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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)

, 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

Relevance Score: 0.84111536

Student Perceptions on the Effectiveness of Incorporating Numerical Computations into an Engineering Linear Algebra Course

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)

engineering students and now includes four practical components, incorporating MATLABas the primary tool for numerical computations. These numerical components have beenintegrated extensively throughout the course, from daily lectures to homework and projects. Wewill refer to this course as Redesigned Linear Algebra (RDLA) hereafter; for more informationabout the course, see [13] (RDLA here is CALM in [13]).Class FormatRDLA incorporates four essential numerical components: 1. Students engage in active learning by solving worksheet problems in MATLAB ("solve WS"), addressing complex issues collaboratively during in-class group sessions. 2. Students write MATLAB codes for fundamental linear algebra concepts (“code core concepts

Relevance Score: 0.83989954

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)

large proportion of first-generation, low-income students,and spanned one semester. The students solved the activity in two teams, which were grouped asfollows: Team 1, consisting of four students [four males] and Team 2, comprised of five students[two females and three males].Context of the MEAIn order to elicit students’ sense-making processes and gather information on the measurementprocedures involved in modeling for this study, a MEA titled “Ram pump: a resource forproviding running water to las Colonias community” was designed. The MEA was craftedconsidering the six design principles of MEAs [12] and comprised three sections. The firstsection included the context where students read and discussed the challenges faced by “lascolonias” [the

Relevance Score: 0.8398534

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)

spaces. Instead, tit just covers a simple introduction of such topcis. • There are a few common linear algebra projects if the class involves the component of application, e.g., Markov Chain, Least Square Regression, and Image Compression by SVD. All other application projects vary from school to school, depending on students’ needs and interests. • Four out of eight universities have discussion sessions in addition to the regular three traditional lectures per week.Bases on all the findings the author investigated, along with the objectives of making thelearning more active, efficient and applicable, the author carefully reconstructed the coursecontents, which is displayed in Figure 1

Relevance Score: 0.839576

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)

engineering course. Two upper-level students were selected to lead theSI sessions while providing peer mentorship and community engagement for the first-yearstudents. The faculty teaching both courses worked together with the peer mentors to develop aplan for the SI sessions.This paper will detail the SS Program and analyze the performance of the students in their firstquarter at the university. Data from common exams given in their precalculus and engineeringcourses will be used to examine the effectiveness of the program.MotivationFirst-year engineering students are at-risk for high attrition rates [1], [2]. Social issues,independence, adapting to a new environment, foundational knowledge, and other factors havebeen determined as possible

Relevance Score: 0.8393737

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)

life, which isuseful for the scientific, technical and civil society in order to help the student to develop insociety in a reasoned, critical, analytical and scientific way. Moreover Camarena [18] statethat the philosophical educational assumption of TMCC is;“... that, throughout their undergraduate program, the student should be able to make thetransfer of knowledge of mathematics to the areas that require it and in this way theprofessional and labor skills are favored, because it is intended to contribute to thecomprehensive training of the student and build a Mathematics for life” [18].In TMCC, according to Camarena [19],[20], the teaching and learning environment isconsidered to consist of a complex system, as shown in Figure 1, which

Relevance Score: 0.8392043

Exploring the Impact of Mastery Grading on Student Performance

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)

., Hurst-Kennedy, J., Barrera, A., Talley, J., Javazon, E., Diaz, M. andAnzovino, M.E., 2021. The effect of specifications grading on students’ learning and attitudes inan undergraduate-level cell biology course. Journal of Microbiology & BiologyEducation, 22(3), pp.e00200-21.[10] Usher, E.L. and Pajares, F., 2009. Sources of self-efficacy in mathematics: A validationstudy. Contemporary educational psychology, 34(1), pp.89-101.[11] Dweck, C.S., 2006. Mindset: The new psychology of success. Random house.[12] Taylor, J. and Deane, F.P., 2002. Development of a short form of the Test AnxietyInventory (TAI). The Journal of general psychology, 129(2), pp.127-136.

