Quality Assessments of Problem Solving Leadership for Classroom Assessment September 21, 2006 Omaha,

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Quality Assessments of Problem SolvingLeadership
for Classroom AssessmentSeptember 21,
2006Omaha, NebraskaLenny VerMaas, ESU 6
John Moon, NEAP CoordinatorNebraska Department
of Education
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On Monday in math class Mrs Fibonacci says,
You know, you can think of almost everything as
a math problem.On Tuesday I start having a
problem.
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I take the milk out for my cereal and wonder

• How many quarts in a gallon?
• How many pints in a quart?
• How many inches in a foot?
• How many feet in a yard?
• How may yards in a neighborhood?
• How many inches in a pint?
• How many feet in my shoes?

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Mrs. Fibonacci has obviously put a Math Curse on
me. Everything I look at or think about has
become a math problem.
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What is Problem Solving?

• On an index card write your definition of problem
  solving.
• Share with others.
• Three definitions from the whole group.
• Not everyone or every school will define problem
  solving the same.
• First step to define Problem Solving

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Problem Solving Is When

• The course of action is not immediately evident.
• The solution may be found in several different
  ways.
• Several strategies may be appropriate.
• More than one answer may be possible.

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Looking at a Continuum

• Exercises
• 15 27 ?
• Word Problems
• There are 15 students in one class and 27
  students in another class. How many students are
  in both classes?
• Problem Solving
• Investigation

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A Mathematical Investigation

• Has multidimensional content
• Is open-ended, with several acceptable solutions
• Is an exploration requiring a full period or
  longer to complete
• Is centered on a theme or event
• Is often embedded in a focus or driving question

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In Addition, A Mathematical Investigation May
Involve

• Researching outside sources
• Collecting data
• Collaborating with peers
• Using multiple strategies to reach conclusions

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How is Problem Solving Different than Solving a
Word Problem

• Traditional word problems.
• One solution and one strategy to get to the
  solution.
• Translate the situation into an arithmetic
  sentence and then solve that sentence.
• Real-life problems or Investigations
• Not all of the information may be provided
• Several paths to arrive at solution
• More than one answer

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More Memorizing
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Steps to Problem Solving

• Understand the problem and the question.
• Find the needed data
• Plan what to do
• Brainstorm possible strategies and select one
• Find the answer
• Check to see if the answer makes sense
• Is the answer reasonable?

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Problem Solving Strategies

• Look for a pattern
• Construct a table
• Make an organized list
• Act it out
• Draw a picture
• Use objects
• Guess and check or trial and error

• Work backwards
• Write an equation
• Solve a simpler (or similar problem
• Make a model
• Break the problem into smaller pieces

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Lotus Notes
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Lotus Notes
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Lotus Notes
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Challenges of Measuring Problem Solving

• Open ended solutions
• Several ways to solve the problem.
• Across strands (algebra, geometry, measurement,
  etc.)
• Across standards
• Purpose for assessment formative or summative

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The Process A Sample Problem

• Lets look at a problem
• Then look at student solutions
• Evaluate student solutions (the process)
• Provide possible feedback

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The Question

• Mr. Goldstein thinks that the area to be carpeted
  in his game room (20 feet by 30 feet) is double
  the area to be carpeted in his living room (10
  feet by 15 feet).
• Is Mr. Goldstein correct?
• Explain your answer and show your work. You may
  use diagrams as a part of your explanation and
  work.

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The real reason why we have rubrics and ask
students to show their work.
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Peanuts by Charles Schultz
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Rubrics with a Purpose

• Holisticlooks at the total process
• Analyticlooks at the parts or steps of the
  process
• Specificis used with single problem.
• Generalcan be used to assess many types of
  problems.

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Double the Carpet Scoring Criteria (Holistic /
Specific)

• Level 4 Explanation, work, or diagram
  completely and correctly compares the areas of
  two rectangular shapes.
• Level 3 Explanation, work, or diagram compares
  the areas of two rectangular shapes but contains
  a minor error or omission.
• Level 2 Explanation, work, or diagram indicates
  some comparison of the areas of the rectangular
  shapes.
• Level 1 Explanation, work, or diagram shows a
  beginning understanding of the area concept
  however, that understanding is limited.
• Level 0 Explanation, work, or diagram reveals
  no understanding of the area concept.

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Double the Carpet Scoring Criteria(Analytic
Specific)
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Assessing the Work

• Use the rubric to provide feedback.
• Provides a way to improve the solution.
• What feedback could you provide based on this
  rubric?
• Explanation is complete
• Work supports the solution
• Diagram adds to the explanation

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John Dewey progressive education reformer from
early 1900s

• Learning does not start and intelligence is not
  engaged until the learner is confronted with a
  problematic situation.

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Why assessment quality is needed.
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• THE SIX QUALITY ASSESSMENT CRITERIA
• Assessments reflect the state or local standards.
• The students have had an opportunity to learn the
  content.
• Assessments are free from bias or offensive
  situations.
• Assessment levels are appropriate for students.
• There is consistency of scoring.
• The mastery levels are appropriate.

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Criterion 1

• Assessments reflect the state or local
  standards.
• 1. Measuring what is intended to be measured.
• 2. Enough opportunity to see what students at
  all levels can do.
• 3. Performance level descriptors advanced,
  proficient, progressing and advanced.
• 4. Breadth and Depth
• 5. Sufficiency for all performance levels on each
  standard

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Criterion 2

• The students have had an opportunity to
  learn the content.
• Identify where standards are found in local
  curriculum/instruction.
• When is it taught?
• When is it assessed?
• Multiple courses and teachers
• Match between Instruction and Assessment (item
  format)

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Criterion 3

• Assessments are free from bias or
  offensive situations.
• Directions, print, clarity.
• Any situation unfair to students.
• Setting
• Context
• Experiences

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Criterion 4

• Assessment levels are appropriate for
  students.
• Fairness of brain power.
• Fairness to get at the right content.
• Professional judgment of subject area experts.

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Criterion 5

• There is consistency of scoring.
• Appropriate methods for assessment type and group
  size.
• Subjective Method Inter-relater Reliability
  (double scoring) any group size.

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Criterion 5

• Decision Consistency Objective Methods any
  size group.
• Plans for improving reliability.
• Internal Consistency
• Objectively scored items only
• 30 students or more
• Not as appropriate for classroom assessment

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Criterion 6

• The mastery levels are
  appropriately set.
• Student-centered Methods
• Test-centered Methods
• Angoff Method test centered
• Any number of students
• Examine proficiency level descriptors
• Examine all items
• Decisions about levels of items

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Resources

• Nebraska Association of Teachers of Mathematics
  NATM
• National Council of Teachers of Mathematics NCTM
  http//nctm.org/
• www.ncacasi.org and search for problem solving.

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Geometric Close

• Name something that squared with what you
  already thought or already do in your classroom.
• Name something that made you view something from
  a new angle.
• Name an action or strategy that you will take as
  a result of todays training.