions of situations, Edited by: Verschaffel, L., Greer, B. W., Dooren, Van and Mukhopadhyay, S. 227-244. Rotterdam, The Netherlands: Sense Publishers.
12. Chazan, D. 1993. F(x) = G(x)?: An approach to modeling with algebra. For the Learning of Mathematics, 13(3): 22-26.
13. Chazan, D. 2000. Beyond formulas in mathematics and teaching, New York, NY: Teachers College Press.
14. Chazan, D. and Hebst, P. 2012. Animations of classroom interaction: Expanding the boundaries of video records of practice. Teachers College Record, 114(3) Retrieved from http://www.tcrecord.org ID Number: 16319
15. Chazan, D. and Lueke, H. M. 2009. "Exploring tensions between disciplinary knowledge and school mathematics: Implications for reasoning and proof in school mathematics". In Teaching and learning mathematics proof across the grades, Edited by: Stylianou, D., Knuth, E. and Blanton, M. 21-39. Hillsdale, NJ: Erlbaum.
16. Chazan, D., Yerushalmy, M. and Leikin, R. 2008. An analytic conception of equation and teachers' views of school algebra. The Journal of Mathematical Behavior, 27(2): 87-100.
17. Cohen, D. and Hill, H. 2000. Instructional policy and classroom performance: The mathematics reform in California. The Teachers College Record, 102(2): 294-343.
18. Common Core State Standards Initiative. 2010. "Common Core State Standards for Mathematics". Retrieved from http://www.corestandards.org/
19. Cook, S. D. and Brown, J. S. 1999. Bridging epistemologies: The generative dance between organizational knowledge and organizational knowing. Organization Science, 10(4): 381-400.
20. Cuban, L. 1993. How teachers taught: Constancy and change in American classrooms 1890-1990, 2nd edition, New York, NY: Teachers College.
21. Dolciani, M. and Wooton, W. 1970. Modern algebra: Structure and method, Boston, MA: Houghton Mifflin.
22. Erickson, F. and Schultz, J. 1997. "When is a context? Some issues and methods in the analysis of social competence". In Mind, culture, and activity: Seminal papers from the laboratory of comparative human cognition, Edited by: Cole, M., Engestrom, Y. and Vasquez, O. 22-31. New York, NY: Cambridge University Press.
23. Ernest, P. 1991. The philosophy of mathematics education, London, UK: Falmer.
24. Gainsburg, J. 2009. "How and why secondary mathematics teachers make (or don't make) real-world connections in teaching". In Words and worlds: Modelling verbal descriptions of situations, Edited by: Verschaffel, L., Greer, B., Van Dooren, W. and Mukhopadhyay, S. 265-281. Rotterdam, The Netherlands: Sense Publishers.
25. Garfinkel, H. 1964. Studies of the routine grounds of everyday activities. Social Problems, 11(3): 225-250.
26. Gerofsky, S. 1996. A linguistic and narrative view of word problems in mathematics education. For the Learning of Mathematics, 16(2): 36-45.
27. Gerofsky, S. 2004. A man left Albuquerque heading east: Word problems as genre in mathematics education, New York, NY: Peter Lang.
28. Gravemeijer, K. 1997. Solving word problems: A case of modelling?. Learning and Instruction, 7(4): 389-397.
29. Greeno, J. G. and Goldman, S. V. 1998. Thinking practices in mathematics and science learning, Hillsdale, NJ: Lawrence Erlbaum.
30. Greer, B. 1997. Modelling reality in mathematics classrooms: The case of word problems. Learning and Instruction, 7(4): 293-307.
31. Grice, H. P. 1975. "Logic and conversation". In Syntax and semantics, Edited by: Cole, P. and Morgan, J. L. Vol. 3, 41-58. New York, NY: Academic Press.
32. Gutstein, E. 2006. Reading and writing the world with mathematics: Toward a pedagogy for social justice, New York, NY: Routledge.
33. Halliday, M. A. K. and Matthiessen, M. I. M. 2004. An introduction to functional grammar, 3rd edition, London, UK: Hodder Arnold.
34. Hall, R., Kibler, D., Wenger, W. and Truxan, C. 1989. Exploring the episodic structure of algebra story problem solving. Cognition and Instruction, 6(3): 223-283.
35. Herbst, P. G. 2002. Establishing a custom of proving in American school geometry: Evolution of the two-column proof in the early twentieth century. Educational Studies in Mathematics, 49(3): 283-312.
36. Herbst, P. G. 2006. Teaching geometry with problems: Negotiating instructional situations and mathematical tasks. Journal for Research in Mathematics Education, 37(4): 313-347.
37. Herbst, P. and Chazan, D. 2003. Exploring the practical rationality of mathematics teaching through conversations about videotaped episodes: The case of engaging students in proving. For the Learning of Mathematics, 23(1): 2-14.
38. Herbst, P. and Chazan, D. 2011. Research on practical rationality: Studying the justification of actions in mathematics teaching. The Montana Mathematics Enthusiast, 8(3): 405-462.
39. Herbst, P. and Kilpatrick, J. 1999. "Pour Lire" Brousseau. For the Learning of Mathematics, 19(1): 3-10.
40. Herbst, P. G., Nachlieli, T. and Chazan, D. 2011. Studying the practical rationality of mathematics teaching: What goes into "installing" a theorem in geometry?. Cognition and Instruction, 29(2): 1-38.
41. Herbst, P. and Miyakawa, T. 2008. When, how, and why prove theorems: A methodology to study the perspective of geometry teachers. ZDM-The International Journal on Mathematics Education, 40(3): 469-486.
42. Hill, H. C., Ball, D. L. and Schilling, S. G. 2008. Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers. Journal for Research in Mathematics Education, 39(4): 372-400.
