Conference Session

Mathematics Division (MATH) Technical Session 1

Collection

2024 ASEE Annual Conference & Exposition

Authors

Meiqin Li, University of Virginia; Heze Chen, University of Virginia

Tagged Divisions

Mathematics Division (MATH)

, enabling them to save a significant amount oftime by benefiting from the insights presented in this paper.In this paper, the examined methods were divided into two broad categories: (1) pedagogicalmethods focusing on specified linear algebra contents such as “span”, “linearly independence”,“linear transformation”, etc., and (2) general instructional pedagogical methods focusing on thecourse instead of specific topics, such as “flipped classroom”, “active learning”, “technologyintegration” etc. We read more than 70 literatures and only included those methods that areapplicable for teaching engineering students in this paper. For instance, we excluded theliterature that investigated different approaches to master proofs of some linear algebra

Conference Session

Mathematics Division (MATH) Technical Session 1

Collection

2024 ASEE Annual Conference & Exposition

Authors

Diana D Morris, University of Virginia; Hui Ma, University of Virginia; Farzad Shafiei Dizaji, University of Virginia

Tagged Divisions

Mathematics Division (MATH)

grading for students with thelowest diagnostic scores going into Calculus I. The final exam itself was structured to containboth straightforward, single-concept “Level 1” questions and more challenging, multi-stepquestions that blended multiple topics, “Level 2” questions. There was no significant differencein the performance between students with traditional grading vs. mastery grading for either levelof questions.IntroductionThe vast majority of students entering the school of engineering at our university take Calculus IIor III in their first semester. However, the number of Calculus I students rose sharply during thepandemic, ultimately reaching 23% in Fall 2023. Students who do take Calculus I enter with awide range of high school math

Conference Session

Mathematics Division (MATH) Technical Session 1

Collection

2024 ASEE Annual Conference & Exposition

Authors

Meiqin Li, University of Virginia

Tagged Divisions

Mathematics Division (MATH)

properties of the transformation, which isparticularly relevant in computer graphics, robotics, and control theory. To learn the concept ofchange of basis, change of basis matrix (CBM) is the foundation since it defines the specificchange from one coordinate system to another coordinate system.There are literatures exploring different approaches, practices, and applications for linear algebraconcepts such as “span” [1], [2], [3], [4], [5] , “linear independence” [1], [2], [4], [6], [7], [8],[9], and “eigenvalues/eigenvectors” [10], [11], [12], [13], [14], [15]. There are also researches onpedagogical innovations of teaching linear algebra with or without programming technologyincorporated into the course to reinforce students’ understanding [16

Conference Session

Mathematics Division (MATH) Technical Session 1

Collection

2024 ASEE Annual Conference & Exposition

Authors

Meiqin Li, University of Virginia; Jessica Taggart, University of Virginia

Tagged Divisions

Mathematics Division (MATH)

science, and statistics. Despite its computationalnature, the subject's topics often delve into abstract and conceptual realms. Recognizing theacknowledged challenges and obstacles associated with learning linear algebra [1], [2], [3],a plethora of teaching practices, strategies, and resources have been explored to address thedifficulties encountered by students in grasping these abstract concepts. In this paper, we explorethe potential, from the student perspective, of one possible strategy: incorporating the use ofMATLAB into an engineering Linear Algebra course.Many efforts have aimed to make the study of linear algebra more accessible, engaging, andconducive to effective learning outcomes. Researchers have also emphasized the

Conference Session

Mathematics Division (MATH) Technical Session 1

Collection

2024 ASEE Annual Conference & Exposition

Authors

Luis E Montero-Moguel, The University of Texas at San Antonio; Joel Alejandro Mejia, The University of Texas at San Antonio; Guadalupe Carmona, The University of Texas at San Antonio

Tagged Topics

Diversity

Tagged Divisions

Mathematics Division (MATH)

engage in these processes as part of mathematicalmodeling, and how this approach can be useful for providing future recommendations forcurricula and learning outcomes alignment in engineering education.IntroductionThe challenges of the 21st century require students to engage in activities that enable them to“learn the importance of such decisions as what to measure, what to keep constant, and how toselect or construct data collection instruments” [1, p. 58]. This activities are especially critical forengineering students because engineers are required to develop measurement processes duringthe mathematical modeling of designs [2]. Despite the significance of developing measurementprocesses in engineering education, ABET student learning outcomes

Conference Session

Mathematics Division (MATH) Technical Session 2

Collection

2024 ASEE Annual Conference & Exposition

Authors

Caleb Wilson Hendrick, University of Maine; Karissa B Tilbury

Tagged Divisions

Mathematics Division (MATH)

including: 1) bio-instrumentation,2) drug kinetics, 3) mechanical systems, and 4) organ models. Undergraduate biomedicalengineering students frequently struggle with the intersection of mathematics in these domains asthe problems require students to freely recall various techniques to solve systems of differentialequations in story-problems. This is in contrast with many differential equations textbooks thatemphasize rote memorization methods or provide subtle hints of the particular method and orprocess to be used to solve pre-written mathematical functions. Within engineering disciplines, itis important for students to actively read story problems or interview stakeholders to identify keyconstraints, and governing physical and biological

