Conference Session

Mathematics Division Technical Session 4

Collection

2016 ASEE Annual Conference & Exposition

Authors

Jennifer B. Daines, Colorado Technical University; Tonya Troka, Colorado Technical University; John M. Santiago Jr., Colorado Technical University

Tagged Divisions

Mathematics

Paper ID #15905Improving Performance in Trigonometry and Pre-Calculus by IncorporatingAdaptive Learning Technology into Blended Models on CampusJennifer B. Daines, Colorado Technical University Jennifer Daines received a B.S. in English from the U.S. Air Force Academy in 1998 and subsequently spent eight and a half years as a Personnel Officer in the Air Force, serving most of that time in the Air Force’s education and training command. In 2005, she went back to school, earning an M.A. in English from the University of Texas at San Antonio. In 2007, Jennifer separated from the Air Force and moved to Colorado Springs, where

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

𝐹𝑦 𝐹𝑧 = (𝑟𝑦 𝐹𝑧 − 𝑟𝑧 𝐹𝑦 )i − (𝑟𝑥 𝐹𝑧 − 𝑟𝑧 𝐹𝑥 )j + (𝑅𝑥 𝐹𝑦 − 𝑟𝑦 𝐹𝑥 )k (3) Figure 1: The z-component of a force can be show to contribute to a rotation about y (a) and x (b) axes. This corresponds to the presence of Fz in the Mx and My terms of the formula in eqns. (3) and (4). Similarly, the component of the force in the y-direction contributes to a rotation about the z axes (c) and x axis, (not shown), and can be matched to the presence of Fy in the Mx and Mz components of the moment vector. = 𝑀𝑥 i + 𝑀𝑦 j_𝑀𝑧 k (4) (The x, y, z, coordinate unit vectors are

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

Game Theory, 2(3) (2013), 23-32.[8] K. Motohashi, Economic Analysis of University-Industry Collaboration: The Role of New Tech- nology Based Firms in Japanese National Innovation Reform, The Research Institution of Econ- omy, Trade and Industry, Discussion Paper Series 04-E-001, (2004).[9] M. Sakakibara, Knowledge Sharing in Cooperative Research and Development, Manage. Decis. Econ., 24 (2003), 117-132.[10] R. Veugelers and B. Cassiman, R&D Cooperation between Firms and Universities: Some Em- pirical Evidence from Belgian Manufacturing, International Journal of Idustrial Organization, 23(5) (2005), 355-379.[11] N. E. A. M. Almi, N. A. Rahman, D. Purusothaman, and S. Sulaiman Software engineer- ing education: The gap

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

calculus students whodownplay the importance of strengthening the precalculus background. Students also needto recognize that the probability of success in the calculus sequence is very low if they donot earn an A or B in Precalculus8. Another barrier to student success in college calculus istheir lack of experience with appropriate learning strategies. Student surveys from thesummer 2013 program showed that students overwhelmingly learned to solve mathematicsproblems in high school by imitating the teacher’s solutions to specific types of problems;however, they believed they needed a different approach for college calculus9. Recentbridge programs at Texas A&M University have one significant difference from mostonline programs. They require

Conference Session

Mathematics Division Technical Session 3

Collection

2016 ASEE Annual Conference & Exposition

Authors

Edmund Tsang, Western Michigan University; Kenneth David Domingue, Western Michigan University ; Sarah Gray Hagen, Western Michigan University; Rebecca A. Scheffers, Western Michigan University; Lenore Yaeger; Katherine Fox, Western Michigan University

Tagged Divisions

Mathematics

33.4 31.9 27.5Algebra II 17.7 13.7 18.9 22.0 19.1 16.8 24.2 20.8 25.6 19.7Algebra I* 10.3 7.2 5.9 7.6 6.8 8.4 --- --- --- --No Math Data 0.3 0.3 1.0 0.3 0.7 0 2.4 2.6 0.4 0.9*Beginning in Fall 2012, students with ACT-MATH sub-score of 18 or less, are not admitted toa CEAS major and instead admitted into the university’s Exploratory Advising program. Henceno data has been kept for 2012 and forward.To better inform students of the academic pathways in engineering, engineering technologyand applied sciences, the admissions requirement into CEAS was revised in Fall 2012. InCEAS Exploratory (CEAS-EXEP), students must achieve a grade of B or better in

