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Problem Solving

Problem Solving: Demonstrations, Proofs, and Stories

Props/Prep: No
Time: 3-5 min
Audience: Any
Physical: No

Begin a lecture with a question, a paradox, an enigma, or a compelling, unfinished human story. Solving the problem, depending on what it is or in what field, may require a scientific demonstration, a mathematical proof, an economic model, the outcome of a novel’s plot, or a historical narrative. You refer back to the problem throughout the lecture, inviting students to fill in imaginative spaces in the story (or model) with their own solutions. Students fill in their successive answers passively, or the instructor elicits responses which are recorded and discussed. Example questions include: “What do you think will happen?” “Which solution, outcome, or explanation makes the most sense to you?”

Time requirements: 3 – 5 minutes (for the story)

Materials needed: None

Special features: Allows students to use their imagination and connect content to a plausible real situation.


  • Tell a story, paradox, enigma, or troubling question.
  • During the course of the class time content, frequently refer back to your story.
  • Ask appropriate questions throughout your course content presentation to foster critical thinking about your story.

Function in the class: Passive engagement at the beginning of the class. May lead to understanding and discussion throughout the lesson. The “hook” that encourages the student to listen to content and participate in learning.