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Exploring Mathematics Through Cases I | |
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Setting | ||
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Professional Development
Strategy Elementary teachers discuss cases of mathematics teaching and learning during a summer institute.
Goals of this Example of Professional Development
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What You Can Gain from Using this Video
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Why teacher cases? Many professions have used cases of practice as learning tools. Patterned after the case methods successfully used to prepare lawyers, physicians, and business professionals, mathematics case discussions focus on experiences from teaching practice that promote analytic thought, reflection, and inquiry. Through discussion with colleagues, teachers become more effective in their pedagogy. |
Case discussion helps teachers: 1. deepen
their own understanding of the math they are teaching, | |
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What is a case discussion like? A group of six to twelve elementary of middle school teachers meets once a month for about two hours to discuss a case. The case, a short narrative written by an anonymous teacher not in the group, describes a classroom experience that had an unexpected outcome or ran into difficulty. The author of the case used dialogue and student work to describe how the instruction was planned and what actually happened. Teachers in the discussion group read the case before coming to the meeting. Before beginning the discussion, they work on a mathematics problem related to the case for a few minutes. The purpose of working on the problem is to think about what might be confusing or difficult from a student's point of view. Participants then pair up and identify issues framed as questions. These issues are used to focus the discussion, which continues for about an hour. A facilitator, usually a teacher from the group who has attended a facilitation seminar, helps ensure that issues are carefully examined. The Mathematics Case Methods Project has a casebook and facilitator's guide to assist participants, and provides seminars on learning to facilitate case discussions. | ||
Cases are narratives in print
or on videotape that offer a picture of a teaching or learning event. They are
not simply stories about teaching or learning but are, as Shulman (1992) states,
focused on a teaching dilemma, student engagement in mathematics investigations,
images of student thought processes, or teaching strategies in action. The
classroom videotapes in the Resource Kit developed to share the results of the
Third International Mathematics and Science Study (TIMSS) are powerful examples
of videos that be used to evoke deep reflection on instructional practice (U.S.
Department of Education, 1997). The process of reflecting on students' thinking
and learning through case discussions often results in teachers trying out the
ideas or activities contained in the cases in their own classrooms (Barnett,
1991; Davenport & Sassi, 1995; Schifter, 1994). The vivid images of students
in the cases prompt teachers to wonder about the thinking of their own students.
Case discussions can also be a powerful tool for helping teachers examine their
own teaching practices. In these instances, cases typically convey a contextual
dilemma, as well as the internal struggles of the case teacher (Schifter,
1996).
Additionally, when teachers
confront mathematics issues through the lens of students' perspectives, they
often deepen their own content knowledge (Schifter & Bastable, 1995). As
teachers reflect on students' approaches, they begin to think through the
mathematics again for themselves, often seeing new aspects of familiar content
and expanding their own understanding (Russell et al., 1995).
Cases can present complete
stories that describe how the case teacher addressed the dilemma (Schifter,
1996). Others end instead with a series of open-ended questions. Some convey the
complexity of teaching (Merseth, 1991), while others focus on discrete instances
of teaching. Finally, some cases are grouped into clusters based on similar
themes. Examining clusters of cases requires teachers to grapple with the theme
in different contexts (Barnett & Friedman, in press).
Case discussions provide a more
focused picture of a specific aspect of teaching or learning than one could
observe in real-time in the classroom. Often, observers in a classroom focus on
management and miss opportunities to address specific teaching or learning
episodes. By using cases, participants focus on the same situation and have the
immediate opportunity to reflect specifically on those experiences during the
case discussion. Whatever the focus of a case, all case discussions share common
goals: to deepen teachers' fundamental understanding about teaching and
learning; to provide opportunities for teachers to become involved in critical
discussions of actual teaching situations; and to encourage teachers to become
problem-solvers who pose questions and examine alternative solutions (Barnett
& Sather, 1992; Shulman & Kepner, 1994).
The Strategy in
Action
Case discussions require a
knowledgeable facilitator who prompts reflection by case discussants.
Facilitators must have a deep understanding of the mathematics content
illustrated in the cases. In addition, they must have the skill to turn
discussions that are intellectually stimulating, and challenging -- at times
even confrontational -- into supportive and ultimately useful dialogs. Handbooks
and training opportunities are available to help facilitators develop these
skills (see the Reference list at the end of each strategy as well as the
Resources section under Technical Assistance).
It is also essential that case
discussion groups create an atmosphere of learning and trust. Since participants
rely on discussion to tease out insights, they and the facilitator need fairly
sophisticated communication skills to challenge assumptions, understand
different perspectives, and dig deeply into underlying structures that support
mathematics teaching and learning. If participants do not have experience with
this type of dialog, they need coaching by the facilitator before beginning
their case discussions.
Another key component is the
use of relevant and recognizable cases. Although some cases depict situations
that reflect the "ideal image" of what teaching and learning can look like,
teachers need, at least initially, to be able to identify aspects of their own
teaching within a case. Once teachers feel a sense of connection with a case,
they can delve deeper into how the situation is related to their own teaching
approaches. Some cases will present notions that conflict with the beliefs of
the teachers. "Wrestling with the resulting disequilibrium" leads to changes in
teachers' thinking (Barnett & Sather, 1992).
Not only is participating in
case discussions a powerful professional development strategy, but the process
of writing cases also enhances teachers' development. Usually, teacher-writers
follow a structured case development process that progresses from identifying an
issue of concern to collaborative work with an editor who helps turn the
narrative into a case that has benefits for a larger audience. Most teachers who
have written cases report that the writing process has a strong impact on their
professional lives (Shulman & Kepner, 1994).
