Conference Session

Mathematics Division Technical Session 4

Collection

2018 ASEE Annual Conference & Exposition

Authors

Sandra B. Nite, Texas A&M University; Brady Creel, Texas A&M University at Qatar; Jim Morgan, Charles Sturt University; Jowaher E. Almarri

Tagged Topics

Diversity

Tagged Divisions

Mathematics

Paper ID #22790Design of an International Bridge Program for Engineering CalculusDr. Sandra B Nite, Texas A&M University Sandra Nite, Ph.D., is a Research Scientist in the Department of Mathematics at Texas A&M University, where she has taught 10 different courses in mathematics and mathematics education. She has served on several committees in the mathematics department, including course development for teacher education in mathematics. Her research agenda includes engineering calculus success, including high school prepa- ration for college. Previously, she taught 8 additional courses at the college level and

Conference Session

Mathematics Division Technical Session 2

Collection

2018 ASEE Annual Conference & Exposition

Authors

Doug Bullock, Boise State University; Janet Callahan, Boise State University; Jocelyn B. S. Cullers, Boise State University

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Diversity

Tagged Divisions

Mathematics

Connecticut. Her educational research interests include retention, mathematics and materials science teaching and learning, first-year programs, accreditation, and faculty development.Ms. Jocelyn B. S. Cullers, Boise State University Jocelyn B. S. Cullers is a Data Analyst at the Institute for STEM & Diversity Initiatives at Boise State University. c American Society for Engineering Education, 2018 The Crux: Promoting Success in Calculus IIAbstractIn the 2013-14 school year, Boise State University (BSU) launched a major overhaul of CalculusI. The details of the reform, described elsewhere, involved both pedagogical and curricularchanges. In subsequent years, we developed several

Conference Session

Mathematics Division Technical Session 2

Collection

2018 ASEE Annual Conference & Exposition

Authors

Ashley Bernal, Rose-Hulman Institute of Technology; Jeffery J. Leader, Rose-Hulman Institute of Technology; Jessa B. Ward, Rose-Hulman Institute of Technology

Tagged Divisions

Mathematics

piezoelectrics, nanomanufacturing, optical measuring techniques, and intercultural design.Dr. Jeffery J. Leader, Rose-Hulman Institute of TechnologyMiss Jessa B. Ward, Rose-Hulman Institute of Technology Jessa Ward is a master’s student in the Biology and Biomedical Engineering Department at Rose-Hulman Institute of Technology. She is interested in biomechanics, prosthetics, and orthotics. More specifically, her thesis work is examining the biomechanics of Kinesio tape. c American Society for Engineering Education, 2018 Creating Laboratories to Aid Student Modeling Ability in Calculus IAbstractIn this paper we will report on the development and deployment of a laboratory sequence forCalculus 1 students

Conference Session

Mathematics Division Technical Session 3

Collection

2018 ASEE Annual Conference & Exposition

Authors

John W. Sanders, California State University, Fullerton

Tagged Divisions

Mathematics

wherever you want, and orient the axes however you want;the value of a scalar remains the same.*If one desires, one can represent this invariance with an equation. Consider two orthonormalcoordinate bases, S and S , which differ by an arbitrary proper, rigid rotation, as shown inFigure 1(a). If a is the value of a certain scalar (such as your pen’s mass) in S, and a is the valueof the same scalar in S , then a = a. (1)This is the transformation rule for scalars under proper, rigid rotations. (a) (b) Figure 1. (a) Two orthonormal coordinate bases S = {ˆ ˆ3 } and S

Conference Session

Mathematics Division Technical Session 3

Collection

2018 ASEE Annual Conference & Exposition

Authors

Guenter Bischof, Joanneum University of Applied Sciences; Benjamin Edelbauer, Joanneum University of Applied Sciences

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Diversity

Tagged Divisions

Mathematics

instance, c = ai bi means c = ∑ i =1 aibi . An index that is not a dummy index is called a free Nindex. As an example, the free index i appears in the vector transformationci = aij b j = ∑ j =1 aij b j together with the dummy index j. This is a preliminary definition that Nneeds to be extended in the course of this section.A set of vectors {ai , i = 1,… , N } is said to be linearly independent if λi ai = 0 only whenλi = 0 ∀i . The vector space is said to be N-dimensional if N is the maximum number oflinearly independent vectors. In this case the vectors ai are said to form a basis, and any othervector may be written as a linear combination that set of vectors.Most important for engineering

