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

Tagged Topics

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 3

Collection

2018 ASEE Annual Conference & Exposition

Authors

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

Tagged Topics

Diversity

Tagged Divisions

Mathematics

purpose of this paper is to recommend adapting new pedagogical methods to theaccepted topics in an introductory probability and statistics course for engineeringundergraduates—methods that better match the learning characteristics of Millennial students inour courses. In a nutshell, those characteristics may be summarized as: (1) They want relevanceto their major, and future engineering career; (2) They want rationale (for the textbook selected,and for specific course policies and assignments); (3) They revel in technology (to collect data,compute, communicate, and multi-task); (4) They want a relaxed, hands-on environment; (5)They prefer instructors who rotate among several classroom delivery methods.Considering the “Five R‟s” learning

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

(PCAST). “Transformation and opportunity: The future of the U. S. research enterprise,” Washington, DC: PCAST, 2012.[2] M. W. Ohland, and E. R. Crockett. “Creating a catalog and meta-analysis of freshman programs for engineering students: Part 1: Summer bridge programs,” in Proceedings of the 2002 American Society for Engineering Education Annual Conference & Exposition. Montreal, Canada: ASEE, June 16-19, 2002.[3] B. P. An. “The Impact of Dual Enrollment on College Degree Attainment Do Low-SES Students Benefit?” Educational Evaluation and Policy Analysis, 0162373712461933, 2012.[4] A. Gamoran, A. C. Porter, J. Smithson, and P. A. White. “Upgrading high school mathematics instruction

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

gradingincentive that works well with students. Therefore, our proposed course structure used aneffective combination of group learning and specially prepared detailed course notes. After thefirst (background check) quiz the following e-mail (boxed below) was sent to the class givingstudents another opportunity to relearn the topics. The quiz 1 mentioned below was multiple-choice type. Many students would guess answers on such questions. But the condition forregrading such quizzes was they must learn the correct reason/s for each of the missed questionby reading notes, or by discussions with groupmates or others. This worked very well. In fact,our data shows a consistent interest among students. Further tracking some of the students fromFluids II to the

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 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

Each CourseFaculty were divided into three math focus groups (leaving College Algebra for the end) wherethey specifically addressed main learning outcomes for the course, the core ideas upon whicheach course is grounded, and the supporting concepts that make up the core idea(s). Thisapproach builds upon a theoretical framework resulting from the work of numerous groups (i.e.,Mathematical Association of America - [MAA]) and individuals, such as Bransford et al., (2000)who, in his National Research Council commissioned book, How People Learn, providedrecommendations based on extensive work addressing learning and teaching in mathematics.Guiding their discussions were a series of questions such as (a) does the course outline reflect thedesired

Conference Session

Mathematics Division Technical Session 1

Collection

2018 ASEE Annual Conference & Exposition

Authors

Franziska Dorothea Wehner, Technische Universität Darmstadt

Tagged Divisions

Mathematics

Curriculum," Journal of Engineering Education, vol. 93, no. 3, pp. 253-257, 2004.[3] C. McLoughlin and B. Loch, "Building cognitive bridges in Mathematics: Exploring the role of screencasting in scaffolding flexible learning and engagement," in Show me the Learning. Proceedings ASCILITE 2016 Adelaide, ASCILITE 33rd International Conference of Innovation, Practice and Research in the Use of Educational Technologies in Tertiary Education 2016, Adelaide, Australia, November 27-30, 2016, S. Barker, S. Dawson, A. Pardo, C. Colvin, Eds. pp. 412-420.[4] M. Anastasakis, C. L. Robinson, and S. Lerman, "Links between students’ goals and their choice of educational resources in undergraduate mathematics

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

instructor is incharge of presenting a clarification of the appeal during the next session.Multiple Application Activities: Besides tRAT, this part is considered the most important part ofthe session. Here, teams apply the gained knowledge to solve carefully designed applicationactivities. These activities are designed following the well-known 4-S Framework, i.e. SignificantProblem, Same Problem, Specific Choice and Simultaneous Report. Michaelsen [13] describesthe 4-S approach as follows: a. Address a significant problem that demonstrates a use of a particular concept. b. Make a specific choice among clear alternatives. c. Work on the same problem as other teams, so each team will care about the conclusions and rationales of the other

