Using novel tasks in teaching mathematics: Three tensions affecting the work of the teacher

American Educational Research Journal

Volumn 40, Issue 1, 2003, Pages 197-238

  Herbst, Patricio G ^a  

^a NONE   (United States)

Author keywords

Argumentation; Didactical contract; Mathematics teaching; Novel tasks; Teaching tensions

Indexed keywords

EID: 0038043814     PISSN: 00028312     EISSN: None     Source Type: Journal    
DOI: 10.3102/00028312040001197     Document Type: Review

References (50)

1. Arsac, G., Balacheff, N., & Mante, M. (1992). Teacher's role and reproducibility of didactical situations. Educational Studies in Mathematics, 23, 5-29.
2. Balacheff, N. (1990). Towards a problématique for research on mathematics teaching. Journal for Research in Mathematics Education, 21, 258-272.
3. Ball, D. L. (1993). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. Elementary School Journal, 93, 373-397.
4. Ball, D. L., & Bass, H. (2000). Making believe: The collective construction of public mathematical knowledge in the elementary classroom. In D. Phillips (Ed.), Constructivism in education: Yearbook of the National Society for the Study of Education (pp. 193-224). Chicago: University of Chicago Press.
5. Bateson, G. (1971). Steps to an ecology of mind. Chicago: University of Chicago Press.
6. Bauersfeld, H. (1988). Interaction, construction, and knowledge: Alternative perspectives in mathematics education. In D. A. Grouws, T. J. Cooney, & D. Jones (Eds.), Perspectives on research on effective mathematics teaching. Reston, VA: National Council of Teachers of Mathematics.
7. Bourdieu, P. (1980). The logic of practice. Palo Alto, CA: Stanford University Press.
8. Brousseau, G. (1984). The crucial role of the didactical contract in the analysis and construction of situations in teaching and learning mathematics. In H.-G. Steiner (Ed.), Theory of mathematics education (pp. 110-119). Bielefeld, Germany: Institut für Didaktikk der Mathematikk.
9. Brousseau, G. (1990). Le contrat didactique: Le milieu [The didactical contract: The milieu]. Recherches en Didactique des Mathematiques, 9, 309-336.
10. Brousseau, G. (1997). Theory of didactical situations in mathematics: Didactique des mathematiques 1970-1990 (N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield, Eds. and Trans.). Dordrecht, the Netherlands: Kluwer.
11. Brousseau, G., & Otte, M. (1991). The fragility of knowledge. In A. Bishop, S. Mellin-Olsen, & J. van Dormolen (Eds.), Mathematical knowledge: Its growth through teaching (pp. 13-36). Dordrecht, the Netherlands: Kluwer.
12. Chazan, D. (2000). Beyond formulas in mathematics and teaching: The dynamics of the high school algebra classroom. New York: Teachers College Press.
13. Chazan, D., & Ball, D. (1999). Beyond being told not to tell. For the Learning of Mathematics, 19(2), 2-10.
14. Chevallard, Y. (1985). La transposition didactique: Du savoir savant au savoir enseigné [The didactic transposition: From the knowledge of the expert to the knowledge taught]. Grenoble, France: La Pensée Sauvage.
15. Cobb, P. (2000). Conducting teaching experiments in collaboration with teachers. In A. Kelly & R. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 307-333). Mahwah, NJ: Erlbaum.
16. Cobb, P., & Bauersfeld, H. (Eds.). (1995). The emergence of mathematical meaning: Interaction in classroom cultures. Hillsdale, NJ: Erlbaum.
17. Cohen, D. K. (1990). A revolution in one classroom: The case of Mrs. Oublier. Educational Evaluation and Policy Analysis, 12, 327-345.
18. Cohen, D. K., & Ball, D. L. (1999). Instruction, capacity, and improvement (CPRE Research Report No, RR-043). Philadelphia: University of Pennsylvania, Consortium for Policy Research in Education.
19. Comiti, C., Grenier, D., & Margolinas, C. (1995). Niveaux de connaissances en jeu lors d'interactions en situation de classe et modelisation de phenomenes didactiques [Levels of knowing at play during interactions in classroom situations and modeling of didactical phenomena]. In G. Arsac, J. Grea, D. Grenier, & A. Tiberghien (Eds.), Differents types de savoirs et leur articulation (pp. 93-127). Grenoble, France: La Pensée Sauvage.
20. Douady, R. (1991). Tool, object, setting, window: Elements for analyzing and constructing didactical situations in mathematics. In A. Bishop, S. Mellin-Olsen, & J. van Dormolen (Eds.), Mathematical knowledge: Its growth through teaching (pp. 109-130). Dordrecht, the Netherlands: Kluwer.
