Conference Session

Improving the Mathematical Preparation of Students

Collection

2006 Annual Conference & Exposition

Authors

Mark Inlow, Rose-Hulman Institute of Technology

Tagged Divisions

Mathematics

. Time Series Plot of Temperature vs. Days into the Year 80 Temperature (degrees Fahrenheit) 70 60 50 40 30 20 10 0 1 18 36 54 72 90 108 126 144 162 180 Days into the YearAlthough there is a trend in

Conference Session

Use of Technology in Teaching Mathematics

Collection

2006 Annual Conference & Exposition

Authors

Paul Wlodkowski, Maine Maritime Academy

Tagged Divisions

Mathematics

case accounts for the viscous resistance of afluid, which is proportional to the projectile’s velocity as shown below. dv F0 + F (v) = m ⋅ (1) dtwhere F0 is any constant force independent of the velocity, and F(v) is a velocitydependent force which is obtained empirically. Typically, it is expressed by thefollowing equation, F (v) = −v ⋅ (c1 + c 2 ⋅ v ) (2)where c1 and c2 are linear and quadratic drag coefficients, respectively, and which dependof the size and shape of the projectile. If a simple

Conference Session

Use of Technology in Teaching Mathematics

Collection

2006 Annual Conference & Exposition

Authors

Melinda Z. Kalainoff, U.S. Military Academy; Dawn E. Riegner, U.S. Military Academy; Matthew Deloia, U.S. Military Academy; Russ Lachance, U.S. Military Academy; Andrew Biaglow, U.S. Military Academy

Tagged Divisions

Mathematics

other words, [+] = [-]. The total molar concentration of acid is F,which must equal the sum of [HA(aq)] and [A-(aq)]. The Mathematica implementation of the system of equations as well as thesolution are shown in Figure 1. Note that we solve the system symbolically first, andthen “numericize” the solution for the special cases we are interested in. In practicalterms this is crucial. Students do not need to spend any time determining initial guessesfor numerical solutions. Nor do they need to simplify the algebraic expressions prior tosolution by making physical or chemical approximations. Page 11.589.4 Figure 1. Mathematica 5.2

Conference Session

Project and Model-Based Mathematics

Collection

2007 Annual Conference & Exposition

Authors

John Schmeelk, Virginia Commonwealth University; Jean Hodges, Virginia Commonwealth University Qatar

Tagged Divisions

Mathematics

principles. The authors demonstrate and illustrate theprocedures for several of these course topics, beginning with sequences and series.Sequences, Series, and Fibonacci NumbersThe Fibonacci sequence is presented as the first sequence since it enjoys such a rich history. Theprofessor and students consider Fibonacci as an Italian mathematician, and the students researchhim on the web. The topic is introduced by showing the Leaning Tower of Pisa to place themathematician in an Italian setting (see Fig. 1 below). This is followed by a discussion of theFibonacci sequence (1, 1, 2, 3, 5, 8, 13, 55, …) and illustrated with past students’ projects on thetopic. One past project is posters used to motivate computing and working problems on the whiteboard

Conference Session

Project and Model-Based Mathematics

Collection

2007 Annual Conference & Exposition

Authors

Sharlene Katz, California State University-Northridge; Bella Klass-Tsirulnikov, Sami Shamoon College of Engineering (formerly Negev Academic College of

Tagged Divisions

Mathematics

, specializing in topological vector spaces, as well as in the research on mathematics education at different levels. Page 12.1557.1© American Society for Engineering Education, 2007 Using Neural Networks to Motivate the Teaching of Matrix Algebra for K-12 and College Engineering StudentsAbstractImproving the retention of engineering students continues to be a topic of interest to engineeringeducators. Reference 1 indicates that seven sessions at the 2006 ASEE Annual Conference weredevoted to this subject. In order to be successful in an engineering program, it is recognized thatstudents must have a solid

Conference Session

Applied Mathematics

Collection

2007 Annual Conference & Exposition

Authors

S.K. Sen, Florida Institute of Technology; Gholam Ali Shaykhian, NASA

Tagged Divisions

Mathematics

generators, and TSPs are specially stressed for a better appreciation.1. IntroductionA given number cannot be just termed random unless we check/test the sequence which itbelongs to. This is unlike the transcendental number r 3.14159265358 or the algebraicnumber l ? (1 - 5 ) / 2 1.61803398874989 (golden ratio) or the Hilbert number 2 22.66514414269023. The word random implies that the predictability (probability of correctprediction) is low and never 100%. As long as there is a finite number of outcomes, thepredictability is never zero. In the case of tossing a fair coin, the predictability is 50% while that 2of rolling a six-faced fair die, it is 16 %. However, an approximate global prediction with