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

representation on their performance,” Edu. Research, vol. 1 (10), pp 505-511, 2010.[8] K. Fisher, “Exercises in drawing and utilizing free-body diagrams,” Physics Teacher,vol . 37 (7), pp 434-435, 1999.[9] D. Rosengrant, A. Van Heuvelen, and E. Etkina, “Do students use and understand free-bodydiagrams?”, Phys. Review. Special Topics - Physics Education Research, vol. 5(1), 13p, 2009.[10] D. Rosengrant, A. Van Heuvelen, and E. Etkina, “Free-Body Diagrams: Necessary orSufficient?”, in 2004 Physics Education Research Conference, Sacramento, California, August4-5, J. Marx, P. Heron, S. Franklin, Eds. American Institute of Physics, 2005, pp 177-180.[11] J. Court, “Free-Body Diagrams Revisited -I,” Physics Teacher, vol. 37, pp 427-433, 1999.[12] T. Litzinger

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

author(s) and do not necessarily reflect the views of the National Science Foundation.We also wish to acknowledge the assistance of the Institutional Research Officers at each campusin gathering the data used in this analysis.References [1] X. Chen and M. Soldner, STEM Attrition: College Students’ Paths Into and Out of STEM Fields (Statistical Analysis Report), ser. National Center for Educational Statistics (NCSE) Statistical Analysis Reports. U.S. Department of Education, 2013. [2] J. Levin and J. H. Wyckof, “Predictors of persistence and success in an engineering program,” NACADA Journal, vol. 15, no. 1, pp. 15–21, 1995. [3] J. Middleton, S. Krause, S. Maass, K. Beeley, J. Collofello, and R. Culbertson, “Early course and grade

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

interpretation of the outcomes. A study to compare and contrast preparednessfor math graded events versus that of other subjects would also be useful. Asking similar-typequestions before and after graded events that are more specific to confidence and preparednesswould also provide a beneficial perspective. Finally, alternative classification schemes may beexamined to identify other patterns between confidence and academic performance.7. Acknowledgement: The views expressed in this paper are those of the authors, and do notrepresent the official policy or position of the United States Army, the Department of Defense, orthe United States Military Academy.8. References[1] S. Austin, The paradox of Socratic ignorance (how to know that you don’t know

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

what the right cross sectionshould look like. Consequently, Tanner’s response was coded as mental action.Guessing. Responses that used the word “guess” or explained that the student arrived at aconclusion by chance or without showing evidence of deliberate reasoning were classified asguessing. For instance, Mia responded with, “No, I just guessed on each question.” In this case,she specifically had “guess” in her response. The other students’ who responses involvedguessing also reported using other strategies. These are further discussed in the section oncombined strategies below.Guiding rule. Guiding rule implies that in the participant responses, the student(s) used astandard or criteria to judge which option is likely to be the answer for

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

student retention in engineering. Ms. Bego is also a registered professional mechanical engineer in New York State.Dr. Patricia A. Ralston, University of Louisville Dr. Patricia A. S. Ralston is Professor and Chair of the Department of Engineering Fundamentals at the University of Louisville. She received her B.S., MEng, and PhD degrees in chemical engineering from the University of Louisville. Dr. Ralston teaches undergraduate engineering mathematics and is currently involved in educational research on the effective use of technology in engineering education, the incorpo- ration of critical thinking in undergraduate engineering education, and retention of engineering students. She leads a research group whose

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

Mathematics Division Technical Session 1

Collection

2018 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University

Tagged Divisions

Mathematics

). Construction of the vector space concept from the viewpoint of APOS theory, Linear Algebra Appl. 432 (8), 2112-2124.15. Piaget, J, & Garcia, R. (1989). Psychogenesis and the history of science (H. Feider, Trans.). New York: Columbia University Press. (Original work published 1983).16. Piaget, J., J.-B.Grize, A., Szeminska, & V.Bang (1977). Epistemology and psychology of functions (J. Castellano`s and V.Anderson:Trans.)17. Slavit, D. (1995). A growth-oriented route to the reification of function. In D. T. Owens, M. K. Reed, and G. M. Millsaps (Eds.), Proceedings of the seventeenth annual meeting of the North American Chapter of the international group for the psychology of mathematics education, 1, 284-290

