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A Comprehensive Approach to Modeling Dynamic Biological Systems: Enhancing Critical Thinking and Mathematical Problem-Solving in Biomedical Engineering Education

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)

students to harness their knowledge of physics, biology, physiology,engineering, and mathematics to formulate dynamic models of physiological systems. Our overallaim is to enhance students’ ability to apply and foster a deep appreciation of the power ofmathematics in addressing real-world biomedical engineering challenges.References[1] L. M. Almeida and L. A. Kato, “Different approaches to mathematical modelling: Deduction of models and studens’ actions,” International Electronic Journal of Mathematics Education, vol. 9, no. 1, pp. 3–11, 2014.[2] S. Andr´as and J. Szil´agyi, “Modelling drug administration regimes for asthma: a romanian experience,” Teaching Mathematics and Its Applications: International Journal of the IMA, vol. 29, no. 1

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The Impact of Inquiry-Oriented, Differential-Equations Instruction on Students' Performance and Beliefs about Mathematics

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)

forTeaching and Learning Ordinary Differential Equations: A Systemic Literature Review andBibliometric Analysis,” Mathematics, vol. 9, no. 7, p. 745, Mar. 2021, doi:https://doi.org/10.3390/math9070745.[5] S. Arslan, “Do students really understand what an ordinary differential equationis?,” International Journal of Mathematical Education in Science and Technology, vol. 41, no. 7,pp. 873–888, Oct. 2010, doi: https://doi.org/10.1080/0020739x.2010.486448.[6] C. L. Rasmussen and K. D. King, “Locating starting points in differential equations: arealistic mathematics education approach,” International Journal of Mathematical Education inScience and Technology, vol. 31, no. 2, pp. 161–172, Mar. 2000, doi:https://doi.org/10.1080/002073900287219.[7] C. L

Relevance Score: 0.018338177

Unlocking Success in Calculus for Engineering Majors: Impact of Engagement Tactics for Underrepresented Undergraduate Engineering Students

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)

exercise of control. New York: W.H. Freeman.[3] Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. Annual Review of Psychology, 53(1), 109-132.[4] Hackett, G. (1995). Self-efficacy in career choice and development. In A. Bandura (Ed.), Self- efficacy in changing societies (pp. 232-258). New York: Cambridge.[5] Rottinghaus, P. J., Larson, I. M., Borgen, F. H. (2003). The relation of self-efficacy and interests: A meta-analysis of 60 samples. Journal of Vocational Behavior, 62, 221-236.[6] Hidi, S., & Renninger, K. A. (2006a). The role of interest in learning and development. Annual Review of Psychology, 57(1), 517-540.[7] Hakkarainen, K., & Malmberg, J. (2004). Communities of networked expertise

Relevance Score: 0.017443085

Exploring Effective Pedagogical Approaches for Teaching Linear Algebra to Engineering Students: A Literature Review

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)

students.Brief History Figure 1. The History of Linear AlgebraIn the 1960s (Figure 1), a group of mathematicians, notably associated with the Bourbaki Schoolsuch as J. Dieudonné and S. Lang, advocated for a significant overhaul in mathematicseducation, labeling it "Modern Mathematics." They believed that what students learned shouldmatch how mathematicians were logically constructing math at the time. Consequently, LinearAlgebra became a highly abstract and formalized subject. Aspects like Analytic Geometry andMatrix Calculus were largely overlooked in favor of emphasizing complex mathematicalstructures. The focus shifted away from intuition towards a more rigorous exploration of thesestructures, making Linear Algebra a

Relevance Score: 0.015992973

Exploiting a Grading Option to Measure Mathematics Confidence of Engineering Students

Conference Session: Mathematics Division (MATH) Technical Session 2
Collection: 2023 ASEE Annual Conference & Exposition
Authors: Gianluca Guadagni, University of Virginia; Deepyaman Maiti, University of Virginia; Farzad Shafiei Dizaji
Tagged Topics: Diversity
Tagged Divisions: Mathematics Division (MATH)

choose the grading option before the end of the semester at a specific deadline: 04/28/2020, 11/06/2020, or 04/30/2021. All deadlines, even in Spring 21, were before Final Exams.Description of SurveyOur study participants (second, third-, and fourth-year students who had taken at least one APMA course)completed a ~50-question online survey [1] early in Spring 22 semester about their experiences in APMAcourse(s) from Spring 20 to Spring 21 semesters. Survey questions were related to demographic data,motivation, technological tools/ applications used, office hours, help sessions, quizzes/tests in an onlinesetting, grading options, and questions comparing APMA courses with major-related core courses.Analysis Methods, Results, and

