ETA Cuisenaire Sponsor Showcase

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• ETA Cuisenaire Sponsor Showcase
• NCSM
• April 20, 2008
• Linda Gojak
• Author Director, CMSETT
• Past President, NCSM
• Sara Delano Moore
• Director of Mathematics and Science
• ETA Cuisenaire

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Think about how you solve a problem.

• What are some strategies you might use?
• Which would be implicit in a 3rd-6th grader?

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Strategies included in Paths to Problem Solving
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Why Problem Solving?

• Provides context for teaching mathematical skills
• Develops critical thinking skills and strategies
• Encourages teaching of process standards

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Instructional Model

• Launch
• Explore
• Summarize

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Getting Ready

• Who has a pet at home?
• How do you keep them safe?
• What kind of numbers are whole numbers?

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Launch

• Introduce the problem
• Quickstart activities on CD for students who need
  more entry into the problem (literacy support)
• Talk about the problem
• Answer the 5 questions in student journal
• Follow-up questions to stimulate thinking
• Select potential strategies (student journal)

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Mooses Play Area

• Tommy and Tessa want to fence in a play area for
  their dog, Moose. Moose is a big dog and they
  want to give him as much room as they can. They
  have 64 feet of fence. They can use up to 36
  feet of the side of their barn as one side of the
  play area. The area must be rectangular and each
  side must be a whole number of feet. Determine
  the best size for Mooses play area.

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Inside the Journal
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What do you know?

• What do I know?
• What do I want to find out?
• Do I need more information?
• Is there extra information?
• Make a prediction

BARN
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EXPLORE

• Students work in groups to solve problem
• Give the students some independent think time
  before starting with the group
• Forming groups
• Teacher role
• Questions in TE for supporting student thinking
• Students should record work in journal
• If there is not enough space.
• Extension problems for those who finish

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Mooses Play Area

• Tommy and Tessa want to fence in a play area for
  their dog, Moose. Moose is a big dog and they
  want to give him as much room as they can. They
  have 64 feet of fence. They can use up to 36
  feet of the side of their barn as one side of the
  play area. The area must be rectangular and each
  side must be a whole number of feet. Determine
  the best size for Mooses play area.

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Mooses Play Area

• What strategy/strategies did you use?
• Was your strategy efficient?
• Did your strategy reveal patterns to help you
  solve other problems like this one?
• Did your strategy help you think more deeply
  about the mathematics involved?
• Did your strategy help you organize your work and
  organize your thinking?

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Mooses Play Area

• What are possible solutions?
• How do you know you found all the possibilities?
• How do you know your solution is the best
  solution?

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Possible play areas

• Moose's Fence Spreadsheet

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Summarize

• Critical part of learning strategies
• Discuss strategy/strategies used
• Students share their approaches to solution
• Teacher orchestrates the order in which groups go
• Not all groups share on each problem
• Chart paper, transparencies, document camera
• Questions to ask
• Is that a reasonable answer?
• Did anyone get a different answer?
• Does this approach make sense?
• Who did this another way?

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What makes Paths different?

• Strong teacher support
• Focus on developing skill with specific problem
  solving strategies
• Moving beyond key word strategies
• Student journal encourages reflection and
  discussion
• Organize by mathematics or by problem solving
  strategy
• Teaching 21st century skills of problem solving,
  collaboration, creative and critical thinking

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Support for Teachers

• Rich problems
• Good questions
• Explicit Strategies
• Student need strategies modeled in explicit ways
• Students need practice using strategies

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Teachers Resource Guide Contents

• Background Information and Research
• Descriptions of strategies
• Guidance for organizing instruction
• Walking through a lesson
• Assessment Resources
• CD ROM

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Assessment Resources

• Rubric to assess student work
• Organization
• Mathematical Accuracy
• Use of Strategy
• Assessment Sheet
• Recording information
• Plans for instruction

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Organization of Problems
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CD-ROM

• Comprehension Support for 50 problems in student
  journal
• 30 additional problems beyond 50 included in
  student journal

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• Comprehension Support
• Make connections to life experience
• Understand the problem
• Focus on features and/or vocabulary

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• Student Resources
• Problem Solving Flow Chart
• Student Journal

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Scaffolding for Student Learning

• First 25 problems on 2 page spreads
• Second 25 problems on single page
• TRG has ThinkSheet for students who need more
  support

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Extended Response Questions

• Format transition in journal moves students to
  extended-response style items
• Effective test preparation is grounded in
  classroom instruction
• Rubric helps provide specific, descriptive
  feedback on student work

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Implementation Ideas

• Use early lessons to teach strategies
• Designate problem solving time each week
• Select problems based on math being taught
• one or two per instructional unit
• These are opportunities for skill practice

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