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Methods course documentation
Planning and implementing a new inquiry unit (D7.5)
Logistics and scheduling information (by Raffaella Borasi)
Expectations about the design and implementation of a new inquiry
unit as part of the participants' field experience
As mentioned elsewhere, the elementary and secondary math pre-service
teachers who participated in our Methods course had different expectations
with respect to their field experiences. In the case of the elementary pre-service
teachers, the Methods course instructor had essentially no responsibilities
(and, thus, no control) over these participants' student teaching experiences.
However, Methods course students were given the option to report on an "innovative
math experience" that they had developed in their concurrent student
teaching as a way to fulfill the "final project" for that course,
and a few students chose that option.
In the case of the secondary math pre-service teachers, instead, the
Methods course instructor was also the student teaching supervisor. As part
of their student teaching requirements (in the semester following the Methods
course), these participants had to design and implement an "innovative
unit", carefully monitor this experience and prepare a written report
about its implementation and evalution. More specifically, the expectations
for this field experience can be summarized as follows (see Instructional
Materials for a more detailed description):
- The unit had to last a minimum of 1 week of instruction and be informed
by the recommendations articulated in the NCTM Standards. (Note that this
meant that these "innovative units" were not necessarily "inquiry"
units -- although the examples included in the Participants' Work for
this section were specifically selected among those falling into that category).
- The student teacher had to prepare a set of detailed written plans
prior to beginning implementation; these plans were to be shared
and discussed with the instructor/supervisor and usually considerably revised
before beginning the implementation.
- The student teacher had to collect a rich documentation on the implementation
of the unit -- including: written record of initial plan; written daily
accounts of each lesson, including copies of all the instructional materials
used in that lesson; copies of students' work (at least for all major assignments).
- The student teacher had to create a detailed report of the instructional
experience, based on the data collected during the implementation of the
unit; this report should cover both the planning and implementation of
the unit, an analysis of what students learned, and a final written reflection
on the experience.
It is also important to keep in mind that the great majority of the students
teachers did not have an opportunity to first adapt and implement
one of our illustrative units. Thus, for most participants this represented
their first "experience as teachers" with teaching math through
inquiry.
Summary of the kind of support provided to participants for this component
of the field experience
Secondary math pre-service teachers benefited from the following support
as they planned and implemented a unit of their own design as part of their
student teaching experience:
- The university supervisor was expected to extensively support
the planning of this unit -- especially considering that this was
the first time that these participants would engage in the process of planning
an innovative instructional experience (let alone a "new" inquiry
unit!).
- The university supervisor was expected to provide some in-class
support as the innovative unit was implemented.
- Participants were offered on-going multiple opportunity for sharing
and reflection with peers -- including: individual meetings with
the university supervisor; weekly forum with other students teachers, weekly
shared journals, as well as specific "sharing sessions" scheduled
to report on the preliminary plans of each participants' innovative unit,
and on the results of their implementation (as part of the mathematics
education course concurrent with these students' field experiences).
- The university supervisor also provided some support specifically in
the preparation of the final report.
In what follows, we provide further detail about the support provided
for each of the categories identified above. Since in some cases this was
essentially the same as what already described in Section D6, in the following
sections we have often reproduced (with adaptations when appropriate) relevant
excerpts from the "Logistics and scheduling information" documents
included in that section of the materials.
Further information on the kind of support provided for planning of
a new inquiry unit
First of all, student teachers were encouraged to identify the topic
of their "innovative unit" early on, and share it with the university
supervisor, so that she could begin to gather possible resources and readings
that could inform the students' planning. Students were also encouraged
to share their beginning ideas with the supervisor and/or peers, so as to
gather feedback at this initial and crucial stage of the planning -- sometimes,
this "sharing/brainstorming" session took place in one of the
early meetings of the seminar and/or math education course concurrent with
the student teaching experience.
Each student teacher was then expected to have at least one meeting with
the university supervisor prior to beginning the implementation of
the unit. In preparation to this meeting, the student had prepared and shared
with the supervisor a detailed written plan for the unit. During the meeting,
this plan was discussed in detail, and several modifications usually made.
At this stage, the university supervisor also helped enriching the unit
by providing further resources and instructional materials as appropriate.
Further support on the planning also occurred during their implementation
of the unit, as student teachers discussed their students' reactions and
input and asked for suggestions as they attempted to modify and improve
their original plans.
Further information on the kind of "in-class support" provided
during the implementation of a new inquiry unit
As much as possible given the limited resources usually allotted to student
teaching supervision, the university supervisor has usually tried to focus
classroom visits during the time the innovative unit is implemented, so
as to provide support to the students in this important occasion -- as well
as to evaluate their teaching in a "best scenario" kind of situation.
