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

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Mathematics Division (MATH)

.), International handbook of emotions in education (pp. 415–436). New York: Routledge.[25] Kesici, S., Baloğlu, M., & Deniz, M. (2011). Self-regulated learning strategies in relation with statistics anxiety. Learning and Individual Differences, 21, 472–477. http://dx.doi.org/10.1016/j.lindif.2011.02.006.[26] Zimmerman, B. J. (2000). Self-efficacy: An essential motive to learn. Contemporary Educational Psychology, 25, 82–91.[27] Graham, S., & Harris, K. R. (2000). The role of self-regulation and the development of literacy and numeracy skills: Results from a longitudinal study. Merrill-Palmer Quarterly, 46(3), 203-224.[28] Fredricks, J. A., Blumenfeld, P. C., & Paris, A. H. (2004). School engagement: Potential of the

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

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Mathematics Division (MATH)

, “Students’ Retention of MathematicalKnowledge and Skills in Differential Equations,” School Science and Mathematics, vol. 105, no.5, pp. 227–239, May 2005, doi: https://doi.org/10.1111/j.1949-8594.2005.tb18163.x.[11] M. Carlson, “Views About Mathematics Survey: Design and Results,” in Proceedings of theEighteenth Annual Meeting of the International Group for the Psychology of MathematicsEducation, vol. 2, pp. 395-402, 1997.[12] M. P. Carlson, “The Mathematical Behavior of Six Successful Mathematics GraduateStudents: Influences Leading to Mathematical Success,” Educational Studies in Mathematics,vol. 40, no. 3, pp. 237–258, 1999, Accessed: Feb. 08, 2024. [Online]. Available:https://www.jstor.org/stable/3483143[13] I. Halloun and D. Hestenes

Conference Session

Mathematics Division (MATH) Technical Session 3

Collection

2023 ASEE Annual Conference & Exposition

Authors

Daniel Blessner, Pennsylvania State University, Wilkes-Barre Campus

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Mathematics Division (MATH)

ratio form. Lastly, they will alsosee that the f in f(x) was replaced by another symbol such as sin or cos or sin -1.References[1] Spangenberg, E. D. (2021). Manifesting of pedagogical content knowledge ontrigonometry in teachers‟ practice. Journal of Pedagogical Research, 5(3), 135-163.[2] Yang, D. C., & Sianturi, I. A. (2017). An Analysis of Singaporean versusIndonesian textbooks based on trigonometry content. EURASIA Journal ofMathematics, Science and Technology Education, 13(7), 3829–3846.[3] Brijlall, D., & Maharaj, A. (2014). Exploring support strategies for high schoolmathematics teachers from underachieving schools. International Journal ofEducational Sciences, 7(1), 99–107.[4] Shulman, L. (1987). Knowledge and teaching

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

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Mathematics Division (MATH)

Mathematical Preparation and Engineering PersistenceAbstractThis work-in-progress research paper is at the early stages seeking to further understand the linksbetween incoming engineering students’ mathematical preparation and their actual degreeattainment in engineering. The importance of mathematical achievement and preparation toengineering persistence has long been studied. This investigation seeks to further enhance thisresearch-base. A sample of 450 incoming engineering majors were divided into three differentengineering tracks by their university based upon their level of mathematics preparation:Engineering Track 1 (Calculus-ready), Engineering Track 2 (Calculus-ready with Precalculusreview), and Engineering Track 3 (College Algebra-ready

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

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Mathematics Division (MATH)

journey. Last but not least, test scores commonlyassess student performance, but they do not provide a complete measure of students' interests andtheir level of engagement in the class [2]. Several approaches have been proposed in theliterature to mitigate this problem. Among them, in this paper, we are interested in the use ofdigital badges to enhance students’ motivation, develop long-lasting enthusiasm for masteringcalculus, and provide an alternative way to showcase their learning progress [3].According to [4], digital badges are essentially virtual artifacts granted to individuals as micro-credentials to record events, such as achievements, competencies, or mastery of skills, whichcould involve completing a course, participating in