21. Doyle, W. (1983), Academic work, Review of Educational Research, 53, 159-199.
22. Doyle, W. (1986). Classroom organization and management. In M. Wittrock (Ed.), Handbook of research on teaching (3rd ed., pp. 392-431). New York: Macmillan.
23. Doyle, W. (1988). Work in mathematics classes: The context of students' thinking during instruction. Educational Psychologist, 23, 167-180.
24. Fenstermacher, G. (1986). Philosophy of research on teaching; Three aspects. In M. Wittrock (Ed.), Handbook of research on teaching (3rd ed., pp. 37-49). New York: Macmillan.
25. Forman, E., Larreamendy-Joerns, J., Stein, M. K., & Brown, C. (1998). "You're going to want to find out which and prove it": Collective argumentation in a mathematics classroom. Learning and Instruction, 8, 527-548.
26. Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht, the Netherlands: Kluwer.
27. Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28, 524-549.
28. Herbst, P. (2002). Engaging students in proving: A double bind on the teacher. Journal for Research in Mathematics Education, 33, 176-203.
29. Herbst, P., & Chazan, D. (in press). Exploring the practical rationality of mathematics teaching through conversations about videotaped episodes: The case of engaging students in proving. For the Learning of Mathematics.
30. Hershkowitz, R., Schwarz, B., & Dreyfus, T. (2001). Abstraction in context: Epistemic actions. Journal for Research in Mathematics Education, 32, 195-222.
31. Krummheuer, G. (1995). The ethnography of argumentation. In P. Cobb & H. Bauersfeld (Eds.), The emergence of mathematical meaning: Interaction in classroom cultures (pp. 229-269). Hillsdale, NJ; Erlbaum.
32. Krummheuer, G. (1998). Formats of argumentation in the mathematics classroom. In H. Steinbring, M. Bartolini-Bussi, & A. Sierpinska (Eds.), Language and communication in the mathematics classroom (pp. 223-234). Reston, VA: National Council of Teachers of Mathematics.
33. Lakatos, I. (1976). Proofs and refutations: The logic of mathematical discovery, Cambridge, England: Cambridge University Press.
34. Lampert, M. (1985). How do teachers manage to teach? Perspectives on problems in practice. Harvard Educational Review, 55, 178-194.
35. Lampert, M. (2001). Teaching problems and the problems of teaching. New Haven, CT: Yale University Press.
36. Lampert, M., & Ball, D. (1998). Teaching, multimedia, and mathematics: Investigations of real practice. New York: Teachers College Press.
37. LeCompte, M., & Preissle, J. (1993). Ethnography and qualitative design in educational research (2nd ed.). San Diego, CA: Academic Press.
38. Mason, J. (1999). The role of labels in promoting learning from experience in teachers and students. In L. Burton (Ed.), Learning mathematics: From hierarchies to networks (pp. 187-208). London: Falmer Press.
39. National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston, VA: Author.
40. Piaget, J., Inhëlder, B., & Szeminska, A. (1960). The child's conception of geometry. New York: Basic Books.
41. Reid, D. (2002). Conjectures and refutations in Grade 5 mathematics. Journal for Research in Mathematics Education, 33, 5-29.
42. Rousseau, J.-J. (1994). Social contract: Discourse on the virtue most necessary for a hero (R. Masters & C. Kelley, Eds., J. Bush, R. Masters, & C. Kelley, Trans.). Hanover, NH: University Press of New England.
43. Serra, M. (1997). Discovering geometry: An inductive approach. Emeryville, CA: Key Curriculum Press.
44. Simon, M., & Tzur, R. (1999). Explicating the teacher's perspective from the researchers' perspectives: Generating accounts of mathematics teachers' practice. Journal for Research in Mathematics Education, 30, 252-264.
45. Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33, 455-488.
46. Thompson, A. G. (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.
47. Thompson, P. (1993). Quantitative reasoning, complexity, and additive structures. Educational Studies in Mathematics, 25, 165-208.
48. Toulmin, S. (1958). The uses of argument. Cambridge, England: Cambridge University Press.
49. Voigt, J. (1985). Patterns and routines in classroom interaction. Recherches en Didactique des Mathematiques, 6, 69-118.
50. Voigt, J. (1994). Negotiation of mathematical meaning and learning mathematics. Educational Studies in Mathematics, 26, 275-298.