Conference Session

Mathematics Division Technical Session 1

Collection

2016 ASEE Annual Conference & Exposition

Authors

Guenter Bischof, Joanneum University of Applied Sciences; Thomas Singraber B.Sc., Joanneum University of Applied Sciences; Christian J. Steinmann, HM&S IT-Consulting; Marton Szabo-Kass B.Sc., Joanneum University of Applied Sciences; Stefan Woerndl B.Sc., Joanneum University of Applied Sciences

Tagged Divisions

Mathematics

University of Applied Sciences Thomas Singraber obtained his B.Sc. in Automotive Engineering at the FH Joanneum, University of Applied Sciences Graz, Austria. Currently he is working on finalizing his Master’s Thesis at the same faculty with a company partner supplying components to top motorsport teams all over the world. During his time at the Formula Student team he focused his work on aerodynamics and chassis developement and achieved therefore practical knowledge on a wide spectrum of racing topics. On completion of his studies, he intends to pursue an interdisciplinary career in the automotive sector with a strong motorsport affiliation.Mr. Christian J. Steinmann, HM&S IT-Consulting Christian Steinmann has

Conference Session

Mathematics Division Technical Session 4

Collection

2016 ASEE Annual Conference & Exposition

Authors

Eliza Gallagher, Clemson University; Lisa Benson, Clemson University; Geoff Potvin, Florida International University

Tagged Divisions

Mathematics

over the course of the semester, ensuring that each GTA workedwith each undergraduate precalculus assistant and with all or nearly all of the otherundergraduates. The content of the combined course was closely connected to the precalculusclassrooms at the university and to cooperating teacher classrooms at the high schools.Pedagogical content knowledge was addressed directly and repeatedly, as were reflection onpractice and professional identity.Use of Cases in the Combined CourseIn the 1990’s, the Harvard Mathematics Case Development Project (HMCDP) sought to establisha basis of cases for the preparation of mathematics teaching professionals. Several of those caseswere published as Windows on Teaching Math: Case Studies in Middle and

Conference Session

Mathematics Division Technical Session 1

Collection

2016 ASEE Annual Conference & Exposition

Authors

Jing Zhang, Virginia State University; Yongjin Lu, Virginia State University ; Zhifu Xie, Virginia State University; Dawit Haile, Virginia State University; Keith Williamson, Virginia State University

Tagged Divisions

Mathematics

increases. Thus we denoteproduction cost as ci (z), where the first derivative ciz < 0. In addition, let s(β, γ)denote the collaboration cost. The mathematical model for the firm’s payoff is: ΠI = b1 z − M − s(β, γ) − ci (z) (2)where b1 is a positive constant and b1 >> 0. We assume furthermore that s(β, γ)is convex with respect to both β and γ. The collaboration cost increases as the GAME THEORY APPROACH ON A UNIVERSITY-INDUSTRY COLLABORATION MODEL 7relevance γ decreases, but at a decay rate. That is, sγ < 0 and sγγ > 0. And ci (z)is also convex with respect to z.2.5. Formulation of the University’s Model. The payoff of the university fromthe collaboration

Collection

2016 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University

Tagged Divisions

Mathematics

-developed knowledge of conceptimage and concept definition of Riemann integrals. The use of absolute value with definite integralis an important aspect of the research question for the area calculations. In this work, the goal is toobserve graduate and senior undergraduate mathematics and engineering students’ ability tocombine integral and absolute value concepts by evaluating their responses to an integral question.____________________________________________________________________Special thanks to Drs. Deborah A. Trytten and Gizem S. Aydin for their valuable discussions andinput during the preparation of the IRB approved form.MethodologyIn pedagogy, researchers needed to observe students’ comprehension of the function concept. Thedefinitions in

Conference Session

Mathematics Division Technical Session 4

Collection

2016 ASEE Annual Conference & Exposition

Authors

Sandra Nite, Texas A&M University; G. Donald Allen; Jim Morgan, Charles Sturt University; Ali Bicer, Texas A&M University; Robert M. Capraro, Texas A&M University

