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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. |
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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).
