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Examining Content and Student Thinking |
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| Setting In this example teachers from the Boston, Massachusetts area participate in the Urban Calculus Initiative. Every month during the school year, the teachers attend a day-long professional development seminar. They explore complex mathematics and the implications for teaching it in their own classrooms, facilitated by Ricardo Nemirovsky. They later engage in a discussion about student work led by Mweusi Willingham. The overall goal of the project is to increase the number of students from urban settings studying calculus. |
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Professional
Development Strategy Goals of this Example
of Professional Development
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What You Can Gain
from Using this Video
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Examining Student Work and Thinking, and Scoring Assessments
"Real student work gives teachers a starting point for conversations
that get to the essence of what happens in classrooms. Samples of student
work are concrete demonstrations of what is known and what is not known"
(Evans, 1993, p. 72). Using the professional development strategy of examining
student work and thinking, and scoring assessments is based on several assumptions
about teaching, learning, and professional development.
The closer a professional development opportunity brings teachers to student
learning, the better. This philosophy is in contrast with professional development
that focuses on teaching practices. Examining student work focuses teachers'
attention on the consequences of their teaching and demonstrates discrepancies
between what teachers believed they were teaching and what students appear
to have learned (Driscoll & Bryant, in press).
It stands to reason that more learning occurs when teachers confront real
problems. Such is the case with student work and assessments, which teachers
use to judge the quality of learning and, in some cases, teaching. As Ball
and Cohen (1995) indicate, there is value in using a real task of practice
as a context for learning.
There are many who see this strategy as the most powerful way to help teachers
improve their practice. Clearly, it is totally "authentic" in
that teachers work with products of student thinking and study closely the
very thing they are responsible for improving. As professional development
becomes more results oriented, there is no better way to focus on learning.
The Strategy in Action
The availability of student work may make this appear to be an easily applied
strategy for professional development. However, professional developers
need to keep in mind that student work samples should be varied in their
nature and quality. Rather than consisting of short answers, the samples
must include students' explanations of their thinking (e.g., why they answered
the way they did).
The focus of teachers' discussion of student work may vary. Sometimes disappointing
student performance on a standardized test will give teachers a compelling
reason to examine the actual examination questions and their students' answers.
At other times, teachers might discuss examples of student classroom work
that puzzle them. In some situations, teachers may begin with a rubric supplied
by others to apply to a set of student work or may take the opportunity
to develop their own rubric through examining student answers. Or, the focus
for a discussion may be a videotape of children's explanations of their
understanding of a problem or situation.
Although individual teachers can certainly examine student work on their
own, there is power in discussing the work as a team. As elementary teacher
Christine Evans (1993) points out, working together greatly enhances the
process. Across her teaching group, ideas differed about the mathematics,
the tasks, and particular students. Together they began to develop shared
standards that could guide their collective efforts. Creating a supportive
environment allows teachers to work with each other and examine their own
values notes Rebecca Corwin (1997, p. 187), "...doing mathematics together
in a responsive group creates a safe professional community in which to
explore issues and raise questions about both mathematics and pedagogy."
The guidance of an expert with deep mathematics content knowledge is especially
important in this strategy. Often, understanding what students are thinking
by analyzing their written work requires substantial knowledge of the mathematics
topic. Similarly, if students' responses on standardized tests or the effectiveness
of the tests themselves are being examined, it is helpful to have the guidance
of someone with experience in assessment.
