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)

modeling of complex physiological systems, bridging mathematics and human biology. He is passionate about finding ways to bring mathematical modeling into more fields of research and educational settings.Prof. Karissa B Tilbury ©American Society for Engineering Education, 2024 A Comprehensive Approach to Modeling Dynamic Biological Systems: Enhancing Critical Thinking and Mathematical Problem-Solving in Biomedical Engineering Education Caleb Hendrick, Karissa Tilbury caleb.hendrick@maine.edu, karissa.tilbury@maine.edu Chemical/Biomedical Engineering University of

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)

Paper ID #41135Exploring Effective Pedagogical Approaches for Teaching Linear Algebra toEngineering Students: A Literature ReviewDr. Meiqin Li, University of Virginia Dr. Li obtained her Ph.D. in Applied Mathematics from Texas A&M University-College Station in 2017. Dr. Li holds a strong interest in STEM education. For example, she is interest in integrating technologies into classrooms to bolster student success, creating an inclusive and diverse learning environment, and fostering student confidence by redeveloping course curricula and assessment methods, etc. Beyond this, her research intertwines numerical

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)

efficient and scaleable manner.References[1] D. Clark and R. Talbert, Grading for growth: A guide to alternative grading practices that promote authentic learning and student engagement in higher education. Taylor & Francis, 2023.[2] L. B. Nilson and C. J. Stanny, Specifications grading: Restoring rigor, motivating students, and saving faculty time. Routledge, 2015.[3] J. Elsinger and D. Lewis, “Applying a standards-based grading framework across lower level mathematics courses,” PRIMUS, vol. 30, no. 8-10, pp. 885–907, 2020.[4] H. Ritz, “WIP: Implementing an alternative grading scheme in a large enrollment differential equations course: Lessons learned,” in 2023 ASEE Annual Conference & Exposition, 2023.[5] S. Wagner and H. Ritz

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)

engineering.Additionally, mathematics courses help students develop skills such as analytical reasoning,accuracy, interpretation, patience, perseverance, and critical thinking, among many other skills.In the following subsections, we explore the design, implementation, and validation process of abadge architecture for MATH 202, highlighting how adherence to the FSBPI recommendationshelped us achieve the intended objectives. b. Badge Instructional DesignOne of the main recommendations of this category of the FSBPI is to establish the purpose ofintroducing badges into a course. As mentioned above, the main objective of developing a badgearchitecture for MATH 202 is to seek a potential strategy to boost students' motivation and, atthe same time, guide their

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)

Paper ID #42816Rethinking Precalculus: A Thematic ApproachMr. Carl Boyet, Louisiana Tech University Carl Boyet is an Instructor of Mathematics who has worked for Louisiana Tech University for nine years.Dr. Jonathan Walters, Louisiana Tech University Senior Lecturer at Louisiana Tech UniversityChristian Smith, Louisiana Tech University ©American Society for Engineering Education, 2024 Rethinking Precalculus: A Thematic ApproachAbstract: Over the last decade, Precalculus at Louisiana Tech University has seen manyrevisions as needs and demands shift for the many STEM majors it services

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)

American Mathematical Society’s noteworthy contribution can be foundin [18]. This comprehensive exploration of diverse pedagogical approaches under-scores the evolving landscape of STEM education and highlights the crucial role ofvisual, intuitive, and interactive methods in enhancing the learning experience.2 The Concept of Inverse FunctionIn simple words: Applying a function f and then its inverse f −1 results in the originalvalue back again. Using mathematical notation: f (a) = b ⇔ f −1 (b) = aIn [19] the basic idea behind inverse function is visually explained. Here we summa-rize the explanations. Refer to Figure 1. Envision a function represented as a ”gray box” at the top,featuring a green square as input

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)

Survey.In Fall 2021, 192 students [123 males, 69 females] out of 236 students [152 males, 84 females]in five sections of APMA2130, completed the same survey.This instrument has been used previously to assess the impact of IODE instruction [1]. EachVAMS item presents a statement and a binary choice and students express their preference forone of the choices on a scale of 1-7 [11][12]. For example, one statement students were asked toreact to was: For me, doing well in mathematics courses depends on: a) How much effort I put into studying. b) How well the teacher explains things in class.Students were asked to react to this by choosing one of the following: 1. Only a 2. Mostly a 3. More a than b 4. Equally a and b 5

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)

⃗ 𝑛 } is a basis of the vector space V, the B-coordinates of𝑥 (the coordinates of 𝑥 with respect to the basis B) are the coefficients in the linear combination 𝑐1 𝑐2of 𝑥 : 𝑥 = 𝑐1 𝑢 ⃗ 𝑛 . Let [𝑥 ]𝐵 = [ ⋮ ], then [𝑥 ]𝐵 is the coordinate vector of 𝑥 (with ⃗ 1 +. . . + 𝑐𝑛 𝑢 𝑐𝑛respect to B), or the B-coordinate vector of 𝑥 .Each basis of a given vector space can viewed as a coordinate system. Take 𝑅3 for example, themost familiar coordinate system in 𝑅3 is 𝑥𝑦𝑧-coordinate system which corresponds to thestandard basis S = {𝑒1, 𝑒2 , 𝑒3 } of 𝑅3 . If a