Conference Session

Applied Mathematics

Collection

2007 Annual Conference & Exposition

Authors

Josue Njock-Libii, Indiana University-Purdue University-Fort Wayne

Tagged Divisions

Mathematics

solutionapproximates the actual motion.1. IntroductionThe motion of a pendulum is studied in the first college physics course; and its governingdifferential equation is amongst the first ones that are solved in an introductory course onordinary differential equations. This equation is encountered again and again in coursessuch as dynamics, controls, vibrations, and acoustics. In all these cases, however, it islinearized by assuming that the amplitude of oscillation is small. As a consequence,students do not see what happens to the oscillation of a pendulum when the amplitudesare large and the restoring force becomes nonlinear. More importantly, they do not knowthe limits of applicability of the linearized solution they have studied.In this article, we present

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

Approaches to Mathematics Curriculum to Include Projects and Technologies

Collection

2014 ASEE Annual Conference & Exposition

Authors

Charles C.Y. Lam, California State University, Bakersfield; Melissa Danforth, California State University, Bakersfield; Ronald Hughes, CSUB STEM Affinity Group

Tagged Divisions

Mathematics

consists of 4 credit hours oflecture, and a 1 credit hour student activity session per week for 10 weeks. The completeCalculus course sequence consists of 4 quarter courses. Class size is normally capped at35. The department used to offer a more comprehensive and longer student activitysession per week until it was removed in 2008 due to budgetary reasons. However, noassessment was carried out to measure the effectiveness of the student activity session inthe past. The Engineering Calculus course is designed such that there is no compromise inthe rigorous treatment of Calculus, while addressing the specific needs of engineeringmajors. The new course includes 4 credit hours of lecture and a 2.5-hour student activitysession per week. The

Conference Session

Approaches to Mathematics Curriculum to Include Projects and Technologies

Collection

2014 ASEE Annual Conference & Exposition

Authors

Jeffrey Lloyd Hieb, University of Louisville; Patricia A Ralston, University of Louisville

Tagged Divisions

Mathematics

the department’s mission is to improve retention of first yearengineering students. Research has shown that for engineering students success in the firstcollege mathematics course is critical for retention.1–3 Therefore, a major retention effort by thedepartment has been to improve the teaching and learning in its engineering mathematics coursesusing educational technologies. Many different sections and courses are taught every semesterby a combination of tenure/tenure track and term faculty. The department has worked to see thatthe use of adopted educational technologies is reasonably consistent across courses and faculty,and that the use of the technologies persists beyond any initial pilot phase. Many factors affectedthe selection and

Conference Session

The Use of Games and Unique Textbooks in Mathematics Education

Collection

2014 ASEE Annual Conference & Exposition

Authors

Erin Shaw, University of Southern California; Jihie Kim, University of Southern California; Zinan Xing, University of Southern California

Tagged Divisions

Mathematics

posttest.Pretest and Posttest DifferencesData from pretests and posttests were analyzed and are shown in Table 1. For the Maze gamecomparison, after unmatched samples were removed, the final sample size was 31 pairs. For theShooter game, the final sample size was 12 pairs. We removed a pair of scores that went from7.9 on the pretest to 1.0 on the posttest, which we agreed was done deliberately.Table 1: Mean score comparisons for Maze and Shooter tests. Game Mean Score Percent Correct T-Test (Sample Size) Pretest Posttest Significance (Max Score) Pretest Posttest Value (std

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

Using Applications and Projects in Teaching Mathematics

Collection

2012 ASEE Annual Conference & Exposition

Authors

Gunter Bischof, Joanneum University of Applied Sciences, Graz, Austria; Christian Steinmann, Joanneum University of Applied Sciences, Graz, Austria

Tagged Divisions

Mathematics

25.642.3equations is obtained when considering an incompressible flow of a Newtonian fluid. Liquidsare often regarded as incompressible because they require such high pressure to compressthem appreciably. However, it is quite legitimate in many applications to consider even agaseous medium such as the atmosphere to be incompressible, in which case theincompressible flow assumption typically holds well at low Mach numbers up to about 0.3.The behavior of a viscous incompressible fluid is governed by the simplified Navier-Stokesequation, which can be written as ∂v 1 + ( v ⋅ ∇) v = − ∇P +ν ∆v , ∂t ρand by the continuity equation

Conference Session

Techniques in Improving Mathematics Education in STEM Curricula

Collection

2012 ASEE Annual Conference & Exposition

Authors

Erin Shaw, University of Southern California; Zachary Boehm, University of Southern California; Hussain Badruddin Penwala, University of Southern California; Jihie Kim, University of Southern California

Tagged Divisions

Mathematics

10 No time 6 8 4 One 1-5 Hours 6 2 Two 4 5-10 Hours 0 Three/Four 2 10-15 Hours 0 Games Texting Phone Page 25.661.4 Figure 2a,b. Types of devices owned by students and number of hours spent