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Leveraging Mathematical Modeling to Expand Measurement-Process Opportunities for Engineering Students

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)

experience as an engineer and a mathematics teacher, he promotes the expansion of equitable and high-quality learning opportunities for both engineering and K–12 students through mathematical modeling. His research focuses on exploring the process of refining mathematical ideas and engineering concepts that engineering students develop while engaging in model development sequences built in real engineering contexts.Dr. Joel Alejandro Mejia, The University of Texas at San Antonio Dr. Joel Alejandro (Alex) Mejia is an associate professor with joint appointment in the Department of Bicultural-Bilingual Studies and the Department of Biomedical and Chemical Engineering at The University of Texas at San Antonio. Dr. Mejiaˆa C™s

Relevance Score: 0.014763636

Developing Active Learning of Linear Algebra in Engineering by Incorporating MATLAB and Autograder

Conference Session: Mathematics Division (MATH) Technical Session 1
Collection: 2023 ASEE Annual Conference & Exposition
Authors: Meiqin Li, University of Virginia
Tagged Divisions: Mathematics Division (MATH)

combinations of three linearly independent vectors, which isthe exercise in Figure 3. By rotate viewing the graph they obtained, they observed that thespan is not a plane any more. All the combinations residue in all possible directions in R3 . 9Then students reflected that: three linearly independent vectors span the whole R3 .4.1.2 Example 2Another important concept in this class is ’subspace’. In order to determine whether a given → −subset S ⊂ Rn is a subspace, three criterion should be checked: (i) 0 ∈ S. (ii

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Elaboration of a contextualized event for teaching eigenvalues and eigenvectors in the control and automation engineering course

Conference Session: Mathematics Division (MATH) Technical Session 1
Collection: 2023 ASEE Annual Conference & Exposition
Authors: Juliana Martins Philot, Instituto Mauá de Tecnologia - Brazil; Barbara Lutaif Bianchini, Pontifícia Universidade Católica de São Paulo - Brasil; Eloiza Gomes, Instituto Mauá de Tecnologia - Brazil; Gabriel Loureiro de Lima, Pontifícia Universidade Católica de São Paulo - Brasil; Octavio Mattasoglio Neto Neto
Tagged Topics: Diversity
Tagged Divisions: Mathematics Division (MATH)

Paper ID #39362Elaboration of a contextualized event for teaching eigenvalues andeigenvectors in the control and automation engineering courseJuliana Martins Philot, Instituto Mau´a de Tecnologia - Brazil I hold a B.A. in Mathematics from Universidade Estadual Paulista J´ulio de Mesquita Filho - UNESP (2007), a M.Sc. in Mathematics from Universidade Estadual Paulista J´ulio de Mesquita Filho - UNESP (2010) and a Ph.D. in Mathematics Education from Pontif´ıcia Universidade Cat´olica de S˜ao Paulo - PUC- SP (2022). I have experience in Mathematics Teaching for Engineering courses since 2009 and currently I am a

Relevance Score: 0.011318568

Understanding Students in Times of Transition: The Impact of the COVID-19 Pandemic on Engineering Students' Math Readiness and Transition into Engineering

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)

curriculum. We argue that the pandemic impacted student math readiness, which‬ ‭subsequently impacted their transition to the university and into engineering, as illustrated in‬ ‭Figure 1.‬‭ igure 1‬F‭Relationship between Pandemic, Math Readiness, and Transition to University/Engineering‬‭ . COVID-19’s Effect on Education‬A‭The COVID-19 pandemic brought unprecedented challenges to the education system, and many‬ ‭students struggled. Due to school and home life disruptions during the pandemic, students‬ ‭reported difficulty completing their schoolwork. Specifically, female and underrepresented‬ ‭minority (URM) students reported having more difficulty completing schoolwork‬‭[9]‬‭. With‬ ‭varying restrictions across states and school

