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

2009 Annual Conference & Exposition

Authors

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

Tagged Divisions

Mathematics

Page 14.865.4attempted if it meant that depth were to be sacrificed.Another critical component in the design of the course was the textbook. Criteria for thetextbook include (1) logical flow with the design of the course, (2) easy for advanced freshmenand sophomore students to read and understand, (3) useful as a reference text for later use, (4)contains the differential equations and calculus topics identified as critical, and (5) includes clearexamples for students to follow. In an ideal world, the textbook would also have an associatedhomework delivery system to provide the practice medium and immediate feedback necessaryfor basic competence and concrete understanding on which to build abstract thought.Thus, the professors gave serious

Conference Session

Engineering and Mathematics Potpourri

Collection

2009 Annual Conference & Exposition

Authors

Murray Teitell, DeVry University, Long Beach

Tagged Divisions

Mathematics

interest group (see Table 1 below). The second step was to apply a fitnessfunction to the system and ascertain the fitness of each plan. The students decided on the general form of the fitness function which was:(1) limit the rate of increase in energy consumption, (2) limit the rate of decrease in energy production, (3) minimize the unit energy cost, (4) maximize the renewable sources, (5) maximize the domestic sources, (6) minimize the air/water/soil pollution including CO2, and (7) maximize the efficiency. These fitnesses were incorporated into matrices and each normalized as a percentage of 1. The third step was to apply the genetic operations. The students implemented the evolutionarychange functions as:Crossover9,10

Conference Session

Integrating Math, Science, and Engineering

Collection

2009 Annual Conference & Exposition

Authors

Paul Kauffmann, East Carolina University; Michael Bosse, East Carolina University

Tagged Divisions

Mathematics

universities discussed below wereidentified based on two criteria. First we started with universities in the ASEE listings of topvolumes in total engineering graduates, female graduates, or minority graduates. Second,information on mathematics course sequences had to be available through search of their websites. In studying mathematics content in engineering programs, an obvious classificationscheme is to begin with the traditional calculus sequence. Using this as a starting point, based onthree or four credit sequences, a number of options are possible. Tables 1 and 2 providerepresentative examples of ten engineering programs which have three and four credit calculussequences respectively.In interpreting the columns in these tables, engineering

Conference Session

Mathematics: Recruitment and Retention

Collection

2009 Annual Conference & Exposition

Authors

Michael Georgiopoulos, University of Central Florida; Cynthia Young, University of Central Florida; Cherie Geiger, University of Central Florida; Scott Hagen, University of Central Florida; Chris Parkinson, University of Central Florida; Alison Morrison-Shetlar, University of Central Florida; Tace Crouse, University of Central Florida; Paula Krist, University of Central Florida; Pat Lancey, University of Central Florida; Melissa Dagley-Falls, University of Central Florida; Pat Ramsey, University of Central Florida; Dahlia Forde, University of Central Florida; Anna Koufakou, University of Central Florida

Tagged Divisions

Mathematics

program that can be sustained at UCF, after the grant’scompletion, and disseminated at other educational institutions. This paper discusses EXCEL’sinfrastructure, the activities pursued to achieve its objectives, the results from these activities,and the lessons learned in the first three years of EXCEL’s operation.1. IntroductionIn the book Talking About Leaving, Why Undergraduates Leave the Sciences (see [1]) it is statedthat nationally 40 percent of undergraduate students leave engineering programs, 50 percentleave the physical and biological sciences and 60 percent leave mathematics. The losses aredisproportionately greater among women and students of color (also seen with the UCFnumbers). The following is a list of some reasons that

Conference Session

Computers and Software in Teaching Mathemathetics

Collection

2009 Annual Conference & Exposition

Authors

Ali Farahani, National University, San Diego

Tagged Divisions

Mathematics

loop. The next code snippet reports on whether Nis a prime number; it simply applies the definition of a prime number to N by looping through aset of integers less that N to see is N has a factor there. for i in [x+1 for x in range(N)]: if N % i==0 and (i!=1 and i!=N): return False return TrueOnce again the syntax and semantics are very intuitive and readily graspable by a computerscience student. In Python set membership can be examined by the command “in”. Students caneasily experiment with introductory set theory concepts using Python’s set object. Here is an