The following considerations can help clarify the nature of these visits
and how the university surpevisor tries to provide classroom support to
the student teacher:
- First, it is critical, prior to entering the classroom, that
the student teacher and cooperating teacher understand that the supervisor
is there to support the student teacher. This view of the supervisor can
be established by making clear from the very beginning that, while they
have considerable experience planning and implementing an inquiry approach,
the supervisor by no means has all the answers. We have found that we can
operationalize this view by making public our expectations that a) we will
all make mistakes but we can "recover" from anything if we identify
it; and, b) learning to teach through inquiry requires that we "problem
solve together", each contributing ideas informed by our previous
experiences and expertise.
- We have also learned some strategies for putting such a collaborative
problem solving model into practice. First, there should be an expectation
that the cooperating teacher be present in the classes attended by the
supervisor and the debriefing meetings. Though it may not always be possible
for the cooperating teacher to attend the entire debriefing meeting we
have found that their attendance significantly enhances the collaboration.
During the debriefing meetings it is very important that the student teacher
begin the discussions by sharing thoughts/reactions to the lesson, questions/concerns
s/he identified, or new ideas. We have found that student teachers frequently
identify the same issues that we would have identified, thus helping us
find the fine line between telling too much and not telling enough as well
as eliminating some potentially uncomfortable situations. However, for
this sharing to be useful the supervisor must make sure that the debriefing
meetings include time for both reflection and planning in light
of the reflections. With respect to the planning, even if they may not
be the best possible choices, it is critical that the supervisor accepts
and supports some of the student teacher's and cooperating teacher's ideas
as well as offering their own suggestions. The point is to remember that
there is no "absolute right way" and we can learn a lot from
both successes and failures. The collaboration can be further supported
if the supervisor and cooperating teacher occasionally accept some of the
responsibility for finding the resources or planning activities.
- Finally, we would like to share some of the things student teachers
have said were helpful:
- discussing with the supervisor, in advance of a series of classroom
visits, what the student teacher would like to get from the collaboration
- having the supervisor or cooperating teacher offer subtle interventions
during a lesson to re-direct the student teacher or make explicit the value
of a student's comment or action (for example, during a discussion the
supervisor might add a comment like "I was just working out what John
suggested and you know what I found…", or "John, I'm confused
about what you mean, could you say more")
- receiving a supervisor/cooperating teacher prepared "script"
of the lesson as it actually played out; student teachers have indicate
that they "missed" some of the comments, or had forgotten that
something took place, or just liked having the record to reflect on
- hearing what the supervisor/cooperating teacher found powerful - valuable
- interesting - problematic in the students' interpretations, understandings,
or processes
- hearing a report of the discussions of small groups or individuals
with whom the facilitator worked
- hearing about the strategies other teachers have used to accomplish
particular tasks
- having the supervisor/cooperating teacher share how they think students
will respond to a particular idea
- grappling with mathematical issues / content together and then helping
them make instructional decisions - what to do, when, how
- knowing that the supervisor was available and interested in discussing
lessons and experiences.
Further information on the opportunities for sharing and reflection
provided with respect to new inquiry units
As discussed at more length in Section D6.5, sharing what was happening
during the field experiences, and reflecting on these experiences, was an
important component of our teacher preparation program. In what follows,
we will briefly summarize the complementary opportunities for such sharing
and reflections offered to our participants with respect to the experience
of planning and implementing a unit of their own design:
- The planning and classroom support sessions involving the individual
student teacher and the school facilitator -- as described in
the previous subsection.
- The weekly meetings of seminar/forum for reflection concurrent with
student teaching, which involved all of the secondary math student
teachers and their university supervisor. These meetings were designed
for the main purpose of providing participants with a forum for sharing
and reflecting on their on-going classroom experiences, and in fact participants
often used these meetings to share some of their tentative plans and get
feedback, as well as to share their impressions after implementing their
innovative lessons.
- The shared journals student teachers were expected to write
and share with each other on a weekly basis.
- Specific sessions of the math education course concurrent with student
teaching were scheduled for presentation on the plans for the innovative
units (prior to their implementation) and on the results of implementing
those plans (after the implementation of participants' own inquiry
units).
Further information on the support provided for monitoring and reporting
on a new inquiry unit
The university supervisor supported the student teachers' creation of
written reports on their units in a variety of ways, including:
- providing suggestions about the possible contents and formats of this
report;
- providing models of reports other student teachers had created in the
past;
- providing feedback on early drafts;
- suggesting revisions to drafts created by the teacher.
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