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Consulting
Services and
Programs
Teaching
Problem Solving and Creating An Inquiry Based Mathematics Classroom
A
Professional Development Program
The
following staff development program was prepared specifically for
Roger's Elementary School in Stamford Connecticut. The program was
designed and implemented as a response to student deficits in select
mathematical abilities as evidenced by standardized tests.
Concern:
As indicated by
the percentages of students reaching the standard on the latest Connecticut
Mastery Test (CMT) in mathematics for 4th graders there is a consistent
weakness in select areas of problem solving and estimating geometric
measurements and numerical calculations.
Response:
The areas of concern in the CMT results are commonly associated with
weaknesses in conceptual understanding, mathematical creativity, and
confidence in students. This program will focus on improving curriculum
and/or the classroom practice of teachers to address these factors.
Strategies will be designed and implemented by teachers with the facilitation
of Scott Beall in a three part staff development sequence. Drawing
from ideas presented in the workshop as well as their own resources,
each teacher will craft a focus according to their personal background,
experience, comfort level, resources, personal teaching style and
the unique needs of their particular students. Key factors that will
be viewed in the workshop are listed below:
Teaching
practice
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The art questioning to stimulate higher order thinking and discussion
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Teacher modeling of the problem solving process for students,
validating the need for persistence, the norm of false starts
and experimentation
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Considering teachers' own perceptions of what it means to "do
mathematics" (questioning, classifying, sorting, creating, modeling,
experimenting, vs. performing memorized procedures)
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Creating a classroom culture that is safe for risk taking
Curriculum
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Availability and knowledge of specific problem solving strategies
that students can resort to in non routine problem situations
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Utilizing authentic activities/games that provide real practice
in estimating
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Experience with inductive, discovery based activities that require
students to think about mathematics as opposed to performing memorized
procedural tasks
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Experience with non routine problems to be solved over time and
presented in written formats and/or class presentations
- Group
work strategies to enhance student discussion and reflection on
issues of problem solving
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Fostering students' reflection on the problem solving process
through discussion, journaling and written problem write-ups.
An
Opening note to workshop participants
It seems that all too often, students' experience their greatest fear
and difficulty in mathematics when they are faced with dreaded "story
problems." Most of us as adults have experienced this as kids; it
has even become a popular topic for comics strips and comedians, such
as the Gary Larson comic playing on a hypothetical nightmare portraying
a young child at the gates of Heaven, with God requiring one last
task for entry: to correctly answer a distance-rate-time story problem
in a limited amount of time. The ability of students to apply mathematical
tools to solve problems in unique situations, to identify relevant
and extraneous information and evaluate the reasonableness of answers
is directly related to the strength of their number sense and conceptual
understanding of mathematics. Conceptual understanding is empowering
to students. With it, fear diminishes and confidence increases. In
this workshop you will have the opportunity to collaborate with your
fellow teachers, reflect on what happens in YOUR classroom and consider
ideas presented in our work session to further expand how you teach
for understanding in your classroom.
FORMAT
Part I: Opening workshop
March 14, 3:30-5:30pm
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1.
Group discussion and reflection
Define areas of concern--
Where are we now?
Where do we need to go? (objectives/outcomes)
2. Presentation/discussion
How will we get there? (curriculum and instruction)
How will we know we are there? (assessment)
a) A process for teacher inquiry--Action Research(AR)
b) Factors and tools for creating an inquiry based classroom
i) The art of questioning
ii) Student generated discussion--The Debra Ball classroom and
Shea numbers
iii) Teacher modeling of non-routine problem solving
iv) Problem solving cycles
v) Open ended Problems of the Week
vi) Student reflection on the problem solving process
3. Teacher work sessions
Teachers group in common areas of focus for individual AR plans
to incorporate strategies into their classroom teaching for
the subsequent 10 days.
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Part
II: Implementation in the classroom
March 15-March 23
Implementation of strategies as planned, making observations and journal
notes as appropriate for sharing out and evaluating the AR plan.
Part III: Follow up workshop--sharing out
and tuning
March 24, 3:30-5:30pm
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