Advertisement

Mathematics Education Research Journal

, Volume 29, Issue 3, pp 283–311 | Cite as

Student reflections on learning with challenging tasks: ‘I think the worksheets were just for practice, and the challenges were for maths’

  • James RussoEmail author
  • Sarah Hopkins
Original Article

Abstract

The current study considered young students’ (7 and 8 years old) experiences and perceptions of mathematics lessons involving challenging (i.e. cognitively demanding) tasks. We used the Constant Comparative Method to analyse the interview responses (n = 73) regarding what work artefacts students were most proud of creating and why. Five themes emerged that characterised student reflections: enjoyment, effort, learning, productivity and meaningful mathematics. Overall, there was evidence that students embraced struggle and persisted when engaged in mathematics lessons involving challenging tasks and, moreover, that many students enjoyed the process of being challenged. In the second section of the paper, the lesson structure preferences of a subset of participants (n = 23) when learning with challenging tasks are considered. Overall, more students preferred the teach-first lesson structure to the task-first lesson structure, primarily because it activated their cognition to prepare them for work on the challenging task. However, a substantial minority of students (42 %) instead endorsed the task-first lesson structure, with several students explaining they preferred this structure precisely because it was so cognitively demanding. Other reasons for preferring the task-first structure included that it allowed the focus of the lesson to be on the challenging task and the subsequent discussion of student work. A key implication of these combined findings is that, for many students, work on challenging tasks appeared to remain cognitively demanding irrespective of the structure of the lesson.

Keywords

Challenging tasks Cognitively demanding tasks Lesson structure Student perceptions Student learning preferences Problem-based learning Early years 

