Monday, April 11, 2011
Quotes
"Problems call forth our courage and our wisdom; indeed, they create our courage and our wisdom. It is only because of problems that we grow mentally and spiritually." - M. Scott Beck
Thursday, April 7, 2011
Definitions
Well-defined problem - "one for which the desired end result is clearly stated, all of the necessary information is readily available, and a particular sequence of operations will (if properly executed) lead to a correct solution" (Ormrod, 2008, p. 402).
Ill-defined problem - "one in which the goal is ambiguous, some essential information is lacking, and no guaranteed means of reaching the goal exists" (Ormrod, 2008, p. 402).
Problem schemas - knowing how to solve different problems different ways. Used to classify a problem in ones mind (Ormrod, 2008).
Importance
"Why is it important to learn problem-solving skills? Because we all have to make decisions. Whether you're a student, a parent, a business person, or the president of the United States, you face problems every day that need solving . . . Whether the issue is big or small, we all set goals for ourselves, face challenges, and strive to overcome them" (Watanabe, 2009). Click here to learn more about Ken Watanabe's simplistic problem solving methods and his book titled Problem Solving 101: A Simple Book for Smart People.
"Problem solving is a fixture in life. You have to be able to solve problems. Problems pop up everyday. Sometimes they are small and sometimes they are large. Sometimes solving a problem is a matter of life and death and other times it is merely a matter of keeping your sanity. Regardless of why you need problem solving, you can not deny that you need it" (mindmentor, 2008).
Usage and Application
It is very important for teachers to encourage, learn, and apply different problem solving strategies.
Examples of problem-solving strategies include:
1. Algorithms - a step-by-step process to follow in order to solve a well-defined problem. Algorithms are "useful with particular problems in a particular content area but are, for the most part, inapplicable to problems in other areas" (Ormrod, 2008, p. 414). Algorithms can be used by themselves, or in combination in order to get the desired effect.
2. Heuristics - a basic problem-solving strategy that allows a person to make a quick and efficient decision. Used when an algorithm is not appropriate or available. Examples include:
- Brainstorming - developing multiple approaches to the problem at hand
- Means-end analysis - dividing a large problem into several small problems, then working on each one individually until the larger problem is solved
- Working backward - working from the goal to the problem state, opposite of means-end analysis.
- Using visual imagery - visualizing the components of the problem
- Drawing an analogy - relating the problem to a previously experienced problem, allowing insight into the new problem.
Marriott, Davies, & Gibson (2009) describe problem solving in four cycling steps: plan, collect, process, and discuss.
They performed a study that led to an easier, more effective way for school age children to learn statistics, by incorporating problem solving into the curriculum. Problem solving was taught based on the diagram above. To review this article, click here.
ITS Tuition School (2011) has a website devoted entirely to problem solving: what is problem solving, the steps to perform in order to achieve problem solving, using a group for problem solving, and assisting with achieving goals with the solved problem. If interested in the several articles posted on the website, click here.
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They performed a study that led to an easier, more effective way for school age children to learn statistics, by incorporating problem solving into the curriculum. Problem solving was taught based on the diagram above. To review this article, click here.
ITS Tuition School (2011) has a website devoted entirely to problem solving: what is problem solving, the steps to perform in order to achieve problem solving, using a group for problem solving, and assisting with achieving goals with the solved problem. If interested in the several articles posted on the website, click here.
Advantages/Disadvantages
Advantages:
There are many problems throughout the world, some that are very simplistic while others are very complicated with many details. In order to be an effective problem solver, a person has to have the ability to use prior problem solving skills on problems in the existing future (Ormrod, 2008). Disadvantages:
There are several things that could lead to problem solving disadvantages.
1.) Inappropriate use of algorithms. While teaching the use of algorithms, teachers often do not explain the reasoning behind the usage nor the way to reapply the algorithm to other problems. This often leads to the algorithm being used inappropriately or an inopportune time (Ormrod, 2008).
2.) Blocks. People often develop "blocks" that make it difficult to develop a solution to the problem. Examples include:
- Perceptual - how people interpret what they see in the world, which often renders decision making biased.
- Emotional - when a person's emotional needs take precedence over the problems at hand.
- Intellectual - not being able to think through the processes required for a particular problem.
- Expressive - the problem solver not having the ability to communicate well enough to produce an effective solution.
- Environmental - anything external (social or physical) that gets in the way of the problem solving procedure.
- Cultural - the inability to veer from the "norm". (ITS Tutorial School, 2011).
Theories and Theorists
Trial-and-Error Learning: Edward Thorndike formulated the law of effect, and is known for his "cat in the puzzle box" project (New World Encyclopedia, 2008). His work showed how animals try different approaches to receive a desired effect, with each attempt taking less time than the previous. This type learning is often observed in children. An example is a small child putting together a puzzle, how they try different angles with each piece until they fit appropriately (Ormrod, 2008).
Response Hierarchies: From trial-and-error learning, people come to the conclusion that some responses work better and quicker than others. These responses are placed in hierarchies, with the most successful at the top. Next time the same problem approaches, the response with the highest success would be attempted first (Ormrod, 2008).
Insight: Wolfgang Kohler developed his theory based on chimpanzee behavior during problem solving activities. He observed the fact that the chimps had a moment of "insight", when they contemplated a problem until a solution was determined. When this insight occurred, the chimp would perform the necessary tasks in order to solve the problem at hand (Ormrod, 2008).
Stages in Problem Solving: Graham Wallace developed four stages of problem solving, revolving around the thought of insight.
Wallace's four steps included:
1.) Preparation: Identifying the problem and finding information to assist with the solution.
2.) Incubation: Letting the thought 'sit' while going on about daily life, but continuing to think about it subconsciously.
3.) Inspiration: 'Insight' into the problem.
4.) Verification: Determining if the solution was appropriate.
George Polya also developed four stages of problem solving, but these steps were more focused on "conscious, controlled mental activities" (Ormrod, 2008, p. 405).
Polya's four steps are:
1.) Understanding the problem: "Identifying the problem's knowns (givens) and unknowns and, if appropriate, using suitable notation, such as mathematical symbols, to represent the problem" (Ormrod, 2008, p. 404).
2. ) Devising a plan: making a plan of actions
3.) Carrying out the plan: "Executing the actions that have been determined to solve the problems and checking their effectiveness" (Ormrod, 2008, p. 404).
4.) Looking backward: "Evaluating the overall effectiveness of the approach to the problem, with the intention of learning something about how similar problems may be solved on future occasions" (Ormrod, 2008, p. 404).
References
ITS Tutorial School. (2011). A Guide To - Problems and How to Solve Them.Retrieved April 13, 2011 from http://www.tuition.com.hk/problem-solving.htm
Mindmentor. (2008). The Importance of Problem Solving. Retrieved on April 11, 2011 from http://mindmentor.wordpress.com/2008/09/10/the-importance-of-problem-solving/
New World Encyclopedia. (2008). Thorndike, Edward L. Retrieved on April 11, 2011 from http://www.newworldencyclopedia.org/entry/Edward_L._Thorndike
Ormrod, J. (2008). Human learning. (5th ed.). Upper Saddle River, NJ: Pearson Education Inc.
Watanabe, K. (2009, April 23). The importance of problem-solving. Huffpost Living. Retrieved on April 11, 2011 from http://www.huffingtonpost.com/ken-watanabe/the-importance-of-problem_b_190514.html
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