Conference Session

Mathematics Division Technical Session 3

Collection

2018 ASEE Annual Conference & Exposition

Authors

Campbell R Bego P.E., University of Louisville; Patricia A. Ralston, University of Louisville; Angela Thompson P.E., University of Louisville; Adrienne Parsons, University of Louisville; Gale J. Crush, University of Louisville, Speed Scientific School

Tagged Divisions

Mathematics

a flipped classroom can be difficult for teachers. Time is needed to developinstructional materials for students to view outside of class, in addition to the time required for developingconstructive in-class activities. Teachers who have persisted with this teaching method often report that theirclassrooms are not optimized until the third or fourth implementation. This paper describes the three-yearprogression from traditional lecture style to flipped classroom design of a large enrollment differential equationscourse at the University of Louisville’s J. B. Speed School of Engineering. The discussion section of the paperreflects on specific implementation difficulties of flipping a classroom, and gives strategic suggestions forinstructors

Conference Session

First-Year Programs Division - Visualization and Mathematics

Collection

2018 ASEE Annual Conference & Exposition

Authors

Adetoun Oludara Yeaman, Virginia Tech; Diana Bairaktarova, Virginia Tech; Tamara Knott, Virginia Tech

Tagged Divisions

First-Year Programs, Mathematics

Paper ID #21999Developing a Coding Rubric for Students’ Spatial Visualization StrategiesMrs. Adetoun Oludara Yeaman, Virginia Polytechnic Institute and State University Adetoun Yeaman is a second year PhD student in Engineering Education at Virginia Polytechnic Institute and State University (Virginia Tech). She received here MS in Mechanical and Nuclear Engineering and her BS in Biomedical Engineering both from Virginia Commonwealth University. She is currently a Graduate Research Assistant. In her first year, she taught two semesters of a freshman engineering course series, Foundations of Engineering. Her research

Conference Session

Mathematics Division Technical Session 1

Collection

2018 ASEE Annual Conference & Exposition

Authors

Lynn Albers, Campbell University

Tagged Divisions

Mathematics

Paper ID #23669Implementing the Wright State Model First-Year Engineering MathematicsCourse in a Startup School of EngineeringDr. Lynn A Albers, Campbell University Dr. Lynn Albers is an Assistant Professor in the newly formed School of Engineering at Campbell Uni- versity. A proponent of Hands-On Activities in the classroom and during out-of-school time programs, she believes that they complement any teaching style thereby reaching all learning styles. She earned her doctorate in Mechanical Engineering from North Carolina State University specializing in thermal sci- ences where her dissertation research spanned three

Conference Session

First-Year Programs Division - Visualization and Mathematics

Collection

2018 ASEE Annual Conference & Exposition

Authors

Kristen L. Sanford Bernhardt P.E., Lafayette College; Mary Roth P.E., Lafayette College

Tagged Divisions

First-Year Programs, Mathematics

Paper ID #22569Using Concept Maps to Assess Student Learning in a Multi-Section Introduc-tion to Engineering CourseDr. Kristen L. Sanford Bernhardt P.E., Lafayette College Dr. Kristen Sanford Bernhardt is chair of the Engineering Studies program and associate professor of Civil and Environmental Engineering at Lafayette College. Her expertise is in sustainable civil infrastructure management and transportation systems. She teaches a variety of courses including sustainability of built systems, transportation systems, transportation planning, civil infrastructure management, engineering economics, and Lafayette’s

Conference Session

First-Year Programs Division - Visualization and Mathematics

Collection

2018 ASEE Annual Conference & Exposition

Authors

Jeffrey A. Davis, Grant MacEwan University; Shelley Lorimer P.Eng., Grant MacEwan University

