Chapter 1 the Nature of Problem Solving

No Slide TitleProblem Solving Chapter 1
Problem Solving Chapter 1
Introduction
Critical and Creative Thinking
A problem is an opportunity for improvement.
A problem is the difference between your current state and your goal state.
A problem results from the recognition of a present imperfect and the belief in the possibility of a better future.
The importance of goals in solving a problem
The management of a problem in a way that successfully meets the goals established for treating it.
*
Problem solving is a process by which the learner discovers a combination of previously learned rules that he/she can apply to achieve a solution. (Holroyd 1985)
stop it
mop it
Problem Exploration
Restate the problem
Clarify the Problem
Articulate the assumptions
Obtain needed information
Explain the Problem
Look at the problem from different viewpoints
Ask a series of whys.
What is the history of the problem?
What is the problem environment?
What are the constraints?
Goal Establishment
Idea Generation
Use idea generation techniques (brainstorming, forced relationships, random stimulation, and so on)
Allow time to incubate during various phases of idea generation
Idea Selection
Implementation
Evaluation
Determine whether the solution worked
Remember that many solutions are better described as partially successful or partially unsuccessful, rather than as an either/or in a success/failure division
Truth Problems
*
Critical thinking is the process to reflect on, assess and judge the assumption underlying our own and others ideas and efforts.
Creative thinking is the process we use to develop ideas that unique, useful, and worthy of further elaboration.
Scrutinizing arguments.
Judging ideas.
Judging the rationality of these justifications by comparing them to a range of varying interpretations and prospective.
Providing positive as well as negative appraisal.
How does this relate to our discussion?
What does this mean?
What do we already know about...?
The Six Types of Socratic Questions for
Critical Thinking
How can you verify or disapprove that assumption?
Explain why...(Explain how...)
Critical Thinking
What would be an example?
What is the nature of this?
Why is this happening?
Why is....happening?
What evidence is there to support your answer?
What would be an alternative?
Is there another way to look at it?
Explain why it is necessary-or beneficial?
Who benefits?
Critical Thinking
How are...and ...similar?
What is a solution to the problem of...?
Compare... and... with regard to...
What is another way to look at...?
Critical Thinking
What generalizations can you make?
What are the consequences of that assumption?
How could...be used to...?
How does...affect...?
Why is... important?
What was the point of this question?
Why do you think I asked this question/
What does...mean?
Critical Thinking
Consider rejecting standardized formats for problem solving.
Have an interest in a wide range of related and divergent fields.
Take multiple perspectives on a problem.
Use trial-and-error methods in their experimentation.
Have a future orientation.
Improving Your Creative Abilities
Keep track of your ideas at all times. Many times ideas come at unexpected times. If an idea is not written down within 24 hours it will usually be forgotten
*
Pose new questions to yourself every day. An inquiring mind is a creatively active one that enlarges its area of awareness.
Keep abreast of your field. Read the magazines, trade journals, and other literature in your field to make sure you are not using yesterday's technology to solve toady's problems.
*
Engage in creative hobbies. Hobbies can also help you relax. An active mind is necessary for creative growth.
Have courage and self-confidence. Be a paradigm pioneer. Assume that you can and will indeed solve the problem Persist and have the tenacity to overcome obstacles that block the solution pathway.
Learn to know and understand yourself. Deepen your self-knowledge by learning your real strengths, skills, weaknesses, dislike, biases, expectations, fears and prejudices.
Learn about things outside your specialty. Use cross-fertilization to bring ideas and concepts from one field or specialty to another.
*
Avoid rigid, set patterns of doing things. Overcome biases and preconceived notions by looking at the problem from a fresh view point, always developing at least two or more alternative solutions to your problem.
Be open and receptive to ideas (yours and others). New ideas are fragile; keep them from breaking by seizing on the tentative, half formed concepts and possibilities and developing them.
*
Be alert in your observations. Look for similarities, differences, as well as unique and distinguishing features in situations and problems.
Adopt a risk taking attitude. Fear of failure is the major impediment to generating solutions which are risky (i.e., small chance of succeeding) but would have a major impact if they are successful. Outlining the ways you could fail and how you would deal with these failures will reduce this obstacle to creativity.
*
Keep your sense of humor. You are more creative when you are relaxed. Humor aids in putting your problems (and yourself) in perspective. Many times it relieves tension and makes you more relaxed.
*
Closed Ended Problems are the type with only one right answer. These are the same types of problems that are usually found at the end of chapters in textbooks, and they reinforce concepts learned in the corresponding chapter.
