skip to main content


Title: Engineering Students’ Perceptions of Mathematical Modeling in a Learning Module Centered on a Hydrologic Design Case Study
Abstract Engineering 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.  more » « less
Award ID(s):
1725989 1726965 1726667
NSF-PAR ID:
10285242
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
International Journal of Research in Undergraduate Mathematics Education
Volume:
7
Issue:
2
ISSN:
2198-9745
Page Range / eLocation ID:
351 to 377
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. null (Ed.)
    Engineering graduates need a deep understanding of key concepts in addition to technical skills to be successful in the workforce. However, traditional methods of instruction (e.g., lecture) do not foster deep conceptual understanding and make it challenging for students to learn the technical skills, (e.g., professional modeling software), that they need to know. This study builds on prior work to assess engineering students’ conceptual and procedural knowledge. The results provide an insight into how the use of authentic online learning modules influence engineering students’ conceptual knowledge and procedural skills. We designed online active learning modules to support and deepen undergraduate students’ understanding of key concepts in hydrology and water resources engineering (e.g., watershed delineation, rainfall-runoff processes, design storms), as well as their technical skills (e.g., obtaining and interpreting relevant information for a watershed, proficiency using HEC-HMS and HEC-RAS modeling tools). These modules integrated instructional content, real data, and modeling resources to support students’ solving of complex, authentic problems. The purpose of our study was to examine changes in students’ self-reported understanding of concepts and skills after completing these modules. The participants in this study were 32 undergraduate students at a southern U.S. university in a civil engineering senior design course who were assigned four of these active learning modules over the course of one semester to be completed outside of class time. Participants completed the Student Assessment of Learning Gains (SALG) survey immediately before starting the first module (time 1) and after completing the last module (time 2). The SALG is a modifiable survey meant to be specific to the learning tasks that are the focus of instruction. We created versions of the SALG for each module, which asked students to self-report their understanding of concepts and ability to implement skills that are the focus of each module. We calculated learning gains by examining differences in students’ self-reported understanding of concepts and skills from time 1 to time 2. Responses were analyzed using eight paired samples t-tests (two for each module used, concepts and skills). The analyses suggested that students reported gains in both conceptual knowledge and procedural skills. The data also indicated that the students’ self-reported gain in skills was greater than their gain in concepts. This study provides support for enhancing student learning in undergraduate hydrology and water resources engineering courses by connecting conceptual knowledge and procedural skills to complex, real-world problems. 
    more » « less
  2. null (Ed.)
    Engineering graduates need a deep understanding of key concepts in addition to technical skills to be successful in the workforce. However, traditional methods of instruction (e.g., lecture) do not foster deep conceptual understanding and make it challenging for students to learn the technical skills, (e.g., professional modeling software), that they need to know. This study builds on prior work to assess engineering students’ conceptual and procedural knowledge. The results provide an insight into how the use of authentic online learning modules influence engineering students’ conceptual knowledge and procedural skills. We designed online active learning modules to support and deepen undergraduate students’ understanding of key concepts in hydrology and water resources engineering (e.g., watershed delineation, rainfall-runoff processes, design storms), as well as their technical skills (e.g., obtaining and interpreting relevant information for a watershed, proficiency using HEC-HMS and HEC-RAS modeling tools). These modules integrated instructional content, real data, and modeling resources to support students’ solving of complex, authentic problems. The purpose of our study was to examine changes in students’ self-reported understanding of concepts and skills after completing these modules. The participants in this study were 32 undergraduate students at a southern U.S. university in a civil engineering senior design course who were assigned four of these active learning modules over the course of one semester to be completed outside of class time. Participants completed the Student Assessment of Learning Gains (SALG) survey immediately before starting the first module (time 1) and after completing the last module (time 2). The SALG is a modifiable survey meant to be specific to the learning tasks that are the focus of instruction. We created versions of the SALG for each module, which asked students to self-report their understanding of concepts and ability to implement skills that are the focus of each module. We calculated learning gains by examining differences in students’ self-reported understanding of concepts and skills from time 1 to time 2. Responses were analyzed using eight paired samples t-tests (two for each module used, concepts and skills). The analyses suggested that students reported gains in both conceptual knowledge and procedural skills. The data also indicated that the students’ self-reported gain in skills was greater than their gain in concepts. This study provides support for enhancing student learning in undergraduate hydrology and water resources engineering courses by connecting conceptual knowledge and procedural skills to complex, real-world problems. 
