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Teaching Through Problem Solving. EDN 322. NCTM process standards. Problem solving Reasoning and proof Communication Connections Representation. What is a problem? (Van De Walle, 2004). A problem is any task or exploration for which the solution has not been explained…

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nctm process standards
NCTM process standards
  • Problem solving
  • Reasoning and proof
  • Communication
  • Connections
  • Representation
what is a problem van de walle 2004
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.
why teach with problems van de walle 2004
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.
  • It’s a lot of fun!!!
lesson plan components
Lesson Plan Components
  • NC Objective(s)
  • Materials
  • Procedures
    • Before
    • During
    • After
  • Assessment(may be including in the “during” and “after” phase of the lesson.)
teaching through problem solving lesson structure

BEFORE

DURING

AFTER

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.
slide7

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

problem solving strategies
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
problem solving strategies1
Problem Solving Strategies
  • Work backwards
  • Try a simpler problem
  • Write an equation or open sentence
  • Logical reasoning