Conference Session

Mathematics Division Technical Session 1

Collection

2013 ASEE Annual Conference & Exposition

Authors

Catherine Matos, Clayton State University; Tamara Pearson, Clayton State University

Tagged Divisions

Mathematics

are required to have access to a laptop computer that they can bring to class withthem each day. Enrollment in the Ordinary Differential Equations class is comprised ofmathematics majors and students in our dual degree and transfer programs for engineering. Asignificant portion of the students are non-traditional and/or have substantial work obligationsthat they need to balance with their coursework. Roughly 55% of our student body is enrolledfull-time (Figure 1), and about 45% falls into the traditional college student age range (Figure2).6 Differential Equations is a 3 hour course with no recitations and no teaching assistants. Whileclass size is thankfully small, many students have to work before and after class time, making itdifficult

Conference Session

Mathematics Division Technical Session 1

Collection

2013 ASEE Annual Conference & Exposition

Authors

Patricia Salinas, ITESM; Eliud Quintero, ITESM

Tagged Divisions

Mathematics

with the 2011 Sim´on Bolivar Award for Doctoral Thesis in Mathematics Education and with the National ANUIES Award for Doctoral Research related with Education at College in 2011. At present she is Member Level 1 of the National Researches System from CONACYT M´exico. She has been addressing several projects promoting the use of technology in the teaching of Calculus and the implications of such innovation on the learning of the fundamental ideas that this scientific discipline encourages. She has also been participating in the development of the Educational Model that Tecnol´ogico de Monterrey promotes through the design of the syllabi of the Mathematics Courses for Engineering and its distribution with the use of

Conference Session

Mathematics Division Technical Session 1

Collection

2013 ASEE Annual Conference & Exposition

Authors

Jenna Tague, Ohio State University; Jennifer Czocher, Ohio State University; Gregory Richard Baker, Ohio State University; Amanda Roble, Ohio State University

Tagged Divisions

Mathematics

outside of the traditional instructional setting. Thus,we sought instructional media that would realize our anywhere/anyplace attitude toward meetingstudents' needs. In our efforts to reconceptualize the course, we aimed to: (1) capitalize onengineering and science points of view to help students utilize mathematics within theirdiscipline, and (2) use instructional technology to help the professor in achieving this goal.Mathematical modeling is theorized as a cycle that links mathematical thinking to science andengineering, and so supports the first goal. In this paper, we report on the means we used tomeet the second goal and on our evaluation of our success. Our contribution to the engineeringeducation community is (i) a description of how we

Conference Session

Mathematics Division Technical Session 1

Collection

2013 ASEE Annual Conference & Exposition

Authors

Ravi T. Shankar, Florida Atlantic University; Don Ploger, Florida Atlantic University; Agnes Nemeth, Florida Atlantic University; Steven Alan Hecht Ph.D., Nova Southeastern University

Tagged Divisions

Mathematics

planned efforts to integrate robotics intohigh school math curriculum. We are driven by two fundamental objectives: (1) Build low costrobots that can be purchased or built incrementally to manage budgetary restrictions. Theserobots should be re liable, robust, and most important of all, be customizable for the specificneeds of the teacher and the student teams; and (2) adapt the approach of “Understanding byDesign” by Wiggins and McTighe1 in integrating robots into math lessons. They recommend athree-stage process: define objectives; determine assessments, and develop tasks (in our case,robotics based exercises).For the first objective, we will provide details of our on-going work on building low cost robotsthat every K-12 school can afford. It

Conference Session

Mathematics Division Technical Session 1

Collection

2013 ASEE Annual Conference & Exposition

Authors

James E. Lewis, University of Louisville; Jeffrey Lloyd Hieb, University of Louisville

Tagged Divisions

Mathematics

I course, the department has long observed that students who attendclass have a higher probability of succeeding. The use of paper-based, daily, in-class problemsto help learning and attendance has been used for many years. A small amount of credit onweekly exams was given for completion of in-class problems. Work on in-class problems wasnot graded for accuracy since the problem was always worked by the instructor during class priorto the students submitting the problem. Since 2007, all incoming freshmen have been required topurchase a Tablet PC. Initial efforts to incorporate Tablet PC technology into the classroomwere focused on the use of DyKnow™ 1, including these in-class problems. Electronic collectionof students’ digital work on the

Conference Session

Mathematics Division Technical Session 3

Collection

2013 ASEE Annual Conference & Exposition

Authors

Kathleen A Harper, The Ohio State University; Gregory Richard Baker, Ohio State University; Deborah M. Grzybowski, The Ohio State University

