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

university engi- neering research team should apply to select a project from a firm to enhance its research capacity and diversify its engineering programs as well. Keywords: Stock of Knowledge, Cooperative Game, Noncooperative Game, Economic Network, Optimization.Date: May, 2016. 12 J. ZHANG, Y. LU, Z. XIE, D. HAILE, K. WILLIAMSON 1. Introduction In the current global knowledge-and-technology intensive marketplace, the Re-search and Development (R&D) department plays a vital role in the developmentof a firm or an industry. During the last decade, we have seen a rapid increase inthe research of R&D collaboration in econometric

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

framework.In the second stage of this work3, the authors began to explore ways to add reflective thinkingand adapt the EFFECTs framework into the math classroom, Math-EFFECTs. The approachincorporated physical applications, geometry-based problems, and estimation techniques intosolution processes to contribute to the “does this answer make sense” aspect of critical thinking.These Math-EFFECTs modules were proposed for courses that still had flexible contentrequirements that allowed for more free form, less time constrained exploration. Studentsreported more enjoyment in learning and that their feelings of creativity in using mathematicshad increased significantly as they (1) completed realistically modeled problems and (2) weregiven the opportunity to

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 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

complexity of the discrete system exceeds a certainlimit, and a summary then closes the paper.Mass spring system and continuum limitTo better understand the physics of such a system it seems to be convenient to employ a one-dimensional system consisting of particles aligned in a straight line. The model can beimagined as beads mounted on a thin wire and connected to neighboring beads by springs(Figure 1).Figure 1: Schematic diagram of a one-dimensional coupled system of masses and springs.The particles have the masses mi and all the springs connecting the particles shall have equalspring constants k. If the equilibrium position of the ith particle is xi, then its position whendisturbed from equilibrium can be denoted xi + ui. In other words, ui(t

Collection

2016 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University

Tagged Divisions

Mathematics

either enrolled or recentlycompleted (i.e. 1 week after the course completion) a Numerical Methods or Analysis course at alarge Midwest university during a particular semester in the United States. Each participant wasasked to complete a questionnaire consisting of calculus concept questions and interviewed forfurther investigation of the written responses to the questionnaire. The research question isdesigned to understand students’ ability to apply Riemann’s limit-sum definition to calculate thedefinite integral of a specific function. Qualitative (participants’ interview responses) andquantitative (statistics used after applying APOS theory) results are presented in this work by usingthe written questionnaire and video recorded interview

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

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

Tagged Divisions

Mathematics

learn in their mathematics classrooms. In addition to these grade-levelcontent standards, there were also standards of mathematical practice that cut across grade levels(See Table 1). These standards described mathematical habits of mind, which are important forcritical consumers of mathematics content.MP1 - Make sense of problems and persevere in solving themMP2 - Reason abstractly and quantitativelyMP3 - Construct viable arguments and critique the reasoning of othersMP4 - Model with mathematicsMP5 - Use appropriate tools strategicallyMP6 - Attend to precisionMP7 - Look for and make use of structureMP8 - Look for and express regularity in repeated reasoning Table 1 – Standards for Mathematical Practice (NGA, 2010)What becomes

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

at improving entering students’ college readinessand mathematics placement. The small scale intervention, A Bridge to Calculus, is intended toimprove students’ placement from College Algebra into Calculus 1. The target population forthis effort are students with high school experience in a Calculus course but whose performanceon placement exams does not reflect this experience. At our institution this is a significantnumber of students and the goal of the project is to develop methods to address and acceleratestudents in this category. The course design, to take advantage of the students’ prior experience,emphasizes practice and mastery using a modified emporium course design and the ALEKSsoftware1. This intervention runs as a summer course

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

programs were noted: 1)bridge programs generally improve assessment scores, 2) most program are notcompulsory and have difficulty recruiting students who need the intervention, and 3)mathematics is the most commonly addressed subject area. In 208 a meta-analysis ofbridge programs focused on mathematics instruction was conducted5. Only 12 summerbridge programs for incoming engineering freshmen were identified for the study. Ofthose programs, 8 lasted 4-6 weeks, while one program was only one week. The one-weekprogram involved approximately 8 hours a day of solving mathematics problems. Thetotal time spent was comparable to the longer programs6. A high percentage of thosecompleting the program increased their mathematics scores, although small

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

.1 Regarding student motivation, it is important for minority studentsto have role models to inspire them and for students to be exposed to STEM subjects early andcontinuously.7 It is also helpful for students to be surrounded by a community of STEMprofessionals.1 Although Active STEM does not aim to replicate or validate the programs of theNMSI, the key factors of student engagement, motivation, and exposure to STEM subjects werecentral to Active STEM’s design.Other sources in the literature have attempted to highlight factors specific to these minoritygroups that may deter interest in STEM. Two primary factors for both black and Hispanicstudents are a lack of financial support and poor academic preparation. Hispanic students, inparticular

