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People often ask us to compare the Problem-Solving Cycle to other models of professional development. We typically respond that, in many ways, the Problem-Solving Cycle is most similar to "lesson study," a type of teacher professional development with which Americans are becoming increasingly familiar. Like lesson study, the Problem-Solving Cycle provides a structure for a group of teachers to work together for a considerable length of time and carefully study issues around teaching and learning that are of interest to them. A key difference between these two models is that lesson study focuses on designing, carrying out, and reflecting on a designated lesson, whereas the PSC focuses on solving, teaching, and learning from a designated mathematics problem. Another important distinction is that a knowledgeable facilitator plays a prominent role in carrying out the PSC, whereas in lesson study there typically is not a facilitator to plan or guide the professional development sessions. What is the time frame for implementing PSC? Each "cycle" of three workshops roughly corresponds to an academic semester, so that teachers would participate in two cycles per school year (six workshops per school year). Each workshop lasts from 3 to 6 hours, depending on teachers' availability. With longer sessions, it is possible to delve deeper into issues and to share more examples from the teachers' videotaped lessons. Successive iterations of the Problem-Solving Cycle build on one another and capitalize on teachers' expanding knowledge, skills, and interests. Each cycle is focused on a unique mathematical task and specific issues related to mathematics teaching and learning. By regularly organizing workshops that are focused, productive, and collegial, facilitators play a critical role in ensuring the long-term participation of their teachers. As they become part of a learning community, we have found that teachers take genuine pleasure in gaining and sharing knowledge and working to improve their craft. Do workshops need a facilitator? The Problem-Solving Cycle is designed to have a facilitator. Facilitators of the Problem-Solving Cycle might be mathematics coaches, department chairs, teacher leaders, district-level leaders, or other teacher educators who are knowledgeable about the model and who are enthusiastic about using it to work with teachers. The PSC model is built on the premise that teachers can and should provide input into each "cycle" and each workshop within a cycle. At the same time, it is the facilitator's role to gather this input and to respond to the participants’ developing needs and interests. Carefully planning each workshop and providing structured guidance during the workshops is essential to the success of the PSC model. For example, in advance of each workshop facilitators need to consider what topics the teachers have been struggling with or seem particularly interested in discussing (including issues related to mathematics content, pedagogy, and students), and what aspects of the community need to be addressed. In addition, facilitators select the mathematical task for each PSC and choose the video clips for the teachers to watch and discuss. How can I use the PSC? The Problem-Solving Cycle is designed to have a facilitator. Facilitators of the Problem-Solving Cycle might be mathematics coaches, department chairs, teacher leaders, district-level leaders, or other teacher educators who are knowledgeable about the model and who are enthusiastic about using it to work with teachers. The PSC model is intentionally designed to be flexibly implemented and responsive to the needs of facilitators, teachers, and school district personnel. It is built on the premise that teachers can and should provide input into each "cycle" and each workshop within a cycle. At the same time, it is the facilitator’s role to gather this input and to respond to the participants’ developing needs and interests. The Problem-Solving Cycle is designed to complement other professional development activities that teachers might be involved in, not compete with them. Because the Problem-Solving Cycle contains so much flexibility, it can be used to complement and reinforce "standards" that are designated by individual schools, districts, and states, and it can be used to support a wide variety of mathematics curricula. Forming a tightly knit community is central to the effectiveness of the professional development; community development is thus a strong focus of this manual. Our best guess is that the Problem-Solving Cycle would work best with a group of teachers that is neither too small nor too large. We suggest including 4 to 15 teachers. Similar to regularly scheduled "department meetings," we imagine that participation in the Problem-Solving Cycle could become part of teachers' professional routines that continue over the duration of their career. The Problem-Solving Cycle model attempts to delicately balance the realistic schedules of teachers with the delivery of workshops that are long and frequent enough to have an impact. |
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