Teaching Through Problem Solving

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Teaching Through Problem Solving

• EDN 322

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NCTM process standards

• Problem solving
• Reasoning and proof
• Communication
• Connections
• Representation

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What is a problem? (Van De Walle, 2004)

• A problem is any task or exploration for which
  the solution has not been explained
• that begins with the ideas that kids 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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Why Teach with Problems? (Van De Walle, 2004)

• Places the focus of attention on ideas and sense
  making rather than on following the directions of
  the teacher.
• Develops mathematical power. All five process
  standards are likely to be employed.
• Develops the belief in students they are capable
  of doing mathematics and that mathematics makes
  sense.
• Provides assessment data on an ongoing basis so
  that instructional decisions can be made.
• Its a lot of fun!!!

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Lesson Plan Components

• NC Objective(s)
• Materials
• Procedures
• Before
• During
• After
• Assessment (may be including in the during
  and after phase of the lesson.)

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Teaching through Problem SolvingLesson Structure

• Getting Ready
• Get students mentally ready to work on the task.
• Be sure all expectations for products are clear.

• Students Work
• Let go!
• Listen carefully.
• Provide hints.
• Observe and assess.

• Class Discourse
• Accept student solutions without evaluation,
• Conduct discussion as students justify and
  evaluate results and methods.

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In this puzzle you must help a farmer get a fox,
a chicken, and a bag of corn safely across a
river in a boat. The farmer may only take one
thing at a time in the boat. She cannot leave the
fox and the chicken together on either side of
the river, or the fox will eat the chicken.
Likewise, she cannot leave the chicken alone with
the bag of corn or the chicken will eat the corn.
How can the farmer get everything across the
river without anything being eaten? AIMS -
http//www.aimsedu.org/puzzle/farmer/farmer2.html
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Problem Solving Strategies

• Guess and check
• Draw a picture, act it out, use models
• Look for a pattern
• Make a table, chart, or original list
• Account for all possibilities

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Problem Solving Strategies

• Work backwards
• Try a simpler problem
• Write an equation or open sentence
• Logical reasoning