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Give Math Problems with Multiple Solutions


Mathematics ^21st Century Skills MS/HS/College Strategy


Flexible Thinking

Give Math Problems with Multiple Solutions

If your student fixates only on the problem answer and not the process or they easily get frustrated when they can't figure out the solution

Instruction And Practice

  1. Adults should expect to provide ongoing support and coaching to help students who struggle with flexible thinking, ambiguity or thirst for a single right answer.
  2. Help them to not over-react or respond impulsively. Help them understand that there can be multiple paths and solutions to a problem.
  3. Find simple, low stakes opportunities to get them comfortable trying familiar things in different ways, such as agreeing to change the rules of a game. Openly discuss differences of opinion and approaches as they arise in daily life. Explain why it might not be the way you would do it, but it could work equally well.
  4. Engage students in class discussions with two sides of an argument. Have the student write down each side's point of view with examples that defend each side. Use prompts such as, "It depends on...." or "If....then..." to provide structure.
  5. Move students away from perceptions that math and science problems have only one right answer or approach. Encourage students to use multiple approaches to solving math problems. Conduct science experiments without a single right outcome. Re-consider how you grade science experiments--do students lose points because their data is off even if they understood? What does that convey? Do they gain extra points for creative responses?
  6. Use mistakes or misconceptions as a launching point for further discussion rather than offering a simple correction and moving on.
  7. Discuss scientific discoveries that arose out of mistakes or were unintentional.
  8. Encourage extra-curricular activities such as debate team and improvisation classes which offer great practice in flexible thinking.

Why It Works (the Science Of Learning)!

Understanding that not all problems have a right or wrong answer is not only important in academic learning. Many social, political and ethical issues are fraught with gray areas that students will need to consider to fully understand the complexity of a situation. Students, regardless of reasoning ability, might be more or less comfortable with ambiguity. Adults can provide ongoing coaching and support in this area. The more students have experience with the discomfort of "not knowing" the better they will handle it.