Conference Session

Mathematics: Recruitment and Retention

Collection

2009 Annual Conference & Exposition

Authors

Doug Bullock, Boise State University; Janet Callahan, Boise State University; Yuguang Ban, Boise State University; Alison Ahlgren, University of Illinois, Urbana-Champaign; Cheryl Schrader, Boise State University

Tagged Divisions

Mathematics

Systems and Control, both from University of Notre Dame. Page 14.1225.1© American Society for Engineering Education, 2009 The Implementation of an Online Mathematics Placement Exam and its Effects on Student Success in Precalculus and CalculusIntroductionEngineering education research on the impact of freshman engineering courses reveals a closeconnection between graduation rate and first semester GPA.1 The same research also explains theimportance of first-semester math placement, so as to provide students with the necessarybackground for success. For example, students at Purdue

Conference Session

Integrating Math, Science, and Engineering

Collection

2009 Annual Conference & Exposition

Authors

Eduardo Chappa, Texas A&M International University; Terutake Abe, Texas A&M International University; Fethi Belkhouche, Texas A&M International University; Rohitha Goonatilake, Texas A&M International University; Qingwen Ni, Texas A&M International University; Rafic Bachnak, Texas A&M International University

Tagged Divisions

Mathematics

wasexplained that the main consideration was not what the department could do at the time, but if facultyagreed that this was an important outcome for a program. If faculty agreed, then the department wouldfind a way to implement it, which includes redesigning courses, training faculty or adding supplies to acomputer lab.The adopted common outcomes were Outcome 1: Students will be able to communicate effectively in written and oral forms, work successfully in teams, and understand ethical responsibilities. Outcome 2: Students will be able to think critically and be prepared for life-long learning. Outcome 3: Students will be able to continue graduate studies in their current major or related

Conference Session

Bridging the Gap and Freshman Programs

Collection

2009 Annual Conference & Exposition

Authors

Seung Youn Chyung, Boise State University; Janet Callahan, Boise State University; Doug Bullock, Boise State University; Kendra Bridges, Boise State University; Joanna Guild, Boise State University; Cheryl Schrader, Boise State University

Tagged Divisions

Mathematics

. Page 14.711.1© American Society for Engineering Education, 2009 Improving Students' Learning in Precalculus with E-Learning Activities and through Analyses of Student Learning Styles and Motivational CharacteristicsAbstractDuring the spring semester of 2008, a quasi-experimental study with 138 students who wereenrolled in 4 sections of an undergraduate Precalculus class was conducted. The studyinvestigated (1) the effectiveness of using a systematically sequenced and managed, self-paced e-learning program, ALEKS, on academic performance of students with different learning styles,and (2) the relationship among the students’ dominant learning styles, motivationalcharacteristics, and overall performance

Conference Session

Integrating Math, Science, and Engineering

Collection

2009 Annual Conference & Exposition

Authors

Evelyn Brown, East Carolina University; Heather Ries, East Carolina University

Tagged Divisions

Mathematics

wereallowed to appeal their placement, and some students who had taken AP Calculus in high school Page 14.1214.6but did not do well on ALEKS were allowed to take Calculus. Not too far into the fall 2007semester, it became evident to the Precalculus instructors that some of the students who placedinto Precalculus did not have the mathematics background to succeed in that class. Althoughthere were good results from the students who placed into Calculus (see Figure 1), there were anumber of students who were unable to pass Precalculus. This led the EMC to believe that theremay need to be a second line established for ALEKS scores. Students who scored

Conference Session

Bridging the Gap and Freshman Programs

Collection

2009 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

students for their engineeringcourses. Before winter term 2008/09 we successfully offered this course for the third time. Thisyear we had no additional financial resources to offer very small classes. On the other hand, inthe week between this course and the final examinations a summer camp has been organizedwhere recitation lessons were voluntarily offered by teaching assistants.In this article, we are comparing the final examination results of Early Bird students and regularstudents. We are presenting the results of the Early Bird courses of the last three years. Theresults will be compared with the data of regular students who took the same written exams.1. Key Features of Early BirdAt the Berlin Institute of Technology we offer an intensive