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Board 134: MATLAB Integration in Sophomore Mathematical Analysis Course

Conference Session: Mathematics Division (MATH) Poster Session
Collection: 2024 ASEE Annual Conference & Exposition
Authors: Djedjiga Belfadel, Fairfield University
Tagged Divisions: Mathematics Division (MATH)

learning. Integrating MathWorks auto-gradedprogramming workshops and requiring completion certificates for these sessions ensures activeparticipation and solidifies learning, making this comprehensive approach conducive to fosteringactive learning and supporting individual advancement in larger classroom contexts.References[1] P. T. Goeser, W. Johnson, S. L. Bernadin, and D. A. Gajdosik-Nivens, “Work-in-Progress:The Impact of MatLab Marina - A Virtual Learning Environment on Student Learning in aComputing for Engineers Course”, ASEE Annual Conference and Exposition, 2013.[2] R. Talbert, “Learning MATLAB in the Inverted Classroom”, ASEE Annual Conference andExposition, 2012.[3] K. Larsen, A. Hossain And M. Weiser, “Teaching an Undergraduate

Relevance Score: 0.010671249

Work in Progress: A Structural Change in Calculus Sequences

Conference Session: Mathematics Division (MATH) Technical Session 3
Collection: 2023 ASEE Annual Conference & Exposition
Authors: Mark Mixer, Wentworth Institute of Technology; Deirdre Donovan, Wentworth Institute of Technology
Tagged Topics: Diversity
Tagged Divisions: Mathematics Division (MATH)

, Leaving College: Rethinking the Causes and Cures of Student Attrition. 2nd ed. Chicago, IL, USA: University of Chicago Press, 1993.[12] J. A. Middleton, S. Krause, S. Maass, K. Beeley, J. Collofello and R. Culbertson, "Early course and grade predictors of persistence in undergraduate engineering majors," 2014 IEEE (Institute of Electrical and Electronic Engineers) Frontiers in Education Conference (FIE) Proceedings, Madrid, Spain, 2014, pp. 1-7, doi: 10.1109/FIE.2014.7044367.[13] M. W. Ohland, A.G. Yuhasz, and B.L. Sill, “Identifying and removing a calculus prerequisite as a bottleneck in Clemson's General Engineering Curriculum.” Journal of Engineering Education, vol. 93, no. 3, pp. 253-257. 2004.[14] J. Pearson, L.A. Giacumo

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Design and Implementation of a Badge Architecture to Motivate Students' Excellence in an Engineering Calculus Course

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)

theirvaluable assistance in incorporating the badge architecture into our LMS and their contributionsto the graphic design process. Finally, our thanks go to the reviewers for their constructivecomments.6. References[1] R. Portillo, C. Andersson, A. Alvarado, G. Kroisandt, and D. Logofatu, “Guatemala vs. Germany-A cross-cultural study of students9 motivation in basic mathematics courses,” in 2022 IEEE World Engineering Education Conference (EDUNINE), IEEE, 2022.[2] Jung Yeop Lee, Chong Un Pyon, Jiyoung Woo, “Digital Twin for Math Education: A Study on the Utilization of Games and Gamification for University Mathematics Education,” https://www.mdpi.com/journal/electronics, 2023.[3] K. Davis and S. Singh, “Digital badges in

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Our Learning Experience with MATH 101, a Virtual and Adaptive Remedial Course

Conference Session: Mathematics Division (MATH) Technical Session 2
Collection: 2023 ASEE Annual Conference & Exposition
Authors: Alberth Alvarado, Universidad Galileo; Jose Roberto Portillo, Universidad Galileo
Tagged Topics: Diversity
Tagged Divisions: Mathematics Division (MATH)

score corresponds to the student's firstattempt to solve the worksheet, where no educational resources are available. In other words,these results come exclusively from the student's prior knowledge. In contrast, the maximumscore may match the student's final try, i.e., when the student solves the worksheet successfullyafter studying MATH 101's material. Of course, there are cases where the students only require asingle attempt to solve the worksheet satisfactorily; in these cases, the minimum and maximumscores are equal. Finally, note that the average number of attempts is a relative measure of thetopic's difficulty; the closer to 1, the easier it was for the student to pass to the next module.With the following topic-by-topic analysis, we can

