scholarly journals Engineering Students’ Perceptions of Mathematical Modeling in a Learning Module Centered on a Hydrologic Design Case Study

2021 ◽  
Author(s):  
Madeline F. Merck ◽  
Melissa A. Gallagher ◽  
Emad Habib ◽  
David Tarboton
Keyword(s):  
Mathematical Modeling ◽  
Real World ◽  
Engineering Students ◽  
Online Module ◽  
Modeling Process ◽  
Online Databases ◽  
Modeling Software ◽  
Authentic Problems ◽  
Design Case Study ◽  
Hydrologic Design

AbstractEngineering students need to spend time engaging in mathematical modeling tasks to reinforce their learning of mathematics through its application to authentic problems and real world design situations. Technological tools and resources can support this kind of learning engagement. We produced an online module that develops students’ mathematical modeling skills while developing knowledge of the fundamentals of rainfall-runoff processes and engineering design. This study examined how 251 students at two United States universities perceived mathematical modeling as implemented through the online module over a 5-year period. We found, subject to the limitation that these are perceptions from not all students, that: (a) the module allowed students to be a part of the modeling process; (b) using technology, such as modeling software and online databases, in the module helped students to understand what they were doing in mathematical modeling; (c) using the technology in the module helped students to develop their skill set; and (d) difficulties with the technology and/or the modeling decisions they had to make in the module activities were in some cases barriers that interfered with students’ ability to learn. We advocate for instructors to create modules that: (a) are situated within a real-world context, requiring students to model mathematically to solve an authentic problem; (b) take advantage of digital tools used by engineers to support students’ development of the mathematical and engineering skills needed in the workforce; and (c) use student feedback to guide module revisions.

Authenticity of Mathematical Modeling

2014 ◽  
Vol 107 (9) ◽  
pp. 672-678 ◽  
Author(s):  
Dung Tran ◽  
Barbara J. Dougherty
Keyword(s):  
Mathematical Modeling ◽  
Modeling Process ◽  
Authentic Problems

The choice and context of authentic problems—such as designing a staircase or a soda can—illustrate the modeling process in several stages.

Call for Manuscripts for the 2015 Focus Issue: Mathematical Modeling

2013 ◽  
Vol 18 (9) ◽  
pp. 571
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Models ◽  
Real World ◽  
The Real

This call for manuscripts is requesting articles that address how to use mathematical models to analyze, predict, and resolve issues arising in the real world.

Accessibility vs. Feasibility: Optimizing Function Allocation for Accommodation of Heterogeneous Populations

2021 ◽  
pp. 1-36
Author(s):  
Benjamin Knisely ◽  
Monifa Vaughn-Cooke
Keyword(s):  
Optimization Model ◽  
Engineering Students ◽  
Product Variety ◽  
Human Beings ◽  
Heterogeneous Populations ◽  
Trade Offs ◽  
Potential System ◽  
Wide Range ◽  
Need To Evaluate ◽  
Design Case Study

Abstract Human beings are physically and cognitively variable, leading to a wide array of potential system use cases. To design safe and effective systems for highly heterogeneous populations, engineers must cater to this variability to minimize the chance of error and system failure. This can be a challenge because of the increasing costs associated with providing additional product variety. Most guidance for navigating these trade-offs is intended for late-stage design, when significant resources have been expended, thus risking expensive redesign or exclusion of users when new human concerns become apparent. Despite the critical need to evaluate accommodation-cost trade-offs in early stages of design, there is currently a lack of structured guidance. In this work, an approach to function modeling is proposed that allows the simultaneous consideration of human and machine functionality. This modeling approach facilitates the allocation of system functions to humans and machines to be used as an accessible baseline for concept development. Further, a multi-objective optimization model was developed to allocate functions with metrics for accommodation and cost. The model was demonstrated on a design case study. 16 senior mechanical engineering students were recruited and tasked with performing the allocation task manually. The results were compared to the output of the optimization model. Results indicated that participants were unable to produce concepts with the same accommodation-cost efficiency as the optimization model. Further, the optimization model successfully produced a wide range of potential product concepts, demonstrating its utility as a decision-aid.

Synergizing Product Design Information and Unit Manufacturing Process Analysis to Support Sustainable Engineering Education

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Kamyar Raoufi ◽  
Sriram Manoharan ◽  
Karl R. Haapala
Keyword(s):  
Instructional Design ◽  
Product Design ◽  
Engineering Students ◽  
Raw Materials ◽  
Process Analysis ◽  
Sustainable Manufacturing ◽  
Educational Training ◽  
Design Changes ◽  
Addie Model ◽  
Design Case Study

Promoting excellence in sustainable manufacturing has emerged as a strategic mission in academia and industry. In particular, universities must prepare the next generation of engineers to contribute to the task of sustaining and improving manufacturing by providing appropriate types of sustainability education and training. However, engineering curricula are challenged in delivering educational training for assessing technical solutions from the three domains that define sustainability: economic, environmental, and social. In the research presented here, an educational framework is developed with an aim to improve student understanding of sustainable product design (PD) and manufacturing. The framework is founded on the analyze, design, develop, implement, and evaluate (ADDIE) model for instructional design. The developed framework is demonstrated using an example of a sustainable PD activity. This instructional design case study illustrates how engineering students would be able to investigate the impacts of raw materials, unit manufacturing processes, manufacturing locations, and design changes on product sustainability performance by integrating PD information and manufacturing analysis methods during the PD phase.

