unexpected responses from their students. Coping with these issues in the classroom pushed
their knowledge, perspectives, and practices beyond what they had experienced before and
provided a rich set of experiences on which to reflect. Subsequent revisions to each learning
activity completed the intended cycles of analytical thinking about their teaching practices.
Implications for Professional Development
We found the following professional development activities to be critical in effecting
significant change for these two teachers. A vital role of professional development is to facilitate
and support these activities.
1) Teachers need to engage in the entire process of design, implementation, reflection, and
revision of instructional materials in their own classrooms. It is not sufficient for teachers to see
this process modeled in a professional development workshop/institute. They must be involved
in all phases in this process.
2) Learning activities and curricula must be designed to complement teachers’ current
textbook materials and standards, yet be adaptable in more than one way to meet differing needs.
The key to this adaptability is to design activities that connect multiple concepts. Pedagogically,
this allows for multiple entry points and multiple extensions. Mathematically, this maximizes
the impact of each activity.
3) Reflections must focus on comparisons of actual experiences with different teaching
practices. It is not enough for a teacher to compare a learning experience in a professional
development institute/workshop to his or her current teaching experiences. It is the
implementation of alternative teaching practices that sheds new light on current teaching
practices, hence fueling the reflective process in a powerful way.
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