    more » « less
  3. Robotics has emerged as one of the most popular subjects in STEM (Science, Technology, Engineering, and Mathematics) education for students in elementary, middle, and high schools, providing them with an opportunity to gain knowledge of engineering and technology. In recent years, flying robots (or drones) have also gained popularity as teaching tool to impart the fundamentals of computer programming to high school students. However, despite completing the programming course, students may still lack an understanding of the working principle of drones. This paper proposes an approach to teach students the basic principles of drone aeronautics through laboratory programming. This course was designed by professors from Vaughn College of Aeronautics and Technology for high school students who work on after-school and weekend programs during the school year or summer. In early 2021, the college applied for and was approved to offer a certificate program in UAS (Unmanned Aerial Systems) Designs, Applications, and Operations to college students by the Education Department of New York State. Later that year, the college also received a grant from the Federal Aviation Administration (FAA) to provide tuition-free early higher education for high school students, allowing them to complete the majority of the credits in the UAS certificate program while still enrolled in high school. The program aims to equip students with the hands-on skills necessary for successful careers as versatile engineers and technicians. Most of the courses in the certificate program are introductory or application-oriented, such as Introduction to Drones, Drone Law, Part 107 License, or Fundamentals of Land Surveying and Photogrammetry. However, one of the courses, Introduction to Drone Aeronautics, is more focused on the theory of drone flight and control. Organizing the lectures and laboratory of the course for high school students who are interested in pursuing the certificate can be a challenge. To create the Introduction to Drone Aeronautics course, a variety of school courses and online resources were examined. After careful consideration, the Robolink Co-drone [1] was chosen as the experimental platform for students to study drone flight, and control and stabilize a drone. However, developing a set of comprehensible lectures proved to be a difficult task. Based on the requirements of the certificate program, the lectures were designed to cover the following topics: (a) an overview of fundamentals of drone flight principles, including the forces acting on a drone such as lift, weight, drag, and thrust, as well as the selection of on-board components and trade-offs for proper payload and force balance; (b) an introduction to the proportional-integral-directive (PID) controller and its role in stabilizing a drone and reducing steady-state errors; (c) an explanation of the forces acting on a drone in different coordinates, along with coordinate transformations; and (d) an opportunity for students to examine the dynamic model of a 3D quadcopter with control parameters, but do not require them to derive the 3D drone dynamic equations. In the future, the course can be improved to cater to the diverse learning needs of the students. More interactive and accessible tools can be developed to help different types of students understand drone aeronautics. For instance, some students may prefer to apply mathematical skills to derive results, while others may find it easier to comprehend the stable flight of a drone by visualizing the continuous changes in forces and balances resulting from the control of DC motor speeds. Despite the differences in students’ mathematical abilities, the course has helped high school students appreciate that mathematics is a powerful tool for solving complex problems in the real world, rather than just a subject of abstract numbers. 
    more » « less
  4. This article describes the design, development, and evaluation of an undergraduate learning module that builds students’ skills on how data analysis and numerical modeling can be used to analyze and design water resources engineering projects. The module follows a project-based approach by using a hydrologic restoration project in a coastal basin in south Louisiana, USA. The module has two main phases, a feasibility analysis phase and a hydraulic design phase, and follows an active learning approach where students perform a set of quantitative learning activities that involve extensive data and modeling analyses. The module is designed using open resources, including online datasets, hydraulic simulation models and geographical information system software that are typically used by the engineering industry and research communities. Upon completing the module, students develop skills that involve model formulation, parameter calibration, sensitivity analysis, and the use of data and models to assess and design a hydrologic a proposed hydrologic engineering project. Guided by design-based research framework, the implementation and evaluation of the module focused primarily on assessing students’ perceptions of the module usability and its design attributes, their perceived contribution of the module to their learning, and their overall receptiveness of the module and how it impacts their interest in the subject and future careers. Following an improvement-focused evaluation approach, design attributes that were found most critical to students included the use of user-support resources and self-checking mechanisms. These aspects were identified as key features that facilitate students’ self-learning and independent completion of tasks, while still enriching their learning experiences when using data and modeling-rich applications. Evaluation data showed that the following attributes contributed the most to students’ learning and potential value for future careers: application of modern engineering data analysis; use of real-world hydrologic datasets; and appreciation of uncertainties and challenges imposed by data scarcity. The evaluation results were used to formulate a set of guiding principles on how to design effective and conducive undergraduate learning experiences that adopt technology-enhanced and data and modeling- based strategies, on how to enhance users’ experiences with free and open-source engineering analysis tools, and on how to strike a pedagogical balance between module complexity, student engagement, and flexibility to fit within existing curricula limitations. 
    more » « less
  5. This NSF IUSE project is on the Exploration and Design Tier and the Engaged Student Learning Track. It is aimed at better preparing the country’s professional workforce in the renaissance of U.S. skilled manufacturing by creating new personnel proficient in additive manufacturing (AM). AM is mainstream; it has the potential to bring jobs back to the U.S. and add to the nation’s global competitiveness. AM is the process of joining materials to make objects from 3D data in a layer upon layer fashion. The objectives are to develop, assess, revise, and disseminate an upper division course and laboratory, “Additive Manufacturing,” and to advance undergraduate and K-12 student research and creative inquiry activities as well as faculty expertise at three diverse participating universities: Texas Tech, California State-Northridge, and Kansas State. This research/pedagogical team contains a mechanical engineering professor at each university to develop and teach the course, as well as a sociologist trained in K-12 outreach, course assessment, and human subjects research to accurately determine the effects on K-12 and undergraduate students. The proposed course will cover extrusion-based, liquid-based, and powder-based AM processes. For each technology, fundamentals, applications, and advances will be discussed. Students will learn solutions to AM of polymers, metals, and ceramics. Two lab projects will be built to provide hands-on experiences on a variety of state-of-the-art 3D printers. To stimulate innovation, students will design, fabricate, and measure test parts, and will perform experiments to explore process limits and tackle real world problems. They will also engage K-12 students through video demonstrations and mentorship, thus developing presentation skills. Through the project, different pedagogical techniques and assessment tools will be utilized to assess and improve engineering education at both the undergraduate and K-12 levels through varied techniques: i) undergraduate module lesson plans that are scalable to K-12 levels, ii) short informational video lessons created by undergraduates for K-12 students with accompanying in-person mentorship activities at local high schools and MakerSpaces, iii) pre- and post-test assessments of undergraduates’ and K-12 participating students’ AM knowledge, skills, and perceptions of self-efficacy, and iv) focus groups to learn about student concerns/learning challenges. We will also track students institutionally and into their early careers to learn about their use of AM technology professionally. 
    more » « less