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)

final exam mandatory in Fall 2023. Students receive a grade before the final based on threefactors: the number of learning targets (including core ones) they have mastered, the completion ofworksheets, and their overall average on WebAssign. The final exam now contributes to their coursegrade, potentially modifying it based on performance. For instance, scoring 88% on the final couldraise a student's grade by one level, from a B to a B+. Conversely, scoring below 65% could lowertheir base grade by one level, from a B to a B-. See Table 1 for details.Table 1: Course Grades, AFTER the Final Scores on the final Scores on the final Scores below this needed to move up needed to

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)

. (−∞, −5) ∪ (2, ∞) A. (−∞, 9) ∪ (14, ∞) B. (−∞, −2) ∪ (−1, ∞) B. (−∞, −5) ∪ (5, ∞) B. (−∞, 2) ∪ (7, ∞) C. (−1,3) C. (−∞, ∞) C. (2, ∞) D. (−2, −1) D. (−5, 2) D. (2,7) Assessment 2 Assessment 3 Assessment 4 Q10: Solve for 𝑥: Q10: Solve for 𝑥: Q10: Solve for 𝑥: 𝑥 2 + 9𝑥 > −14 𝑥 2 + 2𝑥 < 8 𝑥 2 + 7𝑥 + 12 > 0 A. (−7, −2) A. (−∞, −4) ∪ (2

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)

areas: (a) STEM education and identity development; (b) model-based assessment and instruction; (c) the impact of opportunity to learn on learning and achievement; and (d) discipline-based education research for culturally and linguistically diverse students.Melissa Almeida, University of California, Merced Melissa Almeida, a Ph.D. student in Cognitive and Information Sciences at the University of California, Merced, is deeply engaged in the intersection of learning, cognitive science, and STEM education. Her research evaluates the impact of classroom interventions, focusing on embodied cognition and the educational use of augmented and virtual reality technologies. Moving beyond initial feasibility, her work aims to

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)

of its origins, missing the crucial ”why” behind itsapplication. The primary objective of this paper is to deepen students’ understanding ofL’Hopital’s Rule by incorporating visualization and intuition techniques with math-ematical approaches. We explore the background of L’Hopital’s Rule and presentthree different ways to explain the essence of the rule by: a) “zooming-in” on theintersection of two functions, b) employing the Taylor Series, and c) utilizing In-finitesimal Calculus. By using these approaches, it becomes easier to grasp theessence of L’Hopital’s Rule, which is about comparing how fast two functions changeas they approach a particular point. Moreover, to provide a comprehensive perspec-tive we share some practical textbook

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)

Paper ID #41094Understanding Students in Times of Transition: The Impact of the COVID-19Pandemic on Engineering Students’ Math Readiness and Transition into EngineeringOlivia Ryan, Virginia Polytechnic Institute and State University Olivia Ryan is a Ph.D. student in Engineering Education at Virginia Tech. She holds a B.S. in engineering with a specialization in electrical engineering from Roger Williams University. Her research interests include developing professional skills for engineering students and understanding mathematics barriers that exist within engineering.Susan Sajadi, Virginia Polytechnic Institute and State

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)

Paper ID #41119Student Perceptions on the Effectiveness of Incorporating Numerical Computationsinto an Engineering Linear Algebra CourseDr. Meiqin Li, University of Virginia Dr. Li obtained her Ph.D. in Applied Mathematics from Texas A&M University-College Station in 2017. Dr. Li holds a strong interest in STEM education. For example, she is interest in integrating technologies into classrooms to bolster student success, creating an inclusive and diverse learning environment, and fostering student confidence by redeveloping course curricula and assessment methods, etc. Beyond this, her research intertwines numerical

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)

Paper ID #42419Leveraging Mathematical Modeling to Expand Measurement-Process Opportunitiesfor Engineering StudentsLuis E Montero-Moguel, The University of Texas at San Antonio Luis Montero-Moguel is a Ph.D. Candidate in Interdisciplinary Learning and Teaching specializing in STEM education at The University of Texas at San Antonio (UTSA). Luis holds an MSc in Mathematics Education from the University of Guadalajara and a BSc in Mechanical Engineering. Luis is an NSF-CADRE fellow. As part of his doctoral program, Luis has earned a Graduate Certificate in iSTEM Education and a Graduate Certificate in Engineering Education. With

Conference Session

Mathematics Division (MATH) Poster Session

Collection

2024 ASEE Annual Conference & Exposition

Authors

Djedjiga Belfadel, Fairfield University

Tagged Divisions

Mathematics Division (MATH)

Mathematical Analysis course for sophomore engineering students at Fairfield Universitymajoring in electrical, mechanical, and biomedical engineering. Previously, MATLAB wastaught in later years of the engineering program. Now, it is introduced in the first-year course,“Fundamentals of Engineering”, and then fully integrated into the sophomore-level“Mathematical Analysis” course. This redesign prepares students for their future courses.MATLAB provides a diverse array of application-specific functions, graphical user interfaces,debugging tools, and facilitates advanced visualization and matrix manipulation. Additionally, itincludes App Designer and Simulink providing essential programming tools for developingcoding skills and solving complex