Conference Session

Mathematics Division (MATH) Technical Session 3

Collection

2023 ASEE Annual Conference & Exposition

Authors

Hui Ma, University of Virginia

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Mathematics Division (MATH)

engineering students should provide at least five things to lead to students’further academic success and prepare them for the job market: 1) material mastery, 2)communication, and collaboration, 3) software/programming skills, 4) learning andmetacognition, and 5) confidence. Students in traditional lecture-based classrooms may not betaught these skills [1][2]. Numerous studies have shown that active and cooperative learningclasses are better at addressing these than traditional lecture-based classes [3]. Some examples ofActive learning (AL) and Cooperative learning (CL) [4] are 1) Flipped classroom, 2) Studentpresentation, 3) Student projects, 4) Student discussion, and 5) Student group work.A traditional calculus class is often content-driven and

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

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Mathematics Division (MATH)

Education, vol. 86, pp. 139-149, 1997. https://doi.org/10.1002/j.2168-9830.1997.tb00277.x[6] C.P. Veenstra, E.L. Dey, and G.D. Herrin, "A Model for Freshman Engineering Retention,"Advances in Engineering Education, vol. 1, no. 3, 2009.[7] J. Fife, "Calculus and precalculus reform at minority institutions," MAA Notes, vol. 36, pp.36–39, 1994.[8] G. Sonnert and P. Sadler, "The impact of taking a college pre-calculus course on students’college calculus performance," International Journal of Mathematics Education in Science andTechnology, vol. 45, no. 8, pp. 1188-1207, 2014. https://doi.org/10.1080/0020739X.2014.920532[9] E. Jarrett, "Evaluating the persistence and performance of ‘successful’ precalculus students insubsequent mathematics courses," MS

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

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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

Conference Session

Mathematics Division (MATH) Technical Session 2

Collection

2024 ASEE Annual Conference & Exposition

Authors

Caleb Wilson Hendrick, University of Maine; Karissa B Tilbury

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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

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

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Mathematics Division (MATH)

Covid-19 on Applied MathematicsCourses for Engineering Students. In 2022 ASEE Annual Conference & Exposition.[2] Besser, A. et al. (2020) ‘Adaptability to a sudden transition to online learning during the COVID-19pandemic: Understanding the challenges for students.’, Scholarship of Teaching and Learning inPsychology. doi:10.1037/stl0000198.[3] Faulkner, B., Earl, K. and Herman, G. (2019) ‘Mathematical Maturity for Engineering Students’,International Journal of Research in Undergraduate Mathematics Education, 5(1), pp. 97–128.doi:10.1007/s40753-019-00083-8.[4] Jamalpur, B. et al. (2021) ‘A comprehensive overview of online education – Impact on engineeringstudents during COVID-19’, Materials Today: Proceedings. doi:10.1016/j.matpr.2021.01.749

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

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Mathematics Division (MATH)

. J. ’Kemi Ladeji-Osias is Professor in the School of Engineering at Morgan State University in Balti- more. She is a rotating Program Director in the Division of Engineering Education from 2021 - 2023.Frank Efe ©American Society for Engineering Education, 2023Experimental Centric Pedagogy as Scaffolding for a Better Understanding of Calculus in the Mathematics DisciplineAbstractThe field of calculus is critical to the success and advancement of many engineering and statisticalsystems. Calculus provides ways of analyzing transient quantities, including data collected fromsensors, determining the area under a curve, fitting a line for predictive analytics, and price changesin the stock market

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

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Mathematics Division (MATH)

/9780429021381-2.[6] M. Hagena, “Mathematical modelling by fostering measurement sense: An intervention study with pre-service mathematics teachers,” in Mathematical modelling in education research and practice, G. A. Stillman, W. Blum, and M. Salett Biembengut, Eds., in International Perspectives on the Teaching and Learning of Mathematical Modelling. , Cham Heidelberg: Springer International Publishing, 2015, pp. 185–194. doi: 10.1007/978- 3-319-18272-8_14.[7] M. A. Hjalmarson, T. J. Moore, and R. Delmas, “Statistical analysis when the data is an image: Eliciting student thinking about sampling and variability,” Statistics Education Research Journal, vol. 10, no. 1, Art. no. 1, May 2011, doi: 10.52041/serj.v10i1.353.[8] A. W