Tagged Divisions

Mathematics

. Page 23.603.1 c American Society for Engineering Education, 2013 First Steps in Strengthening the Connections Between Mathematics and EngineeringIt is well-documented that students have difficulty transferring their knowledge between thedomains of science, mathematics, and engineering.1-3 This lack of transfer can lead to frictionbetween these departments. Some engineering professors are tempted to blame their colleaguesin math and science for not teaching effectively or not even addressing the proper content.Conversely, colleagues in mathematics and science have been known to say that engineeringstudents do not actually try to learn the material and just plug numbers into

Conference Session

Mathematics Division Technical Session 2

Collection

2013 ASEE Annual Conference & Exposition

Authors

Helen M Doerr, Syracuse University; Jonas Bergman Arleback, Syracuse University; AnnMarie H O'Neil, C.S. Driver Middle School

Tagged Divisions

Mathematics

discharged. Students weregiven a set of resistors and capacitors and were asked to develop a model they could use toanswer these three questions: (1) How does increasing the resistance affect the rate at which acapacitor discharges? (2) Compare the rates at which the capacitor is discharging at thebeginning, middle and end of the total time interval. How does the average rate of change of thefunction change as time increases? (3) How does increasing the capacitance affect the rate atwhich a capacitor discharges? Similar to the multiple tasks within the light intensity applicationactivity, the students engaged in several iterations of interpreting and communicating theirreasoning about three quantities: (1) the values of the exponential decay

Conference Session

Mathematics Division Technical Session 2

Collection

2013 ASEE Annual Conference & Exposition

Authors

Andrew Grossfield P. E., Vaughn College of Aeronautics & Technology

Tagged Divisions

Mathematics

only a few separate points.Piecewise smooth means the curves have a tangent line everywhere except at a few separatepoints.Usually, students learn in high school algebra the different kinds and characteristics of curves;that is, they learn to graph simple curves, to find the zeros of polynomials and rational curvesand to solve for the intersections of simple curves. It is also important that students learn tovisualize the curve which is associated with a particular equation. 4 2As an example, examine the graph of the fourth degree polynomial, y = x – 2x + .2x +1, whichis shown below in Figure 1

Conference Session

Mathematics Division Technical Session 2

Collection

2013 ASEE Annual Conference & Exposition

Authors

Jamiiru Luttamaguzi, Elizabeth City State University; Ka'Ren Ladoris Byrd; Akbar M. Eslami, Elizabeth City State University; Ehsan O Sheybani, Virginia State University; Giti Javidi, Virginia State University

Tagged Divisions

Mathematics

. These areas, as well as others, help to improve the understanding of Page 23.274.2linkages between water, energy and carbon cycles. Data for measurements in SMAP are carriedout by antennas. Specifically the SMAP concept utilizes L-band radar and radiometerinstruments sharing a rotating 6-m mesh reflector antenna to provide high-resolution and high-accuracy global maps of soil moisture and freeze/thaw state every two to three days.A SMAP mission is depicted in Figure 1 as below. Figure 1: SMAP MissionSome basic parameters such as power, radiation pattern and efficiency, directivity, beam solidangle, polarization

Conference Session

Mathematics Division Technical Session 3

Collection

2013 ASEE Annual Conference & Exposition

Authors

Jeremiah J. Neubert, University of North Dakota; Deborah Worley, University of North Dakota; Naima Kaabouch, University of North Dakota; Mohammad Khavanin, Professor of Mathematics at University of North Dakota

Tagged Divisions

Mathematics

note that the questions not only help the students find themathematical solution to the problem, but also often ask them to think more deeply about thesolution. For example, students may find that a structure is not designed correctly and are thenasked how it could be changed to meet the desired design specifications. This process requiresthem to not only solve the equation, but they must also understand its meaning and know how tomanipulate it. An example problem from one of the modules is provided in Fig. 1; the moduleproblem sets can be obtained via the project website12. Page 23.275.3 Search and Rescue

Conference Session

Mathematics Division Technical Session 3

Collection

2013 ASEE Annual Conference & Exposition

Authors

Gregory Richard Baker, Ohio State University

Tagged Divisions

Mathematics

what they need to know mathematically. Thispaper presents just such a documentation of the mathematical content in a typical first-year physics course.1. IntroductionThe Department of Mathematics of a typical large mid-western university teaches alarge number of students each year, of whom about 70% are engineering students. TheDepartment of Physics teaches also teaches many student each year, of which about75% are engineering students. Many of these engineering students are enrolled in thebasic first-year courses in physics and mathematics, and to accommodate such largenumbers, course enrollments are split into multiple large lectures and supplementedwith smaller recitation sections.To ensure uniform teaching, the curriculum in physics and

