Thursday, June 11, 2009

Polya's Army

Problem Solving is a big deal in any math class I teach, and I, like most math teachers, use Georg Polya's problem solving phases as a framework. Though I used to teach it as a four step process, I now recognize it as four phases, which problem solvers can progress through in many different ways, back tracking and skipping. The ultimate reference on this is Polya's book How to Solve It. My handout (adapted from Dave Coffey's) is here; it focuses on Polya's questions. (Questioning being another important comprehension strategy.) The modern day successor to Polya as a researcher and teacher of problem solving is Alan Schoenfeld. The link leads to his site where he generously shares a lot of his research and work. I recommend at least skimming Learning to Think Mathematically: Problem Solving, Metacognition, and Sense-Making In Mathematics (pdf link), a novella of a paper. Around pp 60-67 there's an amazing section on novice and expert problem solvers and teaching interventions.

One of my calc students was taking his final early, on his way to the month duty for army reservists, and commented on how he remembers Polya's steps by a connection with the troop leadership procedure. He sees:
  • understanding the problem - receive the mission, issue the warning
  • make a plan
  • do the plan - start movement, recoineter, complete plan
  • revise and check - issue plan and supervise
How cool is that! I just had to share. Thanks, James!


  1. Hello, can I cite the "ProblemSolving-Polya.jpg" ? Is it from Georg Polya's book or illustrate by yourself ? thank you ^^

  2. The phases are from How to Solve It (follow the link for info). The picture is mine and you're welcome to use it.

  3. thank you very much^^ My name is Doraemonwill, I am a student from Taiwan, I will cite this figure in my paper. Thanks again :)