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This work in progress research paper considers the question, what kind of problems do engineering students commonly solve during their education? Engineering problems have been generally classified as ill-structured/open-ended or well-structured/closed-ended. Various authors have identified the characteristics of ill-structured problems or presented typologies of problems. Simple definitions state that well-structured problems are simple, concrete, and have a single solution, while ill-structured problems are complex, abstract, and have multiple possible solutions (Jonassen, 1997, 2000). More detailed classifications have been provided by Shin, Jonassen, and McGee (2003), Voss (2006), and Johnstone (2001). It is commonly understood that classroom problems are well-structured while workplace problems are ill-structured, but we cannot find any empirical data to confirm or deny this proposition. Engineers commonly encounter ill-structured problems such as design problems in the field therefore problem-solving skills are invaluable and should be taught in engineering courses. This research specifically looks at the types of problems present in the two most commonly used statics textbooks (Hibbeler, 2016; Beer, et al., 2019). All end-of-chapter problems in these textbooks were classified using Jonassen’s (2000) well-known typology of problem types. Out of 3,387 problems between both books, 99% fell into the algorithmic category and the remaining fell into the logic category. These preliminary results provide an understanding of the types of problems engineering students most commonly encounter in their classes. Prior research has documented that textbook example problems exert a strong influence on students' problem-solving strategies (Lee et al., 2013). If instructors only assign textbook problems, students in statics courses do not see any ill-structured problems at that stage in their education. We argue that even in foundational courses such as statics, students should be exposed to ill-structured problems. By providing opportunities for students to solve more ill-structured problems, students can become more familiar with them and become better prepared for the workforce. Moving forward, textbooks from several other courses will be analyzed to determine the difference between a fundamental engineering course such as statics and upper-level courses. This research will allow us to determine how the problem types differ between entry level and advanced classes and reveal if engineering textbooks primarily contain well-structured problems. Keywords: problem solving, textbooks, ill-structured problems
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Enriching Students’ Combinatorial Reasoning through the Use of Loops and Conditional Statements in Python
When solving counting problems, students often struggle with determining what they are trying to count (and thus what problem type they are trying to solve and, ultimately, what formula appropriately applies). There is a need to explore potential interventions to deepen students’ understanding of key distinctions between problem types and to differentiate meaningfully between such problems. In this paper, we investigate undergraduate students’ understanding of sets of outcomes in the context of elementary Python computer programming. We show that four straightforward program conditional statements seemed to reinforce important conceptual understandings of four canonical combinatorial problem types. We also suggest that the findings in this paper represent one example of a way in which a computational setting may facilitate mathematical learning.
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- Award ID(s):
- 1650943
- PAR ID:
- 10148794
- Date Published:
- Journal Name:
- International Journal of Research in Undergraduate Mathematics Education
- ISSN:
- 2198-9745
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s40753-019-00108-2