Relevance Score: 0.8373417

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)

URMsstudents and proportion of first-generation students in classes. Psychosocial Factors Influencing Course PerformanceSTEM Self-Efficacy STEM self-efficacy, defined as an individual's belief in their ability to excel in STEMtasks and activities [1], plays a pivotal role in shaping students' attitudes and behaviors in STEMfields. Anticipations of personal efficacy dictate the initiation, extent, and sustainability of copingbehavior when faced with challenges and adverse experiences [1]. This belief is influenced byInterest & Engagement Tactics for Success 2prior experiences, accomplishments, as well as social and environmental factors [2]. High STEMself-efficacy

Relevance Score: 0.49745792

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)

office hours interactions we’ve everhad. This grading scheme strongly incentivizes students to understand and learn from theirmistakes. Students can engage with the material on a deeper level instead of arguing over points.Table 1: Learning outcomes for the course. Students had to demonstrate mastery of each LO acertain number of times to earn credit for that LO towards their final course grade.LO DescriptionModeling Generate differential equations to model physical problems and use the models to answer relevant questions.Slope fields Use slope fields to sketch differential equation solutions for given initial conditions (ICs).Separable

Relevance Score: 0.49723583

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

Relevance Score: 0.49661478

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)

“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

Relevance Score: 0.49558538

Integrating Precalculus into Calculus II and Its Outcomes

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

Relevance Score: 0.49528074

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)

semester was 20 students, so generally students sat in groups of 4 based on their ownselection. The in-class activities were designed to build on the course notes and provideadditional opportunities for students to analytically and numerical solve LTE ordinary differentialequations. Once students mastered the basic mechanics of analytical and numerical solutionapproaches, the in-class problems focused more on physiological systems. Over the course of thesemester, student teams completed in-class exercises focused on the following physiologicalsystems: 1) Arterial Vascular Dynamics, 2) Body Volumes, 3) Neural Activity of a single neuronusing Hodgkin Huxley Model and 4) Blood Alcohol Dynamics. The physiological modelingassignments contained both an

Relevance Score: 0.49321914

Introducing Omnifinites and the Arithmetic Errorless Infinity Calculator

Conference Session: Mathematics Division (MATH) Technical Session 2
Collection: 2023 ASEE Annual Conference & Exposition
Authors: Hunter Christopher Fred, Western Kentucky University; Ryan Bennett Greenwood, Western Kentucky University; Shane Mathew Palmquist, Western Kentucky University
Tagged Divisions: Mathematics Division (MATH)

infinitesimals workwithin the context of mathematical arithmetic. Of importance throughout this paper is basicfundamental arithmetic, which is what led to the development of the web-based errorless infinitycalculator software tool.For this work in developing and creating the errorless calculator, the authors introduce a new setof numbers referred to as omnifinites. Generally, in mathematics, a number is an arithmeticvalue used to represent a quantity. This definition implicitly implies a concept of size as well asorder, but not explicitly. For omnifinites, this definition is used as well. For the Greeks, indefining and describing a number, the concept of “The part of a number is less than the whole.”was foundational [1-3]. This concept was the governing

Relevance Score: 0.49250808

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)

! , y(7) = 9 (b) (𝑡 − 3𝑦’ + 𝑦𝑙𝑛𝑡 = 𝑡 ! , y(1) = −4The three procedural questions are given below. There were two questions that dealt with linearfirst order equations. The other question asked students to use the Laplace transform to solve aninitial value problem whose forcing term included the unit impulse function.Linear Equation, Test 1: Solve the following initial value problem: 𝑡 " 𝑦’ + 4𝑡𝑦 = 𝑡 ! , y(1) = 3Linear Equation, Final Exam: Find the general solution to the differential equation: 1 𝑦’(𝑡) = 3𝑦(𝑡) = 𝑒

Relevance Score: 0.49250805

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)

. Additionally, using this method, teachers self-organize,examine, assess, and orient learning for students both within and beyond the classroom. This goesbeyond merely transmitting knowledge to students.Calculus has many useful applications. This topic reveals itself in its numerous and significantapplications in practice and in many branches of science, particularly physics, which hashistorically been most closely associated with analysis. According to Kleiner [1] for three centuries(18th, 19th, 20th), the primary quantitative instruments for analyzing scientific issues have beencalculus, modern physics, and engineering. Calculus cannot, then, solely concentrate on solvingproblems of pure mathematics while ignoring the chance to show students the

