A Mathematical Modeling Module with System Engineering Approach for Teaching Undergraduate Students to Conquer Complexity

Liu, Hong; Raghavan, Jayathi

doi:10.1007/978-3-642-01973-9_11

Cited by 5 publications

(6 citation statements)

References 4 publications

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“…and [10]). Liu et al [9] find that a large majority portion of US students were weak in logical reasoning, critical thinking, and analytical thinking.…”

mentioning

confidence: 90%

“…The increasing complexity and rapid change of technology demand our students be more prepared and capable of learning new skills fast and solving complex problems (see, for example, P21—the partnership for 21st century learning at http://www.p21.org/). Unfortunately, many students lack essential algorithmic thinking and problem‐solving skills ( and ). Liu et al find that a large majority portion of US students were weak in logical reasoning, critical thinking, and analytical thinking.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, advances in computer technologies offer possible solutions. Liu and Raghavan introduced a pragmatic strategy to use technologies to integrate content, practice, and problem‐solving. When teaching the Differential Equation course, they integrated small mathematical modeling modules that used a system engineering process and the dynamic system modeling tool Stella to help students represent and solve challenging problems.…”

Section: Introductionmentioning

confidence: 99%

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Computer technologies for model‐based collaborative learning: A research‐based approach with initial findings

Liu

Spector²,

Iklé

2018

Comp Applic In Engineering

Self Cite

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Computer‐based technologies are changing at an accelerating pace and becoming increasingly complex. Smart and context‐aware devices and Internet access enable children and adult learners to gain factual and procedure knowledge about many things anywhere at any time. These computer‐based technologies, if well‐utilized in support of learning, can promote personalized and collaborative education, which research suggests are valuable pedagogies. However, new technologies create a burden on designers and educators to use them effectively in support of learning and instruction. Emphasis on 21st century skills suggests that education should emphasize the development of critical thinking and complex problem‐solving skills. Meanwhile, many educators encounter students who lack motivation and are ill‐prepared in reading and mathematics. In addition, engineering educators face another challenge—namely, the need to frequently update curricula so that students can attain marketable skills and adapt to rapidly changing technologies in the workplace. As it happens, proper use of educational technologies can provide solutions to these challenges. This paper reports one such approach to integrate new technologies in two hybrid synchronous courses using technology‐enabled scaffolds in support of deep learning and enhanced problem‐solving competence in engineering education at small colleges in the United States. The emphasis here is on the developmental approach rather than research analysis.

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“…and [10]). Liu et al [9] find that a large majority portion of US students were weak in logical reasoning, critical thinking, and analytical thinking.…”

mentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Computer technologies for model‐based collaborative learning: A research‐based approach with initial findings

Liu

Spector²,

Iklé

2018

Comp Applic In Engineering

Self Cite

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“…The system engineering modeling methodology in module 1 ( [7]) emphasizes (1) building of conceptual models before the mathematical models to increase traceability of model assumptions and first principles, (2) separating concerns and refining models iteratively to divide and conquer complexity, and (3) verification and validation (V&V) based on empirical data and mathematical analysis. The other four modules were divided into three units and each unit starts with an interesting application and develops a core concept to model.…”

Section: Innovative Learning Environmentmentioning

confidence: 99%

Innovative Model, Tools, and Learning Environments to Promote Active Learning for Undergraduates in Computational Science and Engineering

Hong¹,

Ludu²,

Klein³

et al. 2017

JOCSE

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This paper presents an innovative hybrid learning model as well as the tools, resources, and learning environment to promote active learning for both face-to-face students and online students. Most small universities in the United States lack adequate resources and cost justifiable enrollments to offer Computational Science and Engineering (CSE) courses. The goal of the project was to find an effective and affordable model for small universities to prepare underserved students with marketable analytical skills in CSE. As the primary outcome, the project created a cluster of collaborating institutions that combined students into common classes and used cyberlearning learning tools to deliver and manage instruction. The instrumental tools for educational technologies included Smart Podium, digital projector, teleconference systems such as AdobeConnect, auto tracking camera and high quality audio in both local and remote classrooms. As an innovative active learning environment, an R&D process was used to provide a coherent framework for designing instruction and assessing learning. Course design centered on model-based learning which proposes that students learn complex content by elaborating on their mental model, developing a conceptual model, refining a mathematical model, and conducting experiments to validate and revise their conceptual and mathematical models. A wave lab and underwater robotics lab were used to facilitate the experimental components of hands-on research projects. Course delivery included interactive live online help sessions, immediate feedback to students, peer support, and teamwork which were crucial for student success. Another key feature of instruction of the project was using emerging technologies such as HIMATT (Highly integrated model assessment technology and tools) [11] to evaluate how students think through and model complex, illdefined and ill-structured realistic problems.

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“…We have authored several computational modules which have been presented, published and were used in our undergraduate honors classes. We have also been involved in developing a framework to create computational mathematics modules that help improve students' abstraction capabilities [8][9][10][11] . These workshops and activities served as a springboard for our department to draft and submit the proposal for the degree program in Computational Mathematics.…”

Section: Introductionmentioning

confidence: 99%

An Innovative Undergraduate Computational Mathematics Curriculum For Engineering Students Seeking Dual Major

Raghavan

Hong

2010 Annual Conference &Amp; Exposition Proceedings

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In this paper, we discuss the design of a unique undergraduate curriculum in Computational Mathematics for students in the engineering fields who wish to pursue a dual major. At the institution that the authors teach, an undergraduate program in Computational Mathematics has been recently approved. The trend seems to be that most of the students wishing to pursue the degree program are engineering students interested in pursuing a dual major. The challenges faced by the department are 1) to offer these dual majors an integrated curriculum that would take advantage of their engineering background and 2) to offer a curriculum which will enable them to complete the degree within one additional year without compromising the integrity of the program. In this paper, the authors discuss in detail their Computational Mathematics curriculum and the modification of the curriculum for the dual majors.

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A Mathematical Modeling Module with System Engineering Approach for Teaching Undergraduate Students to Conquer Complexity

Cited by 5 publications

References 4 publications

Computer technologies for model‐based collaborative learning: A research‐based approach with initial findings

Computer technologies for model‐based collaborative learning: A research‐based approach with initial findings

Innovative Model, Tools, and Learning Environments to Promote Active Learning for Undergraduates in Computational Science and Engineering

An Innovative Undergraduate Computational Mathematics Curriculum For Engineering Students Seeking Dual Major

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