Transcript Document

Problem Solving
and
Assessment
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EDC 456 Spring 2006 (Seitsinger)
Introduction
Goals for All Students
 Goals for Problem Solving
 Factors in Problem Solving
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EDC 456 Spring 2006 (Seitsinger)
Goals for All Students
All Students will:
 Learn to value mathematics
 Become confident in their ability to do
mathematics
 Become mathematical problem solvers
 Learn to communicate mathematically
 Learn to reason mathematically
National Council of Teachers of Mathematics. 1989. Curriculum and
Evaluation Standards for School Mathematics. Reston, VA: Author.
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EDC 456 Spring 2006 (Seitsinger)
Knowing mathematics is doing
mathematics
Verbs of Doing Mathematics
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Explore
Investigate
Conjecture
Solve
Justify
Represent
Formulate
Discover
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Construct
Verify
Explain
Predict
Develop
Describe
Use
Discuss
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EDC 456 Spring 2006 (Seitsinger)
Goals of Problem Solving
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Strategy and Process Goals
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Develop problem analysis skills
Develop and be able to select strategies
Justify solutions
Extend and generalize problems
Metacognitive goal
– Monitor and regulate actions
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Attitudinal Goals
– Gain confidence and belief in abilities
– Be willing to try and to persevere
– Enjoy doing mathematics
EDC 456 Spring 2006 (Seitsinger)
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What is a problem?
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A problem is any task or exploration
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for which the solution has not been explained
that begins with the ideas that students have
that is challenging mathematically, and
for which justification and explanations of
answers and methods are the responsibility of
the students.
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EDC 456 Spring 2006 (Seitsinger)
Factors in Problem Solving
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Problem Context
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Problem Structure
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Problems involving
concrete, factual, or
personalized settings
are easier for
children to solve than
hypothetical or
abstract ones
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More difficult problems
might include:
EDC 456 Spring 2006 (Seitsinger)
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Length
Readability
Action
Order of data
Extraneous data
Unfamiliar terms
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Modes of Representation
Pictures
Manipulative
Models
Real World
Situations
Written
Symbols
Oral
Language
Van de Walle, p.30
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EDC 456 Spring 2006 (Seitsinger)
Problem Solving Strategies
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Look for a pattern
Construct a table
Make an organized
list
Act it out
Draw a picture
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Use objects
Guess and check
Work backwards
Write an equation
Solve a simpler or
similar problem
Make a model
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EDC 456 Spring 2006 (Seitsinger)
The Assessment Cycle
Make sure to consider how the
results will be reported, and
Think about how you will
decide how the results will affect
Planning Assessment
determine understanding and
future instructional decisions.
what criteria you will use to
Setting Clear Goals
analyze the evidence.
Using Results
Gathering Evidence
Making Decisions
Multiple
Methods
Think about
the purpose
of the
assessment, what methods you
will use to collect and interpret
evidence, what criteria you
Consider what Interpreting
activities, tasks,Evidence
will use to judge performance,
and procedures you
will use
to
Making
Inferences
and what format you will use
involve students.
to summarize findings.
EDC 456 Spring 2006 (Seitsinger)
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GOT IT
A Four-Point Rubric
4 points
3 points
2 points
1 point
NOT YET
fully accomplishes the purpose of
the task
substantially accomplishes the
purpose of the task
partially accomplishes the
purpose of the task
little or no progress toward
accomplishing the purpose of the
task
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EDC 456 Spring 2006 (Seitsinger)
Summary
Teach mathematics through problem solving
 Use assessments to inform instruction
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EDC 456 Spring 2006 (Seitsinger)