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About the Site
Reflection Topics and Critical
Teaching Questions
Guiding Beliefs
Acknowledgments
Algebra Standards for Grades 3-5
Algebra Standards for Grades 6-8
About the Site
Reflections, NCTM's video-based, professional
development Web site, is designed to help teachers — individually and collectively — examine
their teaching of mathematics. The site’s components are
designed to assist teachers in reflecting on the mathematics they
teach, and
as a tool to systematically observe, analyze, critique, and improve
classroom practices. Reflections focuses on algebra in grades 3-8.
Whether the site is approached through the six individual lessons
or the five across-lesson topics, the heart of Reflections is a
set of Critical Teaching Questions. For example:
- How effectively does the teacher
determine when to clarify, explain, question or let a student
struggle?
- What are the mathematical ideas in
this lesson and how significant are they?
When selected, each Critical Teaching Question provides you with
a set of video clips from the lesson and from pre- and post-lesson
discussions, with accompanying on-screen transcripts, and a set
of reflective tasks and analyses that foster individual or collaborative
reflection and analysis of the lesson, the mathematics taught,
the
pedagogy employed and the learning that occurred.
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Reflection Topics and
Critical Teaching Questions
The five reflective topics and the accompanying critical teaching
questions that form the heart of the site are:
- Reflecting on the mathematical
tasks being used:
- How mathematically appropriate are the tasks for developing
an understanding of the mathematics being taught?
- Reflecting on the classroom discourse
that occurs, including the classroom environment that is created:
- How effectively does the teacher use questioning to
help students develop mathematical understanding?
- What techniques and strategies are used to
orchestrate and promote student discourse and how effective
are these strategies
implemented?
- Are there alternative questions that could
have been asked to further the development of mathematical
understanding? What
are
they?
- Reflecting on student learning:
- What strategies were used to assess student understanding?
- What evidence is there that students have learned the
mathematics being taught?
- Reflecting on the teaching decisions
made:
- What decisions does the teacher make to achieve the
goal of reaching all students?
- How were transitions made and how effectively was this
done?
- How effectively are student mistakes and misconceptions
dealt with?
- How effectively does the teacher determine when to clarify,
explain, question or let a student struggle?
- Reflecting on the mathematics
being taught:
- What are the mathematical ideas in this lesson and how
significant are they?
- How are contexts, representations, connections and applications
used to enhance the mathematics being taught?
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Guiding Beliefs
Many teachers are part of a culture more
often characterized by individualism and professional isolation
than by collegiality
and
professional
sharing and interaction. Drawing from other countries and cultures – most
notably Japan – it is clear that the collegial analysis and
critique of teaching is a powerful mechanism for reducing isolation,
improving practice, and raising levels of student achievement.
Accordingly, NCTM has created a set of guiding
beliefs – aligned
with the vision of NCTM’s Principles
and Standards for School Mathematics – to frame the design and development of Reflections.
We believe
- Reflection entails a detailed
analysis of teaching decisions made and their consequences.
- Collegial discussion of this analysis,
based on lessons that are observed (in person, on tape, or
through a computer),
can
help
lead to new mathematical understandings and teaching insights.
- Teaching is an incredibly complicated
endeavor, involving a vast array of decisions, all with implications
for learning.
- Analyzing and reflecting on these
decisions is one way to make improvement.
- Reflection can be facilitated
by a video record and by individual and collegial analysis
and discussion of such matters
as the mathematics
being taught, the mathematical tasks being used, the classroom
discourse that occurs, the student learning that ensues, and
the teaching decisions
that are made.
Reflections is designed to honor these beliefs
and to help you improve practice – whether you are a teacher,
a prospective teacher, a teacher educator, or a supervisor.
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Acknowledgements
The Reflections Project was created through the generous support
of the Duke Energy Corporation.
In addition, Reflections would not have been possible with
out the extraordinary efforts and courage of the six teachers
featured
on
the site:
- Rosemary Klein and Sandy Allen
from the Charlotte-Mecklenburg Public Schools in North Carolina;
- Bernadette Green and Nancy Barthel
from the Minneapolis Public Schools in Minnesota; and
- Mark Alcorn and Kathleen Gallagher
from the San Diego Public Schools in California.
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