Teachers and Mathematical Modeling

2018 ◽  
pp. 216-236
Author(s):  
Samantha Analuz Quiroz Rivera ◽  
Ruth Rodríguez Gallegos
Keyword(s):  
Mathematical Modeling ◽  
Real World ◽  
Collaborative Work ◽  
Lesson Plans ◽  
Teaching Mathematics ◽  
Learning And Teaching

Mathematics cannot be reduced to the use of algorithms. The main objective of teaching mathematics in school is their application in real world situations. Mathematical modeling was born as an answer of this concerned and implies the relation between mathematics and applications. Because of that, teachers need to be correctly training in the use of mathematical modeling in their daily lesson plans. The aim of this study is to propose a methodology for help teachers purchase mathematical modeling as a strategy to teach mathematics. Our methodology is based on the analysis of teachers' conceptions about learning and teaching mathematics and after that promote their evolution. The main characteristic is the collaborative work between teachers and the researcher in cycles of discussion and classes' implementation. The evidence showed that teachers can actually change their conceptions about what is needed for teaching mathematics and design lesson plans using mathematical modeling.

Teachers and Mathematical Modeling

2017 ◽  
pp. 45-64
Author(s):  
Samantha Analuz Quiroz Rivera ◽  
Ruth Rodríguez Gallegos
Keyword(s):  
Mathematical Modeling ◽  
Real World ◽  
Collaborative Work ◽  
Lesson Plans ◽  
Teaching Mathematics ◽  
Learning And Teaching

Mathematics cannot be reduced to the use of algorithms. The main objective of teaching mathematics in school is their application in real world situations. Mathematical modeling was born as an answer of this concerned and implies the relation between mathematics and applications. Because of that, teachers need to be correctly training in the use of mathematical modeling in their daily lesson plans. The aim of this study is to propose a methodology for help teachers purchase mathematical modeling as a strategy to teach mathematics. Our methodology is based on the analysis of teachers' conceptions about learning and teaching mathematics and after that promote their evolution. The main characteristic is the collaborative work between teachers and the researcher in cycles of discussion and classes' implementation. The evidence showed that teachers can actually change their conceptions about what is needed for teaching mathematics and design lesson plans using mathematical modeling.

On the Identification of Modeler Communities

2014 ◽  
Vol 5 (2) ◽  
pp. 22-40 ◽  
Author(s):  
Dirk van der Linden ◽  
Stijn J.B.A. Hoppenbrouwers ◽  
Henderik A. Proper
Keyword(s):  
Conceptual Understanding ◽  
Real World ◽  
Empirical Support ◽  
Enterprise Modeling ◽  
Modeling Language ◽  
Science Students ◽  
Modeling Process ◽  
Psychometric Data ◽  
Computing Science ◽  
Insight Into

The authors discuss the use and challenges of identifying communities with shared semantics in Enterprise Modeling (EM). People tend to understand modeling meta-concepts (i.e., a modeling language's constructs or types) in a certain way and can be grouped by this conceptual understanding. Having an insight into the typical communities and their composition (e.g., what kind of people constitute such a semantic community) can make it easier to predict how a conceptual modeler with a certain background will generally understand the meta-concepts s/he uses, which is useful for e.g., validating model semantics and improving the efficiency of the modeling process itself. The authors have observed that in practice decisions to group people based on certain shared properties are often made, but are rarely backed up by empirical data demonstrating their supposed efficacy. The authors demonstrate the use of psychometric data from two studies involving experienced (enterprise) modeling practitioners and computing science students to find such communities. The authors also discuss the challenge that arises in finding common real-world factors shared between their members to identify them by and conclude that there is no empirical support for commonly used (and often implicit) grouping properties such as similar background, focus and modeling language.

Experiences of a US-India Team in Developing a Case Study That Illustrates Technical and Global Issues in Weld Design

2008 ◽  
Author(s):  
Pramod Rajan ◽  
P. K. Raju ◽  
Chetan S. Sankar
Keyword(s):  
Real World ◽  
Engineering Students ◽  
Learning Experience ◽  
Real Life ◽  
Inspection Time ◽  
Cd Rom ◽  
Global Issues ◽  
Auburn University ◽  
Institute Of Technology

Understanding the real-world issues in the global industry is one of the ways of enhancing the learning experience of engineering students. This paper describes such an experience. This was a collaborative weld design project between Auburn University, Auburn, Alabama, Indian Institute of Technology (IIT), Madras, India and Bharat Heavy Electricals Limited (BHEL), Tiruchirappalli, India. The main problems BHEL faced were (1) Inspection time of the welds, (2) Inaccessibility of the welds, and (3) Detection of kissing bond or pasty weld. Three possible solutions to these problems were identified by the practitioners. In order to bring this real-world issue into engineering classrooms, the authors developed a case study. The authors also developed a multimedia CD-ROM which brings the problem live into class rooms using video, audio and pictures. This case study has been tested with mechanical engineering students. The majority of the students found the use of case studies to be beneficial, particularly because of the group work and applicability to real life situations. The details of the case study and its implementation in an engineering class room at Auburn University are discussed in the paper.

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