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Measuring the Impact of an Enrichment Program for First-Term Undergraduate Engineering Students in Mathematics and Engineering Curricula

Conference Session: Mathematics Division (MATH) Technical Session 1
Collection: 2023 ASEE Annual Conference & Exposition
Authors: Krystal Corbett Cruse, Louisiana Tech University; Carl Boyet; Levi Savercool; Hylie Jane Holloway
Tagged Topics: Diversity
Tagged Divisions: Mathematics Division (MATH)

Foundation under Grant No.(2221638).Any opinions, findings, and conclusions or recommendations expressed in this material are thoseof the author(s) and do not necessarily reflect the views of the National Science Foundation.References[1] Besterfield-Sacre, M., Atman, C.J. and Shuman, L.J. (1997), Characteristics of FreshmanEngineering Students: Models for Determining Student Attrition in Engineering. Journal ofEngineering Education, 86: 139-149. https://doi.org/10.1002/j.2168-9830.1997.tb00277.x[2] Veenstra, C. P., Dey, E.L., Herrin, G.D.. "A Model for Freshman Engineering Retention."Advances in Engineering Education 1, no. 3 (2009): n3.[3] Nelavai, N., & Ramesh, S. (2020). An Insight into the challenges faced by First Year EngineeringStudents

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Experimental Centric Pedagogy as Scaffolding for a Better Understanding of Calculus in the Mathematics Discipline

Conference Session: Mathematics Division (MATH) Technical Session 2
Collection: 2023 ASEE Annual Conference & Exposition
Authors: Tijesunimi Abraham Adeyemi, Morgan State University; Oludare Adegbola Owolabi P.E., Morgan State University; Neda Bazyar Shourabi, Pennsylvania State University, Berks Campus; Chukwuemeka Duru; Jumoke 'Kemi' Ladeji-Osias, Morgan State University; Frank Efe
Tagged Divisions: Mathematics Division (MATH)

sametravel lane, and when one vehicle passes another, the trajectories will come together. Time-spacediagrams are practical tools for assessing and showing the traffic flow characteristics of a particularroute section over time (e.g., analyzing traffic flow congestion). However, the ruler experimentwill be the one we pay the most attention to using the distance formula.Now, using fundamental calculus knowledge, we can mathematically deduce the equation ofmotion. Acceleration, distance, and velocity are all related to time, as previously mentioned.The velocity is the displacement that an object or particle experiences with respect to time. In theInternational System of Units (SI), the unit of velocity is meters per second (m/s) Figure 1 (Graph

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Understanding students’ experience and achievement in a redesigned engineering math class

Conference Session: Mathematics Division (MATH) Technical Session 3
Collection: 2023 ASEE Annual Conference & Exposition
Authors: Hui Ma, University of Virginia
Tagged Divisions: Mathematics Division (MATH)

in other math courses with active learningstructures. Reference[1] Henshaw, R., 1991, December. Desirable attributes for professional engineers. In Broadeninghorizons of engineering education, 3rd Annual conference of Australasian Association forEngineering Education (pp. 15-18).[2] Lang, J.D., Cruse, S., McVey, F.D. and McMasters, J., 1999. Industry expectations of newengineers: A survey to assist curriculum designers. Journal of Engineering Education, 88(1),pp.43-51.[3] Freeman, S., Eddy, S.L., McDonough, M., Smith, M.K., Okoroafor, N., Jordt, H. andWenderoth, M.P., 2014. Active learning increases student performance in science, engineering,and mathematics. Proceedings of the national academy of

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An Alternative Methodical Approach and Its Effectiveness to Learn Change of Basis Matrices in an Engineering Linear Algebra Class

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

Relevance Score: 0.008086376

Understanding the sin, cos, and tan calculator buttons

Conference Session: Mathematics Division (MATH) Technical Session 3
Collection: 2023 ASEE Annual Conference & Exposition
Authors: Daniel Blessner, Pennsylvania State University, Wilkes-Barre Campus
Tagged Divisions: Mathematics Division (MATH)

