Lesson Plans Archive

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TOPIC: Dr. Brooker's Guide to Teaching Problem Solving

GRADES: K-12

AUTHOR: Dr. Robert Brooker, Professor Emeritus of Chemistry

SCHOOL: University of Indianapolis

Many students progress through kindergarten, grade school, high school and college without learning how to reason or think for themselves. The traditional methods of instruction that have been used to educate these students often are based upon:

- Giving the students a set "chunk" of material,
- Expecting the students to reproduce the materials on tests, and
- Assessing their progress by how much of the material they have been able to retain and reproduce on demand.

As a result, many students leave our schools with the impression that "learning" is the same as memorizing. The purpose of this Problem Solving Guide is to give educators some direction as to how to present problems to promote independent student thinking through reasoning, analysis, thinking and the synthesis of knowledge.

Students will learn:

- Some techniques of solving problems.
- The team approach to problem solving.
- To be more active participants in class.
- To become emotionally involved in class work.
- To use their imagination.
- To be prepared to take and accept the risk of failure.

Students should:

- Read the problem thoroughly or listen carefully when it is given orally.
- Want to solve the problem.
- Avoid mind sets.
- Organize the information.
- Write down what it is that is sought.
- Devise a strategy for solving the problem.
- If the strategy doesn't work, try solving a similar problem that is simpler.
- Work with others on the problem.
- After obtaining a solution, check to see if it meets the problem requirements.

The Student:

- Did not concentrate on the material and does not understand the problem.
- Misread the problem and missed important facts.
- Made errors in reading, working or thinking.
- Was not consistent in interpretation of words or operations.
- Did not check correctness of procedures or answers
- Worked too rapidly.
- Did not break a complex problem into smaller parts.
- Did not use a dictionary or other reference material as needed.
- Did not evaluate the reasonableness of a solution.
- Lacked confidence in his/her ability to solve the problem.
- Solved the problem mechanically without true thought or understanding.
- Jumped to a conclusion without adequate thought.

When presenting a problem to be solved by a group there are hazards that any instructor will run into. If one is not aware of these hazards, time is wasted and the educational effect on students can be lessened. Among these hazards are:

- STUDENTS ASKING FOR THE PROBLEM TO BE REPEATED:
When reading problems to students, don't repeat them. Repeating problems unnecessarily takes extra time, and, students will learn that they do not need to concentrate fully when a problem is initially read. Life's problems are not repeated. Students need to learn this.

- MAKING HUMOROUS REMARKS ABOUT A PROBLEM:
Making a humorous remark about a problem indicates to the students that the problem is beneath their attention. Humorous remarks can disrupt students who otherwise would make a serious attempt to solve the problem.

- GIVING AN IMMEDIATE ANSWER:
Learning to persevere and rework failed solutions is important. Giving an immediate answer will deter most of the students from making more than one attempt to work a problem.

- LAUGHING AT ANOTHER'S ANSWER:
Any answer is better than no answer. No one should be allowed to make a remark about an answer unless they have a better one.

- FAILING TO BECOME INVOLVED:
Student will occasionally argue that they can learn by listening, and that they do not have to participate directly in the process or discussions in order to learn the methods. They are wrong. This puts the student right back in the memorization method. One must participate directly in order to learn how to solve problems. As Mark Twain said: "The person who grabs the cat by the tail learns far more than the person who just thinks about it."

- GUESSING THE CORRECT ANSWER:
Estimation is good, and often necessary, but problems have specific answers. Guessing at answers without actually solving the problems will stop others from trying. Answers to simpler problems may be intuitive to some students, but, when required to actually work through the problems, students will often find out that the basis for even intuitive answers can often be abstract and challenging.

Students should understand that in a problem solving class, getting the answer to a single problem is not as important as learning the problem solving process.

Problem Type #1: Words.

Problem Type #2: Converting Letters to Numbers.

Problem Type #3: Logic.

Problem Type #4: Decoding - Cryptogram.

Problem Type #5: Moving Toothpicks.

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