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TIPM3 Problem Solving

TIPM3 Problem Solving. April 25, 2012. 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.

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TIPM3 Problem Solving

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  1. TIPM3 Problem Solving April 25, 2012

  2. 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.

  3. What is Problem Solving? • Use the Frayer Model Template to record your definition of problem solving

  4. 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.

  5. 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.

  6. Exploring Problem Solving As you do the Wheels problem, consider the following: • What strategies did you use? • What steps did you follow?

  7. 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?

  8. 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

  9. 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

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