TIPM3 Problem Solving

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TIPM3 Problem Solving

• April 25, 2012

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Mathematical Practices

• 1. Make sense of problems and persevere in
  solving them.
• 2. Reason abstractly and quantitatively.
• 3. Construct viable arguments and critique the
  reasoning of others.
• 4. Model with mathematics.
• 5. Use appropriate tools strategically.
• 6. Attend to precision.
• 7. Look for and make use of structure.
• 8. Look for and express regularity in repeated
  reasoning.

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What is Problem Solving?

• Use the Frayer Model Template to record your
  definition of problem solving

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What is Problem Solving?

• Most problems" at the end of a lesson are
  usually an "exercise" for practicing the skill,
  rather than a problem.
• A problem is actually a task for which the means
  to a solution is not known in advance.
• If children do not have to think about the
  situation in order to solve the problem, if they
  can solve the problem by applying the procedure
  taught in the lesson, they are not doing problem
  solving.

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Problem Solving

• (1) Problem solving affords children
  opportunities to make sense of the mathematic
  concepts they are learning by using their own
  strategies as they decide how to proceed.
• (2) Rich problems can be solved in many ways,
  often have more than one correct answer, and
  encourage students to think beyond applying their
  basic skills. This kind of teaching encourages a
  problem-solving disposition that will serve
  children well past the primary grades.

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Exploring Problem Solving

• As you do the Wheels problem, consider the
  following
• What strategies did you use?
• What steps did you follow?

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Wheels Problem

• We have been collecting information about the
  different ways that teachers and students
  traveled to school the in last several days.
  Today I counted the number of wheels in the
  parking lot. There were 24 wheels. How many
  vehicles could be in the parking lot?

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Characteristics of Effective Tasks

• 1. What is problematic must be the mathematics
• Task must focus on mathematical idea embedded in
  it.
• Use context to introduce the problem
• 2. Tasks must be accessible to the students
• Just within students reach
• Challenging, not inaccessible
• 3. Tasks must require justifications and
  explanations for answers or methods

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Signposts for Classrooms that Promote Students
Understanding
 1. Allow mathematics to be problematic for
students 2. Focus on the methods used to solve
problems 3. Tell the right things at the right
time