Conference Session

Bridging and Freshman Programs

Collection

2008 Annual Conference & Exposition

Authors

Wendy James, Oklahoma State University; Karen High, Oklahoma State University

Tagged Divisions

Mathematics

the following questions: 1. What aspects of freshman-level mathematics did the authors identify as problematic in their courses? 2. What did the paper position as the underlying problem? 3. What interventions or changes served as the impetus for publishing? 4. What was studied? 5. What did the paper suggest as direction for future research? 6. What sources of literature did the paper reference? 7. To what degree was the paper and study situated in literature?The greatest goal while analyzing the papers was to list any problematic areas authors mentionedabout freshman-level mathematics. The goal of the remaining six questions was to explore andreport the assumptions, actions, and future vision of the authors for

Conference Session

Innovative Instructional Strategies

Collection

2008 Annual Conference & Exposition

Authors

Taskin Padir, Lake Superior State University; Kimberly O. Muller, Lake Superior State University; Collette Coullard, Lake Superior State University

Tagged Divisions

Mathematics

teaching. It is a prerequisite for many othercourses such as vibrations, fluid mechanics, advanced calculus, mathematical modeling, networkanalysis and electromagnetics.A total of 99 students have been enrolled in the course since 2005 fall semester. An analysis ofthe student demographics showed that 26 mechanical engineering, 24 electrical engineering, 18computer engineering, 11 mathematics secondary education, 8 mathematics, 5 geology, 3computer science, 3 chemistry and 1 sociology student took the course. Moreover, the averageclass size was 16. Figure 1 illustrates the distribution of students enrolled in MATH 310according to their majors.It is noted that a substantial number of students majoring in programs outside engineering andmathematics

Conference Session

Bridging and Freshman Programs

Collection

2008 Annual Conference & Exposition

Authors

Christopher Papadopoulos; John Reisel, University of Wisconsin - Milwaukee

Tagged Divisions

Mathematics

attempting to learn more about the efficacy of summer bridge programs, we discovered ageneral dearth of relevant performance data in the literature. We identified and examined 12engineering summer bridge programs that serve new freshmen whose math placement is at orbelow pre-calculus, and for which meaningful student performance data has been published. Thedata that we compiled suggests that bridge programs are very successful in helping students toadvance in math placement by at least one level. Less clear is whether bridge studentsoutperform control group students in the years beyond the bridge program (as measured byretention, graduation, and grades), but some evidence suggests that this is the case.1. IntroductionNew freshmen in many engineering

Conference Session

Engineering and Math Potpouri

Collection

2008 Annual Conference & Exposition

Authors

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

Tagged Divisions

Mathematics

AC 2008-1657: VIDEO LECTURE ON THE PYTHAGOREAN THEORYBertram Pariser, Technical Career Institute, Inc.Cyrus Meherji, Technical Career Institute, Inc. Page 13.1383.1© American Society for Engineering Education, 2008 Video Lecture on PYTHAGOREAN THEORYAbstractPythagoras derived the famous equation a2 +b2 =c2. This discovery enabled the Greeks tobuild the Acropolis and the Parthenon. This equation is probably the most famous equation inmathematics. There are hundreds of proofs to the Pythagorean Theorem in mathematical literature.My derivation of "A GEOMETRICAL PROOF OF PYTHAGORAS’ THEOREM" 1 is difficult for ourstudents to understand. Students, who use the video

Conference Session

Bridging and Freshman Programs

Collection

2008 Annual Conference & Exposition

Authors

Phillip Mlsna, Northern Arizona University; Janet McShane, Northern Arizona University; Jennifer Maynard, Northern Arizona University; Maya Lanzetta, Northern Arizona University; Chester Ismay, Northern Arizona University; Sarah Brown, Northern Arizona University

