How does lesson structure shape teacher perceptions of teaching with challenging tasks?


  • James Anthony Russo Monash University
  • Sarah Hopkins Monash University


Cognitively demanding tasks, teacher perceptions, lesson structure, instructional approaches, mathematical knowledge for teaching


Despite reforms in mathematics education, many teachers remain reluctant to incorporate challenging (i.e., more cognitively demanding) tasks into their mathematics instruction. The current study examines how lesson structure shapes teacher perceptions of teaching with challenging tasks. Participants included three Year 1/2 classroom teachers who observed the researcher (first author) deliver two units of mathematical work. Teacher-participants were given an opportunity to observe the use of challenging tasks to both launch lessons (Task-First Approach) and extend student thinking (Teach-First Approach). It was revealed that teacher-participants perceived both the Task-First Approach and the Teach-First Approach to teaching with challenging tasks to have particular strengths. Specifically, the Task-First Approach was viewed as engaging and empowering for students, providing an opportunity to build student persistence whilst fostering student mathematical creativity. Teachers also placed value on the quality of the mathematical discussion which emerged, and the value of the Task-First Approach for supporting an authentic assessment of student mathematical knowledge. By contrast, the Teach-First Approach was viewed as highly focussed, and an efficient approach to learning. It was also perceived as providing an opportunity for lower-achieving and less confident students to be successful. Although there appear to be distinct advantages to both the Task-First and Teach-First Approaches, the study revealed that the most dramatic shift in teaching practice for some teachers may be the incorporation of more cognitively demanding tasks into their mathematics instruction in any capacity.


Alfieri, L., Brooks, P. J., Aldrich, N. J., & Tenenbaum, H. R. (2011). Does discovery-based instruction enhance learning? Journal of Educational Psychology, 103(1), 1-18.

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.

Charalambous, C. Y. (2008). Mathematical knowledge for teaching and the unfolding of tasks in mathematics lessons: Integrating two lines of research. In O. Figueras, J. Cortina, S. Alatorre, T. Rojano & A. Sepúlveda (Eds.), Proceedings of the 32nd conference of the International Group for the Psychology of Mathematics Education (pp. 281-288). Morelia, Mexico: PME.

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.

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.

Dweck, C. S. (2000). Self-theories: Their role in motivation, personality, and development. Philadelphia, United States: Psychology Press.

Forman, E. A., Larreamendy-Joerns, J., Stein, M. K., & Brown, C. A. (1998). “You're going to want to find out which and prove it”: Collective argumentation in a mathematics classroom. Learning and Instruction, 8(6), 527-548.

Forrester, P. A., & Chinnappan, M. (2010). The predominance of procedural knowledge in fractions. In L. Sparrow, B. Kissane & C. Hurst (Eds.), Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia (pp. 185-192). Fremantle, Australia: MERGA.

Hmelo-Silver, C. E., Duncan, R. G., & Chinn, C. A. (2007). Scaffolding and achievement in problem-based and inquiry learning: A response to Kirschner, Sweller, and Clark (2006). Educational Psychologist, 42(2), 99-107.

Hollingsworth, H., McCrae, B., & Lokan, J. (2003). Teaching mathematics in Australia: Results from the TIMSS 1999 video study. Camberwell, Australia: Australian Council for Educational Research.

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.

Kuhn, D. (2007). Is direct instruction an answer to the right question? Educational Psychologist, 42(2), 109-113.

Leikin, R. (2009). Exploring mathematical creativity using multiple solution tasks. In R. Leikin, A. Berman & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 129-145). Rotterdam, the Netherlands: Sense Publisher.

Marshall, J. C., & Horton, R. M. (2011). The relationship of teacher‐facilitated, inquiry‐based instruction to student higher‐order thinking. School Science and Mathematics, 111(3), 93-101.

Pichon, C. (2014). What do teachers value and perceive to be the purpose of Foreign Languages in Key Stage Two–a multi-case study. Language Issues: The ESOL Journal, 25(2), 59-60.