Conference Session

Mathematics Division (MATH) Poster Session

Collection

2024 ASEE Annual Conference & Exposition

Authors

Djedjiga Belfadel, Fairfield University

Tagged Divisions

Mathematics Division (MATH)

students' proficiency inboth areas.Analytical data from assignment evaluations and student feedback indicate that integratingMATLAB into the mathematical analysis course effectively develops sophomore students'programming skills. 1. Introduction:The integration of computer programming in engineering education has become increasinglyessential, especially in the sophomore year when students are expected to tackle more complexengineering problems. Recognizing this need, most engineering curricula require a computerprogramming course, often taught using traditional languages like Python, C, or JAVA. Whilethese languages have their merits, their complexity can be a barrier for students who are stilldeveloping their engineering problem-solving skills

Conference Session

Mathematics Division (MATH) Technical Session 3

Collection

2024 ASEE Annual Conference & Exposition

Authors

Alberth Alvarado, Universidad Galileo; Jose Roberto Portillo, Universidad Galileo; Byron Haroldo Linares Roman

Tagged Divisions

Mathematics Division (MATH)

' Excellence in an Engineering Calculus Course1. IntroductionIt is well known that a significant number of freshmen engineering students often face a lack ofmotivation while studying calculus due to different factors that can be discouraging and affecttheir performance not only in this course but also in their overall university experience. A limitedmathematical background coupled with the theoretical and abstract nature of calculus may leadsome students to feel overwhelmed and demotivated [1]. Furthermore, most first-yearengineering students aim to solve real-world problems from their first days of class; however,they find themselves loaded with theoretical courses that seem distant from engineeringapplications at the early stage of their academic

Conference Session

Mathematics Division (MATH) Technical Session 2

Collection

2024 ASEE Annual Conference & Exposition

Authors

Juan David Yepes, Florida Atlantic University; Daniel Raviv, Florida Atlantic University

Tagged Divisions

Mathematics Division (MATH)

textbooks [1–10] have embraced visual ex-planations, with notable contributions from Apostol and Mamikon [10]. Their workstands out for explaining the integration of certain functions without heavy relianceon mathematical formulas, marking a noteworthy departure from conventional in-structional methods. Expanding on the incorporation of visual and intuitive methodologies, the fieldsof ”Control Systems” Physics have seen insightful contributions from works such as[11, 12]. In the digital domain, content creators like 3Blue1Brown [13] leveraging theopen-source Python library Manim for interactive animations, have made significantstrides in teaching foundational STEM concepts. It stands out for its clear visualiza-tions and comprehensible

Conference Session

Mathematics Division (MATH) Technical Session 3

Collection

2024 ASEE Annual Conference & Exposition

Authors

Carl Boyet, Louisiana Tech University; Jonathan Walters, Louisiana Tech University; Christian Smith, Louisiana Tech University

Tagged Divisions

Mathematics Division (MATH)

and discussed.Introduction/MotivationLouisiana Tech University operates on a quarter calendar but awards semester credit hours(SCH). This is accomplished by extending the meeting time for classes. For example, a 3 SCHclass will typically meet for 75 minutes three times a week, or for 110 minutes twice a week for10 weeks. One advantage this affords is students majoring in engineering and other STEMprograms can begin in Precalculus without being behind in their curriculum, leading to benefitsin retention [1]. This and other contributing factors have led to Precalculus serving as a gatewayfor most incoming freshmen into engineering and other STEM programs.In the 2022-2023 academic year, well over 50% of incoming students in the College

Conference Session

Mathematics Division (MATH) Technical Session 3

Collection

2024 ASEE Annual Conference & Exposition

Authors

Zenaida Aguirre Munoz Ph.D., University of California, Merced; Melissa Almeida, University of California, Merced; Comlan de Souza, California State University, Fresno; Keith Collins Thompson, University of California Merced; Khang Tran, California State University, Fresno; Yue Lei, University of California, Merced; Erica M Rutter, University of California, Merced; Lalita G Oka, California State University, Fresno; Maribel Viveros, University of California Merced; Bianca Estella Salazar, University of California, Merced; Changho Kim, University of California, Merced

Tagged Topics

Diversity

Tagged Divisions

Mathematics Division (MATH)

include experimental geotechnics, numerical modeling, liquefaction assessments, and dam safety. She is also interested in issues related to women in engineering and has published numerous articles in ASEE conferences.Maribel Viveros, University of California MercedBianca Estella Salazar, University of California, MercedChangho Kim, University of California, Merced Changho Kim is Assistant Professor of Applied Mathematics at the University of California, Merced. He is participating in the ”Why, What and How” Calculus project as co-PI. ©American Society for Engineering Education, 2024Interest & Engagement Tactics for Success 1