Tagged Divisions

Mathematics

– Introduction to Engineering Design, andCENE 150 – Introduction to Environmental Engineering. In each course, a pre-test wasadministered during the first two weeks of the semester to all students in the course. The pre-testcovered the mathematical skills that the engineering faculty judged most useful for success in theengineering courses. These were: (1) fractions, (2) unit conversions, (3) graphing of basicpolynomial functions, (4) systems of equations, (5) exponentials and logarithms, and (6)estimation and problem solving. Based on the student’s performance on the questions coveringthese topics, they were deemed to have either satisfactory knowledge in the area or a need forimprovement.Students and their instructors were given notification of the

Conference Session

The Use of Computers in Teaching Mathematics

Collection

2008 Annual Conference & Exposition

Authors

Janet Callahan, Boise State University; Seung Youn Chyung, Boise State University; Joanna Guild, Boise State University; William Clement, Boise State University; Joe Guarino, Boise State University; Doug Bullock, Boise State University; Cheryl Schrader, Boise State University

Tagged Divisions

Mathematics

. Presently, e-learning is already deeply integrated into schoolcurricula to motivate students and facilitate learning. Numerous studies have revealed thebenefits of implementing self-paced e-learning strategies in traditional curricula for improvingcritical learning variables such as motivation, self-efficacy, goal-orientation, satisfaction, andpersistence.1 Especially, there has been a fair amount of acceptance and practice among thecommunity of science and engineering education community that traditional teaching can begreatly benefited by incorporating e-learning strategies.2-6 Leading academic organizations suchas the Sloan Consortium also advocate that incorporating online learning strategies into theengineering curricula can augment some of

Conference Session

Innovative Instructional Strategies

Collection

2008 Annual Conference & Exposition

Authors

Alejandra J. Magana; Sean Brophy, Purdue University; Timothy Newby, Purdue University

Tagged Divisions

Mathematics

(AmericanAssociation for the Advancement of Science [AAAS] 2006) 1 . Scaling related concepts aredirectly applied to the study of phenomena in the micro, nano, and atomic level. As new tools,techniques, and instrumentations that allow study of phenomena in the micro and nano world aredeveloped, new and complex technologies rise resulting in new fields of science and technology.As a consequence, new global markets emerge as well as the need of a workforce to meet them.Engineering is one of these disciplines that requires a strong spatial ability involving scale, aswell as the ability to reason proportionally when using scale models. In addition, advancingnanosciences is opening new opportunities for engineers to pursue opportunities for

Conference Session

Innovative Instructional Strategies

Collection

2008 Annual Conference & Exposition

Authors

Sabina Jeschke, University of Stuttgart; Akiko Kato, Technische Universitaet Berlin; Olivier Pfeiffer, Technische Universitaet Berlin; Erhard Zorn, Technische Universitaet Berlin

Tagged Divisions

Mathematics

allowing beginners to use the often unused period between“Abitur” (German high-school graduation) and beginning of studies in the winter term forattending the mathematics modules of the first semester (Linear Algebra and Calculus I) beforethe official beginning of studies. With this project, students have the in-depth mathematicalknowledge at their disposal considerably earlier. Students of engineering can reduce the durationof their education in mathematics by one semester by preponing the mathematics classes ofhigher semesters as well.1. MotivationMathematics is one of the most important foundations for engineering. From the first semesterson a sound knowledge in mathematics is necessary for being successful in the basic subjects ofengineering

Conference Session

Innovative Instructional Strategies

Collection

2008 Annual Conference & Exposition

Authors

Martha Allen, Georgia College & State University; Amy Kelley, Georgia College & State University

Tagged Divisions

Mathematics

engineering majors,mathematics majors, chemistry majors, and computer science majors. Engineering, chemistry,and computer science majors have an inherent need for an understanding of the practicalapplications of the theory in a particular discipline. In fact, many of the ABET program criteriaspecifically list the knowledge and application of linear algebra as a necessary skill.1 In additionto applications, the theory and mathematical reasoning skills developed in an introductory linearalgebra course will be invaluable to math majors as they progress to more proof oriented contentcourses.At Georgia College & State University, there are approximately 110 mathematics majors.Roughly half of these majors are enrolled in the pre-engineering program

