Open Ended Problems in Mechanics of Materials





Problem solving is one learning activity that is extensively employed by engineering educators. “Problem-solving is defined as a process used to obtain a best answer to an unknown or a decision subject to some constraints” (Mourtos 2004). Through problem solving students learn to apply the theoretical equations in both hypothetical and real-world scenarios. Assigning problem sets provides students the opportunity to test their understanding of the theory and concepts. The type of problems assigned to students addresses various levels of thinking and outcomes. Traditionally, problems are designed with given parameters and students are required to determine an unknown quantity. The solution usually involves substitution of known values to an equation to solve for the unknown parameter. Problems of this type are said to be “close-ended.” Close-ended questions usually have a unique answer and the procedure of obtaining the answer is limited or straight-forward. Close-ended problems address lower levels of thinking (based on Bloom’s taxonomy) like “remembering”, “understanding” and “applying” and some higher mode of thinking like “analyzing”.



To address higher levels of thinking like “evaluating” and “creating” and transformative outcomes experienced in the real-world, “open-ended” questions should also be included in the problem sets. Sobek and Jain (2004) emphasized the need for open-ended problems. “Employers look for engineers who are effective at solving open-ended problems. Engineering accreditation demands evidence that students can tackle open-ended problems proficiently.” Open-ended problems address considerably the student outcomes on “an ability to recognize, formulate, and solve civil engineering problems” and “an ability to engage in lifelong learning.” Open-ended questions are usually ill-defined and there may be more than one valid approach to obtain the solution. As a matter of fact, the solution may not be unique because of varying assumptions made regarding some parameters. Mourtos (2004) noted in their study that “traditional exercises (close-ended) found in most engineering texts, although useful, do not adequately prepare engineering students for real-world problems. Students seem to have great difficulty approaching these (open-ended) problems; however, they also seem to enjoy the challenge and perform reasonably well if given proper guidance.”

Problem : If you were to install a

steel Z-purlin, which arrangement

would you choose to maximize the

moment capacity of the section?

In the problem sets in my structural analysis course, open-ended problems are given. The problem shown about a Z-purlin is related to analysis of beams due to unsymmetrical bending which is similar to a problem by Singer. Deciding on the most effective set-up of the Z-section whether upright or inverted would require application of concepts in moment of inertia, equilibrium, bending moment and elastic bending stress analysis. There are various ways of determining the more efficient arrangement of the Z-section. You may compute which arrangment has the larger moment capacity. You can assume a moment and compute the maximum stresses and compare.

References:

Mourtos, N. et al. (2004). “Open-ended problem solving skills in thermal-fluids engineering,” Global Journal of Egg Education, UICEE

Sobek, D and Jain V. (2004). “The Engineering Problem Solving Process: Good for Students?” Proc.2004 American Society for Engineering Education (ASEE) Annual Conference & Exposition

NOTE: An updated version of this article - "Challenging Students' Thinking Through Open-ended Problems" was published as e-notes in The Philippine Engineering Education (Vol. 1, No. 1, Sept 2013) - the official news magazine of the Philippines Association for Technological Education (PATE).