Conference Session

Mathematics Division (MATH) Technical Session 2

Collection

2024 ASEE Annual Conference & Exposition

Authors

Olivia Ryan, Virginia Polytechnic Institute and State University; Susan Sajadi, Virginia Polytechnic Institute and State University

Tagged Topics

Diversity

Tagged Divisions

Mathematics Division (MATH)

an online format, and many‬ ‭students struggled in this environment. Mathematics was one of the subjects most affected by‬ ‭online learning. At a large R1 university in the mid-Atlantic region, more engineering students‬ ‭than ever before entered their first year, placing in Pre-Calculus instead of Calculus 1, and were‬ ‭classified as pre-math-ready. Being ‘math ready’ and placing into Calculus 1 is critical for‬ ‭engineering students due to the engineering curriculum's reliance on mathematics and the‬ ‭barriers related to the subject. This study shares the experiences of 15 first-year engineering‬ ‭students who were behind in math during the 2022-2023 academic year. Most participants were‬ ‭in their

Conference Session

Mathematics Division (MATH) Technical Session 3

Collection

2024 ASEE Annual Conference & Exposition

Authors

Julia Spencer, University of Virginia; Megan Ryals, University of Virginia; Gianluca Guadagni, University of Virginia

Tagged Topics

Diversity

Tagged Divisions

Mathematics Division (MATH)

Students' Performance and Beliefs about MathematicsInquiry-oriented (IO) instruction is one of many inductive teaching approaches that relies heavilyon active student learning. However, there are key features that distinguish IO instruction fromactive learning in other classrooms. Traditionally, if students actively participate in a universitymathematics class, it is after an instructor has presented key concepts and procedures. That is,their engagement is that of practice. In an IO classroom, however, students are expected toreinvent mathematics in their quest to solve real-world problems [1]. Therefore, the applicationsprecede and motivate, rather than follow, the theory.In an IO course, students are presented with novel problems; they are not

Conference Session

Mathematics Division (MATH) Technical Session 2

Collection

2024 ASEE Annual Conference & Exposition

Authors

Hadas Ritz, Cornell University; Stephan Wagner, Cornell University

Tagged Divisions

Mathematics Division (MATH)

“lessons learned” from two versions of this alternativegrading scheme are presented here as “best practices” which we hope will be useful for otherfaculty wishing to implement standards-based grading on a large scale.IntroductionAlternative grading schemes encompass a large variety of course assessment rubrics and a largevariety of implementations of the different styles. Some examples include Mastery BasedGrading, Standards Based Grading, Specifications Grading, and Ungrading, among others [1, 2].Motivations for implementing a course assessment scheme different from a traditionalpoint-based rubric include encouraging a growth mindset in students, reducing testing anxietywhich may occur due to high-stakes exams, and requiring students to solve

Conference Session

Mathematics Division (MATH) Technical Session 3

Collection

2024 ASEE Annual Conference & Exposition

Authors

Meiqin Li, University of Virginia; Stacie Pisano, University of Virginia; Jennifer Felder Marley, University of Virginia; Anne M Fernando, University of Virginia; Lindsay Wheeler, University of Virginia

Tagged Topics

Diversity

Tagged Divisions

Mathematics Division (MATH)

implementation of a dedicated precalculus course.To address these obstacles, the aim of this study is to understand the impact of accessibleprecalculus practice opportunities to all students, with the goal of enabling them to enhance theirprecalculus skills without feeling overwhelmed. This objective was achieved by integratingprecalculus instruction into the curriculum of Calculus II and assessing its outcomes.Literature ReviewThere is acknowledgement that the math course entry point in curricula for engineering studentsmay differ among students based on socio-economic and minority classifications. Those who arefirst generation college students, Underrepresented Minority (URM)1 students, or those with feweracademic opportunities in secondary education

Conference Session

Mathematics Division (MATH) Technical Session 2

Collection

2024 ASEE Annual Conference & Exposition

Authors

Juan David Yepes, Florida Atlantic University; Daniel Raviv, Florida Atlantic University

Tagged Divisions

Mathematics Division (MATH)

get some intuition/visualization for it. For example, when we try to take thelimit of the ratio of the function of f1 (x) = x + 2 and the function of f2 (x) = 2x + 3as x approaches infinity, we simply apply L’Hˆopital’s rule to get: d f1 (x) x+2 dx (x + 2) 1 1 lim = lim = lim d = lim = (1) x→∞ f2 (x) x→∞ 2x + 3 x→∞ (2x + 3) x→∞ 2 2 dx Another example, when x approaches 0: d 1 − ex