Abstract
In this article, we describe a task-centric approach to professional development for mathematics teachers in which teachers’ learning experiences are focused on the selection and implementation of cognitively challenging mathematical tasks. We examined teachers’ selection and implementation of cognitively challenging tasks at three points in time: before and after their participation in the professional development initiative and during a follow-up data collection 2 years later. Data included instructional tasks, samples of student work, and classroom observations, and were compared between the time points to identify changes in teachers’ task selection and implementation and to determine whether these changes were sustained over time. Results indicate that teachers increased and sustained their ability to select high-level instructional tasks and to maintain the level of cognitive demand during instruction. All teachers, however, did not exhibit this pattern. Portraits of teachers who continued to select and enact tasks at a high level are contrasted with those who did not, and factors are identified to account for teachers’ current practices.
Similar content being viewed by others
Notes
A task can be a single problem or activity, or a set of related problems or exercises.
Teachers with at least 3 years of teaching experiences and an interest in improving their classroom instruction were recruited from the region. Not all teachers participating in ESP elected to participate in the data collection. At time points 1 and 2, only one teacher elected not to participate because she was on maternity leave and was not teaching. At time point 3, only seven teachers elected to participate. There are many reasons for this including unwillingness of school districts to allow researchers into their schools and teachers feeling overwhelmed with responsibilities.
Data were also collected from the 18 teachers during the winter of 2005, but is not the focus of the current analysis. For a complete analysis of data on the 18 teachers, see Boston (2006).
References
Arbaugh, F., & Brown, C. A. (2005). Analyzing mathematical tasks: A catalyst for change? Journal of Mathematics Teacher Education, 8, 499–536.
Ball, D. L., & Cohen, D. K. (1999). Developing practice, developing practitioners: Towards a practice-based theory of professional education. In L. Darling-Hammond & G. Sykes (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 3–32). San Francisco: Jossey-Bass.
Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside School. Teachers College Record, 110, 608–645.
Borasi, R., & Fonzi, J. (2002). Engaging in scaffolded instructional innovation. Foundations: Professional development that supports school reform (pp. 83–98). Washington, DC: National Science Foundation.
Boston, M. D. (2006). Developing secondary mathematics teachers’ knowledge of and capacity of implement instructional tasks with high-level cognitive demands. Unpublished doctoral dissertation, (University of Pittsburgh). UMI Dissertation Services, #3223943.
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, 119–156.
Boston, M. D., & Wolf, M. K. (2006). Assessing academic rigor in mathematics instruction: The development of Instructional Quality Assessment Toolkit. National Center for Research on Evaluation, Standards, and Student Testing (CRESST) Report #672.
Clare, L., & Aschbacher, P. R. (2001). Exploring the technical quality of using assignments and student work as indicators of classroom practice. Educational Assessment, 7, 39–59.
Farmer, J. D., Gerretston, H., & Lassak, M. (2003). What teachers take from professional development: Cases and implications. Journal of Mathematics Teacher Education, 6, 331–360.
Henningsen, M. A., & 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, 524–549.
Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K. C., Wearne, D., Murray, H., et al. (1997). Making sense: Teaching and learning mathematics with understanding. Portsmouth: Heinemann.
Hiebert, J., Gallimore, R., Garnier, H., Givvin, K. B., Hollingsworth, H., Jacobs, J., et al. (2003). Teaching mathematics in seven countries: Results from the TIMSS 1999 video study. Washington, DC: NCES.
Hiebert, J., & Wearne, D. (1993). Instructional tasks, classroom discourse, and students’ learning in second-grade arithmetic. American Educational Research Journal, 30, 393–425.
Lappan, G., & Briars, D. (1995). How should mathematics be taught? In M. Carl (Ed.), Prospects for school mathematics (pp. 131–156). Reston, VA: National Council of Teachers of Mathematics.
Matsumura, L. C. (2003). Teachers’ assignments and student work: Opening a window on classroom practice (CSE Tech. Rep. No. 602). Los Angeles: University of California, National Center for Research on Evaluation, Standards, and Student Testing (CRESST).
Simon, M., & Schifter, D. (1991). Towards a constructivist perspective: An intervention study of mathematics teacher development. Educational Studies in Mathematics, 22, 309–331.
Smith, M. S. (2000). Balancing the old and new: An experienced middle school teacher’s learning in the context of mathematics instructional reform. The Elementary School Journal, 100, 351–375.
Smith, M. S. (2001). Practice-based professional development for teachers of mathematics. Reston, VA: NCTM.
Smith, M. S., Bill, V., & Hughes, E. K. (2008). Thinking through a lesson protocol: A key for successfully implementing high-level tasks. Mathematics Teaching in the Middle School, 14, 132–138.
Stein, M. K., Grover, B., & 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, 455–488.
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 mathematics project. Educational Research and Evaluation, 2, 50–80.
Stein, M. K., Smith, M. S., Henningsen, M., & Silver, E. A. (2000, 2009). Implementing standards-based mathematics instruction: A casebook for professional development. New York: Teachers College Press.
Stigler, J. W., & Hiebert, J. (2004). Improving mathematics teaching. Educational Leadership, 61, 12–16.
Sykes, G., & Bird, T. (1992). Teacher education and the case idea. In G. Grant (Ed.), Review of Research in Education (Vol. 18, pp. 457–521). Washington, DC: American Educational Research Association.
Tarr, J. E., Reys, R. E., Reys, B. J., Chavez, O., Shih, J., & Osterlind, (2008). The impact of middles grades mathematics curricula on student achievement and the classroom learning environment. Journal for Research in Mathematics Education, 39, 247–280.
Thompson, C. L., & Zeuli, J. S. (1999). The frame and the tapestry: Standards-based reform and professional development. In L. Darling-Hammond & G. Sykes (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 341–375). San Francisco: Jossey-Bass.
Watson, A., & Sullivan, P. (2008). Teachers learning about tasks and lessons. In D. Tirosh & T. Wood (Eds.), International handbook of mathematics teacher education: Vol. 2: Tools and Processes in Mathematics Teacher Education (pp. 109–134). Rotterdam: Sense Publishers.
Weiss, I. R., & Pasley, J. P. (2004). What is high quality instruction? Educational Leadership, 61, 24–28.
Zaslavsky, O. (1995). Open-ended tasks as a trigger for mathematics teachers’ professional development. For the Learning of Mathematics, 15, 15–20.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Boston, M.D., Smith, M.S. A ‘task-centric approach’ to professional development: enhancing and sustaining mathematics teachers’ ability to implement cognitively challenging mathematical tasks. ZDM Mathematics Education 43, 965–977 (2011). https://doi.org/10.1007/s11858-011-0353-2
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11858-011-0353-2