Ill Structured Problems

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When I had originally seen on the syllabus the word “Wicked Problem,” I wasn’t quite sure what to make of that assignment.   What was a wicked problem?  Sure enough as class started to wind down, the introduction of the wicked problem came.  In society there are 3 types of problems: well structured, ill structured, and wicked problems.  Well-structured problems are ones that can be solve fairly easily and have one route to that solution.  Ill structured problems require a little more work, but there are several paths that can get you to an answer.  In this video below, Jon Kolko gives a great explanation.

And finally wicked problems, ones that you could never solve, but provide several solutions to get to a more desirable atmosphere.  For a more in depth look at wicked problems, you can listen to the other my colleagues and I tried to solve.

What sparked my interest was this idea of ill structured problems.  In my math pedagogical classes when I was in undergrad, we constantly emphasized that there were several ways for someone to solve a math problem and still provide a correct answer.  However, reflecting on my first year of teaching, I hadn’t provided many opportunities for my students to do this.  And then I remembered when I was in high school.

When I was in high school, we followed the Interactive Math Program, IMP for short, which was a discovery based, problem solving curriculum.  Every week we were posed with these “Problems of the Week.”  Here is an example of one.  A brief introduction to the POW, as they were called, is that you were given a problem at the beginning of the week and on Friday you were asked to turn in a description of the steps you took to solve it and your finished product.  From what I recall in high school, these explanations ended up taking up 3 or more sheets of paper and often gave me terrible headaches on Thursday nights.   The problems usually required a lot of problem solving skills because they often didn’t relate to anything you had just learned, but lead you into the next topic of discussion.  In the example provided earlier, you are trying to figure out how many eggs were in a cart knowing only that it is divisible by 7 and gives various remainders for various numbers that you would divide by.  Students possess the basic skills of division, but this will lead into systems of equations and divisibility laws.

So why am I trying to pass my old headaches onto my new students?  Well it certainly isn’t because I enjoy dealing with frustrated teenagers, but to make them better thinkers.  One of the major themes of this program has been getting to make your students think more critical about not only their subjects, but the world around them as well.  Students constantly question me why they are learning what they are learning and where it is applicable; well here it is!

I think these will be great to implement slowly over the years because it fosters creativity and collaboration.  I remember talking to my fellow students and seeing a variety of ways that people solved these problems.  For all of these POW’s, there wasn’t one correct of going about it—just one correct solution.  My goal is to implement one of these during a block of class time over a week and see how that works and then slowly assign it for homework.

 

References:

Program, I. (2008, June 3). POW 1: The Broken Eggs. Retrieved from the Connexions Web site: http://cnx.org/content/m15963/1.3/

 

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