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R & D Activities: Project Details


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Beyond Implementation: Focusing On Challenge And Learning

When school districts adopt innovative curriculum materials, some professional development support is typically offered in order to familiarize teachers with the content and character (e.g., sequence, lesson style) of the new materials. Teachers often become comfortable implementing innovative curriculum materials after a year or two of initial support, but then they hit a plateau. What is frequently missing at this critical point, which we identify as the implementation plateau, is help for teachers in supporting student engagement with the complex intellectual tasks that are included in the curriculum materials. This absence has been particularly noticeable in U. S. mathematics classrooms. BIFOCAL (Beyond Implementation: Focusing On Challenge And Learning), a multi-year advanced professional development project, provides support to local teachers, schools, and districts that assists in the movement beyond the initial implementation. Our project addresses the needs of middle school mathematics teachers who are experienced users of an innovative mathematics curriculum for the middle grades, Connected Mathematics (Lappan et al., 1998).

BIFOCAL has unfolded in three phases. In Phase 1 (July 2002 to June 2004), we identified local school districts that had been using standards-based middle grades curriculum materials for at least three years and contacted them to solicit indications of potential interest in participating in the project. Four small school districts with a total of five middle schools, each of which had been using Connected Mathematics for several years, agreed to participate. In this first phase we aimed at preparing these participants to become mathematics teacher leaders in their schools and districts. In Phase 2 (July 2004 to June 2005), the project was expanded in two ways: First, additional participants from he already participating schools and districts joined the project. Second, in addition to the large group sessions, school-based professional development sessions were led by the participants from year one. In Phase 3 (July 2005 to date), we incorporated assessment for learning as an additional focus of the project, with the goal provide an iterative and adaptive professional development approach (i.e., an approach that addresses participants’ needs and also offers them significant and recurrent opportunities to dwell on critical aspects of their work). During the current year more emphasis has also been placed on providing year-one participants with more structured opportunities to successfully undertake the role of mathematics teacher leaders in their schools and districts.

Our work so far has been informed by several frameworks and perspectives, including Practice-Based approaches (Ball & Cohen, 1999; Smith, 2003), the Mathematical Task Framework (Silver & Stein, 1996), Case Analysis and Discussion (Shulman, 2003), and Lesson Study (Hughes & Smith, 2004; Lewis, 2002; Lewis, Perry, and Murata, 2006). In particular, our teacher participants have had the opportunity to use case studies as well as their on-going lesson planning to identify the features of intellectually challenging tasks, understand the teacher moves that sustain or diminish the challenge of these tasks, and the role that anticipation of and building on students’ thinking play in successful implementation of such tasks. The cases, based on documented episodes of teaching in racially and linguistically diverse urban 6th-8th grade classrooms in the QUASAR project (Silver, Smith, & Nelson, 1995; Smith, Silver, & Stein, 2005a, 2005b, 2005c; Stein, Smith, Henningsen, & Silver, 2000), were developed as part of COMET (Cases of Mathematics Instruction to Enhance Teaching), another NSF-funded research project (Stein et al., 2000).

The BIFOCAL research team is led by principal investigators Valerie Mills (Oakland Schools) and Edward Silver (University of Michigan). Current graduate and postgraduate student research assistants are Alison Castro, Charalambos Charalambous, Lawrence Clark, Hala Ghousseini, Melissa Gilbert, Dana Gosen, and Jenny Sealy. Beatriz Font Strawhun serves as the project coordinator.

Download NCSM Presentation on BI:FOCAL


Ball, D., & Cohen, D. (1999). Developing practice, developing practitioners. In L. Darling-Hammond & G. Sykes (Eds.), Teaching as the learning profession (pp. 3-32). San Francisco, CA: Jossey-Bass Publishers.

Hughes, E. K., & Smith, M. S. (2004). Thinking through a lesson: Lesson planning as evidence of and a vehicle for teacher learning. Paper presented at the annual meeting of the American Educational Research Association. San Diego, CA.

Lappan, G., Fey, J. T., Fitzgerald, W. M., et al. (1998). Connected mathematics project. White Plains, NY: Dale Seymour.

Lewis, C. (2002). Lesson Study: A handbook of teacher-led instructional change. Philadepphia: Research for Better Schools.

Lewis, C., Perry, R., & Murata, A. (2006). How should research contribute to instructional improvement? The case of lesson study. Educational Researcher, 35(3). 3-14.

Shulman, J. H. (2003, April). From practice to theory and back again: Cases as instruments for professional development. Paper presented at the annual meeting of the American Educational Research Association, Chicago, IL.

Silver, E. A., Smith, M. S., & Nelson, B. S. (1995). The QUASAR project: Equity concerns meet mathematics education reform in the middle school. In W. Secada, E. Fennema, & L. Byrd Adajian (Eds.), New directions in equity in mathematics education (pp. 9-56). New York: Cambridge University Press.

Silver, E. A., & Stein, M. K. (1996). The QUASAR project: The "revolution of the possible" in mathematics instructional reform in urban middle schools. Urban Education, 30(4), 476-521.

Smith, M.S. (2003). Practice-based professional development for teachers of mathematics. Reston: NCTM.

Smith, M.S., Silver, E.A., & Stein, M.K. (2005a). Improving instruction in geometry and measurement: Using cases to transform mathematics teaching and learning (Vol. 3). New York: Teachers College Press.

Smith, M.S., Silver, E.A., & Stein, M.K. (2005b). Improving instruction in rational numbers and proportionality: Using cases to transform mathematics teaching and learning (Vol. 1). New York: Teachers College Press.

Smith, M.S., Silver, E.A., & Stein, M.K (2005c). Improving instruction in algebra: Using cases to transform mathematics teaching and learning (Vol. 2). New York: Teachers College Press.

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

Additional References:

Articles on BIFOCAL:

Silver, E. A., Ghousseini, H., Gosen, D., Charalambous, C., & Strawhun, B.T.F. (2005) Moving from rhetoric to praxis: Issues faced by teachers in having students consider multiple solutions for problems in the mathematics classroom. Journal of Mathematical Behavior, 24, 287-301.

Silver, E. A., Mills, V., Castro, A., & Ghousseini, H. (In press). Blending elements of lesson study with case analysis and discussion: A promising professional development synergy. In K. Lynch-Davis & R. L. Ryder (Eds.), The work of mathematics teacher educators: Continuing the conversation. San Diego, CA: Association of Mathematics Teacher Educators.

Articles on Origins of QUASAR/MTF:

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, 524-549.

Stein, M.K., Grover, B.W., & Henningsen, M.A. (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., & Silver, E. A. (1999). The development of professional developers: Learning to assist teachers in new settings in new ways. Harvard Educational Review, 69(3), 237-269.