Advertisement

Mathematics Education Research Journal

, Volume 26, Issue 2, pp 193–213 | Cite as

Exploring teachers’ use of, and students’ reactions to, challenging mathematics tasks

  • Peter Sullivan
  • Angela Mornane
Original Article
First Online:

Abstract

This is the report of an investigation in partnership with a team of junior secondary classroom teachers of the potential of posing more challenging tasks to their students. A range of data sources are used to represent the experience of teachers and students in a unit of work that incorporated a range of challenging tasks. Students learned the intended mathematics and they reacted positively to the challenges. The teachers identified both opportunities and constraints in such teaching, especially those related to changes to their pedagogies and assessment of student work.

Keywords

Mathematics teaching Mathematics tasks Mathematics pedagogies 
This is a preview of subscription content, log in to check access.

References

  1. City, E. A., Elmore, R. F., Fiarman, S. E., & Teitel, L. (2009). Instructional rounds in education. Boston, MA: Harvard Educational Press.Google Scholar
  2. Clarke, D. (1988). Assessment alternatives in mathematics. Canberra: Curriculum Development Centre:Google Scholar
  3. Clarke, D. M., & Clarke, B. A. (2004). Mathematics teaching in Grades K–2: Painting a picture of challenging, supportive, and effective classrooms. In R. N. Rubenstein & G. W. Bright (Eds.), Perspectives on the teaching of mathematics (66th Yearbook of the National Council of Teachers of Mathematics (pp. 67–81). Reston, VA: NCTM.Google Scholar
  4. Delpit, L. (1988). The silenced dialogue: Power and pedagogy in educating other people’s children. Harvard Educational Review, 58(3), 280–298.Google Scholar
  5. Desforges, C., & Cockburn, A. (1987). Understanding the mathematics teacher: A study of practice in first schools (p. 26). London: The Palmer Press.Google Scholar
  6. Dooley, T. (2012). Constructing and consolidating mathematical entities in the context of whole class discussion. In J. Dindyal, L. P. Cheng, & S.F. Ng (Eds). Mathematics education: expanding horizons (Proceedings of the 35th conference of the Mathematics Education Group of Australasia, pp. 234-241): Singapore: MERGA.Google Scholar
  7. Doyle, W. (1986). Classroom organisation and management. In M. C. Wittrock (Ed.), Handbook of research on teaching (pp. 392–431). New York: Macmillan.Google Scholar
  8. Dweck, C. S. (2000). Self-theories: Their role in motivation, personality, and development. Philadelphia: Psychology Press.Google Scholar
  9. Education Queensland. (2010). Productive pedagogies. Downloaded in January 2010 from http://education.qld.gov.au/corporate/newbasics/html/pedagogies/pedagog.html
  10. Elliot, A. J. (1999). Approach and avoidance motivation and achievement goals. Educational Psychologist, 34(3), 169–189.CrossRefGoogle Scholar
  11. Hannula, M. (2004). Affect in mathematical thinking and learning. Turku: Turun Yliopisto.Google Scholar
  12. Hill, H., Ball, D., & Schilling, S. (2008). Unpacking pedagogical content knowledge: Conceptualising and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372–400.Google Scholar
  13. Inoue, N. (2010). Zen and the art of neriage: Facilitating consensus building in mathematics inquiry lessons through lesson study. Journal of Mathematics Teacher Education, Retrieved online from http://www.springerlink.com/content/g33022h2k1384461/.polt
  14. Kelly, A. (2003). Research as design. Educational Researcher, 32(1), 3–4.CrossRefGoogle Scholar
  15. Marshall, J., & Horton, R. (2011). The relationship of teacher-facilitated, inquiry-based instruction to student higher-order thinking. School Science and Mathematics, 111. Retrieved from http://www.freepatentsonline.com/article/School-Science-Mathematics/250321509.html
  16. Middleton, J. A. (1999). Curricular influences on the motivational beliefs and practice of two middle school mathematics teachers: A follow-up study. Journal for Research in Mathematics Education, 30(3), 349–358.CrossRefGoogle Scholar
  17. Ruthven, K., Hoffmann, R., & Mercer, N. (2011). A dialogic approach to plenary problem synthesis. In B. Ubuz (Ed.), Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 81–89). Ankara, Turkey: PME.Google Scholar
  18. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.CrossRefGoogle Scholar
  19. Stein, M. K., & Lane, S. (1996). Instructional tasks and the development of student capacity to think and reason and analysis of the relationship between teaching and learning in a reform mathematics project. Educational Research and Evaluation, 2(1), 50–80.CrossRefGoogle Scholar
  20. 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.CrossRefGoogle Scholar
  21. Sullivan, P. (2011). Teaching mathematics: Using research informed strategies. Australian Education Review. Melbourne: ACER Press.Google Scholar
  22. Sullivan, P., Cheeseman, J., Michels, D., Mornane, A., Clarke, D., Roche, A., et al. (2011). Challenging mathematics tasks: What they are and how to use them. In L. Bragg (Ed.), Maths is multi-dimensional (pp. 33–46). Melbourne: Mathematical Association of Victoria.Google Scholar
  23. Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127–146). New York: Macmillan.Google Scholar

Copyright information

© Mathematics Education Research Group of Australasia, Inc. 2013

Authors and Affiliations

  1. 1.Monash UniversityMelbourneAustralia

Personalised recommendations

Cite article

Buy options