
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 multiyear 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 standardsbased 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, schoolbased 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
participantsâ€™ 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 yearone 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 PracticeBased 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 ongoing
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 studentsâ€™ thinking play in successful implementation
of such tasks. The cases, based on documented episodes of teaching
in racially and linguistically diverse urban 6th8th 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 NSFfunded 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
References:
Ball, D., & Cohen, D. (1999). Developing practice, developing
practitioners. In L. DarlingHammond & G. Sykes (Eds.), Teaching
as the learning profession (pp. 332). San Francisco, CA: JosseyBass
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 teacherled 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). 314.
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.
956). 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), 476521.
Smith, M.S. (2003). Practicebased 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 standardsbased 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, 287301.
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. LynchDavis
& 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: Classroombased factors that support and inhibit
highlevel mathematical thinking and reasoning. Journal for Research
in Mathematics Education, 28, 524549.
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, 455488.
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, 5080.
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), 237269.