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

calculate the Head Injury Criterion (HIC). The HIC number is based on theaverage value of time-dependent acceleration 𝑎(𝑡) experienced by the head of a person during animpact. The HIC associates different likelihoods of head injury to different ranges of values ofthe HIC number.In a car safety crash test, anthropomorphic test devices, or simply dummies are placed in thedriver’s and/or passenger’s seat(s). A demonstration video is available for students athttps://www.youtube.com/watch?v=kj9xqrRskrY.The HIC number is defined in equation (2) as follows, 1 𝑡 2.5 HIC = Max[(𝑡2 − 𝑡1 ) × (𝑎̅)2.5 ] = 𝑀𝑎𝑥 {(𝑡2 − 𝑡1 ) × [𝑡 2

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

mathematics placement test to all incoming first time full-time first yearstudents, except those with proof of advanced placement or transfer credits for calculus courses.Performance on this placement test determines students’ starting point in the calculus sequence.Students will either be placed in Calculus-I, which is the preferred scenario, or one of the twopre-calculus courses. Students that are placed in pre-calculus courses start 1-2 courses behind ascompared to those placed in Calculus-I. In addition, performance in the mathematics placementtest also drives placement in physics and chemistry. All this put together means that students thatdo not do well on the mathematics placement test are looking at 1-2 added semester(s) to theirgraduation

Conference Session

Mathematics Division Technical Session 3

Collection

2018 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University

Tagged Divisions

Mathematics

convergence of Taylor series yesterday, today, and tomorrow, Ph.D. thesis, University of Oklahoma, 2009.12. Jason Martin, Michael Oehrtman, Kyeong Hah Roh, Craig Swinyard, and Catherine Hart-Weber, Students’ reinvention of formal definitions of series and pointwise convergence, in Proceedings of the 14th Annual Conference on Research in Undergraduate Mathematics Education, edited by S. Brown, S. Larsen, Karen Marrongelle, and Michael Oehrtman (SIGMAA on RUME, Portland, OR, 2011), Vol. 1, pp. 239–254 [http://sigmaa.maa.org/rume/RUME_XIV_Proceedings_ Volume_1.pdf].13. Danielle Champney and Eric Kuo, An evolving visual image of approximation with Taylor series: A case study, in Proceedings of the 15th Annual Conference on

Conference Session

Mathematics Division Technical Session 2

Collection

2018 ASEE Annual Conference & Exposition

Authors

Daniel Raviv, Florida Atlantic University

Tagged Divisions

Mathematics

𝑑𝑑𝑑𝑑the angular velocity, 𝜔𝜔, as well as to the angle θ of the motor shaft. Since 𝜔𝜔 = 𝑑𝑑𝑑𝑑 it means thatthe relationship at all times between 𝜔𝜔 and θ is differentiation or integration depends on how welook at it. By plotting the input voltage V𝑎𝑎, and the outputs ω, and θ of the DC motor we get a clearvisualization of integration and differentiation (Figure 19).Figure 19: Relation between angular velocity and angular position of a DC motorAfter transforming the equations to the s-domain and then to block diagram we obtain (Figure20): Figure 20: Integrator block diagram – DC motorTo complement the understanding of

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

Paper ID #23801Infusion of Big Data Concepts Across the Undergraduate Computer ScienceMathematics and Statistics CurriculumDr. Carl Pettis, Alabama State University Dr. Carl S. Pettis is a Professor of Mathematics at Alabama State University. He received his BS degree in 2001 and his MS degree in 2003 both from Alabama State University in Mathematics. Dr. Pettis received his PhD in Mathematics from Auburn University in 2006. He currently serves as the Interim Associate Provost for the Office of Academic Affairs.Dr. Rajendran Swamidurai, Alabama State University Dr. Rajendran Swamidurai is an Associate Professor of Computer

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

, S. (1992). The function concept as a prototype for problems in mathematical learning. In E. Dubinsky & G. Harel (Eds.), The concept of function: Aspects of epistemology and pedagogy (195-213). Washington, DC: Mathematical Association of America.