Ridlon, C. L. (2009). Learning mathematics via a problem-centered approach: A two-year study. Mathematical Thinking and Learning, 11(4), 188-225.

Roche, A., Clarke, D.M., Sullivan, P., & Cheeseman, J. (2013). Strategies for encouraging students to persist on challenging tasks: Some insights from work in classrooms. Australian Primary Mathematics Classroom, 18(4), 27-32.

Russo, J. (2015). Teaching with challenging tasks: Two 'how many' problems. Prime Number, 30(4), 9-11.

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.

Russo, J. (2016b). Teaching with challenging tasks: Baskets and boundaries. Prime Number, 31(3), 7.

Russo, J. (2016c). Teaching with challenging tasks: Hopping with Fiona the Frog. Prime Number, 31(2), 10-11.

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.

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).

Russo, J., & Hopkins, S. (in press). Student reflections on learning with challenging tasks: “I think the worksheets were just for practice, and the challenges were for maths” Mathematics Education Research Journal.

Schmidt, H. G., Van der Molen, H. T., Te Winkel, W. W., & Wijnen, W. H. (2009). Constructivist, problem-based learning does work: A meta-analysis of curricular comparisons involving a single medical school. Educational Psychologist, 44(4), 227-249.

Smith, J. A., & Osborn, M. (2008). Interpretative phenomenological analysis. In J. A. Smith (Ed.), Qualitative psychology: A practical guide to methods (pp. 53-80). London: Sage.

Star, J. R., & Rittle-Johnson, B. (2008). Flexibility in problem solving: The case of equation solving. Learning and Instruction, 18(6), 565-579.

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.

Stein, M. K., Smith, M., Henningsen, M., & Silver, E. A. (2009). Implementing standards-based mathematics instruction. New York, United States: Teachers College Press.

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, 1-18.

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.

Sullivan, P., Clarke, D. M., Clarke, B., & O'Shea, H. (2010). Exploring the relationship between task, teacher actions, and student learning. PNA, 4(4), 133-142.

Sullivan, P., Clarke, D. M., Michaels, D., Mornane, A., & Roche, A. (2012). Supporting teachers in choosing and using challenging mathematics tasks. In J. Dindyal, L. Cheng & S. Ng (Eds.), Proceedings of the 35th annual conference of the Mathematics Education Research Group of Australasia (pp. 688-695). Singapore: MERGA.

Sullivan, P., & Davidson, A. (2014). The role of challenging mathematical tasks in creating opportunities for student reasoning. In J. Anderson, M. Cavanagh & A. Prescott (Eds.), Proceedings of the 37th annual conference of the Mathematics Education Research Group of Australasia (pp. 605-612). Sydney, Australia: MERGA.

Sullivan, P., & Mornane, A. (2013). Exploring teachers’ use of, and students’ reactions to, challenging mathematics tasks. Mathematics Education Research Journal, 25, 1-21.

Sweller, J. (2010). Element interactivity and intrinsic, extraneous, and germane cognitive load. Educational Psychology Review, 22(2), 123-138. doi:

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.

Thomas, J. A., & Monroe, E. E. (2006). Self-study of a teacher's journey toward standards-based mathematics teaching. Studying Teacher Education, 2(2), 169-181.

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.

Warwick, P., & Kershner, R. (2008). Primary teachers’ understanding of the interactive whiteboard as a tool for children’s collaborative learning and knowledge‐building. Learning, Media and Technology, 33(4), 269-287.

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.

Woodward, J., & Irwin, K. (2005). Language appropriate for the New Zealand numeracy project. In P. Clarkson, A. Downton, D. Gronn, M. Home, A. McDonough, R. Pierce & A. Roche (Eds.), Proceedings of the 28th annual conference of the Mathematics Education Research Group of Australasia (pp. 799-806). Melbourne, Australia: MERGA.