I have never loved the summer months more than I do as a teacher.

It’s not because I don’t have to go to work, see the students, or plan lessons. Nope. I love summer because I can take a step back from planning lessons, writing reports, meeting with colleagues – and I can reflect deeply on my program – and make changes which will support student growth. I can look to research articles, read blogs and links from twitter posts, and fine-tune my approach for the fall.

For instance – I’m going to work hard to develop a classroom community where we embrace problems and problem solving activities. Not just math games, puzzles, or design challenges (like the super-cool Novel Engineering – but more on that later). No – embracing the problems everywhere – from social-emotional situations to prioritizing one’s time to meeting curricular outcome-related tasks.

The thing is – how do I teach Problem Solving skills for the many varied problems we’ll face as a class, or my students will encounter as individuals?

There are resources like the General Problem Solver and the IDEAL Problem Solving Method, but these systems are flawed as guides. They assume that all problems are similar (which they are not), and that problem solving is an easily recognizable, repeatable process because of problem uniformity (which it is not). Furthermore – these resources were developed to explain the process, generally; they should not be viewed as prescriptive guides to problem solving.

I’m working my way through this TED Talk List on Problem Solving, but everything so far assumes that the problem solver is familiar with the type of problem. There’s nothing yet on how do we teach students to recognize the problem type? I’m not talking about “is this a subtraction or an addition” word problem – I’m looking at much larger problem categories here.

So – I have to show my students a variety of problems, and teach them to recognize differences across the types. This has to be a goal: work through as many varied problems as possible; show that not all problems can be solved the same way; and share strategies and possible solution schemes for the different types.

UNDERSTANDING PROBLEM DIFFERENCES

 

Lucky for me, there is David Jonassen’s Toward a Design Theory of Problem Solving (Educational Technology Research & Development; 2000, Vol. 48 Issue 4, p63-85). Jonassen shows that problems can differ in three main categories: Structure, Complexity, and Domain Specificity. Furthermore, Jonassen identified eleven general problem types (each with their own variations in the aforementioned categories).

The eleven problem types are:

  • Logical Problems “Divide a triangular cake into four equal pieces”
  • Algorithms “Convert Fahrenheit to Celsius”
  • Story Problems “How long for Car A to overtake Car B travelling at different speeds”
  • Rule-Using Problems “Expand a recipe for four to prepare the meal for 10 guests”
  • Decision-Making Problems “How am I going to pay this bill”
  • Troubleshooting Problems “Why won’t my car start”
  • Diagnosis-Solution Problems “How should I study for the final exam”
  • Strategic Performance “Flying an airplane”
  • Situated Case-Policy Problems “Develop policy for a condo corporation”
  • Design Problems “Design a vehicle that flies”
  • Dilemmas “Negotiate peace between Israelis and Palestinians”

Knowing the different types I hope to show my class is step one. Next up is thinking about how to teach students to recognize the differences in problems… this step may take a little longer.