Title:
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Using Case Inquiry Approach (CIA) for In-Service Education of Mathematics Teachers: A Critical Inquiry
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This study aims to examine, detennine the efficacy of, and ultimately improve one of
the forms of teacher education that was developed in Israel to address the problems
revealed by the poor achievements of Israeli elementary school children in
international tests. It focuses on a reflective model I designed, comprised of a series
of Case Inquiry Approach (CIA) workshops. The goal of these workshops was to
enrich teachers' knowledge (content and pedagogical), develop their ability to reflect
on their own practice, and encourage professional collaboration between mathematics
teachers working together in schools. The CIA model is based on the analysis of
teaching and learning 'cases' from mathematics lessons, usually in the form of an
unexpected in-class occurrence. The 'case' analysis consists of three main stages:
Recognizing a case within a lesson; considering possible reasons for the case's
occurrence; and thinking of possible solutions.
The purpose ofthis study was to discover to what extent the stated goals of this
teaching model were fulfilled.
The study was performed according to an action research method, which allowed me,
as both researcher and creator ofthe model in question, to examine my own practice
and comprehend the strengths and weaknesses ofmy design. The data analysis
' yielded several positive results, showing that the CIA workshops deepened and
enriched the mathematical and pedagogical knowledge ofthe teachers, and expanded
their pedagogical abilities by focusing their reflection on students' thought processes.
The reflective discussions in the workshops focused either on the story ofthe
experience of an unknown teacher, (a case taken from professional literature), or on a
story taken from a participating teacher's personal experience. The study shows that
teachers were reluctant to bring their personal cases forward for discussion. It seems
that the teachers were threatened by the exposure of unexpected occurrences in their
classrooms, worrying that these cases were harmful to their professional identity.
They appeared to view the occurrence of a 'case' as symptomatic ofan inadequacy on
the teacher's part, and were unwilling to reveal such a weakness in themselves. Instead of discussing 'cases', they offered 'substitute stories' -'cases' that occurred in
other teachers' classes, 'cases' initiated purposely by themselves, or 'nice stories'.
Another unexpected phenomenon relates to the later implementation ofthe
workshops' ideas in class. While some teachers apparently adopted and implemented
the ideas they had learned, others were able to report only their intentions of
changing, or merely identify what they should be doing differently.
'These two unexpected problems (self-reflection and imple~entation), led to a third
phenomenon regarding the study's third goal- the development ofprofessional
collaboration amongst teaching staff. Professrtmal collaboration was meant to occur
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in weekly meetings held by each school's teaching staff for reflective discussion of
the teachers' personal 'cases'. The study showed that such meetings were not being
held, due to the same reservations amongst teachers that hampered their reflective
processes in the workshops.
The recurrence ofthe problem of teachers' confidence as an impediment to reflection
led me to rethink the conditions under which my model should work if it is to achieve
its goals, and undertake several key changes. First, changing the defInition of a 'case'
from an unexpected event or problem, to any interesting classroom occurrence,
making it less threatening to teachers. Second, avoiding discussion ofpersonal cases
until a sufficiently supportive and 'safe' environment has developed in the group.
Third, training the mathematics coordinators to lead the reflective discussion in
schools -making sure meetings are allotted a time and a place, and are carried out
according to the CIA model. Fourth, to gain the interest and support of the school
principals in maintaining these staff meetings. Finally, in-service providers must
begin monitoring and guiding the implementation ofthe workshops' ideas in schools,
even after the workshops themselves have concluded.
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