Exploring relationships between setting up complex tasks and opportunities to learn in concluding whole-class discussions in middle-grades mathematics instruction

Journal for Research in Mathematics Education

Volumn 44, Issue 4, 2013, Pages 646-682

  Jackson, Kara ^a   Garrison, Anne ^b   Wilson, Jonee ^b   Gibbons, Lynsey ^c   Shahan, Emily ^b  

^a MCGILL UNIVERSITY   (Canada)

^b VANDERBILT UNIVERSITY   (United States)

^c UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Cognitive demand; Instruction; Opportunity to learn; Tasks

Indexed keywords

EID: 84880369532     PISSN: 00218251     EISSN: None     Source Type: Journal    
DOI: 10.5951/jresematheduc.44.4.0646     Document Type: Article

References (52)

1. Ball, D. L. (2001). Teaching, with respect to mathematics and students. In T. Wood, B. S. Nelson, & J. Warfield (Eds.), Beyond classical pedagogy: Teaching elementary school mathematics (pp. 11-22). Mahwah, NJ: Erlbaum.
2. Ball, D. L., & Bass, H. (2000). Making believe: The collective construction of public mathematical knowledge in the elementary classroom. In D. C. Phillips (Ed.), Constructivism in education: Opinions and second opinions on controversial issues (pp. 193-224). Chicago, IL: The University of Chicago Press.
3. Ball, D. L., Goffney, I. M., & Bass, H. (2005). The role of mathematics instruction in building a socially just and diverse democracy. The Mathematics Educator, 15(1), 2-6.
4. Ball, D. L., Sleep, L., Boerst, T., & Bass, H. (2009). Combining the development of practice and the practice of development in teacher education. Elementary School Journal, 109(5), 458-474. doi:10.1086/596996
5. Boaler, J. (2002). Learning from teaching: Exploring the relationship between reform curriculum and equity. Journal for Research in Mathematics Education, 33(4), 239-258. doi: 10.2307/749740
6. Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside School. Teachers College Record, 110(3), 608-645.
7. Boston, M. D. (2012). Assessing the quality of mathematics instruction. Elementary School Journal, 113(1), 76-104.
8. Boston, M. D., & Wolf, M. K. (2006). Assessing academic rigor in mathematics instruction: The development of Instructional Quality Assessment Toolkit (Report No. 672). Los Angeles, CA: National Center for Research on Evaluation, Standards, and Student Testing.
9. Chapin, S. H., O'Connor, C., & Anderson, N. C. (2003). Classroom discussions: Using math talk to help students learn. Sausalito, CA: Math Solutions.
10. Cobb, P., & Jackson, K. (2011). Towards an empirically grounded theory of action for improving the quality of mathematics teaching at scale. Mathematics Teacher Education and Development, 13(1), 6-33.
11. Cobb, P., & Smith, T. (2008). The challenge of scale: Designing schools and districts as learning organizations for instructional improvement in mathematics. In T. Wood, B. Jaworski, K. Krainer, P. Sullivan, & D. Tirosh (Eds.), International handbook of mathematics teacher education (Vol. 3, pp. 231-254). Rotterdam, the Netherlands: Sense.
12. Cobb, P., Stephan, M., McClain, K., & Gravemeijer, K. (2001). Participating in classroom mathematical practices. The Journal of the Learning Sciences, 70(1/2), 113-163. doi:10.1207/SI5327809JLS10-1-2-6 (Pubitemid 33625754)
13. Cobb, P., Wood, T., Yackel, E., & McNeal, B. (1992). Characteristics of classroom mathematics traditions: An interactional analysis. American Educational Research Journal, 29(3), 573-604.
14. Cobb, P., Yackel, E., & Wood, T. (1992). A constructivist alternative to the representational view of mind in mathematics education. Journal for Research in Mathematics Education, 23(1), 2-33. doi:10.2307/749161
15. Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences. Mahwah, NJ: Erlbaum.
16. Darling-Hammond, L. (2007). The flat earth and education: How America's commitment to equity will determine our future. Educational Researcher, 36(6), 318-334. doi: 10.3102/0013189X07308253
17. Doyle, W. (1988). Work in mathematics classes: The context of students' thinking during instruction. Educational Psychologist, 23(2), 167-180. doi:10.1207/sl5326985ep2302-6
18. Franke, M. L. (2006). Unpacking practice [Web page]. Retrieved from http://www.cfkeep.org/html/stitch.php?s=11093407507142
19. Franke, M. L., Kazemi, E., & Battey, D. (2007). Mathematics teaching and classroom practice. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 225-256). Greenwich, CT: Information Age.
20. Garrison, A. (2011, September). The cognitive demand of mathematical tasks: Investigating links to teacher characteristics and contextual factors. Paper presented at the Society for Research on Educational Effectiveness, Washington, DC.
21. Gravemeijer, K., & Doorman, M. (1999). Context problems in realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics, 39(1-3), 111-129. doi: 10.1023/A: 1003749919816
22. Grossman, P., Compton, C., Igra, D., Ronfeldt, M., Shahan, E., & Williamson, P. W. (2009). Teaching practice: A cross-professional perspective. Teachers College Record, 111(9), 2055-2100.
23. Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K. C, Weame, D., Murray, H.,... Human, P. (1997). Making sense: Teaching and learning mathematics with understanding. Portsmouth, NH: Heinemann.
24. Hill, H. C., Schilling, S. G., & Ball, D. L. (2004). Developing measures of teachers' mathematics knowledge for teaching. The Elementary School Journal, 105(1), 11-30. doi:10.1086/428763 (Pubitemid 39427416)