References

  1. Baxter, J. A., & Williams, S. (2010). Social and analytic scaffolding in middle school mathematics: managing the dilemma of telling. Journal of Mathematics Teacher Education, 13(1), 7–26.CrossRefGoogle Scholar
  2. Boston, M. D., & Smith, M. S. (2011). A ‘task-centric approach’ to professional development: enhancing and sustaining mathematics teachers’ ability to implement cognitively challenging mathematical tasks. ZDM, 43(6–7), 965–977.CrossRefGoogle Scholar
  3. Cheeseman, J., Clarke, D.M., Roche, A., & Wilson, K. (2013). Teachers’ views of the challenging elements of a task. In V. Steinle, L. Ball & C. Bardini (Eds.), Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia (pp. 154–161). Melbourne, Australia: MERGA.Google Scholar
  4. Clarke, D. M., & Clarke, B. A. (2003). Encouraging perseverance in elementary mathematics: a tale of two problems. Teaching Children Mathematics, 10(4), 204–209.Google Scholar
  5. Clarke, D. M., Cheeseman, J., Roche, A., & van der Schans, S. (2014). Teaching strategies for building student persistence on challenging tasks: insights emerging from two approaches to teacher professional learning. Mathematics Teacher Education and Development, 16(2), 46–70.Google Scholar
  6. Darragh, L. (2013). Sticking with it or doing it quickly: what performances do we encourage in our mathematics learners? In V. Steinle, L. Ball & C. Bardini (Eds.), Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia (pp. 218–225). Melbourne, Australia: MERGA.Google Scholar
  7. Glaser, B. G. (1965). The constant comparative method of qualitative analysis. Social Problems, 12(4), 436–445.CrossRefGoogle Scholar
  8. Glaser, B. G. (1969). The constant comparative method of qualitative analysis. In G. McCall & J. Simmons (Eds.), Issues in participant observation: a text and reader. Reading: Addison-Wesley Pub. Co..Google Scholar
  9. Hatfield, E., Cacioppo, J. T., & Rapson, R. L. (1994). Emotional contagion. New York: Cambridge University Press.Google Scholar
  10. 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(5), 524–549.CrossRefGoogle Scholar
  11. Hollingsworth, H., McCrae, B., & Lokan, J. (2003). Teaching mathematics in Australia: results from the TIMSS 1999 video study. Camberwell: Australian Council for Educational Research.Google Scholar
  12. Jackson, K., Garrison, A., Wilson, J., Gibbons, L., & Shahan, E. (2013). 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, 44(4), 646–682.CrossRefGoogle Scholar
  13. Ke, F. (2014). An implementation of design-based learning through creating educational computer games: a case study on mathematics learning during design and computing. Computers and Education, 73, 26–39.CrossRefGoogle Scholar
  14. Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work: an analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational Psychologist, 41(2), 75–86.CrossRefGoogle Scholar
  15. Krapp, A. (2005). Basic needs and the development of interest and intrinsic motivational orientations. Learning and Instruction, 15(5), 381–395.CrossRefGoogle Scholar
  16. Lambert, R., & Stylianou, D. A. (2013). Posing cognitively demanding tasks to all students. Mathematics Teaching in the Middle School, 18(8), 500–506.CrossRefGoogle Scholar
  17. Leikin, R., Levav-Waynberg, A., Gurevich, I., & Mednikov, L. (2006). Implementation of multiple solution connecting tasks: do students’ attitudes support teachers’ reluctance? Focus on Learning Problems in Mathematics, 28(1), 1–22.Google Scholar
  18. McClain, K. (2002). Teacher’s and students’ understanding: the role of tools and inscriptions in supporting effective communication. Journal of the Learning Sciences, 11(2–3), 217–249.CrossRefGoogle Scholar
  19. Middleton, M. J., & Midgley, C. (2002). Beyond motivation: middle school students’ perceptions of press for understanding in math. Contemporary Educational Psychology, 27(3), 373–391.CrossRefGoogle Scholar
  20. Muis, K. R., Psaradellis, C., Lajoie, S. P., Di Leo, I., & Chevrier, M. (2015). The role of epistemic emotions in mathematics problem solving. Contemporary Educational Psychology, 42, 172–185.CrossRefGoogle Scholar
  21. NRC (National Research Council Staff). (1989). Everybody counts: a report to the nation on the future of mathematics education. Washington: National Academies Press.Google Scholar
  22. Pekrun, R. (2006). The control-value theory of achievement emotions: assumptions, corollaries, and implications for educational research and practice. Educational Psychology Review, 18(4), 315–341. doi: 10.1007/s10648-006-9029-9.CrossRefGoogle Scholar
  23. Ridlon, C. L. (2009). Learning mathematics via a problem-centered approach: a two-year study. Mathematical Thinking and Learning, 11(4), 188–225.CrossRefGoogle Scholar
  24. Russo, J. (2015). Teaching with challenging tasks: Two 'how many' problems. Prime Number, 30(4), 9–11.Google Scholar
  25. Russo, J. (2016a). Teaching mathematics in primary schools with challenging tasks: the big (not so) friendly giant. Australian Primary Mathematics Classroom, 21(3), 8–15.Google Scholar
  26. Russo, J. (2016b). Teaching with challenging tasks: baskets and boundaries. Prime Number, 31(3), 7–9.Google Scholar