Tagged Divisions

Mathematics

interventions because of theimportance of mathematics knowledge and skills in science and engineering coursesrequired for successfully completing the coursework leading to a degree in engineering.Recruitment and retention of engineering students is vital to the progress of Americaneconomy and ability to solve problems to address the needs of an ever-changingtechnological world1, 2. College calculus success is highly correlated to engineeringretention3. Bridge programs designed to increase success for engineering majors werepopular in the 1990's but then waned to some degree. A thorough classification ofprograms in use was conducted in 2002, but insufficient data was reported for researchersto conduct a meta-analysis4. Several common characteristics of

Collection

2016 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University

Tagged Divisions

Mathematics

: b n ∫ f ( x)dx = lim ∑ f (a + i∆x)∆x. a n→∞ i =1This definition will be called the limit definition of Riemann integral throughout this work. Thisdefinition of Riemann integral is taught at early stages of calculus education, therefore Riemannsum approximation needs to be known by the Numerical Methods/Analysis students to be able tosolve a question related to the Riemann integral’s limit definition.___________________________________________________________________________Special thanks to Drs. Deborah A. Trytten and Gizem S. Aydin for their valuable discussions and input during thepreparation of the IRB approved form.This definition

Conference Session

Mathematics Division Technical Session 2

Collection

2016 ASEE Annual Conference & Exposition

Authors

Aimee Cloutier, Texas Tech University; Jerry Dwyer, George Washington University; Sonya E. Sherrod, Texas Tech University

Tagged Topics

Diversity

Tagged Divisions

Mathematics

, interested readers are welcome to contact the authorswho will be happy to share lesson plans and suggestions.References 1. National Math and Science Initiative. (2013). Increasing the achievement and presence of under- represented minorities in STEM fields. Report by the National Math and Science Initiative. 2. Crawford, M. Transformations: Women, Gender and Psychology. New York: McGraw-Hill: 2006. 3. Nassar-McMillan, S. C., Wyer, M., Oliver-Hoyo, M., Schneider, J. (2011). New tools for examining undergraduate students’ STEM stereotypes: Implications for women and other underrepresented groups. New Directions for Institutional Research, 2011(152), 87-98. 4. Blickenstaff, J. C. (2005). Women and science careers

Conference Session

Mathematics Division Technical Session 3

Collection

2016 ASEE Annual Conference & Exposition

Authors

James E. Lewis, University of Louisville; Gerold Willing, University of Louisville; Thomas D. Rockaway, University of Louisville

Tagged Divisions

Mathematics

anticipated that the deeper understanding of the materials gained by being aUTA will entice them to enroll in more rigorous courses as they matriculate. It is possible thatthe teaching experience may influence them to pursue an academic career at either the primary,secondary or collegiate levels.5. AcknowledgementsPartnership for Retention Improvement in Mathematics, Engineering, and Science (PRIMES),National Science Foundation Project NSF-08569, $1,997,451, June 1, 2011 – May 31, 2016.Bibliography1. Otero, V., Pollock, S. & Finkelstein, N. A physics department’s role in preparing physics teachers: The Colorado learning assistant model. Am. J. Phys. 78, 1218 (2010).2. Otero, V., Finkelstein, N., McCray, R. & Pollock, S

Conference Session

Mathematics Division Technical Session 3

Collection

2016 ASEE Annual Conference & Exposition

Authors

Larry G. Richards, University of Virginia; Susan K. Donohue, University of Virginia

Tagged Divisions

Mathematics

Reality: Quantification and Western Society 1250 – 1600. Cambridge University Press, 1997. 2. Dantzig, T. and Mazur, J. Number: The Language of Science. Plume Books, January 30, 2007. 3. Donohue, S.K. and Richards, L.G. A Parent/Teacher ’s Guide to That’s How We Roll: Learning About Linear Motion and Underlying Concepts Using Engineering Design Activities, Virginia Middle School Engineering Education Initiative, University of Virginia, 2014. 4. Donohue, S.K. and Richards, L.G., “FIE 2015 Special Session – Movin’ Along: Investigating Motion and Mechanisms Using Engineering Design Activities,” Proceedings of the 2015 Frontiers in Engineering Conference. 5. Ferguson, E. S. Engineering and the Mind's Eye. MIT