: Foundations of the new reform.Harvard Educational Review, 57(1), 1–23.[5] Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A.,Klusmann, U., Krauss, S., Neubrand, M., & Tsai, Y. M. (2010). Teachers‟mathematical knowledge, Cognitive activation in the classroom, and studentprogress. American Educational Research Journal, 47(1), 133–180.[6] Ball, D. L. (2000). Bridging practices intertwining content and pedagogy inteaching and learning to teach. Journal of Teacher Education, 51(3), 241–247.[7] Hauk, S., Toney, A., Jackson, B., Nair, R., & Tsay, J. (2014). Developing amodel of pedagogical content knowledge for secondary and post-secondarymathematics instruction. Dialogic Pedagogy: An International Online Journal, 2

Relevance Score: 0.007545712

Work in Progress: Uncovering Links between Mathematical Preparation and Engineering Persistence

Conference Session: Mathematics Division (MATH) Technical Session 3
Collection: 2023 ASEE Annual Conference & Exposition
Authors: Mary E. Lockhart, Texas A&M University; Noor Hakim; Vainavi Chilukuri, Texas A&M University; Jason Champagne; Karen E. Rambo-Hernandez, Texas A&M University; Robin A.M. Hensel, West Virginia University
Tagged Topics: Diversity
Tagged Divisions: Mathematics Division (MATH)

National Academies Gathering Storm committee concluded several years ago that theprimary driver of the future economy, security of the United States (US) as a nation, andconcomitant creation of jobs would be innovation—largely derived from advances in scienceand, particularly, in engineering [1]. It has been estimated that close to 50% of the students whobegin their education in engineering do not follow through to the completion of an engineeringdegree [2]-[5]. Some studies have further documented that the propensity for engineeringstudents to attrit is particularly high during their first two years of college [2], [4]. Givenengineers’ critical role in the growth of the U.S.’s economy, security as a nation, and creation ofjobs, this high-level of

Relevance Score: 0.006602498

Mastery Grading Approach in a Calculus Course

Conference Session: Mathematics Division (MATH) Technical Session 2
Collection: 2023 ASEE Annual Conference & Exposition
Authors: Hui Ma, University of Virginia
Tagged Topics: Diversity
Tagged Divisions: Mathematics Division (MATH)

(2020) Raisingthe Bar with Standards-Based Grading, PRIMUS, 30:8-10, 1110-1126, DOI: 10.1080/10511970.2019.1695237[6] Carlisle, S. 2020. Simple specifications grading. PRIMUS. 30(8–10): 926–951. https://doi.org/10.1080/10511970.2019.1695238.[7] Lewis, D. (2022). Impacts of Standards-Based Grading on Students’ Mindset and TestAnxiety. Journal of the Scholarship of Teaching and Learning, 22(2), 67-77.[8] Krathwohl, D. R. (2002). A revision of Bloom's taxonomy: An overview. Theory intopractice, 41(4), 212-218.[9] Usher, E. L., & Pajares, F. (2009). Sources of self-efficacy in mathematics: A validationstudy. Contemporary educational psychology, 34(1), 89-101.[10] Dweck, C. S. (2014). Mindsets and math/science achievement.[11] Taylor, J., &

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WIP: Implementing an Alternative Grading Scheme in a Large Enrollment Differential Equations Course: Lessons Learned

Conference Session: Mathematics Division (MATH) Technical Session 3
Collection: 2023 ASEE Annual Conference & Exposition
Authors: Hadas Ritz, Cornell University
Tagged Divisions: Mathematics Division (MATH)

end of the semester when the full extent of the course trouble becameclear, absorbed communications from many angry students (and parents), and never gave me ahard time about the trouble I caused. I’m sincerely grateful for her support and forbearance.References[1] The Mathematical Association of America, “What is webwork?” Available at https://webwork.maa.org/intro.html (2023/02/28).[2] S. Clontz, “Checkit,” Available at https://checkit.clontz.org (2023/02/28).

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Keys to Success for an Alternative Grading Scheme in a Large Enrollment Differential Equations Course

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