43. Hinsley, D. A., Hayes, J. R. and Simon, H. A. 1976. "From words to equations: Meaning and representation in algebra word problems". In Cognitive processes in comprehension, Edited by: Just, M. A. and Carpenter, P. A. 89-106. Hillsdale, NJ: Lawrence Erlbaum.
44. Hymes, D. 1977. Foundations in sociolinguistics: An ethnographic approach, London, UK: Tavistock Publications.
45. Katz, V. J. 1997. Algebra and its teaching: An historical survey. Journal of Mathematical Behavior, 16(1): 25-38.
46. Koedinger, K. R., Alibali, M. W. and Nathan, M. J. 2008. Trade-offs between grounded and abstract representations: Evidence from algebra problem solving. Cognitive Science, 32(2): 259-457.
47. Lampert, M. 1985. How do teachers manage to teach? Perspectives on problems in practice. Harvard Educational Review, 55: 178-194.
48. Lemke, J. L. 1990. Talking science: Language, learning, and values, Westport, CT: Ablex Publishing Corporation.
49. Lester, F. K. Jr. 1994. Musings about mathematical problem-solving research: 1970-1994. Journal for Research in Mathematics Education, 25(6): 660-675.
50. Lesh, R. A. and Doerr, H. M. 2003. Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching, Mahwah, NJ: Lawrence Erlbaum.
51. Linde, C. 2001. Narrative and social tacit knowledge. Journal of Knowledge Management, 5(2): 160-170.
52. Little, J. 1990. The persistence of privacy: Autonomy and initiative in teachers' professional relations. Teachers College Record, 91(4): 511-536.
53. Martin, J. R. and Rose, D. 2002. Working with discourse, New York, NY: Continuum International Publishing Group.
54. Mehan, H. and Wood, H. 1975. The reality of ethnomethodology, Malabar, FL: Krieger.
55. Nachlieli, T. 2011. Co-facilitation of study groups around animated scenes: The discourse of a moderator and researcher. ZDM-The International Journal of Mathematics Education, 43(1): 53-64.
56. Nathan, M. J., Kintsch, W. and Young, E. 1992. A theory of algebra-word-problem comprehension and its implications for the design of learning environments. Cognition and Instruction, 9(4): 329-389.
57. Nathan, M. J. and Koedinger, K. R. 2000. Teachers' and researchers' beliefs about the development of algebraic reasoning. Journal for Research in Mathematics Education, 31(2): 168-190.
58. National Council of Teachers of Mathematics. 2009. Focus in high school mathematics: Reasoning and sense making, Reston, VA: Author.
59. National Council of Teachers of Mathematics. 2000. Principles and standards for school mathematics, Reston, VA: Author.
60. National Council of Teachers of Mathematics. 1989. Curriculum and evaluation standards for school mathematics, Reston, VA: Author.
61. National Council of Teachers of Mathematics. 1980. Agenda for action, Reston, VA: Author.
62. Palm, T. 2009. "Theory of authentic task situations". In Words and worlds: Modelling verbal descriptions of situations, Edited by: Verschaffel, L., Greer, B., Van Dooren, W. and Mukhopadhyay, S. 3-19. Rotterdam, The Netherlands: Sense Publishers.
63. Pollak, H., Albers, D. J. and Thibodeaux, M. J. 1984. A conversation with Henry Pollak. The College Mathematics Journal, 15(3): 194-217.
64. Reed, S. K. 1999. Word problems: Research and curriculum reform, Mahwah, NJ: Lawrence Erlbaum Associates.
65. Reusser, K. and Stebler, R. 1997. Every word problem has a solution-The social rationality of mathematical modeling in schools. Learning and Instruction, 7(4): 309-327.
66. Robson, E. 1999. Mesopotamian mathematics, 2100-1600 BC: Technical constants in bureaucracy and education, Oxford, UK: Clarendon Press.
67. Roth, W.-M. 1996. Where IS the context in contextual word problem?: Mathematical practices and products in Grade 8 students' answers to story problems. Cognition and Instruction, 14(4): 487-527.
68. Rowland, T. 1995. Hedges in mathematical talk: Linguistic pointers to uncertainty. Educational Studies in Mathematics, 29(4): 327-353.
69. Schoenfeld, A. and Arcavi, A. 1988. On the meaning of variable. Mathematics Teacher, 81(6): 420-427.
70. Shulman, L. S. 1986. Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2): 4-14.
71. Silver, E. A. 1995. The nature and use of open problems in mathematics education: Mathematical and pedagogical perspectives. Zentralblatt fur Didaktik der Mathematik/International Reviews on Mathematical Education, 27(2): 67-72.
72. Simosi, M. 2003. Using Toulmin's framework for the analysis of everyday argumentation: Some methodological considerations. Argumentation, 17(2): 185-202.
73. Tate, W. F. 1995. Returning to the root: A culturally relevant approach to mathematics pedagogy. Theory into Practice, 34(3): 166-173.
74. Thompson, P. 1993. Quantitative reasoning, complexity, and additive structures. Educational Studies in Mathematics, 25(3): 165-208.
75. Toulmin, S. E. 1969. The uses of argument, Cambridge, MA: Cambridge University Press.
76. Usiskin, Z. 1988. "Conceptions of school algebra and uses of variables". In The ideas of algebra, K-12, Edited by: Coxford, A. and Shulte, A. 8-19. Reston, VA: National Council of Teachers of Mathematics.
77. Wenger, E. 1998. Communities of practice: Learning, meaning, and identity, New York, NY: Cambridge University Press.
78. Yackel, E. and Cobb, P. 1996. Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4): 458-477.