Tagged Divisions

First-Year Programs, Mathematics

Paper ID #21855Student performance on drawing Free Body Diagrams and the effect on Prob-lem SolvingDr. Jeffrey A Davis P.Eng., Grant MacEwan University Dr Davis obtained his PhD at ETH Zurich specializing in numerical simulation of multiphase flow. With a passion for teaching, Dr. Davis’ research focuses on pedagogical topics such as student engagement, active learning, and cognitive development. Projects he is currently working on include ”Development of a risk assessment model for the retention of students”, ”Development of Student Assessment Software”, and ”Improving Student Engagement through Active Learning”.Dr

Conference Session

Mathematics Division Technical Session 4

Collection

2018 ASEE Annual Conference & Exposition

Authors

Eliza Gallagher, Clemson University; Christy Brown; D. Andrew Brown, Clemson University; Kristin Kelly Frady, Clemson University; Patrick Bass, The Citadel; Michael A. Matthews P.E., University of South Carolina; Thomas T Peters, South Carolina's Coalition for Mathematics & Science; Robert J. Rabb P.E., The Citadel; Ikhalfani Solan; Ronald W. Welch P.E., The Citadel; Anand K. Gramopadhye, Clemson University

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Diversity

Tagged Divisions

Mathematics

associated with businessprofessionals are nearlyidentical to those associatedwith engineering professionals.Moreover, recruitingstudents into engineering frombusiness would increase overallSTEM enrollment, ratherthan simply shifting enrollment (a) Engineeringwithin STEM fields. In SouthCarolina, nine counties againproduce 75% of all businessmajors among the populationof interest (Figure 6b).In this case, however, only fiveof those counties (Charleston,Greenville, Lexington,Richland, and York) are amongthe most populous. The otherfour (Darlington, Dorchester,Florence, and Orangeburg) (b) Businessare all along the I-95 Figure 6 Pareto charts of major selection among students entering“Corridor of Shame

Conference Session

Mathematics Division Technical Session 1

Collection

2018 ASEE Annual Conference & Exposition

Authors

Nancy Romance, Florida Atlantic University; Ali Zilouchian, Florida Atlantic University; Michael Vitale, East Carolina University; Lisa Greenberg, Florida Atlantic University

Tagged Topics

Diversity

Tagged Divisions

Mathematics

gateway mathematics courses, (b) providing participants course-specific mentoringsupport offered by the University’s engineering majors for the same gateway courses, (c)working with math faculty across all three institutions by forming a learning community that isaddressing issues involving curricular coherence across the gateway courses which, in turn,provides an additional academic support for project participants who are enrolled in coursestaught by the faculty, and (d) refining the gateway mathematics courses with an emphasis oncore concepts, curricular coherence and curricular alignment that supports student conceptualunderstanding.Project InterventionGateway Mathematics Course Curricular RefinementThe mathematics partnership includes

Conference Session

Mathematics Division Technical Session 2

Collection

2018 ASEE Annual Conference & Exposition

Authors

Jose Roberto Portillo, Universidad Galileo; Alberth E Alvarado, Universidad Galileo; Jorge Samayoa Ranero, Universidad Galileo

Tagged Topics

Diversity

Tagged Divisions

Mathematics

Differential Calculus) offered for part-time students during the first semester of 2017.This section was comprised of 15 students from different specializations within engineering and itis offered in a suitable schedule (during evenings) for part-time students.GL - TBLIn order to implement the GL-TBL, we created groups of five students which we formed takinginto account the following characteristics: a. Academic profile (measured using a diagnostic test [14]) b. Gender c. Age d. Years of enrollment in the university (some students may have been held back in the course)In GL-TBL, group formation is crucial. This methodology requires that the students workinteractively, with a common goal: to learn while helping other students in their

Conference Session

Mathematics Division Technical Session 1

Collection

2018 ASEE Annual Conference & Exposition

Authors

Amitabha Ghosh, Rochester Institute of Technology (COE)

Tagged Topics

Diversity

Tagged Divisions

Mathematics

compound angles (e.g., how sin (A+B) may be used to yield sin 2A or, sin 3A)4. Clearly establish the understanding of a well-posed problem using a lumped, differential orintegral approach.4. Sketch a tiny volume and write conservation laws using first order approximations, then showthe transition to differential equations including dividing by the volume before limits. As anexample, each term of Navier-Stokes equation for incompressible flows expresses force per unitvolume. Continue with simplifications to various applications in two and three dimensions.5. Discuss concepts in creation of a boundary condition by using a stretched CV.6. Thoroughly review dimensional analysis for algebraic and differential equations.7. Discuss regimes of fluid flows