Conference Session

Using Computers, Software, and Writing to Improve Mathematical Understanding

Collection

2012 ASEE Annual Conference & Exposition

Authors

N. Jean Hodges, Virginia Commonwealth University, Qatar

Tagged Divisions

Mathematics

to do so.One teaching strategy shown by researchers since the 1960s and 1970s to be an effective learningand thinking tool is writing. Writing enables the writer to capture otherwise random thoughts byplacing them on a writing surface where they become concrete and thus more readily examined andmanipulated. Consequently, writing should be an effective tool for enabling math students to retainthe mathematical principles being developed in the classroom as well as for aiding them to improvetheir critical thinking abilities needed for applying their mathematical understandings to problems ofthe modern world.By incorporating writing that emphasizes critical thinking into the math classroom, this study seeksan answer to two questions: (1) how can

Conference Session

Techniques in Improving Mathematics Education in STEM Curricula

Collection

2012 ASEE Annual Conference & Exposition

Authors

Yonghui Wang, Prairie View A&M University; Jian-ao Lian, Prairie View A&M University; Yonggao Yang, Prairie View A&M University

Tagged Divisions

Mathematics

Algebra and Calculus I. For each course a certain amountof time will be set aside for students to reinforce the concepts they just learned during the normallecture time. The learning modules are designed to be user friendly in order to attract students’attention to math learning instead of texting in classrooms. The benefits of this pedagogyinclude: 1) interactive modules make students actively involved in the math learning process; 2)the unlimited randomly generated questions and examples give students more opportunities onpracticing and reinforcing the concepts they just learned; 3) the quick answer checking functionhelps students build confidence by immediately identifying their learning progress; and 4) themobility of the modules ensures that

Conference Session

Innovative Instructional Strategies and Curricula

Collection

2010 Annual Conference & Exposition

Authors

Jayathi Raghavan, Embry-Riddle Aeronautical University, Daytona Beach; Hong Liu, Embry-Riddle Aeronautical University, Daytona Beach

Tagged Divisions

Mathematics

undergraduate program in Computational Mathematics hasbeen recently approved. The trend seems to be that most of the students wishing to pursue thedegree program are engineering students interested in pursuing a dual major. The challengesfaced by the department are 1) to offer these dual majors an integrated curriculum that wouldtake advantage of their engineering background and 2) to offer a curriculum which will enablethem to complete the degree within one additional year without compromising the integrity ofthe program. In this paper, the authors discuss in detail their Computational Mathematicscurriculum and the modification of the curriculum for the dual majors.IntroductionComputational Mathematics is a multidisciplinary field that applies the

Conference Session

Computers and Software in Teaching Mathematics

Collection

2010 Annual Conference & Exposition

Authors

Bertram Pariser, Technical Career Institute, Inc.; Cyrus Meherji, Technical Career Institute, Inc.

Tagged Divisions

Mathematics

8342 342.75 1931 78 20.67 1967 905 35.00 2003 10454 417.25 Page 15.1241.5Figure 1 Data of the Dow Jones Averages and the Price of Gold from 1896 to 2008Figure 2 is a graph of the Dow Jones Industrial Average and the Price of Gold from 1896 to2008 The price of gold increase from $37.40 to $589.50 an increase of 970% while the DowJones Industrial Average increased $838.92 to $963.99 an increase of 15%. 1970 838.92 37.40 1971 890.20 43.55 1972 1020.02 65.00 1973 850.86 111.75 1974 616.24 193.00 1975 852.41 140.75 1976 1004.65 134.63 1977 831.17 165.15 1978 805.01 226.40 1979 838.74

Conference Session

Integrating Mathematics, Science, and Engineering

Collection

2010 Annual Conference & Exposition

Authors

Elton Graves, Rose-Hulman Institute of Technology

Tagged Divisions

Mathematics

∞ −n π t n2π 2t Ux, t = ∑ Ane 9 C n sin nπx  = 6 ∑ Bne− 9 sin nπx  6 n=1 n=1 Setting t = 0 and Ux, t = 6x − x 2 we arrive at Page 15.1263.3 ∞ n2π 20 6x − x 2

Conference Session

Computers and Software in Teaching Mathematics

Collection

2010 Annual Conference & Exposition

Authors

Cynthia Young, University of Central Florida; Michael Georgiopoulos, University of Central Florida; Tace Crouse, University of Central Florida; Alvaro Islas, University of Central Florida; Scott Hagen, University of Central Florida; Cherie Geiger, University of Central Florida; Melissa Dagley-Falls, University of Central Florida; Patricia Ramsey, University of Central Florida; Patrice Lancey, University of Central Florida

Tagged Divisions

Mathematics

. Page 15.548.2© American Society for Engineering Education, 2010   EXCEL in Mathematics: Applications of Calculus  Abstract Nationally only 40% of the incoming freshmen STEM majors are successful in earning aSTEM degree [1]. The University of Central Florida (UCF) EXCEL program is an NSF fundedSTEP (Science, Technology, Engineering and Mathematics Talent Expansion Program) whosegoal is to increase the number of UCF STEM graduates. One of the activities that EXCEL hasidentified as essential in retaining students in science and engineering disciplines is thedevelopment and teaching of special courses at the freshman level, called