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

own sense of what should be taught in calculus, which guided their teaching,assignments and examinations.There was agreement about what c text should be used, and a common syllabus was on file. Yet,as a result of both growth and lack of coordination between instructional faculty, a situation haddeveloped by 2005-6 which students, the mathematics department, and others recognized asbeing problematic. At that time, from a student’s perspective, it appeared to matter more, “whoyou took,” than “what you learned” in terms of their chances of passing the course.1 This wassupported by pass rate data; the average pass rate in 2005-6 was 51% and ranged from 30% to90% depending on who taught the course.2 The variation in pass rate was a confounding

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

meeting times where students are required to attend the assembly much like atraditional course. This past semester there were six sections of this course taught. All sixsections were led by UTAs, with four sections utilizing three person groups. The other twosections used the same materials and were led by UTAs without the three person groups. Thecourse also uses online interactive and educational software to deliver the material andautomatically grade the students’ assignments.1. IntroductionThe Partnership for Retention Improvement in Mathematics, Engineering, and Science(PRIMES) is a University of Louisville cross-college collaboration aimed at reducing attritionamong our STEM majors. This project unites faculty from the College of Arts &

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

direct them what to do. In the design challenge, the teams are very creativeand devise many unique solutions to the defined problem.RaPower 12, 13In the RaPower ETK, pre-college student teams design and build model solar cars. Through aseries of hands-on activities, they learn how solar cells and motors work: they conductexperiments and take measurements, analyze data, and draw conclusions. Figure 1 shows thetypes of solar cells used in this experiment. They determine which solar cells, motors and tireswould work best for their car. In one experiment, they use multimeters to measure the voltageproduced by three solar cells under four lighting conditions (ambient, incandescent, halogen, andsolar). Each team constructs a 3x4 matrix and enters

Collection

2016 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University

Tagged Divisions

Mathematics

enrolled or recently completed (i.e. 1 week after thecompletion of the course) a Numerical Methods or Numerical Analysis course at a large Midwestuniversity during a particular semester. The participants completed a questionnaire and eachparticipant is interviewed to explain his/her written responses to the questionnaire questions.Qualitative and quantitative results are displayed in this paper by using the written and videorecorded interview responses to the question stated above. The connection between participants’concept image and concept definition knowledge is evaluated in this work. Next section is devotedto the literature review on triad classification and APOS theory.Relevant Literature By relying on Piaget`s study of functions in 1977

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

“Moderately Selective” institution, about 20-30% of the incoming first-year CEAS studentsfor the past 10 years were placed into Algebra II or Algebra I during their first semester. Table 1below shows the percent of the first-year CEAS students’ enrollment in mathematics courses intheir first-semester at WMU from 2006 to 2015.Table 1. Percent of First-Year CEAS Students and First-Semester Mathematics Enrollment from2006 to 2015 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015Calculus II or 5.4 5.1 5.2 7.9 7.5 3.4 4.5 8.0 7.0 13.8HigherCalculus I 35.3 42.7 39.2 34.3 40.7 38.0 37.2 35.1 35.0 38.1Pre-Calculus 31.0 31.1 29.8 27.9 25.2 34.0 31.7

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

Likert-type items (with scores from 1 “not anxious atall” to 5 “very anxious”) on the first and last days of the four week course. The survey wasdistributed during class time just before a test. The first survey distribution was the very first dayof the course, before a diagnostic test (which is not part of the final grade). The final survey wasdistributed the last day of the course, right before the final test. Twenty items from a validatedmath anxiety survey, the 30-item Mathematics Anxiety Rating Scale (MARS 30-item)9, wereselected based on relevance to the context in the Mexican university. The survey was structuredaround math problems that students were likely to encounter in school or daily life, whichstudents then had to rate in terms of

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

the currentpaper.We embedded four first-year GTAs in a senior-level course for secondary mathematics educationmajors and used classroom mathematics case studies as a central component of the course. In thiscontext, we seek to answer these questions: 1. To what extent, and in what manner, did the nature of the graduate students’ comments during case analysis change over time? 2. To what extent, and in what manner, did the graduate students’ perceptions of teaching and of themselves as teachers shift over time? 3. How did the graduate participants perform as first-time teachers of record, compared to first-time teachers of record who were not embedded in the secondary education course?Two of our research questions are

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

has seen promising results in boththe pilot courses as well as the follow on initial Calculus course. The goal in conductingthese pilots was to improve student retention and performance in Trigonometry and Pre-calculus. Since the integration of Intellipath into the campus-based classes in January of2015, average pass rates in Trigonometry have increased from 76% to 94%, and averagewithdraw rates have decreased from 36% to 17%, as indicated in Figure 1. Figure 1. Trigonometry Pass and Withdraw Rates 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% January, April, July, 2014 October, January, April, July, 2015 October, 2014 2014 2014