Conference Session

Integrating Math, Science and Engineering

Collection

2008 Annual Conference & Exposition

Authors

Hong Liu, Embry-Riddle Aeronautical University, Daytona Beach

Tagged Divisions

Mathematics

asking the honors program students whotake that course to learn some extra content and do some extra work. With either solution the actof mixing a significant number of honors students with non-honors students usually results in abi-modal distribution based on the students’ level of academic preparation. To teach such aclass, instructors often face more challenges balancing the content so that the strong honorsstudents can be adequately motivated without intimidating the other relatively weaker students.This paper reports on the first year’s experience offering an honors course option within anordinary mathematics course that had a mix of both honors and non-honors engineering students.1. IntroductionTypical calculus or differential equation

Conference Session

The Use of Computers in Teaching Mathematics

Collection

2008 Annual Conference & Exposition

Authors

Jayathi Raghavan, Embry-Riddle Aeronautical University, Daytona Beach; Leslie Sena, Bethune Cookman College; Hong Liu, Embry-Riddle Aeronautical University, Daytona Beach; David Bethelmy, Bethune Cookman College

Tagged Divisions

Mathematics

modules3,4,5,6,7,8,9,10,11. The authors observed that many students enrolled in entry-levelengineering and computer science courses tend to plug in data without considering the purposeof the analysis and demonstrate little ability to extend mathematical concepts beyond analgorithmic level. These observations motivated the authors to form an interdisciplinary team ofuniversity faculty to discuss the development of instructional mathematics and computer sciencemodules that would enhance students’ ability to apply complex mathematical reasoning whenpresented with novel real world problems. The authors met once a week for six months inroundtable discussions. In these discussions the authors identified the following challengesteachers face when teaching mathematics : 1

Conference Session

Engineering and Math Potpouri

Collection

2008 Annual Conference & Exposition

Authors

Jeffrey Fong, National Institute of Standards and Technology; James Filliben, National Institute of Standards and Technology; Alan Heckert, National Institute of Standards and Technology; Roland deWit, National Institute of Standards and Technology

Tagged Divisions

Mathematics

design. Two examples of this FEM-specific approach are included: (1) The free vibration of an isotropic elastic cantilever beam witha known theoretical solution, and (2) The calculation of the first resonance frequency of theelastic bending of a single-crystal silicon cantilever beam without known solutions. In eachexample, the FEM-simulated result is accompanied by a prediction 95 % confidence interval.Significance and limitations of this metrological approach to advancing FEM as a precisionsimulation tool for improving engineering design appear at the end of this paper.(*) Contribution of the National Institute of Standards & Technology. Not subject to copyright.Introduction A fundamental mathematical modeling and computational tool

Conference Session

The Use of Computers in Teaching Mathematics

Collection

2008 Annual Conference & Exposition

Authors

Jenna Carpenter, Louisiana Tech University; Brian Camp, Louisiana Tech University

Tagged Divisions

Mathematics

at Louisiana Tech University has historically spent approximately $20,000 each year onstudent paper graders to grade homework assignments. The use of WeBWorK would, thereforefree up most of these funds to be used in other, hopefully more effective, ways to improvestudent retention and success in mathematics. For the 2007-2008 academic year, for example,these funds are being used to support Supplemental Instruction for the calculus courses. Thus,the goals of this effort were to 1) increase student mastery of course content, 2) increaseindividual student accountability on out-of-class assignments, and 3) more effectively utilize theprogram budget to enhance student retention and success in mathematics.WeBWorK1 is a web-based (versus software

Conference Session

Integrating Math, Science and Engineering

Collection

2008 Annual Conference & Exposition

Authors

Gregg Janowski, University of Alabama at Birmingham; Melinda Lalor, University of Alabama at Birmingham; Hassan Moore, University of Alabama at Birmingham