Collection

2016 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University

Tagged Divisions

Mathematics

(1989). In addition, Triad classification of the participants aredetermined to obtain the qualitative and quantitative results presented in this work.Key Words: Riemann integral, area, functions, concept image, concept definition, APOS theoryIntroductionAn important application of Riemann integral is determining the area between a single variablecontinuous function and the input axis. Given a continuous function f on the interval [a, b], thearea between the function and the input axis can be calculated by using the formula b Area = ∫ f ( x)dx aThis definition of area by using integral concept requires a well

Collection

2016 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University

Tagged Divisions

Mathematics

responses. Participants are asked tocalculate the definite integral of the function f(x) = x2 on the interval [1, 2] by using the limitdefinition of Riemann integral. Missing conceptual knowledge of the participants in calculus areobserved when they were incapable of determining the solution to the problem.Key Words: Riemann integral, functions, derivative, triad classification, APOS theory.IntroductionRiemann integral is an important concept in calculus that is often used by engineering andmathematics majors during their undergraduate and graduate studies. Given a continuous functionf on an interval [a, b], the Riemann integral (for definite integral) of f on the given interval can bedetermined by using the limit of sums

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

Paper ID #15737Peer-Led Team Learning in an Introductory Calculus CourseDr. James E. Lewis, University of Louisville James E. Lewis, Ph.D. is an Assistant Professor in the Department of Engineering Fundamentals in the J. B. Speed School of Engineering at the University of Louisville. His research interests include paral- lel and distributed computer systems, cryptography, engineering education, undergraduate retention and technology (Tablet PCs) used in the classroom.Dr. Gerold Willing, University of Louisville Gerold (Jerry) A. Willing is an Associate Professor in the Chemical Engineering Department at the Uni

Conference Session

Mathematics Division Technical Session 4

Collection

2016 ASEE Annual Conference & Exposition

Authors

Virgil U. Pierce, University of Texas, Rio Grande Valley; Javier Angel Kypuros, University of Texas, Rio Grande Valley; Shirley J. Mills, University of Texas, Rio Grande Valley

Tagged Topics

Diversity

Tagged Divisions

Mathematics

than 35%). While a goal is to be producing students with a higher than expected degree ofsuccess in Calculus 1, we are producing students whose success in Calculus 1 is comparable to © American Society for Engineering Education, 2016 2016 ASEE National Conferencethat of students who have placed into Calculus 1 via more traditional means (mainlycoursework).Table1:GradedistributionintheFall2014andFall2015Calculuscourses. A B C D DR/W F Total % ABC Fall 2014 Calculus 1 64 63 78 42 114 55 416 49% Summer Bridge Students 1

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

Paper ID #16176The Use of Classroom Case Studies in Preparing First-Year MathematicsGraduate Teaching AssistantsEliza Gallagher, Clemson University Although my mathematical research was in topological algebra, my first faculty position was a joint ap- pointment in Mathematics and Mathematics Education housed within the Mathematics Department at California State University, Chico. Currently the Coordinator of Undergraduate Studies for the Depart- ment of Mathematical Sciences at Clemson University, my research interests are in the field of STEM education, and particularly the development of a teacher identity among

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

Arthur B. Powell Rutgers University Rutgers University muteb.alqahtani@gse.rutgers.edu powellab@andromeda.rutgers.eduDynamic geometry environments can support learning of geometry through meditating learners’activity. To understand how dynamic geometry environment mediate the activity of mathematicsteachers, we used Rabardel’s categories of instrument mediations in an instrument-mediatedactivity [1, 2]. We analyzed the discursive and inscriptive interactions of 4 mathematics teacherswho worked for 15 weeks in a team to construct geometric figures and solve open-endedgeometrical problems in a collaborative, dynamic geometry environment. In addition

