Teacher Toolbox
Learning Strategies - Problem Solving

Work through problem space

The mental representations help to maintain the background information and the elements needed to solve the problem.  To solve the problem, the student is required to select the most appropriate strategy to determine the solution.  General thinking skills are necessary. Problem solving strategies are often task specific.

Determining the Strategy
  • Teach students to look for keywords to guide their problem solving.  For example, keep a chart on their desk of common words used to indicate a math procedure.
  • Teach the students to recognize the purpose of the problem.  For example, have the students ask themselves, "Can I find a definite answer?"
  • Have the students reword the problem in their own words.
  • Have the students create checklists or diagrams showing the steps to the problem and list their evidence in order of relevance. 
  • Direct the students to create an argument or a defense if they are working with opinions, judgments, and claims.
  • Have the students write or show their predicted outcomes.
Adjusting/Shifting the Strategy
  • Take a thinking break.  Engage the students in a discussion about their method of solving the problem and have them tell why they chose that strategy.
  • If a strategy isn’t successful, have the students circle or mark the area where they are stuck.  Direct them to work backwards through the problem.
  • Have students highlight the keywords in the problem to see if they understood correctly the procedure or purpose.
  • Encourage students not to erase when they made a mistake.  Have them circle the error and write the correct answer next to the error.  Go back and work through the problem with the student to see where the breakdown occurred.
  • Direct them to ask themselves, "What if…" to change the approach to the problem and to change their perspective.
  • Encourage students to talk with others in the class. At times, others may see things differently and help with a solution.
  • Make a pro and con list and select the next most viable option to use to solve the problem.  Have students provide reasons as to why they support trying the different method.
Restructuring Mental Space
  • After clarifying the information, the students will need to adjust their representation.
  • Have them make lists of choices to help them think about the problem in a different way. 
  • Have them use a different color of pencil, or highlight changes, or use different types of blocks, for their representation.