  27. Russo, J. (2016c). Teaching with challenging tasks: hopping with fiona the frog. Prime Number, 31(2), 10–11.Google Scholar
  28. Russo, J., & Hopkins, S. (2017a). Task-First vs Teach-First: Does lesson structure matter for student mathematical performance when teaching with challenging tasks? Manuscript submitted for publication.Google Scholar
  29. Russo, J., & Hopkins, S. (2017b). Class challenging tasks: Using cognitive Load theory to inform the design of challenging mathematical tasks. Australian Primary Mathematics Classroom, 22(1).Google Scholar
  30. Russo, J., &amp Hopkins, S. (in press). How does lesson structure impact teachers’ willingness to teach with Challenging Tasks? Mathematics Teacher Education and Development.Google Scholar
  31. Sherin, M. G. (2002). When teaching becomes learning. Cognition and Instruction, 20(2), 119–150.CrossRefGoogle Scholar
  32. 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
  33. 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, 10(4), 313–340.CrossRefGoogle Scholar
  34. Stein, M. K., Smith, M., Henningsen, M., & Silver, E. A. (2009). Implementing standards-based mathematics instruction. New York: Teachers College Press.Google Scholar
  35. Strauss, A., & Corbin, J. (1994). Grounded theory methodology. In N. Denzin & Y. Lincoln (Eds.), Handbook of qualitative research (pp. 273–285). Thousand Oaks: Sage.Google Scholar
  36. Sullivan, P., & Mornane, A. (2013). Exploring teachers’ use of, and students’ reactions to, challenging mathematics tasks. Mathematics Education Research Journal, 25, 1–21.CrossRefGoogle Scholar
  37. Sullivan, P., Tobias, S., & McDonough, A. (2006). Perhaps the decision of some students not to engage in learning mathematics in school is deliberate. Educational Studies in Mathematics, 62(1), 81–99.CrossRefGoogle Scholar
  38. Sullivan, P., Clarke, D. M., & Clarke, B. (2009). Converting mathematics tasks to learning opportunities: an important aspect of knowledge for mathematics teaching. Mathematics Education Research Journal, 21(1), 85–105.CrossRefGoogle Scholar
  39. Sullivan, P., Cheeseman, J., Michels, D., Mornane, A., Clarke, D.M., Roche, A., & Middleton, J. (2011). Challenging mathematics tasks: what they are and how to use them. Paper presented at the Maths is multidimensional (Mathematical Association of Victoria), Melbourne, Australia: MAV.Google Scholar
  40. Sullivan, P., Aulert, A., Lehmann, A., Hislop, B., Shepherd, O., & Stubbs, A. (2013). Classroom culture, challenging mathematical tasks and student persistence. In V. Steinle, L. Ball & C. Bardini (Eds.), Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia (pp. 618–625). Melbourne, Australia: MERGA.Google Scholar
  41. Sullivan, P., Askew, M., Cheeseman, J., Clarke, D. M., Mornane, A., Roche, A., & Walker, N. (2014). Supporting teachers in structuring mathematics lessons involving challenging tasks. Journal of Mathematics Teacher Education, 18(2), 1–18.Google Scholar
  42. Sweller, J. (2010). Element interactivity and intrinsic, extraneous, and germane cognitive load. Educational Psychology Review, 22(2), 123–138. doi: 10.1007/s10648-010-9128-5.CrossRefGoogle Scholar
  43. Sweller, J., Kirschner, P. A., & Clark, R. E. (2007). Why minimally guided teaching techniques do not work: a reply to commentaries. Educational Psychologist, 42(2), 115–121.CrossRefGoogle Scholar
  44. Teddlie, C., & Tashakkori, A. (2009). Foundations of mixed methods research: integrating quantitative and qualitative approaches in the social and behavioral sciences. Thousand Oaks: Sage.Google Scholar
  45. Tzur, R. (2008). A researcher perplexity: why do mathematical tasks undergo metamorphosis in teacher hands? In O. Figuras, J. Cortina, S. Alatorre, T. Rojano & A. Sepulveda (Eds.), Proceedings of 32nd conference of the International Group for the Psychology of Mathematics Education (pp. 139–147). Morelia, Mexico: PME.Google Scholar
  46. Valås, H., & Søvik, N. (1993). Variables affecting students’ intrinsic motivation for school mathematics: two empirical studies based on Deci and Ryan’s theory on motivation. Learning and Instruction, 3(4), 281–298.CrossRefGoogle Scholar
  47. Westwood, P. (2011). The problem with problems: potential difficulties in implementing problem-based learning as the core method in primary school mathematics. Australian Journal of Learning Difficulties, 16(1), 5–18.CrossRefGoogle Scholar
  48. Wilhelm, A. G. (2014). Mathematics teachers’ enactment of cognitively demanding tasks: investigating links to teachers’ knowledge and conceptions. Journal for Research in Mathematics Education, 45(5), 636–674.CrossRefGoogle Scholar
  49. Woolley, M. E., Strutchens, M. E., Gilbert, M. C., & Martin, W. G. (2010). Mathematics success of black middle school students: direct and indirect effects of teacher expectations and reform practices. Negro Educational Review, 61, 41–59.Google Scholar

Copyright information

© Mathematics Education Research Group of Australasia, Inc. 2017

Authors and Affiliations

  1. 1.Faculty of EducationMonash UniversityClaytonAustralia

Personalised recommendations