Conference Session

Mathematics Division Technical Session 4

Collection

2018 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University; Hazal Ceyhan, Ankara University

Tagged Topics

Diversity

Tagged Divisions

Mathematics

points of f(x).c) Intervals where f (x) is increasing and decreasing.d) Intervals where f (x) is convex and concave.e) Please draw the graph of f ( x ) = x x +1 by using the information you have in parts (a), (b), (c), and (d) if they are applicable.The written responses of the participants to this research question indicated misconceptions of first derivative,second derivative and limit knowledge. Students encountered difficulty in determining the intervals of increaseand decrease, determining the horizontal asymptote of the function, and sketching the horizontal asymptote onthe graph. The first derivative knowledge observed to be

Conference Session

Mathematics Division Technical Session 1

Collection

2018 ASEE Annual Conference & Exposition

Authors

Franziska Dorothea Wehner, Technische Universität Darmstadt

Tagged Divisions

Mathematics

-existing knowledge and assumptions without ignoring the individualcontributions of the participants. First, main categories were created based on research andinterview questions. Among the main categories, there were three with relevance to thecurrent study as they referred to a) the way students used different learning resources, b) thefrequency with which students used these resources, and c) students’ satisfaction with theseresources. For all categories, subcategories covering different learning resources with onereferring specifically to video tutorials were created a priori. After this, all transcripts wereread and summarized by the author. Then, the initial coding frame was applied to threeinterviews and revised where needed. In the next

Conference Session

Mathematics Division Technical Session 2

Collection

2018 ASEE Annual Conference & Exposition

Authors

Daniel Raviv, Florida Atlantic University

Tagged Divisions

Mathematics

examples that relay to very basicdaily observations such as the relation between moving shadows to differentiation andintegration. (b) First order differential equation and time constant of first order system. Based onaccumulated teaching experience, some helpful examples are: (1) battery charging a mobilephone at different initial charging values, and (2) cooling rate of coffee. There are of coursemany other examples, but less related to students’ everyday experiences (e.g., radioactive decayand carbon dating). These ideas are shared so that instructors can use them to enhanceunderstanding of engineering-related math concepts, and to show their relevance.We refer to this approach as “work in progress.” When using the above examples (and

Conference Session

Mathematics Division Technical Session 1

Collection

2018 ASEE Annual Conference & Exposition

Authors

Paul L. Goethals, United States Military Academy; Karoline Hood, United States Military Academy

Tagged Divisions

Mathematics

),Philosophical Topics, vol. XV, no. 2, pp. 23-34, 1987.[2] S. Lichtenstein, B. Fischhoff, Do those who know more also know more about how muchthey know?, Organizational Behavior and Human Performance, vol. 20, no. 2, pp. 159-183,1977.[3] G. Gigerenzer, U. Hoffrage, H. Kleinbolting, Probabilistic mental models: a brunswikiantheory of confidence, Psychological Review, vol. 98, pp. 506-528.[4] P. Juslin, H. Olsson, Thurstonian and bruswikian origins of uncertainty in judgment: asampling model of confidence in sensory discrimination, Psychological Review, vol. 10, pp.344-366.[5] D. Kahneman, P. Slovic, A. Tversky, Judgments under uncertainty: heuristics and biases,Cambridge University Press, Cambridge, England, 1982.[6] J.B. Soll, Determinants of

Conference Session

Mathematics Division Technical Session 2

Collection

2018 ASEE Annual Conference & Exposition

Authors

Leszek Gawarecki, Kettering University; Yaomin Dong, Kettering University; Gina Rablau, Kettering

Tagged Divisions

Mathematics

plane.The distribution of grades in this section was as follows; Grade Frequency A 9 B 7 C 6 D 5 F/W 9The results are not indicative of any change in grades distribution in this course.The Likert-type scale results for question on engagement and enhanced learning are statisticallysignificantly positively correlated with the Spearman correlation coefficient 𝜌 = 0.688 (𝑝 −value < 0.005). 6 5 Enhanced Learning 4 3 Enhanced Learning 2

