Skip to main content
SpringerLink
Log in

Investigating how secondary prospective teachers plan to launch cognitively demanding tasks

  • Published:
Journal of Mathematics Teacher Education Aims and scope Submit manuscript

Abstract

Cognitively demanding tasks have been shown to support students’ understanding of mathematics. How a task is launched, or introduced, determines how students engage with the task, as well as the type of work the teacher engages in during the task implementation. The authors designed a unit focused on launching a task where prospective teachers (PSTs) planned and enacted a task launch as part of their methods of teaching secondary mathematics courses. Participants in the study spanned three institutions. Using a curricular noticing framework, this paper describes how the prospective teachers (PSTs) interpreted their task by identifying key contextual features, mathematical relationships, and common language, and then focuses on how they responded to their interpretations as they planned to elicit and develop their students’ understanding of those key aspects. This paper also describes how the PSTs responded to their interpretations in planning to maintain the cognitive demand of the task. Findings suggest that the prospective teachers valued student-centered approaches and used a range of pedagogical methods to launch cognitively demanding tasks. We also found the prospective teachers needed support identifying context in tasks and in determining how much to tell while maintaining the cognitive demand of the task. We conclude with implications and suggestions for methods courses on both launching a cognitively demanding task and on teaching practices more generally.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Notes

  1. One task, the Toothpick Task, had limited contextual features.

  2. The sum for instances of specific (n = 28) and non-specific (n = 11) questioning does not add to 34 instances because in some cases, PSTs plans included both specific and non-specific questioning for a particular aspect.

References

  • Amador, J. M., & Earnest, D. (2018). Launch forth: Preservice teachers translating elementary mathematics curriculum into lessons. Mathematics Education Research Journal, 31(3), 301–323.

    Article  Google Scholar 

  • Creager, M. A., Snider, R. B., Parrish, C. W. (2021). Learning to launch cognitively demanding tasks: A practicebased unit for secondary methods. Mathematics Teacher Educator, 9(2), 127–144. https://doi.org/10.5951/MTE.2019.0002

  • 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.

  • Boston, M. D., & Smith, M. S. (2009). Transforming secondary mathematics teaching: Increasing the cognitive demands of instructional tasks used in teachers’ classrooms. Journal for Research in Mathematics Education, 40(2), 119–156.

    Google Scholar 

  • 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. The International Journal on Mathematics Education, 43(6–7), 965–977.

    Google Scholar 

  • Chapin, S., & O’Connor, C. (2007). Academically productive talk: Supporting student learning in mathematics. In W. G. Martin, M. Strutchens, & P. Elliott (Eds.), The learning of mathematics, 69th NCTM yearbook (pp. 113–128). National Council of Teachers of Mathematics.

    Google Scholar 

  • Corbin, J., & Strauss, A. (2008). Basics of qualitative research: Techniques and procedures for developing grounded theory (3rd ed.). Sage.

  • Dietiker, L., Males, L. M., Amador, J. M., & Earnest, D. (2018). Curricular noticing: A framework to describe teachers’ interactions with curriculum materials. Journal for Research in Mathematics Education, 49(5), 521–532.

    Article  Google Scholar 

  • Doyle, W. (1983). Academic work. Review of Educational Research, 53(2), 159–199.

    Article  Google Scholar 

  • Faith, C., Cleverdon, J., & Parrish, C. W. (2020). Lessons learned from launching tasks. Banneker Banner, 32(1), 10–18.

  • González, G., & Eli, J. A. (2015). Prospective and in-service teachers’ perspectives about launching a problem. Journal of Mathematics Teacher Education, 20(2), 159–201.

    Article  Google Scholar 

  • Grossman, P., Compton, C., Igra, D., Ronfeldt, M., Shahan, E., & Williamson, P. (2009). Teaching practice: A cross-professional perspective. Teachers College Record, 111(9), 2055–2100.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Herbel-Eisenmann, B. A., Steele, M. D., & Cirillo, M. (2013). (Developing) teacher discourse moves: A framework for professional development. Mathematics Teacher Educator, 1(2), 181–196.

    Article  Google Scholar 

  • Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371–404). NCTM.

    Google Scholar 

  • Jackson, K. J., Shahan, E. C., Gibbons, L. K., & Cobb, P. A. (2012). Launching complex tasks. Mathematics Teaching in the Middle School, 18(1), 24–29.

    Article  Google Scholar 

  • Jackson, K. J., Garrison, A., Wilson, J., Gibbons, L. K., & Shahan, E. C. (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.

    Article  Google Scholar 

  • Jacobs, V. R., Lamb, L. L. C., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169–202.

    Article  Google Scholar 

  • Lobato, J., Clarke, D., & Ellis, A. (2005). Initiating and eliciting in teaching: A reformation of telling. Journal for Research in Mathematics Education, 36(2), 101–136.

    Google Scholar 

  • Lortie, D. C. (1975). Schoolteacher: A sociological study. University of Chicago Press.

    Google Scholar 

  • Munter, C. (2014). Developing visions of high-quality mathematics instruction. Journal for Research in Mathematics Education, 45(4), 584–635.

    Article  Google Scholar 

  • Nathan, M. J., & Petrosino, A. (2003). Expert blind spot among preservice teachers. American Educational Research Journal, 40(4), 905–928.

    Article  Google Scholar 

  • National Council of Teachers of Mathematics [NCTM]. (2014). Principles to actions: Ensuring mathematical success for all. Author.

  • Smith, M. S., & Stein, M. K. (2018). 5 Practices for orchestrating productive mathematics discussions (2nd ed.). The National Council of Teachers of Mathematics.

  • 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.

    Article  Google Scholar 

  • 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 mathematical project. Educational Research and Evaluation, 2(1), 50–80.

    Article  Google Scholar 

  • Stein, M. K., Smith, M., Henningsen, M., & Silver, E. (2000). Implementing standards-based mathematics instruction: A casebook for professional development. Teachers College Press.

  • Tarr, J. E., Reys, R. E., Reys, B. J., Chavez, O., Shih, J., & Osterlind, S. J. (2008). The impact of middle-grades mathematics curricula and the classroom learning environment on student achievement. Journal for Research in Mathematics Education, 39(3), 247–280.

    Google Scholar 

  • Troki, A., Taylor, C., Starlin, T., Sztajn, P., & Heck, D. (2014/2015). Launching a discourse-rich mathematics lesson: Adapted from literacy instruction for use in mathematics, the think-aloud strategy models mathematical thinking. Teaching children mathematics, 21(5), 276–281.

  • Woods, D. M., & Wilhelm, A. G. (2020). Learning to launch complex tasks: How instructional visions influence the exploration of the practice. Mathematics Teacher Educator, 8(3), 105–119.

    Article  Google Scholar 

Download references

Funding

None.

Author information

Authors and Affiliations

  1. Department of Leadership and Teacher Education, University of South Alabama, UCOM 3100, 307 University Blvd., N, Mobile, AL, 36688-0002, USA

    Christopher W. Parrish

  2. Department of Mathematics and Statistics, The College of New Jersey, Ewing Township, NJ, USA

    Rachel B. Snider

  3. Mathematical Sciences, University of Southern Indiana, Evansville, IN, USA

    Mark A. Creager

Authors
  1. Christopher W. Parrish
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rachel B. Snider
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mark A. Creager
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Christopher W. Parrish.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Parrish, C.W., Snider, R.B. & Creager, M.A. Investigating how secondary prospective teachers plan to launch cognitively demanding tasks. J Math Teacher Educ 26, 395–423 (2023). https://doi.org/10.1007/s10857-022-09534-7

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10857-022-09534-7

Keywords

Search

Navigation