Vol. 30 No. 2 (2022)

Preservice Teachers’ Conceptualizations of Mathematical Tasks

Bima Kumari Sapkota
Purdue University

Published 2022-03-04


  • task frameworks,
  • mathematical tasks,
  • preservice teachers,
  • task description


This study reports how 12 secondary mathematics preservice teachers (M-PSTs) described characteristics of Mathematical Tasks after participating in instructional activities, including reading, reflecting, and discussing task characteristics from two mathematics task frameworks and related book chapters. The findings demonstrated that after engaging in these activities, M-PSTs used formal, research-informed language in a way that highlighted student-related factors (e.g., student prior knowledge) and contextual factors (e.g., class time constraints), suggesting that the language and concepts offered through the task frameworks initiated M-PSTs’ nuanced task descriptions. The implications of the instructional activities in teacher education programs to enhance M-PSTs’ conceptions of tasks are discussed.


  1. Anhalt, C. O., & Cortez, R. (2016). Developing understanding of mathematical modeling in secondary teacher preparation. Journal of Mathematics Teacher Education, 19(6), 523-545. https://doi.org/10.1007/s10857-015-9309-8
  2. Anhalt, C. O., Ward, R. A., & Vinson, K. D. (2006). Teacher candidates’ growth in designing mathematical tasks as exhibited in their lesson planning. The Teacher Educator, 41(3), 172-186. https://doi.org/10.1080/08878730609555382
  3. Arbaugh, F., & Brown, C. A. (2005). Analyzing mathematical tasks: A catalyst for change? Journal of Mathematics Teacher Education, 8(6), 499-536. https://doi.org/10.1007/s10857-006-6585-3
  4. Boaler, J. (2016). Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages and innovative teaching. Jossey-Bass.
  5. Chi, M. T. H. (1997). Quantifying qualitative analyses of verbal data: A practical guide. The Journal of Learning Science, 6(3), 271-315. https://doi.org/10.1207/s15327809jls0603_1
  6. Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers’ practices. Educational Studies in Mathematics, 52(3), 243-270. https://doi.org/10.1023/A:1024364304664
  7. Crespo, S., & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal of Mathematics Teacher Education, 11(5), 395-415. https://doi.org/10.1007/s10857-008-9081-0
  8. 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. https://doi.org/10.2307/749690
  9. Hiebert, J., & Wearne, D. (1993). Instructional tasks, classroom discourse, and students’ learning in second-grade arithmetic. American Educational Research Journal, 30(2), 393-425. https://doi.org/10.3102%2F00028312030002393
  10. Lee, E.-J., Lee, K.-H., & Park, M. (2019). Developing preservice teachers’ abilities to modify mathematical tasks: Using noticing-oriented activities. International Journal of Science and Mathematics Education, 17(5), 965-985. https://doi.org/10.1007/s10763-018-9891-1
  11. Leinwand, S., & Wiggins, G. (1991). Criteria for performance tasks. In J. K. Stenmark (Ed.), Mathematics assessment: Myths, models, good questions, and practical suggestions (pp.16-16). National Council of Teachers of Mathematics.
  12. National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Author.
  13. National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Author.
  14. Norton, A., & Kastberg, S. (2012). Learning to pose cognitively demanding tasks through letter writing. Journal of Mathematics Teacher Education, 15(2), 109-130. https://doi.org/10.1007/s10857-011-9193-9
  15. Saldaña, J. (2016). The coding manual for qualitative researchers. Sage.
  16. Smith, M. S., Stein, M. K., Arbaugh, F., Brown, C., & Mossgrove, J. (2004). Characterizing the cognitive demands of mathematical tasks: A task sorting activity. In G. Bright & R. Rubenstein (Eds.), Professional development guidebook for perspectives on teaching of mathematics: Companion to the sixty-sixth yearbook (pp. 45-72). National Council of Teachers of Mathematics.
  17. 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. https://doi.org/10.3102%2F00028312033002455
  18. Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2000). Implementing standards-based math instruction: A casebook for professional development. Teachers College Press.
  19. Wieman, R., & Arbaugh, F. (2013). Success from the start: Your first years teaching secondary mathematics. National Council of Teachers of Mathematics.
  20. Yin, R. K. (2017). Case study research and applications: Design and methods (6th ed.). Sage.