Problem Solving





A Discipline of Study
People tend to use the term discipline when talking about a large and inclusive discipline of study, a sub-discipline, an interdisciplinary discipline, and so on. Each academic discipline or area of study can be defined by a combination of general things such as:


 * The types of problems, tasks, and activities it addresses.
 * Its accumulated accomplishments such as results, achievements, products, performances, scope, power, uses, impact on the societies of the world, and so on.
 * Its history, culture, and language, including notation and special vocabulary.
 * Its methods of teaching, learning, assessment, and thinking. What it does to preserve and sustain its work and pass it on to future generations.
 * Its tools, methodologies, and types of evidence and arguments used in solving problems, accomplishing tasks, and recording and sharing accumulated results.
 * The knowledge and skills that separate and distinguish among: a) a novice; b) a person who has a personally useful level of competence; c) a reasonably competent person, employable in the discipline; d) an expert; and e) a world-class expert.

As in the above list, people tend to use the term problem rather loosely, assuming that everybody knows what a problem is. The term is applicable in every area of human endeavor. So, in this IAE-pedia document we are giving a definition that is very broadly applicable.

Expertise
The last item in the bulleted list above provides a scale that a learner works up through as he or she gains in expertise in a particular area.

Each discipline has its own ideas as to what constitutes an increasing level of expertise and how to go about helping students to achieve this increasing level of expertise. Each discipline has its own ideas on what constitutes being a novice, reasonably good, very good, and "world class" within the discipline. Depending on the discipline, one might demonstrate their level of expertise through performances, presentations, competitions, products produced, knowing about the culture and history of the discipline, and so on.

It is common to quote the number "10,000 hours" of study and practice as being necessary to move from a novice level to an expert level. Some areas take much longer than this. To become a world class chess player may take 20,000 hours or more. A tenured research professor in a good university will have spent 20,000 hours or more of study and research to achieve this position.

Definition of Problem
Here is a definition of "problem" that fits well in many different disciplines. You (personally) have a problem if the following four conditions are satisfied:


 * 1) You have a clearly defined given initial situation.
 * 2) You have a clearly defined goal (a desired end situation). Some writers talk about having multiple goals in a problem. However, such a multiple-goal situation can be broken down into a number of single-goal problems.
 * 3) You have a clearly defined set of resources that may be applicable in helping you move from the given initial situation to the desired goal situation. These typically include some of your time, knowledge, and skills. Resources might include money, the Web, the telecommunication system, computers, friends, teachers, and so on. There may be specified limitations on resources, such as rules, regulations, guidelines, and time lines for what you are allowed to do in attempting to solve a particular problem.
 * 4) You have some ownership—you are committed to using some of your own resources, such as your knowledge, skills, time, and energy, to achieve the desired final goal.

This document considers problem solving to include:


 * Question situations: recognizing, posing, clarifying, and answering questions.
 * Problem situations: recognizing, posing, clarifying, and then solving problems.
 * Task situations: recognizing, posing, clarifying, and accomplishing tasks.
 * Decision situations: recognizing, posing, clarifying, and making good decisions.
 * Using higher-order critical, creative, wise, and foresightful thinking to do all of the above. Often the results are shared, demonstrated, or used as a product, performance, or presentation.

In many problem-solving situations, Information and Communication Technology (ICT) and computerized tools are resources of the type mentioned in the third part of the definition. These resources have grown more powerful over the years. That is one reason why it is so important to integrate teaching the use of computers in problem solving thoroughly into the basic fabric of academic courses.

The fourth part of the definition of a problem is particularly important. Unless you have ownership—through an appropriate combination of intrinsic and extrinsic motivation—you do not have a problem. Motivation, especially intrinsic motivation, is a huge topic in its own right.

For example, you glance at the headlines in your local newspaper and see that a drought in a particular country in Africa is causing widespread hunger. Hundreds of thousands of people are on the verge of starvation.

This hunger and starvation situation meets the first three components of the definition of a problem. Moreover, the story touches your heart. But what—if anything—can or will you do about it? It is one thing for a problem situation to touch your heart. It is another situation entirely for you to make a decision to commit some of your resources such as time and money to do something about helping to solve the problem.

Now, think about the types of "problems" that we assign students in school. Many students look at the tasks assigned as homework and mentally respond, "I couldn't care less. These are just make-work busy work—a hoop that I am supposed to jump through." That is, these students have no ownership.

A good teacher creates learning situations in which students are willingly engaged in working on problems and tasks that they feel are personally relevant and important.

A Free Book by David Moursund

 * Moursund, D.G. (2007). Introduction to Problem Solving in the Information Age. Eugene, OR: Information Age Education. Access at http://i-a-e.org/downloads/doc_download/7-introduction-to-problem-solving-in-the-information-age.html.

This short (99-page) book is intended primarily for preservice and inservice teachers of K-12 students, and the teachers of these teachers. In this book, the term "problem solving" includes posing and solving problems, posing and accomplishing tasks, posing and answering questions, and posing and making decisions.

Problem solving is an integral component of every academic discipline. Humans solve problems using their physical and mental capabilities, and tools that they have developed. The Information Age has brought us a wide range of computer-based tools that are powerful aids to problem solving. Now, more than ever, it is important to stress problem solving and higher-order critical thinking throughout our educational system.

Computer Systems that Solve Problems
The IAE-pedia document Two Brains Are Better Than One discusses the individual and joint capabilities of human brains, computer brains, and the two working together in solving problems and accomplishing tasks. Human brains get better at problem solving by study and practice. This is a one-brain-at-a-time process. Once researchers and developers develop software to make a computer better at problem solving, then the software can be mass distributed. This brings an entirely new dimension to the concept of a person becoming better at problem solving.

What this means is that our educational system needs to fully integrate computers as an aid to problem solving into every discipline that students study.

Moreover, consider the problem of helping students to learn. We now have Highly-interactive Intelligent Computer-assisted Learning (HIICAL) systems that are quite good and are steadily improving (http://i-a-e.org/iae-blog/entry/education-for-the-future.html). They are an aid to helping to solve the problem of children throughout the world needing and wanting to get a good education.

Author or Authors
The initial version of this article was written by David Moursund.