Conference Session

Engineering and Mathematics Potpourri

Collection

2009 Annual Conference & Exposition

Authors

Athanasios Tsalatsanis, University of South Florida; Ali Yalcin, University of South Florida; Autar Kaw, University of South Florida

Tagged Divisions

Mathematics

approaches.Our preliminary results indicate that knowledge discovery methodologies can be successfullyused in predicting student performance. Based on the experiences gained from this work, specificfuture research directions and tasks to ensure a successful comprehensive implementation arediscussed.1. IntroductionCan we reliably predict the performance of a student in a particular course before he/she startsthe course? Or can we recommend a specific set of course materials to certain students toimprove their learning? What are the key factors that help answer these questions? Is it astudent’s past academic performance? Or is it their current work and/or class load? Or maybe itis their existing knowledge regarding the course material. More than likely it

Conference Session

Bridging the Gap and Freshman Programs

Collection

2009 Annual Conference & Exposition

Authors

Nelson Baker, Georgia Institute of Technology; Marion Usselman, Georgia Institute of Technology; Thomas Morley, Georgia Institute of Technology; Rick Clark, Georgia Institute of Technology

Tagged Divisions

Mathematics

movements have often promoted amath sequence in which the standard 8th grade math course is Algebra 1. If “on-grade-level”students are taking algebra in the 8th grade, then “advanced” and “gifted” students typically startthe course a year earlier, namely in 7th grade, and sometimes even earlier. By their senior year inhigh school, these students have exhausted the mathematics course offerings of the high school.Few school systems can reliably guarantee that they will have a teacher capable of teachingAdvanced Calculus, and even if they do, colleges and universities have no way to judge thecaliber of the course.In the fall of 2004, a conversation between a staff member from Georgia Tech’s Center forEducation Integrating Science, Mathematics and

Conference Session

Bridging the Gap and Freshman Programs

Collection

2009 Annual Conference & Exposition

Authors

James Sullivan, Dallas Independent School District

Tagged Divisions

Mathematics

master standards for 8th grade coordinate geometry, “Students who areunsuccessful have the greatest difficulty with setting up and solving proportions from real-worldexamples involving similar triangles” (in addition to three other factors). 1 Furthermore, one ofthe report’s recommendations is “For Grades 6–8, students need more experience setting up andsolving proportions from problems presented in a real-world context.” 2 And with respect to theFlorida Comprehensive Assessment Test (FCAT) 10th grade level standard of understandingmathematical operations, “Students who are successful are able to … understand and applyproportion concepts” (in addition to other skills). 3 Finally, ratio/proportion skills are importantto the successful performance

Conference Session

Mathematics: Recruitment and Retention

Collection

2009 Annual Conference & Exposition

Authors

Sabina Jeschke, University of Stuttgart; Ndjeka Manya

Tagged Divisions

Mathematics

! ∀ ! # # # # ! ∃% ∃% ∃! ∃ # & ∋ ∋ # # ( ) ∗ +,,, −,,. ! −,,/−,,. Page 14.1248.2 0 1 1 2 # 1 ! ∋ ∋ ( ) ∋3 ! 4 ∋ ∋5 6.∋5 ∋ ∋ ∀ ∀ ∋5

Conference Session

Innovative Instructional Strategies

Collection

2009 Annual Conference & Exposition

Authors

Elton Graves, Rose-Hulman Institute of Technology

Tagged Divisions

Mathematics

; tenminutes; and fifteen minutes; we have the student announce the temperature of the water in theflask. While the class is waiting for the temperature readings, we derive the differential equationfor Newton’s Law of Cooling. Using the temperature data provided by our student we now solvethe differential equation and check the theoretical results. It is not uncommon for the theoreticalresults at ten minutes to have a relative error of 0.1% of the actual temperature the studentmeasured. We have never had a relative error of more than 1%, and once we actually had exactagreement between the theoretical and actual temperature of the water. Again our purpose is tonot only show the derivation of Newton’s Law of Cooling, but to show that mathematical models

Conference Session

Innovative Instructional Strategies

Collection

2009 Annual Conference & Exposition

Authors

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

Tagged Divisions

Mathematics

, and engineering courses1-3.We consider the ordinary differential equation given byx + 2ςx + ω 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, and ω n2 andς are constants that characterize the system. Page 14.1325.2Picture A. Photo of a smooth sphere on a linear spring oscillating in the open air of a laboratory.Eq. (1) can represent the motion of a mass, m

