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.
