Problem solving is more than the ability to compute.
When the learner is confronted with a problem situation whose solution is not known, the student must rely on his or her problem solving skills. One, problem solving is the ability to pick out the important facts that are given and disregard the facts that are not pertinent. Another skill is to recognize what information is missing and how to find it. Another is the ability of the learner to recognize similarities between problems which are being solved and have been solved.
There are several techniques, methods and strategies used in problem solving. Problem solving involves trying several ways to solve the problem before deciding on which to use. It involves putting together the facts that the learner has with the mathematics that he or she knows in such a way that the result is a solution that was unknown to begin with. A model of a problem can be a picture worth five hundred words, a sketch, a scale drawing a chart or graph. It’s whatever helps the student. There are times when information is missing and the skill is the ability to recognize what additional information is necessary.
Problem solving situations are likely to be representative of those which the learner will face sometime in the future. Problem solving will give the students experiences to help them in their thinking and decision making processes. The main thrust of problem solving should be toward the development of logical thinking. Taking the numbers out of problems seems to be one way of doing this without the negative reaction that usually accompanies mathematical problems.
In New Haven, we have found that teaching problem solving is a problem, but like anything else, it can be solved. No automatic formula can be applied to guarantee success in teaching problem solving.
It is common knowledge that when the learner is trying to solve a problem he must:
1. Understand the problem.
2. Plan to solve the problem.
3. Solve the problem.
4. Review the problem and the solution.
The learner must apply some strategies. We’ve considered five strategies that we have found to be helpful. The learner can make a model of the problem by using commercial or teacher made materials. Needed information can be gained by asking questions whose answers will provide the necessary information.
Some problems must be broken down into smaller parts. Once the answer for each part has been found, the information can be used to solve the original problem. In order to simplify the problem eliminate extraneous information and list the facts that remain. There are times when problems can be simplified by making assumptions.
In research the learner identifies what information is needed, decides what information is necessary, and finds that information in reference books or by collecting data.
This unit is designed to help students gain insight into problem solving through handson materials based upon careers. Speakers and visitations will be included.
Six careers are utilized. They are:
1. Sales Person
3. Stock Clerk
4. Purchasing Agent
5. Bank Teller
Six different professionals will be invited to speak to the classes based upon their career. Each will be asked to speak on the math problems that he or she has to encounter daily and give some examples. They will also be asked to discuss the firm that they work for and give some information about themselves.
There will be scheduled visits to receptive local businesses. Transportation will be provided by the city through its educational system, between the hours of nine and twelve.
As a culminating activity an out of state trip will be planned to the World Trade Center, Stock Exchange and/ or United Nations.
Lesson plans will be constructed for each career listed in this unit in the form of word problems. Objectives and strategies will be listed and the strategies will be based upon a model.
Certain skills are necessary for the development of problem solving. Students must be able to denote details, recognize sequence and know what is given in the problem.
The learner needs to know what is asked for in the problem and plan a solution. In order to plan a solution the learner has to answer questions such as: how, when, where, what time, and how many.
Special emphasis will be placed on number facts, operation techniques, to ensure that the learner will have a general idea what the problem is about.
Key words will play a major role in helping students to understand the problem and have some thoughts relative to the reasonable steps leading to a solution.
Receptive local businesses will give the students on the job training. Local businesses will be asked to take at least two students for a school day thus giving them handson experience. Once this has been done the students will prepare a report for the class. A discussion of their experience will take place as to positive and negative aspects of the experience.
A definition of each career will be stated as well as information concerning each career.
A wide range of practical applications will include consumer activities such as: finding income, take home pay, installment buying, sales, and exercises in banking.
The unit includes a list of speakers, their phone numbers and addresses; also a receptive list of individuals for visitations; a reading list for students and teachers, a bibliography and a resource list.