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2-Minute Mentor: Teaching Problem Solving

Teaching problem solving

How can I help students...

  • See the steps they need to follow to solve problems?
  • Transfer skills from one problem to another?
  • Identify the processes they need to use for problem solving?

 

Click below to watch CTE’s 2-Minute Mentor video on this topic:

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Teaching Problem Solving video transcript (doc)

 

Thinking and problem solving

In his book Engaging Ideas, John Bean (2011) summarizes several key works that link critical thinking and problem solving, beginning with John Dewey. Dewey rooted critical thinking in students’ engagement with a problem: “Only by wrestling with the conditions of the problem at first hand, seeking and finding his way out, does the student think” (quoted p. 3). Bean believes that presenting students with problems “taps into something natural and self-fulfilling in our beings” (p. 3). Bean continues by quoting Ken Bain, who showed that the best college teachers confront students with “intriguing, beautiful, or important problems, authentic tasks that will challenge them to grapple with ideas, rethink their assumptions, and examine their mental models of reality (quoted p. 3). At the right level of difficulty, “beautiful problems” create a “natural learning environment” that engages students.

Bean suggests that teachers develop a repertoire of ways to give critical thinking tasks to students, including:

  • Problems as formal writing assignments
  • Problems as thought-provokers for exploratory writing
  • Problems as small group tasks
  • Problems as starters for class discussions
  • Problems as practice exam questions

Solving homework problems

Barbara Gross Davis (2009) recommends that teachers help students figure out how to approach a difficult problem (adapted from Andrews, 1989; Brown and Atkins, 1988, p. 185):

  • Write out the information specifically requested by the problem.
  • List all the givens, both explicit and implicit.
  • Distinguish key points.
  • Try to explain the problem to someone else.
  • Make a flowchart, draw a diagram, or represent the problem in a graph or mathematically.
  • Think of similar problems you have solved.
  • Break the problem into smaller parts.
  • Do the easiest parts first.
  • Make a rough approximation of what the solution should look like.
  • Work backward from the goal.
  • Work backward and forward from the midpoint.
  • Systematically use trial and error.
  • After you have solved the problem: Verbally summarize the solution to reinforce what you learned. Check to see if there is a simpler or alternative method. Keep a log of problems you found difficult; look for commonalities among these problems and use this information to identify areas you need to work on.

References:

Bean, J.C. (2011). Engaging ideas, 2nd ed. San Francisco: Jossey-Bass.

Davis, B.G. (2009). Tools for teaching, 2nd ed. San Francisco: Jossey-Bass.

 

More about teaching problem solving

CTE Resources:

Portfolios that illustrate ways to incorporate problem solving in your courses:


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