Open-ended problems are those which have many solutions or no solution for the problem as defined.
1. Write out the problem statement.
Include information on what you
are to solve, and consider why you need to solve the problem.
*
2. Make sure you are solving the real problem as opposed to the perceived problem.
3. Draw and label a sketch. Define and name all variables and/or symbols. Show numerical values of variables if known.
Systems and subsystems
*
5. List assumptions and approximations involved in solving the problem. Question the assumptions and then state which ones are the most reasonable for your purposes.
*
6. Check to see if the problem is either under-specified or over-specified. If it is under-specified, figure out how
to find the missing information. If over-specified, identify the extra information that isn't needed.
7. Relate problem to a similar problem
or experience (compare to an example problem in lecture or in the book).
8. Develop/derive/integrate and/or
from which the desired variable can
be determined.
*
9. Substitute numerical values and calculate the desired variable. Check your units at each step in the solution to find possible errors.
10. Examine and evaluate the answer to see it makes sense. Is it reasonable, considering the problem statement? Does it consider safety and ethical issues?
1. Write out the problem statement.
Include information on what you
are to solve, and consider why you need to solve the problem.
2. Make sure you are solving the real problem as opposed to the perceived problem.
3. Generate Solutions
a. Understand what conceptual blocks can occur so that you will be aware of them when they surface. Perceptual, Emotional, Cultural, Environmental, Intellectual, Expressive
b. Brainstorm. Use Osborn’s checklist.
Osborn's Checklist for Adding New Ideas
Adapt?.... How can This (product, idea, plan, etc.) be used as is? What are other uses it could be adapted to?
Modify?.... Change the meaning, material, color, shape, odor, etc.?
Magnify?.... Add new ingredient? Make longer, stronger, thicker, higher, etc.?
Minify?.... Split up? Take something out? Make lighter, lower, shorter, etc.?
*
Substitute?..... Who else, where else or what else? Other ingredient, material, or approach?
Rearrange?.... Interchange parts? Other patterns, layouts? Transpose cause and effect? Change positives to negatives? Reverse roles? Turn it backwards or upside down? Sort?
Combine?.... Combine parts, units, ideas? Blend? Compromise? Combine from different categories?
*
Example: Imagine that you have been given the task of designing safe playground equipment entirely out of old cars. How wold you approach this problem?
*
Adapt: Take the hood off and use it as a toboggan in winter
Modify: Remove the engines and side panels and make go-carts
*
Magnify: Over inflate the inner tubes from the tires and use them to create a "romper room"/jumping pit.
Minify: Crush the cars into cubes and allow the kids to climb on the blocks
Substitute: Use the car's seats in swings
Rearrange: Turn the car upside down and use it as a teeter-totter
Combine: Use the side panels or roof to make a huge canopy or fort
*
c. Analogy. State the problem, Generate analogies, Solve the analogy, Transfer the analogy to the solution.
d. Cross Fertilize. Draw analogies from other disciplines.
*
e. Futuring. Today's constraints (e.g. computing speed, communications) may be limiting the generation of creative solutions. Think to the future when these constraints may no longer exist. Remove all possible constraints from the problem statement and solution criteria.
f. Incubate. Take a break. Let your subconscious work on the problem while you do something else. Sometimes all you need is a breather to achieve that final breakthrough!
a. Decision Making: Musts, Wants, Adverse, Consequences
b. Planning: Potential Problem, Consequences, Preventative Action, Contingent Action
c. Evaluate: Does the solution satisfy all the
stated and implied criteria? Is the solution safe to people and property? Is the solution ethical?
B
A
2. Who is our greatest president?
3. What is the rated tensile strength of an E6011 electrode?
4. Which wood is the hardest?
5. Which wood is the hardest to work with?
6. How can a chair be re-designed to eliminate back ache?
PROBLEM #4: Determine whether the problem is open-ended or closed ended
*
7. Would it be more cost effective to use a robotic welder, or a human welder?
8. What is the greatest volume that can be produced by cutting squares out of the corners, and folding a 10" x 12" sheet of steel into a rectangular box with an open top?
9. What is the sum of the interior angles of a triangle?
10. Do parallel lines converge?
11. What is the sum of 1 + 1?
Polya’s Heuristics
The first and most important step in solving a problem is to understand the problem, that is, identify exactly which quantity the problem is asking you to find or solve for (make sure you read the whole problem).
Polya’s Heuristics
Next you need to devise a plan, that is, identify which skills and techniques you have learned can be applied to solve the problem at hand.
Carry out the plan
Look back: Does the answer you found seem reasonable? Also review the problem and method of solution so that you will be able to more easily recognize and solve a similar problem.

Chapter 1 the Nature of Problem Solving

Documents

Transcript of Chapter 1 the Nature of Problem Solving