Problem-Solving

Instructional Strategies

  • Teach the PIES Strategy for word problems.
  • Have the student verbally explain his/her reasoning and steps in solving the problem.
  • Teach the student the definitions of specific mathematical vocabulary using examples and nonexamples, as well as non-linguistic representations. See Vocabulary section.
  • Provide the student with real-life problems to solve.
  • Teach the student the SQRQCQ Strategy.
  • Teach the student the four steps to solving a problem, as well as strategies within each step. Step 1: Understanding the problem (using SQR, , Visualizing, etc.), Step 2: Devising a plan to solve the problem (estimating, use guess/check, make an organized list, eliminate possibilities, look for a pattern, work backwards), Step 3: Implementing a solution plan (experiment with different plans, allow for mistakes, work collaboratively, check answer), Step 4: Reflecting on the problem.
  • Explicitly teach problem solving strategies like those listed above: guess/check, make an organized list, eliminate possibilities, look for a pattern, etc.
  • Teach students to solve algebraic equations using the Concrete-Representational-Abstract process and SUMLOWS (go to p158+).
  • Have the student write word problems when given a numerical equation.
  • Ask the student to paraphrase/restate a problem in his/her own words.
  • Provide the student with a mnemonic to scaffold the steps of an operation or have the student create his/her own. E.g. COSMIC for algebraic problem solving, RIDE or STAR for word problems (STAR for algebraic word problems).
  • Use schema-based instruction to teach the underlying structure of problems.
  • Using the Think Board, vary the information provided to the student and the information required of him/her to produce.

Scaffolds

  • Allow the student to use a calculator for computation if that is also a challenge when focusing on problem-solving is the goal.
  • Simplify the computational demands to allow the student to focus on problem solving.
  • Ensure that a student’s reading ability is not negatively impacting his/her math problem solving.

Additional Resources

Focus Area/Sample SMART Goal/Sample Tier 2 Intervention Plan:

Focus Area

Sample SMART Goal

Sample Tier 2 Intervention Plan

Problem-solving strategies

Student will increase her accuracy in solving multi-step word problems from 58% accuracy to 80% accuracy as measured by classroom-based problem sets by January 2020.

Teach the student to use the SQRQCQ Strategy

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