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All the options listed above can support the efforts of teachers engaging in instructional innovation. The choice of specific options, however, will depend for the most part on the available personnel and financial resources and the expressed needs of the teachers.

The variations discussed in this section show that supported field experiences do not just take place in the teacher’s own classroom or in one-on-one interactions with a teacher educator. Rather, important scaffolding can occur before and after the field experience in different settings, such as Summer Institutes or other large group meetings and in small groups, too.

Scaffolded field experiences are probably one of the most challenging forms of professional development because the provider must have high levels of expertise in multiple areas. In order to evaluate and guide other teachers’ efforts toward instructional innovation, teacher educators facilitating these experiences need to have a good understanding of mathematics in a wide variety of areas and considerable pedagogical expertise. Specific training in classroom observation and mentoring strategies is also advisable.

Teacher learning needs addressed

Our discussion thus far suggests that, depending on the nature of the innovative teaching experience and the support provided for it, scaffolded field experiences may effectively address several of the teacher learning needs we identified in Chapter 1:

Developing a vision and commitment to school mathematics reform. For many teachers, seeing a non-traditional approach to teaching mathematics succeed in their classrooms and witnessing their students’ enthusiastic responses may be the most powerful way to grasp what school mathematics reform is all about. Indeed, once teachers see what their students can do when given the opportunity to explore and make sense of mathematics, they are hooked!
Nevertheless, certain conditions need to occur for this to happen. First, the innovations that teachers implement in their classes need to truly enact school mathematics reform. Second, they have to be sufficiently well-designed and implemented, so that students actually have new opportunities to learn and thus to show their teacher what they can do. Either conditions are difficult to ensure in the case of teacher-designed experiences. Therefore, having teachers begin with field-tested materials, in addition to receiving sufficient in-class support, may be advisable to ensure that teachers’ first attempts at innovation are successful.

It is also critical to offer opportunities for individual reflection and sharing so that teachers can recognize the significance of the changes they witness in their classrooms and the implications for school mathematics reform. Such cognizance is illustrated by the conversations that took place when teachers shared their first experience with inquiry in Illustration 7.

Strengthening one’s knowledge of mathematics. From years of offering scaffolded field experiences, we know that the maxim, “You learn something best when you have to teach it,” is really true. After they use open-ended problems and a student-centered approach in their classrooms, teachers regularly report learning new solutions and strategies from their own students! Even more substantial opportunities to learn new mathematics occur when the scaffolded field experience entails implementing replacement units or units from one of the new Standards-based comprehensive curricula. Since these materials have been designed to address new learning standards and to highlight “big mathematical ideas,” they offer new perspectives and insights on familiar – and not so familiar – mathematical topics for both teachers and students. Again, opportunities to learn new mathematics and to challenge dysfunctional mathematical beliefs are enhanced when providers build time for reflection and sharing into the field experiences that focuses on mathematical issues.
Understanding the pedagogical theories that underlie school mathematics reform. While scaffolded field experiences by themselves are not sufficient to teach teachers the theories that underlie the teaching and learning practices of mathematics reform, they can help further this goal. First, scaffolded experiences can motivate teachers to learn more about pedagogical theories not only as a way to make sense of what they witness in their classes but also to justify their instructional choices to other teachers, parents and administrators. Consequently, teachers may be more willing to attend presentations or read articles they may have previously dismissed as “too theoretical” and, therefore, irrelevant to classroom practice. Second, these classroom experiences can provide an experiential base for teachers to interpret and critically examine competing pedagogical theories.
Understanding students’ mathematical thinking. Scaffolded field experiences can provide teachers with multiple opportunities to understand their students’ thinking. This understanding occurs to some extent any time teachers listen to their students’ explain how they solved complex and open-ended tasks, which is one of the key practices promoted by school mathematics reform. However, this teacher learning need is supported best when the scaffolded field experience includes opportunities to examine students’ work systematically with other teachers.
Learning to use effective teaching and assessment strategies. Addressing this teacher learning need is probably the most obvious goal of scaffolded field experiences, especially at the beginning of a professional development program. No matter how effectively a new teaching practice is modeled in an experience-as-learners or in a classroom video, it is only when teachers try it out in their own classrooms that they really understand what it takes to make it work. However, the extent to which this happens depends once again on the design of the innovative teaching experience and teachers’ opportunities for receiving feedback on their implementations of the new teaching practice.
Becoming familiar with exemplary instructional materials and resources. Scaffolded field experiences are the best way for teachers to become acquainted with exemplary instructional materials and to appreciate fully the role these materials can play in supporting instructional innovation. Many of the teachers who participated in the experiences reported in Illustrations 7 and 8 voiced the belief that they could not have come up with a unit of the same quality on their own. To a lesser extent, scaffolded field experiences based on teacher-designed units might also provide motivation and opportunities to examine exemplary instructional materials, especially when teachers are encouraged to look at these resources for ideas to adapt for their own unit.
Understanding equity issues and their classroom implications. Scaffolded field experiences have the potential to contribute greatly to teachers’ understanding issues of equality in the classroom, especially when the implementation takes place in a diverse instructional setting and strategies for differentiated instruction are explicitly introduced. Implementing a unit that has been designed to address multiple learning styles and needs can allow all students in the class to show what they are capable of doing. This, in turn, may surprise many teachers and invite them to critically examine their expectations and biases. Explicit reflections about equity issues and their implications in each teacher’s specific context are also critical to capitalize on the potential of scaffolded field experiences to address this teacher learning need.
Coping with the emotional aspects of engaging in instructional innovation. Teachers are likely to experience emotions ranging from elation to despair as they try innovative instructional experiences, especially the first time. Consequently, it is especially important that any scaffolded field experience include ongoing opportunities for teachers to share their experiences and feelings with peers. They need reassurance that their reactions are not unique. They also need to hear from more experienced peers and mentors that there is “light at the end of the tunnel.” Scaffolded field experiences should include a reflective component to meet this teacher learning need.
Developing an attitude of inquiry towards one’s practice. Helping teachers become more reflective about their practice should indeed be one of the main goals of any scaffolded field experience. The extent to which such experiences can promote the habit of inquiry, however, depends on the structures and opportunities for reflecting and sharing provided to participants. The more teachers are invited to critically examine what they have done in their field experiences, whether in reflective journals, discussions with peer-support groups, or debriefing meetings, the more they can appreciate the value of such reflections and learn strategies to continue reflecting on their own.