25. Jackson, K., & Cobb, P. (2010, April). Refining a vision of ambitious mathematics instruction to address issues of equity. Paper presented at the annual meeting of the American Educational Research Association, Denver, CO.
26. Jackson, K., Shahan, E., Gibbons, L., & Cobb, P. (2012). Launching complex tasks. Mathematics Teachingin the Middle School, 18(1), 24-29. doi: 10.5951/mathteacmiddscho. 18.1.0024
27. Kane, M. T. (2006). Validation. In R. E. Brennan (Ed.), Educational measurement (4th ed., pp. 17-64). Westport, CT: American Council of Education and Praeger Publishers.
28. Kazemi, E., Franke, M. L., & Lampert, M. (2009). Developing pedagogies in teacher education to support novice teachers' ability to enact ambitious instruction. In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Crossing Divides: Proceedings of the 32nd Annual Conference of the Mathematics Education Research Group of Australasia (Vol. 1, pp. 12-30). Palmerston North, NZ: MERGA.
29. Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
30. Lampert, M. (2001). Teaching problems and the problems of teaching. New Haven, CT: Yale University Press.
31. Lampert, M., Beasley, H., Ghousseini, H., Kazemi, E., & Franke, M. L. (2010). Using designed instructional activities to enable novices to manage ambitious mathematics teaching. In M. K. Stein & L. Kucan (Eds.), Instructional explanations in the disciplines (pp. 129-141). New York: Springer, doi: 10.1007/978-1-4419-0594-9-9
32. Lampert, M., & Graziani, F. (2009). Instructional activities as a tool for teachers' and teacher educators' learning. The Elementary School Journal, 109(5), 491-509. doi:10.1086/596998
33. Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., & Phillips, E. D. (2009). Moving straight ahead: Linear relationships (Connected Mathematics Project 2, Grade 7). Upper Saddle River, NJ: Prentice Hall.
34. Lubienski, S. T. (2000). Problem solving as a means toward mathematics for all: An exploratory look through a class lens. Journal for Research in Mathematics Education, 31(4), 454-482. doi: 10.2307/749653
35. Matsumura, L. C., Gamier, H. E., Slater, S. C., & Boston, M. D. (2008). Toward measuring instructional interactions "at-scale." Educational Assessment, 13(4), 267-300. doi:10.1080/10627190802602541
36. Matsumura, L. C., Slater, S. C., Junker, B., Peterson, M., Boston, M. D., Steele, M., & Resnick, L. (2006). Measuring reading comprehension and mathematics instruction in urban middle schools: A pilot study of the Instructional Quality Assessment. Los Angeles, CA: National Center for Research on Evaluation, Standards, and Student Testing.
37. McClain, K. (2002). Teacher's and students' understanding: The role of tool use in communication. Journal of the Learning Sciences, 11(2/3), 217-249. (Pubitemid 36618864)
38. McClain, K., & Cobb, P. (1998). The role of imagery and discourse in supporting students' mathematical development. In M. Lampert & M. Blunk (Eds.), Talking mathematics in school: Studies of teaching and learning (pp. 56-81). New York, NY: Cambridge University Press.
39. Moschkovich, J. (1999). Supporting the participation of English language learners in mathematical discussion. For the Learning of Mathematics, 19(1), 11-19.
40. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
41. National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Retrieved from http://www.corestandards.org
42. Silver, E. A., Smith, M. S., & Nelson, B. S. (1995). The QUASAR project: Equity concerns meet mathematics reforms in the middle school. In W. G. Secada, E. Fennema, & L. B. Adajian (Eds.), New directions in equity in mathematics education (pp. 9-56). New York, NY: Cambridge University Press.
43. Smith, M. S., Bill, V., & Hughes, E. K. (2008). Thinking through a lesson: Successfully implementing high-level tasks. Mathematics Teaching in the Middle School, 14(2), 132-138.
44. Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 70(4), 313-340. doi:10.1080/10986060802229675
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(2), 455-488.
46. Stein, M. K., & Lane, S. (1996). Instructional tasks and the development of student capacity to think and reason: An analysis of the relationship between teaching and learning in a reform mathematics project. Educational Research and Evaluation, 2(1), 50-80. doi:10.1080/1380361960020103
47. Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2000). Implementing standards-based mathematics instruction: A casebook for professional development. New York, NY: Teachers College Press.
48. Sztajn, P., Confrey, J., Wilson, P. H., & Edgington, C. (2012). Learning trajectory based instruction: Toward a theory of teaching. Educational Researcher, 41(5), 147-156. doi:10.3102/0013189X12442801
49. Tate, W. F. (1995). Returning to the root: A culturally relevant approach to mathematics pedagogy. Theory into Practice, 34(3), 166-173. doi: 10.1080/00405849509543676
50. Thompson, A. G., Philipp, R. A., Thompson, P. W., & Boyd, B. (1994). Calculational and conceptual orientations in teaching mathematics. In A. Coxford (Ed.), Professional development for teachers of mathematics, 1994 yearbook of the National Council of Teachers of Mathematics (pp. 79-92). Reston, VA: NCTM.
51. Thompson, P. W. (1996). Imagery and the development of mathematical reasoning. In L. P. Steffe, P. Nesher, P. Cobb, G. Goldin, & B. Greer (Eds.), Theories of mathematical learning (pp. 267-283). Hillsdale, NJ: Erlbaum.
52. Van De Walle, J. A., Folk, S., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics: Teaching developmentally. Upper Saddle River, NJ: Pearson Education.