Conference Session

Mathematics Division (MATH) Technical Session 1

Collection

2023 ASEE Annual Conference & Exposition

Authors

Meiqin Li, University of Virginia

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Mathematics Division (MATH)

, including engineering, computerscience, operations research, economics, and statistics. The knowledge and application oflinear algebra is particularly emphasized by various ABET program criteria, making it arequired skill. To address the need for improving the undergraduate linear algebra curriculum, the Lin-ear Algebra Curriculum Study Group (LACSG) was established in January 1990[1] . Thisgroup had a significant impact on the design of linear algebra textbooks and courses. Mean-while, due to the unique characteristics of the course, various teaching experiments andapproaches have been implemented to overcome obstacles encountered by students when 2learning linear algebra[2][3][18][13][18]. Many

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

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Mathematics Division (MATH)

algebra as a necessary skill.Teaching linear algebra poses unique challenges due to the abstract nature of its core conceptssuch as vector spaces, linear transformations, and eigenvalues/eigenvectors. Research by Carlsonet al. [1], Dorier [2], and Wawro et al. [3] has documented the difficulty students face in graspingthese foundational principles.One major issue is the struggle to visualize abstract concepts, which is crucial for understandingthe geometric implications of vector spaces, linear independence, and transformations. Thisdifficulty in visualization has been extensively discussed in studies by Dubinsky [4], Dorier andSierpinska [5], Klasa [6], Dogan [7], and Harel [8]. Moreover, there is a noticeable trend amongstudents to prioritize

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

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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 2

Collection

2023 ASEE Annual Conference & Exposition

Authors

Alberth Alvarado, Universidad Galileo; Jose Roberto Portillo, Universidad Galileo

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Mathematics Division (MATH)

obstacle is evenmore complex; low pass rates may translate not only into demotivated students but also into highdropout rates. In recent years, Galileo University has put much effort into mitigating these issuesby designing and implementing non-traditional remedial courses (e.g., [2]).Traditional remedial mathematics courses have long been a pillar of educational institutions,allowing students to improve their mathematics skills and catch up with their peers [3]. However,these courses often rely on a one-size-fits-all approach that may only be effective for somestudents. Fortunately, since their introduction, adaptive learning through intelligent tutoringsystems, introduced in [4], offered a new way forward. By combining technology andalgorithms

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

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Mathematics Division (MATH)

, there is no way to reverse the haircut damage. Figure 3 serves as a clearillustration of a haircut function lacking an inverse. 5 Figure 2: Inverse function: An inspiring cartoon [20] Figure 3: Haircut - Demonstrating the absence of an inverse function3 Explanation of the FTOCThe fundamental theorem of calculus is a powerful theorem that establishes theconnection between differentiation and integration. We explain the two parts of theFTOC:FTOC Part I: It asserts that if you have a function defined R as the integral ofanother function with a variable upper limit (i.e., F (x) = [a, x] f (t)dt), then itsderivative is equal to the original function: F ′ (x) = f (x). Figure

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

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Mathematics Division (MATH)

Group.Dr. Octavio Mattasoglio Neto Neto Undergraduate in Physics (1983), master in Science (1989) and phd at Education (1998) all of them from Universidade de S˜ao Paulo. Professor of Physics at Mau´a Institute of Technology, since 1994 and President of Teacher’s Academy of the same Institute, ©American Society for Engineering Education, 2023 Elaboration of a Contextualized Event for teaching eigenvalues and eigenvectors in the Control and Automation Engineering programIntroductionResearch in Mathematics Education, for example, [1], [2], [3], [4], [5], [6] have explored thesubject of Linear Algebra