Summary

Scaffolded field experiences can be extremely effective in addressing many of the teacher learning needs we identified in Chapter 1. At the same time, the potential of this type of professional development for providing teachers with opportunities to learn new mathematics, to try out new teaching practices and materials, and to understand equity is greatly increased when teachers use exemplary instructional materials rather than units of their own design. Structures for teachers to talk and share with others, both peers and experts, also ensure that teachers can not only learn from their experiences but also get emotional support. The success of scaffolded field experiences also depends on sufficient resources being available to provide the support that teachers need.

Suggested follow-up resources

Most of the new Standards-based exemplary materials now available (including all the NSF-funded comprehensive curricula listed earlier in Figure 7, along with the address of their respective websites) come together with information designed to provide support to the teachers implementing them. These may include explanations about the mathematics addressed in various units, examples of lesson plans, suggestions about how to implement certain activities, and even recommendations about how specific tasks may be modified to meet the needs of students disadvantaged by some disabilities or limited language proficiency. These supporting materials can also be extremely helpful for teacher educators who want to support the implementation of any of these curricula.

There are not, instead, many professional development materials that have been published specifically to support teacher educators in orchestrating effective field experiences. If you are interested in learning more about ways to organize and support innovative teaching experiences, we recommend the following unpublished resources:

Fonzi, J. & Borasi, R. (2000). Providing in-class support (videotape + facilitator’s guide) (available from the authors)
This 40-minute videotape captures a classroom experience in which a teacher educator plays a number of different roles to support the classroom teacher in implementing an inquiry unit with her sixth grade class. The accompanying guide offers additional information and a commentary on this experience and a set of questions to help teacher educators use this illustration as a catalyst for an inquiry on providing effective in-class support.
Fonzi, J. & Borasi, R. (2000). Debriefing classroom observations (videotape + facilitator’s guide) (available from the authors)
This 40-minute videotape features excerpts from a series of classroom observations and debriefing meetings about the implementation of an inquiry unit in a eighth-grade class. The accompanying guide offers additional information, a commentary on this experience and a set of questions to help teacher educators use this illustration for an inquiry on conducting classroom observations. The goal of the inquiry is to show how debriefings can be a vehicle for professional development rather than teacher evaluation.
Borasi, R. & Fonzi, J. (in preparation). Introducing math teachers to inquiry: A framework and supporting materials for teacher educators. (multimedia package) (available from the authors)
These materials provide descriptions and supporting materials for orchestrating a supported field experience similar to the one portrayed in Illustration 7.
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CHAPTER 7 continued