You may get sick or your brain may freeze up when your teacher says that you will be doing problem solving today. Do not worry, take heart we are going to learn how to deal with these problems and how to actively solve these problems. When teachers mention problem solving most people have a case of math anxiety. They just sit there and hope some plan of action pops into their mind. Usually it dosen't. Most of the time our brains just freeze up and nothing comes to mind. That is what we are going to look at here. A plan of action.
Identifying the problem is one of the most difficult and challenging aspects of problem solving. There are several obstacles to overcome inorder to solve problems effectively. One common obstacle is the lack of background information. When we are faced with a problem we need sufficient information to attack the problem. Make sure that you know exactly what your problem is asking and then research to find all the information needed to begin to solve this problem.
Another obstacle in many students' way is the lack of determination to solve the problem. Many people do not take the time necessary to reflect carefully on the nature of the problem at hand. As with mathematics, most students will attempt the problem for about five minutes and then determine that they cannot complete the problem. Solving problems takes time, be determined to solve the problem. Most of the most difficult thinking occurs at the beginning of the problem. Take your time, wade through all the information. Make a list of all the information that you are given at the beginning of the problem. Then write down the question that you want to answer. Writing things down help free your mind from trying to remember them. At this stage you want all the cognitive resource that you can get.
We can represent the problem in many different ways. One form
could be to simply think about the problem abstractly. Another is to commit
one's thoughts to paper and organize them like we discussed in the above paragraph.
Representing the problem on paper has many advantages. Many problem are so
complex it is too much of a strain on our brains to keep all that information
organized. That is too much for our working memory to handle.
Draw pictures whenever possible. This allows you to see the problem at hand. One way to write down this information is to define our Problem space. First we want to define our goal state: what we want to accomplish. Next is the initial state: what is known about the problem before one attempts to solve it (the given). The operators are what we want to look at now: all the objects or concepts in the problem that can be manipulated to reach a solution. Finally all the constraints on the operators.
People use all kinds of different strategies to solve problems. Some are highly structured and refered to as algortithms. This is just another name for a rule. At other times when no rule is available some rely on heuristics, or rules of thumb. Two common heuristics are trial-and-error and means-ends analysis. Clearly trial and error is the least effective because there is no strategic plan whatsoever. However this may be the only option when students are faced with a new and unfamiliar problem. This is a good steping stone in problem solving. Most students use this at the onset of the problem and then switch to a more effective strategy. Means ends analysis is more efficient than trial and error in that the problem solver tries to reduce the distance to the goal by making a sequence of steps that can be evaluated individually. Means ends analysis requires the learner to do three things: (1) keep the goal in mind, (2) take the problem and break it down into smaller problems, (3) evaluate each step along the way to make sure that there are no mistakes. These are only a couple of strategies, but these are a great place to begin.
At this stage in the game it is very important to evaluate your solution. Does it make sense? Are your answers reasonable? Go back and evaluate your processes and look for mistakes or ways to improve your strategy.
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