Conference Session

Mathematics Division Technical Session 4

Collection

2013 ASEE Annual Conference & Exposition

Authors

Rebecca Bourn, Tribeca Flashpoint Media Arts Academy; Sarah C. Baxter, University of South Carolina

Tagged Divisions

Mathematics

approach suggestedby Polya in How to Solve It8. Polya boils problem solving down to four simple steps thatprovide an algorithm to approaching any type of complex problem. These are: 1) understand theproblem; 2) devise a plan; 3) carry out the plan; and 4) look back and evaluate your results andprocess. The emphasis on evaluating progress against goal is helpful, in particular, for lessexperienced students when dealing with larger-scale problems. However, students still haveissues with evaluating the correctness, or reasonableness of their answers, often because theyhave not developed the often estimation- based skills necessary to support the development ofmathematical intuition, which would guide their judgment. Consequently, we knew we needed

Conference Session

Mathematics Division Technical Session 3

Collection

2013 ASEE Annual Conference & Exposition

Authors

Samantha Nacole Andrews, Georgia Institute of Technology; Greg Mayer, Georgia Tech; Rui Hu, CEISMC, Georgia Institute of Technology; Connelly Hunter Connelly, Google, Inc.; Nathaniel William Tindall III; Neva Rose, Georgia Institute of Tecnology - CEISMC

Tagged Divisions

Mathematics

efforts have been researched to integrate math,engineering, and science courses for the K12 environment[1-4]. Students often do not understand Page 23.430.2the connection between subjects, such as math and science, because they are taught as separateentities. Course integration helps students to gain a better understanding of the application oftopics within the physical world and not just in the context of one subject[4]. Subject integrationhas been shown to increase student interest and test scores and we are hoping for the sameoutcome for this course[3].MethodsI. Development of Course StandardsSince this a new Georgia Virtual School class

Conference Session

Mathematics Division Technical Session 2

Collection

2013 ASEE Annual Conference & Exposition

Authors

Zohra Manseur, Oswego State University College

Tagged Divisions

Mathematics

, called metrons, is discussedin 8 and an extensive textbook treatment of units in mathematics is given in 9.As an example, consider a type of vector commonly used to describe the position and orientation Page 23.436.2of an object in 3-dimensional space. The vector consists of 3 coordinates x, y, and z with unitsof distance, and 3 orientation angles , , and  which are unitless values typically expressed inradians or degrees. The derivative of such a vector is itself non-uniform with units ofdistance/time combined with units of 1/time. The Euclidian norm of these vectors does not exist.Consequently any process that tends to minimize or maximize

Conference Session

Mathematics Division Technical Session 3

Collection

2013 ASEE Annual Conference & Exposition

Authors

Ryan Boyd Cartwright, General Electric; Autar Kaw, University of South Florida; Ali Yalcin, University of South Florida

Tagged Divisions

Mathematics

majors and these include: 1. “cramsorption learning”, where students listen to professors lecturing and then regurgitate the formulas to solve problems in a test, 2. concepts that are not learned through experience but by sitting in a lecture hall, 3. lower grades because of hard courses and hence not qualifying to enter the engineering major, 4. entry level salaries in engineering being lower than other majors such as business, and 5. coursework has a higher difficultly level compared to other majors.So, coupled with the above reasons for dropping out or switching majors and having a small poolof potential students to begin with, it is imperative that state universities increase their retentionrate for greater use

Conference Session

Mathematics Division Technical Session 4

Collection

2013 ASEE Annual Conference & Exposition

Authors

Jennifer Vandenbussche, Southern Polytechnic State University; William George Griffiths IV, Southern Polytechnic State University; Christina R Scherrer, Southern Polytechnic State University

Tagged Divisions

Mathematics

professional programs.A large majority of students major in STEM (science, technology, engineering, andmathematics) fields. Table 1: Self-reported demographics for engineering and engineering technology majors. (n=610) Course Lower level courses 29.6% College Algebra 13.8% Precalculus 10.4% Probability and Statistics 5.4% Intermediate level courses 69.9% Calculus I 21.8

