Cultivating inquiry about space in a middle school mathematics classroom

ZDM - International Journal on Mathematics Education

Volumn 45, Issue 3, 2013, Pages 365-376

  Lehrer, Richard ^a   Kobiela, Marta ^a   Weinberg, Paul J ^a  

^a VANDERBILT UNIVERSITY   (United States)

Author keywords

Interest and disposition; Mathematical habits of mind; Mathematical inquiry; Mathematical practices; Spatial mathematics

Indexed keywords

EID: 84892836103     PISSN: 18639690     EISSN: 18639704     Source Type: Journal    
DOI: 10.1007/s11858-012-0479-x     Document Type: Article

References (37)

1. Abelson, H. & diSessa, A. A. (1980). Turtle geometry: The computer as a medium for exploring mathematics. The Massachusetts Institute of Technology.
2. Azevedo, F. S. (2006). Personal excursions: Investigating the dynamics of student engagement. International Journal of Computers for Mathematical Learning, 11, 57-98.
3. Ball, D. L. (1993). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. The Elementary School Journal, 4, 373-397.
4. Barron, B. (2006). Interest and self-sustained learning as catalysts of development: A learning ecology perspective. Human Development, 49, 193-224.
5. Boaler, J. (2002). Experiencing school mathematics: Traditional and reform approaches to teaching and their impact on student learning (Revised and Expanded Edition ed.). Mahwah, NJ: Lawrence Erlbaum Association.
6. Borasi, R. (1992). Learning mathematics through inquiry. New Hampshire: Heinemann Educational Books, Inc.
7. Chapin, S. H., O'Connor, C., & Anderson, N. C. (2003). Classroom discussions. Using MATH TALK to help students learn. Sausalito, CA: Math Solutions.
8. de Villiers, M. (1998). An alternative approach to proof in dynamic geometry. In R. Lehrer & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 369-393). Mahwah, NJ: Erlbaum.
9. diSessa, A. A. (2004). Metarepresentation: Native competence and targets for instruction. Cognition & Instruction, 22(3), 293-331.
10. Driscoll, M., DiMatteo, R. W., Nikula, J. E., & Egan, M. (2007). Fostering geometric thinking: A guide for teachers grades 5-10. Portsmouth, NH: Heinemann.
11. Ellis, A. B. (2011). Generalizing-promoting actions: How classroom collaborations can support students' mathematical generalizations. Journal for Research in Mathematics Education., 42(4), 308-345.
12. Goldenberg, E. P., & Cuoco, A. A. (1998). What is dynamic geometry? In R. Lehrer & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 351-367). Mahwah, NJ: Erlbaum.
13. Goldenberg, E. P., Cuoco, A. A., & Mark, J. (1998). A role for geometry in general education. In R. Lehrer & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 3-44). Mahwah, NJ: Erlbaum.
14. Gresalfi, M. S. (2009). Taking up opportunities to learn: Constructing dispositions in mathematics classrooms. The Journal of the Learning Sciences, 18(3), 327-369.
15. Hadas, N., Hershkowitz, R., & Schwarz, B. B. (2000). The role of contradiction and uncertainty in promoting the need to prove in dynamic geometry environments. Educational Studies in Mathematics, 44, 127-150.
16. Harel, G. (2008). What is mathematics? A pedagogical answer to a philosophical question. In B. Gold & R. Simons (Eds.), Current issues in the philosophy of mathematics from the perspective of mathematicians. Washington, DC: Mathematical American Association.
17. Henderson, D. W., & Taimina, D. (2005). Experiencing geometry: Euclidean and non-euclidean with history. Upper Saddle River, NJ: Pearson Prentice Hall.
18. Hidi, S., & Renninger, K. A. (2006). The four-phase model of interest development. Educational Psychologist, 41(2), 111-127.
19. Hufferd-Ackles, K., Fuson, K. C., & Sherin, M. G. (2004). Describing levels and components of a math-talk learning community. Journal for Research in Mathematics Education, 35, 81-116.
20. Hwang, S., & Roth, W.-M. (2011). Scientific and mathematical bodies. Rotterdam: Sense Publishers.
21. Knorr Cetina, K. (1999). Epistemic cultures: How the sciences make knowledge. Cambridge: Harvard University Press.
22. Lakatos, I. (1976). Proofs and refutations: The logic of mathematical discovery. Cambridge: Cambridge University Press.
23. Lakoff, G., & Nunez, R. (2000). Where mathematics comes from. How the embodied mind brings mathematics into being. New York: Basic.
24. Latour, B. (1990). Drawing things together. In M. Lynch & S. Woolgar (Eds.), Representation in scientific practice (pp. 19-68). Cambridge, MA: MIT Press.
25. Lehrer, R. (2009). Designing to develop disciplinary knowledge: Modeling natural systems. American Psychologist, 64(8), 759-771.
26. Lehrer, R., Jacobson, C., Kemeny, V., & Strom, D. (1999). Building on children's intuitions to develop mathematical understanding of space. In E. Fennema & T. A. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 63-87). Mahwah, NJ: Lawrence Erlbaum Associates.
27. Lehrer, R., Randle, L., & Sancilio, L. (1989). Learning preproof geometry with LOGO. Cognition and Instruction, 6(2), 159-184.
28. O'Connor, M. K., & Michaels, S. (1996). Shifting participant frameworks: Orchestrating thinking practices in group discussion. In D. Hicks (Ed.), Discourse, learning and schooling (pp. 63-103). New York: Cambridge University Press.
29. Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas. New York, NY: Basic Books.
30. Renninger, K. A. (2009). Interest and identity development in instruction: An inductive model. Educational Psychologist, 44(2), 1-14.
31. Roth, W.-M., & McGinn, M. K. (1998). Inscriptions: Toward a theory of representing as social practice. Review of Educational Research, 68, 35-59.
32. Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114-145.
33. Sinclair, N. (2004). The roles of the aesthetic in mathematical inquiry. Mathematical Thinking and Learning, 6(3), 261-284.
34. Staples, M. (2007). Supporting whole-class collaborative inquiry in a secondary mathematics classroom. Cognition and Instruction, 25(2), 161-217.
35. Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive matheamtical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313-340.
36. van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education. New York: Academic Press.
37. Yackel, E., & Cobb, P. (1996). Sociomath norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27, 458-477.