Conference Session

Mathematics Division Technical Session 2

Collection

2016 ASEE Annual Conference & Exposition

Authors

Muteb M. Alqahtani, Rutgers University; Arthur Belford Powell, Rutgers University

Tagged Divisions

Mathematics

and meta-tasks to promote productive mathematical discourse in collaborative digital environments, in Proceedings of the International Conference on Education in Mathematics, Science & Technology, I. Sahin, A. Kiray, and S. Alan, Editors. 2015: Antalya, Turkey. p. 84-94.11. Powell, A.B. and M.M. Alqahtani, Tasks promoting productive mathematical discourse in collaborative digital environments, in Proceedings of the 12th International Conference on Technology in Mathematics Teaching, N. Amado and S. Carreira, Editors. 2015, University of Algarve: Faro, Portugal. p. 68-76.12. Gattegno, C., The science of education: Part 1: Theoretical considerations. 1987, New York: Educational Solutions.

Conference Session

Mathematics Division Technical Session 1

Collection

2016 ASEE Annual Conference & Exposition

Authors

Rebecca Bourn, University of Wisconsin - Milwaukee; Sarah Baxter, University of St. Thomas

Tagged Divisions

Mathematics

formal assessments. Several possible metrics are concept exams andmore consistent student surveys.Future WorkThe main focus of future work will be to develop a library of simple visual examples,specifically for the mathematics classroom, and to experiment with approaches to include studentreflection on their understanding as well as on their own learning styles. These modules easilyfall into the category of an active learning exercise, but additional assessment metrics, perhapswith more focus on the degree to which students recognize this type of approach as valid, areneeded.References[1] Bourn, R., and Baxter, S. C. (2013), Developing Mathematical Intuition by Building Estimation Skills, Paperpresented at 2013 ASEE Annual Conference, Atlanta

Conference Session

Mathematics Division Technical Session 3

Collection

2016 ASEE Annual Conference & Exposition

Authors

Doug Bullock, Boise State University; Kathrine E. Johnson; Janet Callahan, Boise State University

Tagged Topics

Diversity

Tagged Divisions

Mathematics

(3) face-to-face but taught in parallel with the online section. 600 500 400 300 Other 200 Reform 100 0Figure 2: Calculus I enrollment by semester.Total students “captured” by the reform project, as a percent of enrollment is shown in Figure 3.It appears to be stabilizing in the low to mid 70’s, which currently reflects the portion of calculusthat Boise State University has chosen to offer as honors, online, or face-to-face but parallel toonline. 100% 90% 80% 70% 60% 50% 40

Conference Session

Mathematics Division Technical Session 2

Collection

2016 ASEE Annual Conference & Exposition

Authors

Gustavo Moran, Clemson University; Lisa Benson, Clemson University

Tagged Topics

Diversity

Tagged Divisions

Mathematics

. NAE Grand Challenges for Engineering. (2015). at 3. Lent, R. W., Lopez, F. G. & Bieschke, K. J. Mathematics self-efficacy: Sources and relation to science- based career choice. Journal of Counseling Psychology. 38, 424–430 (1991).4. Hackett, G. Role of mathematics self-efficacy in the choice of math-related majors of college women and men: A path analysis. Journal of Counseling Psycholy. 32, 47–56 (1985).5. Lent, R. W., Brown, S. D. & Hackett, G. Toward a unifying social cognitive theory of career and academic interest, choice, and performance. Journal Vocational Behavior. 45, 79–122 (1994).6. Richardson, F. C. & Suinn, R. M. The Mathematics Anxiety Rating Scale : Psychometric Data. Journal of