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Summary
Cases discussions have a multitude of
possible uses in professional development. Depending on the
content of the case and the focus of the discussion, this type
of activity can address all the teacher learning needs we
identified in Chapter 1. The extreme flexibility in using cases
is one of its greatest strengths as a professional development
tool. At the same time, because cases can vary so much, it is
more difficult to evaluate their effectiveness without
context-specific information.
Suggested follow-up resources
If you are interested in learning more
about how to use cases for a variety of professional
development goals, we recommend the following resources, in
addition to the Developing
Mathematics Ideas (DMI) materials
already mentioned in Chapter 5:
Barnett, C., Goldenstein, D., and
Jackson, B. (Eds.) (1994b). Fractions, decimals, ratios, and percents:
Hard to teach and hard to learn? (casebook
and facilitator’s guide) Portsmouth, NH: Heinemann.
This set of 29 teacher-written cases
illustrates recurring dilemmas and problems in teaching and
learning fractions, decimals, ratios and percents. The editors
primarily intend these cases for mathematics teachers in grades
4 – 8; however, we find them to be beneficial for
teachers from kindergarten through grade 12. The
facilitator’s guide identifies the central mathematical
and pedagogical issues addressed by each case, offers
suggestions for facilitating the discussions, and identifies
some of the common misconceptions that can emerge during the
discussions.
Stein, M. K., Smith, M. S., Henningsen,
M. A., and Silver, E. A. (2000). Implementing standards-based mathematics
instruction: A casebook for professional development. New York: Teachers College Press.
This book, intended for teacher educators
and teachers, is more than a set of cases. The authors
introduce their mathematical task framework and describe the
typical pedagogical patterns teachers use in implementing
tasks, uncovered as the result of their research of middle
school mathematics classrooms. The explicit description of the
task framework and the pedagogical patterns helps teachers
become aware of the cognitive demands of a mathematical task
and of the issues involved in maintaining the cognitive level
of a task. The cases, inspired by real classroom experiences,
provide opportunities for teachers to practice identifying the
cognitive demands of a particular mathematical task, to see
firsthand how pedagogical practices impact the task, and to
grapple with the issues raised by the example. Each case
includes a section in which the featured teacher discusses her
class and a section describing her implementation. In addition,
each case is accompanied by a set of discussion questions and
notes to support the case discussion.
Harvard Mathematics Case Development
Project (in press). Cases
in secondary mathematics classrooms. New York: Teachers College Press.
This book includes several cases at each
level of high school mathematics (i.e., Pre-Algebra and
Algebra, geometry, Algebra II and Trigonometry, Probability and
Statistics, Pre-Calculus and Calculus). Before presenting the
cases, the authors outline in detail their theoretical
framework for constructing them. They examine the mathematical,
pedagogical, student assessment and contextual issues they
believe teachers need in order to promote learning at high
levels. The book also includes a guide for case facilitators
and for participants in case discussions, and it lists the
major mathematical and pedagogical issues raised by each case.
Each case is supplemented by notes for the facilitator that
include a prediscussion activity, tips for teaching the case,
suggested discussion questions, possible extensions and
annotated references for further reading on either the
mathematics content or the pedagogy.
Miller, B., and Kantrov, I. (1998). Casebook on school reform. Portsmouth, NH: Heinemann.
This
book includes six ready-to-use cases that describe teachers’ reform
efforts in mathematics or science. The introduction of the book provides
a rationale for using cases, an explanation of why and how the cases
were developed and some suggestions for how to use them. The cases,
developed to highlight issues raised when educators engage in school
reform, are intended to stimulate thinking and discussions from multiple
perspectives. Each case is accompanied by a facilitator’s guide
that suggests ways to elicit discussion about the “big ideas”
underlying the case.
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CHAPTER 6 continued