Conference Session

First-Year Programs Division - Visualization and Mathematics

Collection

2018 ASEE Annual Conference & Exposition

Authors

Jaskirat Sodhi, New Jersey Institute of Technology; Ashish Borgaonkar, New Jersey Institute of Technology; Edwin Hou, New Jersey Institute of Technology; Moshe Kam P.E., New Jersey Institute of Technology

Tagged Divisions

First-Year Programs, Mathematics

further suggestions and recommendations.References[1] Borgaonkar, A., Hou, E., Vandermark, S., Kam, M., 2015, “Engineering Math Summer Boot Camp to help Students Succeed in Remedial Courses,” Proceedings 2015 7th First Year Engineering Experience Conference, Roanoke, VA, August 3-4, 2015.[2] Borgaonkar, A., Sodhi J. S., Hou, E.,Baldwin R,, Kam, M., 2017, “Helping First Year Students Start on Track in the Mathematics Sequence,” Proceedings 2017 9th First Year Engineering Experience Conference, Daytona Beach, FL, August 6-8, 2017.[3] Klingbeil, N., Rattan, K., Raymer, M., Reynolds, D., Mercer, R., Kukreti, A. and Randolph, B., 2008, “The WSU Model for Engineering Mathematics Education: A Multiyear Assessment and Expansion to

Conference Session

First-Year Programs Division - Visualization and Mathematics

Collection

2018 ASEE Annual Conference & Exposition

Authors

Ashish Borgaonkar, New Jersey Institute of Technology; Jaskirat Sodhi, New Jersey Institute of Technology; Moshe Kam P.E., New Jersey Institute of Technology; Edwin Hou, New Jersey Institute of Technology

Tagged Divisions

First-Year Programs, Mathematics

receiveddiscount on tuition fees, free tutoring, meals (breakfast and lunch) and various opportunities toparticipate in activities designed to increase their interest in and enthusiasm for engineering.Analysis of the performance of students is presented in tables 3, 4, 5 and figure 5 below. Ingeneral, students did quite well and most of them were able to reach one mathematics coursehigher than their original placement.Table 3: MATH108 and MATH110 Grades Breakdown 2015-2017 2015 2016 2017 Pass (A/B/C) 37 28 24 Not Passing (D/F) 7 2 10 Total Students 44 30

Conference Session

Mathematics Division Technical Session 3

Collection

2018 ASEE Annual Conference & Exposition

Authors

Robert G. Batson P.E., University of Alabama

Tagged Topics

Diversity

Tagged Divisions

Mathematics

possible combinations of component settings. If theclass is small enough, then teams of 2-6 students can be turned loose to repeat the simpleexperiments as illustrated by the instructor. This introduces some hands-on “fun” to the math-oriented engineering statistics course.Figure 3. (a)Image of a Statapult and its Components; (b) How it is Used to Launch a BallRotate among Delivery Methods To the disdain of many college instructors, Millennials have ashorter attention span than students from earlier decades. They want variety—in fact, surveyshave shown they lose interest unless the delivery method changes every 10 minutes! So, in atypical 50-minute lecture, one should consider an appropriate rotation sequence among lecture(knowledge transfer

Conference Session

Mathematics Division Technical Session 1

Collection

2018 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University

Tagged Divisions

Mathematics

, 16(4), 399-431.3. Aspinwall, L., Shaw, K. L., & Presmeg, N. C. (1997). Uncontrollable mental imagery: Graphical connections between a function and its derivative, Educational studies in mathematics, 33, 301-317.4. Baker, B., Cooley, L., & Trigueros, M. (2000). A calculus graphing schema, Journal for Research in Mathematics Education, 31(5), 557-578.5. Breidenbach, D., Dubinsky, E., Hawks, J., & Nichols, D. (1992). Development of the process of function, Educational Studies in Mathematics, 23(3), 247-285.6. Clark, J. M., Cordero, F., Cottrill, J., Czarnocha, B., DeVries, D. J., St. John, D., Tolias, G., & Vidakovic, D. (1997). Constructing a schema: The case of the chain rule? Journal of

