It seems like practically every day we read in both the popular media and academic reports that thinking and problem solving skills need to taught in our schools, rather than memorization and standardized testing. But what exactly is problem solving, what does it entail?

The process of finding solutions to difficult or complex issues:
an expert at creative problem-solving
[AS MODIFIER]: problem-solving skills
oxforddictionaries.com

Generally speaking to teach, learn, or solve anything, we have to be able to describe it. We have to be able to talk about it. We need to assess our current situation. Accurately assessing any problem can be easier said than done; however, we need to make an objective assessment of the relevant set of circumstances in order to change them. Can we identify the root cause(s) of the problem? If we're able to do this, then a plan of action can be developed. Being open to the problem solving process, and realizing that some problems are more complex than others, are key concepts in problem-solving. Many problems are moving targets. We will need to accept that adjustments, throughout the problem solving process, will need to be made.

In order to fully understand problem solving techniques, one must attempt to consider the many varieties of problems that can be encountered. Like most skills, the more practice we have at problem-solving situations, the more experience and confidence we build. The more pattern processes of analysis we handle, the more we will recognize and understand. You, the problem solver, can often manipulate, re-define and transform the problem or situation. The first step of solving any problem is having the patience and fortitude to believe that finding a solution is possible. Attitude is your first tool in solving any problem.

A central goal of problem-solving research involves specifying when and how the processes of analysis and transformation are applied, in order to resolve the problem. It should probably be stated that failure, though painful, can be an useful experience. It's the lessons learned or insight gleaned from failure that can lead to solutions and better outcomes.  We will always need to be wary of dogmatic approaches that fail.

Problem solving is the analysis and transformation of information towards a specific goal. The goal may be more or less well-defined. Solving problems may be directly attainable, or require some insight or special body of knowledge. Quite often re-defining the problem in a new light, will yield a better set of attainable goals, which can lead to a solution. Just as one does not need to know the mechanics of an automobile to drive, one does not need to necessarily be an expert on all subjects to solve problems! Consulting those who have knowledge, or obtaining just the knowledge required to accomplish the task or solve a particular step of the problem at hand, needs to be considered.

A Four-Step Process

Billstein, Libeskind and Lott have adopted these problem solving steps in their book A Problem Solving Approach to Mathematics for Elementary School Teachers (The Benjamin/Cummings Publishing Co.). They are based on the problem-solving steps first outlined by George Polya in 1945.

1. Understanding the Problem
   • Can you state the problem in your own words?
   • What are you trying to find or do?
   • What are the unknowns?
   • What information do you obtain from the problem?
   • What information, if any, is missing or not needed?
2. Devising a Plan
   The following list of strategies, although not exhaustive, is very useful.
   • Look for a pattern.
   • Examine related problems, and determine if the same technique can be applied.
   • Examine a simpler or special case of the problem to gain insight into the solution of the original problem.
   • Make a table.
   • Make a diagram.
   • Write an equation.
   • Use guess and check.
   • Work backward.
   • Identify a subgoal.
3. Carrying Out the Plan
   • Implement the strategy or strategies in step 2, and perform any necessary actions or computations.
   • Check each step of the plan as you proceed. This may be intuitive checking or a formal proof of each step.
   • Keep an accurate record of your work.
4. Looking Back
   • Check the results in the original problem. (In some cases this will require a proof.)
   • Interpret the solution in terms of the original problem. Does your answer make sense? Is it reasonable?
   • Determine whether there is another method of finding the solution.
   • If possible, determine other related or more general problems for which the techniques will work.

Much of the research used for this post was generated from our database, Literati. One of the reasons I like this database is the "brainstorming" tool that can give a" visual map" or an overview of related concepts. For the concept of
"Problem Solving" related concepts include, Problem, Lateral thinking, How to Solve it, Ellis Paul Torrance, Edward de Bono, Educational Psychology, Creativity, Creative Problem Solving, and Creative Problem Solving Process.
Correctly defining the problem and assessment can be the most crucial stages of the Problem Solving Process.

Recently I was following the story in the news about the artificial intelligence computer, Google's AlphaGo, that beat Go Champion, Lee Se-dol in March of 2016, and the historic 1997 Deep Blue re-match against World Chess Champion Gary Kasparov. The problem solving techniques that the computer programmers used to defeat the human champions rely on deep search knowledge. Both Go and Chess are games which have so many permutations and possibilities, that even the massive computing ability of today's computers cannot solve these games. Games such as checkers and tic-tac-toe are not as complex and thus lend themselves to brute force calculations. As our world faces increasingly complex issues, we will need to employ problem-solving skills and emotional compassion to discover the solutions for our present and future environments. Find the solutions and answers to your problems and questions at your library. If you don't like the future you see, build one in its place, and if you don't see a title in our catalog, please recommend it to us.

See also

accountability; behaviorism; case studies; critical theory; curriculum, theories of; decision making; empiricism; feedback; globalism; Interstate School Leaders Licensure Consortium; knowledge base, of the field; leadership, theories of; management theories; organizational theories; politics, of education; principalship; rational organizational theory; role conflict; school districts, history and development; superintendency; workplace trends in Credo Reference.

Further Readings and References

Making Better Business Decisions: Understanding and Improving Critical Thinking and Problem Solving Skills

Great Games for Young Children: Over 100 Games to Develop Self-Confidence, Problem-Solving skills, and Cooperation by Rae Pica; illustrations, Kathy Ferrell; photographs, Mary Duru.

Teaching Kids to Think: Raising Confident, Independent, and Thoughtful Children in the Age of Instant Gratification by Darlene Sweetland, Ron Stolberg.