Tagged Divisions

Mathematics

process, instructors of all courses with CalculusIII or Differential Equations as direct or indirect prerequisites were interviewed to (1) determinetheir views of the current preparation of students, (2) identify the mathematics skills that wereexpected of students in their courses, and (3) discuss the possibility of introducing mathematicstopics using engineering problems and incorporating both problem-based and active learningtechniques. Faculty were very satisfied with the capabilities of the better students to carry outsymbolic manipulations of common problems, particularly if the student had recently completedupper-level mathematics courses. However, most students were very poor at applying themathematics in their engineering courses. There

Conference Session

Bridging and Freshman Programs

Collection

2008 Annual Conference & Exposition

Authors

Dale Buechler, University of Wisconsin-Platteville; Christa James-Byrnes, University of Wisconsin - Barboo/Sauk County

Tagged Divisions

Mathematics

the needs of underrepresented groups.University of Wisconsin System ModelThe University of Wisconsin system is made up of thirteen two-year schools (UW-Colleges) andthirteen four-year schools (See Figure 1). Of the thirteen four-year schools, only three havemultiple engineering programs. The University of Wisconsin-Madison (Madison) and theUniversity of Wisconsin-Milwaukee (Milwaukee) have both undergraduate and graduateprograms in engineering. The University of Wisconsin-Platteville (Platteville) located in thesouthwest corner of the state, is primarily focused on undergraduate engineering education.After receiving IRB approval, data was requested from both the UW-Colleges and each of theengineering schools with all person information

Conference Session

Integrating Math, Science and Engineering

Collection

2008 Annual Conference & Exposition

Authors

Josue Njock-Libii

Tagged Divisions

Mathematics

engineering courses.We consider the ordinary differential equation given byx - y n2 x ? 0,%% (1)with the following initial conditionsx (t ? 0) ? x0 (2)x%(t ? 0) ? v0where x is a function of time, the dots indicate derivatives of x with respect to time, andy n2 is a quantity that is independent of time. Page 13.1364.2 This equation has been used to model a variety of physical phenomena. For example, itcan represent the motion of a mass, m, suspended onto a linear spring of stiffness k, whenlosses

Conference Session

Engineering and Math Potpouri

Collection

2008 Annual Conference & Exposition

Authors

John Schmeelk, Virginia Commonwealth University; Jean Hodges, VCU\Qatar Campus

Tagged Divisions

Mathematics

were very much impressed by the past projects and wantedto compete with each other to find new projects that illustrate mathematical principles. Theauthors demonstrate and illustrate the procedures for several of these course topics, beginningwith sequences and series.Sequences, Series, and Fibonacci NumbersTo motivate students’ interest, the instructor then begins with discussing mathematics in theMuslim Community, since most of the students are Muslims and VCUQ exists in a Muslimcountry. The first (Fig. 1 below) indicates several Muslim achievements such as inventingAlgebra and the notion of zero, etc. Muhammad ibn Musa al-Khwarzimi wrote the famous Kitabal-Jabr wa al-Mugabala, the first book on algebra 6.The Fibonacci sequence is presented

Conference Session

Engineering and Math Potpouri

Collection

2008 Annual Conference & Exposition

Authors

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

Tagged Divisions

Mathematics

changing based on thetools/power of tools  often innovative  available to mankind. We discuss here briefly howthe computing scenes go on evolving based on the availability and usage of newer and newercomputing tools leading to early twenty-first century computing scene due to electronicsupercomputing devices.1 IntroductionComputing has been the necessity since time immemorial, even before the dawn of civilization.It must have come to exist when a human being realized the concept of his/herpossession/property such as children, food items, and places for dwelling. Computing alongwith counting started evolving since then. We present here the pre-computer agemethodology/psychology of computing based on the then available tools [1] along with