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Problem-Solving Models

Description 

Many students struggle when asked to solve problems that do not have a clear and prescriptive solution, and they may give up easily since they cannot envision a path or strategy to follow. This activity helps students to learn a clear set of general steps they can use to solve problems independently and confidently. Students learn to follow these steps: 1. Translate the Problem 2. Integrate the Problem 3. Plan and Monitor the Solution 4. Execute the Plan 5. Look Back

Author 

Catherine Ullman-Shade

Learning Strategies 

  • Connecting
  • Inferring
  • Visualizing
Skills 
Note Taking

Lesson Plan Stages 

  • Investigation
  • Reflection
  • Synthesis

Common Core Instructional Shifts 

  • Metacognition
  • Staircase of Complexity

Preparation 

Create a display of the steps of problem solving that will be available to students. This can be a set of handouts, a poster, or a projection. Identify the problem(s) that you would like students to focus on for this activity.

Activity Steps 
  1. Teacher displays the steps of problem solving. Teacher reviews each step. Teacher models solving a problem and thinks aloud going through each step.

    When this strategy is first introduced, students may need to focus on one or two steps at a time until they are each mastered. You will want to prepare to model each step extensively so that students understand them well. Students may need to practice these steps initially on a problem that is relatively easy for them so that they can focus on the steps rather than the problem itself, and then gradually work towards solving more difficult problems.

  2. Students read the target problem(s) individually or in small groups.

    Circulate as students are working, asking them about what they think the problem is asking.

  3. Step 1: Translate the problem. Individually or in small groups students identify what information is given, and the problem’s goal. Students restate the “givens” and restate the goal that they are trying to achieve. Students translate any confusing state

    This step is slightly different for mathematical vs. non-mathematical problem solving. For mathematical problem solving this may include translating mathematical expressions into language, or vice versa, or it might include redefining terms with common variables. For non-mathematical problem solving this means identifying provided information as simply as possible and restating the problem as simply as possible.

  4. Step 2: Integrate the Problem. In groups or individually, students use the givens and the goal to create a coherent and integrated representation of the problem.

    Depending on the type of problem, problem integration may include describing a situational model of the problem, creating a visual representation of the problem, or formally representing the problem with mathematical equations.

  5. Step 3: Plan and Monitor the Solution. In groups or individually, students devise a plan for solving the problem. They record their plan.

    Students may benefit from learning general strategies that can help them to arrive at solutions, such as establishing sub-goals, drawing a diagram, or considering a simpler version of the same problem.

  6. Step 4: Execute the Plan. In groups or individually, students execute their plan to solve the problem.

    Encourage students to monitor their execution and to determine whether and how well the plan is working. Encourage them to consider how to alter their plan if it is not successful.

  7. Step 5: Look Back. In groups or individually, students look back at their work and determine if they solved the problem, and how well.

    As you confer with students, push them to identify how they can tell if their plan worked or not, and what they might do differently next time.

  8. Alone or in groups, in writing or in conversation, students reflect on their learning process.

    Students respond to questions including: · How does this process affect your ability to solve problems? · How might it be useful to memorize a set of problem-solving steps? · In what other context might this strategy be useful to you?

Downloadable Resources 
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