Conference Session

Computers and Software in Teaching Mathemathetics

Collection

2009 Annual Conference & Exposition

Authors

Jenna Carpenter, Louisiana Tech University

Tagged Divisions

Mathematics

university, including come-and-go tutoring sessions andthe more formal Supplemental Instruction program (both of which averaged 10 – 20 students perday total from all lower-level mathematics courses, including calculus).Homework/E-Mail: In the Fall of 2006 the Mathematics and Statistics Program at LouisianaTech University began piloting a web-based homework system in an effort to increase studentmastery of course content and increase individual student accountability on out-of-classassignments. They chose a program called WeBWorK14, developed in the mid-1990’s atUniversity of Rochester by Arnold Pizer and Michael Gage. Two of the primary goals of thisproject were: 1) to increase student mastery of course content, and 2) to increase individualstudent

Conference Session

Engineering and Mathematics Potpourri

Collection

2009 Annual Conference & Exposition

Authors

Andrew Grossfield, Vaughn College of Aeronautics

Tagged Divisions

Mathematics

functions. This same student may become more open tostudying other aspects of polynomials and other functions. These techniques can provide a quickcheck of computer-generated graphs or be employed when a computer is unavailable orinconvenient. If we desire to recruit more students into the analytical and other sciences, weneed to discover better, easier and more pleasurable ways to present conventional math conceptsbefore attempting to accelerate curricula by moving advanced differential concepts into thelower grades.Contents 1. Introduction 2. Polynomials 3. Arithmetic operations on functions and their effect on curves Addition, subtraction, multiplication and division 4. Elementary operations on curves and

Conference Session

Innovative Instructional Strategies

Collection

2009 Annual Conference & Exposition

Authors

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

Tagged Divisions

Mathematics

and because writing is aunique mode of learning, the authors hypothesize that requiring students to engage with thetopics in MATH 131 through writing will improve both (1) the professor’s delivery of instructionby alerting him to problems with students’ language mastery as well as their mathematicalthinking and (2) the students’ mastery of the MATH 131 concepts by requiring deeper and morediverse mental engagement with them.BackgroundThe university and students. Virginia Commonwealth University in Qatar (VCUQatar) is theflagship school of Education City, an innovative and expanding community of United Statesuniversities invited to operate branches in Doha, Qatar. Doha is the capital city of Qatar, apeninsula of 4,400 square miles (comparable

Conference Session

Computers and Software in Teaching Mathemathetics

Collection

2009 Annual Conference & Exposition

Authors

Marilyn Reba, Clemson University

Tagged Divisions

Mathematics

, attributable to a new instructional model and a new placement procedureimplemented by the Department of Mathematics in Fall 2006. All sections of Calculus I adopteda variation of the SCALE-UP active-learning instructional model which includes short lectures,student collaboration at round tables, and graded group activities.1 The placement procedure wasaltered so that more students had to enroll in "Long Calculus,” a one-year course interspersingAlgebra review into a slow-paced Calculus I. Performance statistics (like the 20% DFW ratecited above) indicate that these have been important improvements, but we have not stoppedthere in trying to address the needs of at-risk students. With a 2006 Hewlett-PackardTechnology for Teaching grant, we placed Tablet

Conference Session

Computers and Software in Teaching Mathemathetics

Collection

2009 Annual Conference & Exposition

Authors

Raymond Jacquot, University of Wyoming; Jeffrey Anderson, University of Wyoming; David Walrath, University of Wyoming

Tagged Divisions

Mathematics

Page 14.1044.1© American Society for Engineering Education, 2009 Scripts in MATLAB for Animation of the Solutions to Partial Differential EquationsIntroductionTeaching of mathematics at all levels can be enhanced by the use of graphical techniques. Thatis particularly true for engineering mathematics, since well over half of engineering students aregraphical learners and many presentations of mathematical concepts employ only symbolicpresentations. Geometry and graphics were important parts of the Calculus Reform movementand can be used to advantage in the teaching of concepts of differentiation and integration asreflected in modern calculus texts.1 Differential equation pedagogy can be enhanced by use