Relevance Score: 0.4917613

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)

engineering students, weadopted the mastery grading approach to reduce stress, foster learning over grades, and enhancegrowth. This paper reports the key aspects of the mastery grading design and presents initialfindings on its impact. Results show that students from the mastery grading sections experienceda significant decrease in test anxiety and a significant improvement in self-efficacy across threecategories. No significant changes in performance were observed.Keywords: Calculus, mastery grading, anxiety, growth mindset, self-efficacyIntroductionOur university’s School of Engineering assumes that most incoming students begin withCalculus II. In general, we have less than 15% of students who begin with Calculus I. Since thepandemic, the number of

Relevance Score: 0.4917613

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)

col- laborations between countries in Latin American and the European Union (EU). ©American Society for Engineering Education, 2023Our Learning Experience with MATH 101, a Virtual and Adaptive Remedial Course1. IntroductionThe lack of mathematics proficiency among high school students in Guatemala is a significantconcern (see [1] for details). Some students wishing to pursue a university degree in science orengineering face difficulties in their first year, as a strong background in mathematics is requiredto succeed in these fields. This problem is also evident at Galileo University, where many first-year engineering students struggle to pass their first mathematics course. This

Relevance Score: 0.4917252

Toward Better Understanding of the Fundamental Theorem of Calculus

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)

important. Moststudents praised the visualization approach for teaching FTOC. Even though we havenot used activities and exercises, students felt that more hands-on activities and in-class exercises could be very helpful. In general, they like traditional presentations,but not as excited as we thought about Powerpoint presentations. Surprisingly mostof them prefer not to read texbooks. Overall, we feel that visualizations were verywell-accepted and preferred by students as an additional way of learning. Refer toTable 1 for the percentage of very important and important activities as perceivedby students. For more details please refer to the Appendix. Percentage Activity 69.0% Understanding the concept of FTOC 75.9

Relevance Score: 0.491526

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)

and 2 were offered. Learning Labs was a program initially financially sponsored bythe NSF, then funded by the university. These learning labs are 2-hour long review sessions, runby upper class student leaders for students in these calculus classes. The Learning Labs were anadditional resource which supplements the FSGs, CAE peer tutoring, and faculty office hours.Split Calculus SequenceDespite the changes described, WF rates did not improve to desired levels (See Table 1). Facultyexplored multiple options. After researching calculus initiatives at other institutions, oneinstitution’s structural changes were an excellent model to emulate. Binghamton UniversitySUNY implemented several changes in its calculus sequence offerings in fall 2014. In

Relevance Score: 0.49111548

Rethinking Precalculus: A Thematic Approach

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)

developing more supporting resourcesin the future.Table 1: Pass rates for pilot and non-pilot sections of Precalculus for the 2022-2023 academicyear. 2022-2023 Pass rate Sample Size Pilot 69.25% 348 Non-Pilot 60.21% 377 Pilot vs Non-Pilot p-value = 0.005509References:[1] M.W. Ohland, A.G. Yuhasz, and B.L. Sill, "Identifying and Removing a CalculusPrerequisite as a Bottleneck in Clemson's General Engineering Curriculum," Journal ofEngineering Education, vol. 93, 2004.[2] M. Kopparla, "Role of Mathematics in Retention of Undergraduate STEM Majors: A Meta-Analysis

Relevance Score: 0.4905641

On Teaching and Learning the Fundamentals of L’Hopital’s Rule in Visual and Intuitive Ways

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)

examples that highlight the applications ofL’Hopital’s Rule. This is followed by a real-life engineering problem that utilizesL’Hopital’s Rule. To assess the effectiveness of the new approach for learning L’Hopital’s Rule weconducted an in-class anonymous questionnaire. 58 students responded. The resultsclearly show that understanding the concept of L’Hopital’s Rule is either importantor very important to students. Most of them praised the visualization and intu-ition approach for teaching the rule. Even though we did not used activities andexercises, students felt that more hands-on activities and in-class exercises could be 1very helpful as well. In general, they liked traditional presentations, but