Some thoughts on problem solving - Chemical Engineering ...

<strong>Some</strong> <strong>thoughts</strong> on problem solving
(Material compiled from Fogler's book on elements of chemical reaction engineering)
Problem solving is an activity whereby a best value is determined for an unknown, which is
subject to a set of constraints. Problems, in general, are of two types: Closed ended or Open ended
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 solutions for the problem as
defined. These are the problems often found in industry, design and graduate research etc.
Skills required for solving problems can be classified into 6 categories. Each successive skill level
calls for more advanced intellectual ability.
1. Knowledge: The remembering of previously learned material. Can the problem be solved
simply by defining terms and by recalling specific facts, trends, criteria, sequences, or
procedures This is the lowest intellectual skill level. Other words used in posing knowledge
questions: Who..., When..., Where..., Identify..., What formula
2. Comprehension: This is the first level of understanding. Given a familiar piece of
information, such as a scientific principle, can the problem be solved by recalling the
appropriate information and using it in conjunction with manipulation, translation,
interpretation, or extrapolation of the equation or scientific principle Other comprehension
words: ... Relate..., Show..., Distinguish..., Reconstruct..., Extrapolate... This is skill level 2.
3. Application: The next higher level of understanding is recognizing which set of principles
ideas, rules, equations, or methods should be applied, given all the pertinent data. Once the
principle is identified, the necessary knowledge is recalled and the problem is solved as if it
were a comprehension problem (skill level 2). Other words: ... Apply..., Demonstrate...,
Determine..., Illustrate....
4. Analysis: This is the process of breaking the problem into parts such that a hierarchy of
subproblems or ideas is made clear and the relationships between these ideas is made
explicit. In analysis, one identities missing, redundant, and contradictory information. Once
the analysis of a problem is completed, the various subproblems are then reduced to
problems requiring the use of skill level 3 (application). Other words: ... Organize...,
Arrange..., What are the causes ..., What are the components....
5. Synthesis: This is the putting together of parts to form a new whole. Synthesis enters
problem solving in many ways. Given a fuzzy situation, synthesis is the ability to formulate
(synthesize) a problem statement and/or the ability to propose a method of testing
hypotheses. Once the various parts are synthesized, each part (problem) now uses the
intellectual skill described in level 4 (analysis) to continue toward the complete solution.
Other words: ... Speculate..., Devise..., Design..., Develop..., What alternative..., Suppose...,
Create..., What would it be like..., Imagine..., What might you see....
6. Evaluation: Once the solution to the problem has been synthesized, the solution must be
evaluated. Qualitative and quantitative judgments about the extent to which the materials
and methods satisfy the external and internal criteria should be made. Other Words: ... Was it
wrong..., Will it work..., Does it solve the real problem..., Argue both sides..., Which do you
like best..., Judge..., Rate....

A simple heuristic algorithm for solving close ended
problems
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. Use
techniques such as Finding out Where the Problem Came From
3. Draw and label a sketch. Define and name all variables and/or symbols. Show numerical
values of variables if known.
4. Identify and name: Relevent principles, theories and equations, Systems and subsytems,
Dependent and independent variables, Knowns and unknowns, Inputs and outputs,
Necessary (missing) information
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 manipulate an equation or equations 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
What if you are stuck
Very often one finds that no progress is being made and you are stuck. Don't worry, you are not
alone. Everybody goes through such stages. Here are few tips which may help you overcome this
stage
1. Persevere! Keep trying different strategies and stay open to creative ideas. Try not to get
frustrated.
2. Be more active in the solution!! Ask yourself questions about the problem. Is this problem a
routine one What data are missing What equations can I use Explore the problem. Draw
sketches of what you think that the solution should look like. Write equations. Keep track of
your progress.
3. Re-focus on the fundamentals. Review the textbook and lecture material. Look for similar
examples. Study the examples given. Change what is given in the example and what is
asked, then try to see how it might relate to the problem you are addressing.
4. Break the problem into parts. Analyze the parts of the problem. Concentrate on the parts of
the problem you understand and that can be solved.
5. Verbalize the problem to yourself and others. Describe... what the problem is what you have
done, and where you are stuck

6. Paraphrase. Re-describe the problem. Think of simpler ways to describe the problem. Ask
others to describe the problem to you in their own words.
7. Look at extreme cases that could give insight and understanding. For instance: What
happens if x = 0 x = infinity
8. Simplify the problem and solve a limiting case. Break up the problem into simpler pieces
and solve each piece by itself. Find a related but simpler example and work from there.
9. Look for hidden assumptions or for what information you have forgotten to use. After
reading each phrase or sentence of the problem statement, ask yourself if any assumptions
can be inferred from that phrase.
10. Alternate working forward towards a solution and backwards from a solution you assumed.
Working backwards may at least give you clues as to how you should approach the problem
while working forward.
11. Take a break. Incubate. Let your subconscious work on the problem while you do something
else, like exercising, talking to friends, or just relaxing! <strong>Some</strong>times all you need is a break to
achieve that final breakthrough!
<strong>Some</strong> ideas for dealing with open ended problems
1. Write an initial problem statement. Include information on what you are to solve, and
consider why you need to solve the problem.
2. Make sure you are proceeding to solve the real problem as opposed to the perceived problem
Find out where the problem came from, Explore the problem.
3. Generate solutions Understand what conceptual blocks can occur so that you will be aware
of them when they surface. Try Analogy: State the problem, Generate analogies, Solve the
analogy, Transfer the analogy to the solution. Organize the ideas/solutions that have been
generated. 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. Take
a break. Let your subconscious work on the problem while you do something else.
<strong>Some</strong>times all you need is a breather to achieve that final breakthrough!
4. Choose best alternative from the ideas generated (chapter 5) Decision Making: Musts,
Wants, Adverse Consequences Planning: Potential Problem, Consequences, Preventative
Action, Contingent Action.
5. Evaluation - Is the problem you are solving still relevant Does the solution satisfy all the
stated and implied criteria
<strong>Some</strong>thing about creative thinking
1. 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
2. Pose new questions to yourself every day. An inquiring mind is a creatively active one that
enlarges its area of awareness.
3. 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.
4. Engage in creative hobbies. Hobbies can also help you relax. An active mind is necessary for
creative growth.

5. 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.
6. Learn to know and understand yourself. Deepen your self-knowledge by learning your real
strengths, skills, weaknesses, dislike, biases, expectations, fears and prejudices.
7. Learn about things outside your specialty. Use cross-fertilization to bring ideas and concepts
from one field or specialty to another.
8. 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.
9. 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.
10. Be alert in your observations. Look for similarities, differences, as well as unique and
distinguishing features in situations and problems.
11. 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.
12. 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.