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

., Hall, R. V. (1983). The peer tutoring spelling game: a classroom procedure for increasing opportunity to respond and spelling performance. Education and Treatment of Children, 6(3), 224-39.16. Kamii, C., Lewis, B. A., Livingston, S. J. (1993). Primary arithmetic: children inventing their own procedures. Arithmetic Teacher, 41(4), 200-03.17. Klein, J. D. and Freitag, E. (1991). Effects of using an instructional game on motivation and performance. Journal of Educational Research, 84(5), 303-08.18. Liedtke, W. W. (1995). Developing spatial abilities in early grades. Teaching Children Mathematics, 2(1), 12-18.19. Mackay, M. and Watson, J. (1989). Game for promoting communication. British Journal of Special

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

Counseling Psycholy. 19, 551–554 (1972).7. Pajares, F. Exploratory factor analysis of the Mathematics Anxiety Scale. Measurement and Evaluation in Counseling and Development. 29, 35–47 (1996).8. Hoffman, B. ‘I think I can, but I’m afraid to try’: The role of self-efficacy beliefs and mathematics anxiety in mathematics problem-solving efficiency. Learning and Individual Differences. 20, 276–283 (2010).9. Suinn, R. & Winston, E. The mathematics anxiety rating scale, a brief version: Psychometric data. Psychological Reports. 92, 167–173 (2003).10. Sherman, J. & Fennema, E. The Study of Mathematics By High School Girls and Boys: Related Variables. American Educational Research Journal. 14, 159–168 (1977).11. Betz

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

+/-grades, so the conversion is A+ = 4.0, A = 4.0, A- = 3.7, B+ = 3.3, etc. We count W’s and CW’sas 0.0, along with F’s. This is consistent with DWF used more generally as a student successmetric, in that it considers an F and a W to be equally unsuccessful.Calc II Grade = (Total grade points) / (Cohort size – Audits – Incompletes)It is possible that there one cohortcould be better prepared for college level work than anothercohort. So we tracked four control variables for each cohort: GenACT: About 70% of our students have either an ACT or an SAT Math score. SAT Math scores are converted to ACT using published concordances.7 If this results in two scores (some students have both ACT and SAT) we take the higher. This is averaged

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 1

Collection

2016 ASEE Annual Conference & Exposition

Authors

Roes Arief Budiman P.Eng., University of Calgary

Tagged Divisions

Mathematics

Paper ID #15903Using Card Games for Conditional Probability, Explaining Gamma vs. Pois-son Distributions, and Weighing Central Limit TheoryDr. Roes Arief Budiman P.Eng., University of Calgary Received PhD in Materials Science and Engineering at University of Toronto in 2001. Currently a Senior Instructor at University of Calgary and have been teaching Probability & Statistics for Engineers course in the past three years. Maintain a small research group (1 PhD, 1 MEng) on pipeline failure and reliability. c American Society for Engineering Education, 2016 USING CARD GAMES FOR CONDITIONAL

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

Paper ID #16439Embedding Mathematics in Engineering Design ProjectsDr. Larry G. Richards, University of Virginia Larry G Richards is a Professor in the Department of Mechanical and Aerospace Engineering at the University of Virginia. He leads the Virginia Middle School Engineering Education Initiative, and is active in K 12 outreach and professional development activities locally and nationally. Larry’s research interests include creativity, entrepreneurship, engineering design, innovation, and K-12 engineering education. He is a founding member of the K-12 Division and is a Fellow of ASEE.Prof. Susan K. Donohue

Conference Session

Mathematics Division Technical Session 2

Collection

2016 ASEE Annual Conference & Exposition

Authors

Aaron Brakoniecki, Boston University; Michael Ward, Boston University; Gretchen Fougere, Boston University

Tagged Divisions

Mathematics

Paper ID #16670Using the Engineering Design Process to Complement the Teaching and Learn-ing of MathematicsDr. Aaron Brakoniecki, Boston University Dr. Aaron Brakoniecki is a Lecturer at Boston University. His research focuses on preservice teachers’ uses of technology (specifically, the Internet) to support their learning of mathematics. He is also involved with the Noyce BEST project at BU, which focuses on training engineers to become mathematics teachers in high needs classrooms.Mr. Michael Ward, Boston University Michael Ward is currently entering his senior year of Mechanical Engineering while simultaneously earn