Conference Session

Mathematics Division Technical Session 4

Collection

2013 ASEE Annual Conference & Exposition

Authors

Jennifer Vandenbussche, Southern Polytechnic State University

Tagged Divisions

Mathematics

engineering students.In this paper, the author describes an approach to early remediation in prerequisite material in aCalculus I course at a polytechnic institution. Preliminary results are presented regarding thesuccess of this approach, including a comparison of course grades to comparable groups,student feedback, and instructor observations.IntroductionSuccess in introductory mathematics courses (College Algebra, Precalculus, Calculus I, andCalculus II) is essential to success in engineering disciplines5. It is also widely acknowledgedthat more graduates in engineering and related fields are needed. For example, the Obamaadministration has announced a goal of increasing the number of students who receiveundergraduate degrees in STEM fields by 1

Conference Session

Mathematics Division Technical Session 3

Collection

2013 ASEE Annual Conference & Exposition

Authors

Michael R. Allen, Department of Mathematics; Dale A. Wilson, Tennessee Technological University

Tagged Divisions

Mathematics

Mechanical Engineering. While a student, again, he worked on the Formula SAE team and assisted them in designing and building a half scale Formula 1 race car using a 610 cc motorcycle engine.Dr. Dale A. Wilson, Tennessee Technological University Page 23.882.1 c American Society for Engineering Education, 2013 Making Mathematics Relevant to Engineering Students Abstract: In 2004, the author, an Associate Professor of Mathematics and a truly nontradi-tional student, started an adventure by going back to school and majoring in Mechanical Engineer-ing. The author, along with his advisor and co

Conference Session

Mathematics Division Technical Session 4

Collection

2013 ASEE Annual Conference & Exposition

Authors

Murray Teitell, DeVry University, Long Beach; William S. Sullivan, DeVry University, Long Beach

Tagged Divisions

Mathematics

success,preparedness, and overall achievement of the outcomes of their degree program.Introduction Metrics are used to make measurements about performance in order to evaluate andcompare.1 They are widely used in sports to compare the performance of athletes in a game (e.g.batting averages and slugging average).2 Likewise, Metrics are used to compare the performanceof a task. 3 Software metrics are applied to measure the efficiency of the software/algorithm bymeasuring parameters such as speed and storage use.4, 5 A simple metric can measure how long ittakes to perform a task in actual time or man-hours (quantity), the number of resources required(quantity) and the quality of the outcome. A metric therefore usually measures quantity and

Conference Session

Mathematics Division Technical Session 2

Collection

2013 ASEE Annual Conference & Exposition

Authors

Shirley B. Pomeranz, University of Tulsa

Tagged Divisions

Mathematics

Conference Session

Mathematics Division Technical Session 4

Collection

2013 ASEE Annual Conference & Exposition

Authors

Hassan Moore, University of Alabama, Birmingham

Tagged Divisions

Mathematics

at the University of Alabama at Birmingham, co-authoring the textbook used in the course. As a National Director with the Mathematics Division of ASEE, he works tirelessly to grow and develop the STEM workforce in the Cen- tral Alabama area. Dr. Moore teaches (1) Engineering Mathematics and (2) Engineering Computation using MATLAB at UAB. Work Background / Experience: He interned at UNC/Chapel Hill, Argonne National Laboratory (Atomic Physics Division), and Entergy Corporation in Transmission and Distribution, and then Standards. He then began serving as a high school physics teacher for three (3) years where his students would inspire him to continue his education. Upon completing his doctoral studies, Dr

Conference Session

Mathematics Division Technical Session 4

Collection

2013 ASEE Annual Conference & Exposition

Authors

Kendrick T. Aung, Lamar University; Ryan Underdown, Lamar University; Qin Qian, Lamar University

Tagged Divisions

Mathematics

/2003 – 05/2003), University of Minnesota, Department of Geology and Geophysics • Research/Teaching Assistant (07/1998 – 02/2000), Nanjing University, Department of Earth Science, China • Construction Engineer and Geotechnical En- gineer (06/1994 – 06/1998) Nanjing Construction Company, China PUBLICATIONS Book Chapter Sediment pollution, Handbook of Hydrology, 2012 Journal paper 1. Qian, Q., Voller, V. and Stefan, H., 2010, Can the ”dispersion tensor model” for solute exchange in the sediment bed of a stream or lake be simplified? Advances in Water Resources 33 (2010) 1542–1550. DOI:10.1016/j.advwatres.2010.09.001 2. Qian, Q., Voller, V. and Stefan, H., 2009, Mod- eling of vertical solute dispersion in a sediment