Open-ended problems

The following are summaries of open-ended problems ihat have been used as tenn problems ai Ihe University of Michigan. The complete problem statement of the problems can be found in the DVD-ROM Appendix G. 

The educational literature provides frequent references to individuals, particularly practicing engineers and scientists, that have different learning styles, and in order to successfully draw on these different styles, a variety of approaches can be employed. One such approach involves the use of open-ended problems. 

The term open-ended problem has come to mean different things to different people. It basically describes an approach to the solution of a problem and/or situation for which there is usually not a unique solution. Three literature sources (novide sample problems that can be used when this educational tool is employed. 

The author of this book has applied this somewhat unique approach and included numerous open-ended problems in several earlier course offerings at Manhattan College. Student comments for the graduate course Accident and Emergency Management were tabulated for one such course. Student (unedited) responses to the question What aspects of thi-s course were most beneficial to you are listed below. 

The open-ended questions gave engineers a creative license. We don t come across many of these opportunities.  

Open-ended questions allowed for candid discussions and viewpoints that the class may not have been otherwise exposed to.  

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Insofar as complex adaptive systems can be regarded as being essentially open-ended problem-solvers, their lifeblood consists mostly of novelty. The ability of a complex adaptive system to survive and evolve in a constantly changing environment is determiimd by its ability to continually find — either by chance, or experience, or more typically both insightful new strategies to increase its overall fitness (which is, of course, a constantly changing function in time). 

Encourage flexibility in thinking about alternative solutions to problems. Perhaps it might be possible to develop a set of open-ended problems, much like the case-study approach used so effectively by business schools. 

To emphasize the difference in scale, the different classes of problems are here classified as confined problems and open-ended problems. Confined problems are those where the probability and magnitude of the risks can be quantitatively studied and are found to be limited in scope. Reactor safety and nuclear waste disposal are in this category. 

In contrast, for the open-ended problems it is difficult to evaluate the magnitude of the potential consequences, but in plausible scenarios they may involve great harm on a global scale. These problems include ... 

OPEN-ENDED PROBLEMS Nuclear weapons proliferation... 

The first of the open-ended problems to be considered is nuclear weapons proliferation, in the context of its relation to commercial nuclear power. There is a connection, because a country with an active nuclear power program has a head start, in terms of equipment and technically trained people, should it decide to embark upon a weapons program. This has been a live issue in the case of han.5... 

Comparison ofthe confined and open-ended problems... 

It must again be emphasized that the numbers in the quantitative discussions of the preceding paragraphs provide nothing more than a cmdc hint as to the scale of the problems. But they are consistent with what is probably obvious without numbers the risks from the open-ended problems are far greater than those from the confined problems. For the former, the potential worldwide toll is probably on the scale of millions of lives per century while for the latter it probably is on the scale of a thousand lives per century. 

Solution This is an open-ended problem, which has many possible solutions. We need to find the diameter of the barrel, the channel depth, and the screw speed needed to generate the head pressure. We shall assume a square pitched screw, and use British units (in, s, Btu, lbf). 

The numerical comparison is an open-ended problem, the scope of which must be decided by the instructor. 

This is a challenging and open-ended problem for which we offer no solution. Problem 8.21 may offer some insight. 

Open-ended problems that encourage students to practice creative probiem-solving shills... 

This time there are so many possibilities that we don t want to push any one solution. We hi mind the asymmetric reduction of an acetylenic ketone by CBS or some other asymmetric red-.-m agent and then using the alkyne to make the tram alkene. You also have to consider at what stac -introduce the ester group. This open-ended problem cannot have a more defined solution. 

Something to ponder is whether the cafeteria should have been included in the above answers. A good reference (if available) for this open-ended problem is Guides to Pollution Prevention—Research and Educational Institutions, EPA/625/7-90/010, Office of Pollution Prevention, Washington, DC, 1990. 

Classify the reaction below into one of the four archetypes, and list the possible paths. Using the path restrictions, pick the only path or common path combination that fits for this reaction. Notice how this analysis process turns what appears to be an open-ended problem into a multiple-choice problem. Write out all the steps of the mechanism. 

P7-2Sf (Open-ended problem) You may have to look up/guess/vary some of the coo-s(ants. if methanol is ingested, it can be metabolized to formaldehyde, which can cause blindness if the formaldehyde reaches a conceniralion of 0,16 tt/dm of fluid in the body. A concentration of 0.75 g/dm will be lethal. After ail the methanol ha,s been removed from the stomach, the primary [neaimeni is to inject ethanol inirasenously to tie up (competitive inhibition) the enzyme alcohol dehydrogenase (ADH so that methanol is not converted lo formaldehyde and is eliminated from the body through the kidney and bladder (iy). We will assume as a lirsi approximation that the body is a well-mixed C.5TR of 40 dm [total body fluid i. In Section 7.5, we applied a more rigorous model-... 

The complete data set for this reaction is given on the CD-ROM, P7-25 and the open-ended problem H. 10. After tunning the base case, vary the parameters and describe what you find. 

The purpose of this open-ended problem is for the students to apply their knowledge of reaction kinetics to the problem of modeling the metabolism of alcohol in humans. In addition, the students will present their findings in a poster session. The poster presentations will be designed to bring a greater awareness to the university community of the dangers associated with alcohol... 

The emergency room treatment for methanol poisoning is to inject ethanol intravenously to tie up the alcohol dehydrogenase enzyme so that methanol will not be converted to formic acid and formate, which causes blindness. The goal of this open-ended problem is to build on the physiological-based model for ethanol metabolism to predict the ethanol injection rate for methanol poisoning. One can find a start on this problem by reading problem P7-25c. 

Probiem Solving. Here students can learn different strategies for problem solving in both dosed- and open-ended problem.s. See the ten different types of home problems and suggestions for approaching them. Extensive information on critical and creative thinking can also be found in this section. 

Open-ended) Problem 5-3 addresses in a qualitative fashion the predicted effects of tensile stress on Tg. This problem calls for a quantification of these predictions using a polymer of your choice. The following steps are suggested ... 

The authors experience has shown that by far the most effective way to master the material in the text is to work as many problems as possible, hence the increased emphasis on this aspect in the 3rd Edition. The problems range from relatively straightforward use of an equation included in the book, to far more challenging problems requiring detailed analysis and/or numerical methods. Some of these would even be suitable for term projects. Problems requiring the use of the computer are clearly marked, as are open-ended problems that have no one correct answer. This type of problem, which is required in many undergraduate curricula, provides the student with an opportunity to search, assume, approximate and innovate. As in past editions, answers to many of the problems are provided in an appendix. These answers form an important part of the book, and contain in some cases more details concerning the subject phenomena. 

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