Conference Session

Mathematics Division Technical Session 4

Collection

2018 ASEE Annual Conference & Exposition

Authors

Gianluca Guadagni, University of Virginia; Hui Ma, University of Virginia; Lindsay Wheeler, University of Virginia

Tagged Topics

Diversity

Tagged Divisions

Mathematics

(UVA), she worked as an assistant professor at Black Hills State University for two years. In her current role as an APMA faculty member at UVA, she teaches applied math courses to engineering students. Her goals in teaching are to help students develop the confidence in their own ability to do mathematics and to make mathematics a joyful and successful experience.Prof. Lindsay Wheeler, University of Virginia c American Society for Engineering Education, 2018 The benefit of training Undergraduate Teaching AssistantsAbstractWe report on a new program to train Undergraduate Teaching Assistants (UTAs) that we areimplementing at our institution, the University of Virginia. The mixed methods

Conference Session

Mathematics Division Technical Session 3

Collection

2018 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University

Tagged Divisions

Mathematics

approaching from or number of computationsyou can count here? …in terms of location, what is the difference?RP 15: This is around zero (pointing the Maclaurin series), this (pointing the series centered at x=2) is 2.Interviewer: ….is there a difference between them in terms of function?RP 15: This is (pointing the series centered at x=2) bigger than this one (pointing the Maclaurin)Overall only 16 out of 17 participants responded to question (c). Only 37.5 % of the participants had the correctresponse to question (b). Majority of the participants corrected or responded right to the question during theinterviews. One of the participants preferred to not answer the question.Finite & Infinite Maclaurin Series DifferenceIn this section participating

Conference Session

Mathematics Division Technical Session 3

Collection

2018 ASEE Annual Conference & Exposition

Authors

Carl Pettis, Alabama State University; Rajendran Swamidurai, Alabama State University; Ash Abebe, Auburn University; David Shannon, Auburn University

Tagged Divisions

Mathematics

solutions obtained using hand calculation.Lab-2: In this lab, the main contents include graphical visualization for some real data. Manydatasets are publically available from sites such as kaggle.com and data.gov. Graphicalvisualization ranges from simple graphics such as histogram, boxplot, and scatterplot toadvanced graphics such as PCA projection plots, trellis plots, maps, etc. Students need to exploresome real data using graphics to explore and discover information from the real data.Take-home project: Students were used some simulation examples relevant to the real world.Topics for recommendation include (a) gambling games; (b) biological evolution; (c) finance; (d)social network; (e) forensic science; etc. Depending on the students

Conference Session

Mathematics Division Technical Session 4

Collection

2018 ASEE Annual Conference & Exposition

Authors

Andrew H. Phillips, Ohio State University

Tagged Divisions

Mathematics

Paper ID #23944Technology’s Role in Student Understanding of Mathematics in Modern Un-dergraduate Engineering CoursesAndrew Phillips, The Ohio State University Andrew H. Phillips graduated summa cum laude from The Ohio State University in May 2016 with a B.S. in Electrical and Computer Engineering and with Honors Research Distinction. He is currently fin- ishing his M.S. in Electrical and Computer Engineering, and then he will pursue a Ph.D. in Engineering Education. His engineering education interests include first-year engineering, active learning, learning theory, and teaching design, programming, and mathematics. As a

Conference Session

Mathematics Division Technical Session 2

Collection

2018 ASEE Annual Conference & Exposition

Authors

Stacie Pisano, University of Virginia; Hui Ma, University of Virginia; Bernard Fulgham, University of Virginia; Gianluca Guadagni, University of Virginia; Diana D Morris, University of Virginia; Monika Abramenko, University of Virginia

Tagged Divisions

Mathematics

Paper ID #23750Redesigning the Calculus Curriculum for Engineering StudentsStacie Pisano, University of Virginia After receiving a Master of Science in Electrical Engineering from Stanford University, Stacie Pisano worked as an Electrical Engineer and Technical Manager at AT&T and Lucent Technologies Bell Labo- ratories for 16 years, designing and developing telecommunications equipment for the business market. After moving to Charlottesville, VA, she had the opportunity to teach Multivariable Calculus for UVA SEAS, and she was hooked. She has been teaching Applied Math from that point on and enjoying every