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Unformatted text preview: 5' Read the prabiem i Analyze and try to understand the probiem l Review and write down key features is Draw a diagram of flowsl variaoles I State whot the problem is; the objectivetsl
Enter known data on diogram ' Enter symbols for unknown data on diagram
List relevant physical laws, principles
Employ soitabie notation
Fix the system
List assumptions, inferred conditions
Locote missing information . Pick a basis Plan the problem solving strategy. identity
the problem type ‘ Stondord or known
problem type
(recall from memory) Yes Con the problem be
converted to a
stondaro type No Generate alternative ways to solve the problems Review other key relations, principles
Hypothesize, Visualize Divide the problem up into simpier subproolems
Simpiify, approximate Eliminate olternatives that are too expensive or
will not reach objectives Select strategy from
among options Design o new strategy; list the steps Execute the strategy; check
each step to eliminate bianders: ﬂ Obtoin and check onswer ls it reasonable in magnitude
Try alternote path to answer
Interpret results
Doss it satisfy assumptions,
constraints ' TABLE 1.12 A Comparison of the ProblemSolving Habits of a Novice and an Expert WWWWHMW A novice: An expert: WWMW Starts solving a problem before fully
understanding what is wanted
and/or what a good route for
solution will be «t Focuses only on a known problem set
that he or she has seen before and
trys to match the problem with one
in the set Chooses one procedure without
exploring alternatives Emphasizes speed of solutions
unaware of blunders Does not follow an organized plan of
attack such as outlined in Fig. 1.14,
jumps about, and mixes problem~
solving strategies ls unaware of missing data, concepts,
laws Exhibits bad judgment, makes
unsound assumptions, poor
approximations Gives up solving the problem because
he or she does not know enough 1‘ Gives up solving the problem because
he or she does not have skills to
branch away from a dead~end
strategy Reviews the entire plan outlined in Fig. i.14, mentally explores alternative
strategies, and clearly understands
what result is to be obtained Concentrates on similarities to and
differences from known problems;
uses generic principles rather than
problem matching Examinesseveral procedures serially or
in parallel Emphasizes care and accuracy in the
solution ‘ Goes through the problem—solving
process step by step, checking,
reevaluating, and recycling from
‘dead ends to another valid path Knows what principles might be
involved and where to get missing
data Carefully evaluates the necessary
assumptions and approximations Knows what the difﬁculty is and is
willing to learn more that will
provide the information needed Aware that a dead end may exist for a
strategy and has planned alternative
strategies if a dead end is reached TABLE 2.1 Diagnosis of Reasons for Failing to Solve Problems
(“Experience is the name everyone gives to their mistakes.” Oscar Wilde) g Failure to work on a problem in a systematic rather than a scatterbrained way
(start too soon; skip essentiai steps) g Failure to read/understand the problem thoroughly % Failure to draw a diagram and enter all data thereon and the symbois for the unknowns Failure to ascertain the unknown as Fixing on the ﬁrst, a poor, or an incorrect strategy of solution without considering
alternative strategies Selection of the wrong principle or equation to use (total moles instead of total mass, ideal gas instead of real gas) and solution of the
wrong problem Working with false information Picking the wrong entry frorn a data base, chart, or table
(wrong sign, wrong units, decirnal misplaced, etc.) Entering incorrect inputs/parameters into calculations
(transpose numbers, wrong units, etc.) % Failure to include units in each step of the calculations Sloppy execution of calculations introduce errors
(add instead of subtract, invert coefﬁcients, etc) Difﬁculty in distinguishing new features in a problem that superficially looks familiar Incorrect algebraic manipulations Use of unsatisfactory computer code for the problem
(too much error, premature termination) Unable to locate needed data, coefﬁcients by not reading the problem thoroughly or
looking in the wrong data base Unable to estimate what the answer should be to use in comparison with calculated
answer Knowledge (your data base) is inadequate (you have forgotten, or never learned, some essential laws, equations, values of
coefﬁcients, conversion factors, etc.) Only forward reasoning rather than both forward and backward reasoning is employed % Emotional stress
(fear of making a mistake, looking foolish or stupid) Lack of motivation Inability to relax e i TABLE 2.2 Techniques Used by Experts to Overcome Barriers to Problem
Solving Read the problem over several times but at different times. Be sure to understand all
facets of it. Emphasize different features each time. Restate the problem in your own words. List assumptions. Draw a comprehensive diagram of the process and enter all known information on the
diagram. Enter symbols for unknown variables and parameters. Formally write down what you are going to solve for: “I want to calculate . . . Choose a basis. Relate the problem to similar problems you have encountered before, but note any
differences. Plan a strategy for solution; write it down if necessary. Consider different strategies.
Write down all the equations and rules that might apply to the problem. Formally write down everything you know about the problem and what you believe is
needed to execute a solutiOn. Talk to yourself as you proceed to solve the problem. Ask yourself questions as you go along concerning the data, procedures, equations
involved, etc. Talk to other people about the problem.
Break off problem solving for a few minutes and carry out some other activity. Break up the solution of the problem into more manageable parts, and start at a familiar stage. Write down the objective for each subprobiem (i.e., convert mole fraction to mass
fraction, ﬁnd the pressure in tank 2, etc) Repeat the calculations but in a different order.
Work both forward and backward in the solution scheme. Cousider if the results you obtained are reasonable. Check both units and order of
magnitude of the calculations. Are the boundary conditions satisﬁed? Use alternatiVe paths to verify your solution. Maintain a positive attitude~you know the problem can be solved—just how is the
question. ., w..." ..._.......____.,____....._.__..._._._. TABLE 2.3 A‘ Checklist of Personal Traits to Avoid In Problem Solving 1. When i fail to solve a problem, i do not examine how i went wrong. 2. When confronted with a complex problem, I do not develop a strategy of ﬁnding
out exactly what the problem is. 3. When my ﬁrst efforts to solve a problem fail, I become uneasy about my ability to
solve the problem (or i panic!) 4. I am unable to think of effective alternatives to solve a problem. 5. When I become confused about a problem, i do not try to formalize vague ideas or
feelings into concrete terms 6. When confronted with a problem, I tend to do the ﬁrst thing i can think of to
solve it.  7. Often I do not stop and take time to deal with a problem, but just muddle ahead. 8. i do not try to predict the overall result of carrying out a particular course of
action. 9. When I try to think of possible techniques of solving a problem, l do not come up
with very many alternatives. 10. When faced with a novel problem, i do not have the conﬁdence that I can resolve
it. 11. When I work on a problem, I feel that I am grasping or wandering, and not getting
a good lead on what to do. 12. I make snap judgments (and regret them later).
13. I do not think of ways to combine different ideas or rules into a whole.
14. Sometimes I get so charged up emotionally that i am unable to deal with my 15. ljump into a problem so fast, 1 solve the wrong problem. 16. I depend entirely on the workedmout sample problems to serve as models for other
problems. W SOURCE: Based on the ideas in a questionnaire in RP. Heppner, P.S.I., Department of Psychology,
University of Missouri—Columbia, 1982. l
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i x ‘Weiler’s Law: Nothng is impossible for the person who doesn’t have to do it. Howe’s Law: Every person has a scheme which will not work. The 90/90 Law: Theﬁrst 10% of the task takes 90% of the time. The remaining 90%
takes the remaining 10%. Gordon’s Law: If a project is not worth doing, it’s not worth doing well.
Slack’s Law: The least you will settle for is the most you can expect to get. O’Toole’s Commentary: Murphy was an optimist.7 ...
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 Fall '07
 Monbouquette

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