Conference Session

Integrating Math, Science and Engineering

Collection

2008 Annual Conference & Exposition

Authors

Josue Njock-Libii

Tagged Divisions

Mathematics

13.1364.7Table 3(a). Experimental Fourier coefficientsn a b cn n n0 0.0548641 0 0.05486411 -0.957223 -0.0100514 1.00373662 -0.00173248 0.0034438 0.0973333 0.00308254 0.00475898 0.08774364 0.00142011 0.00109271 0.07670175 0.00257423 -0.000909756 0.07639746 -0.000637367 0.000949299 0.0554893Table 3(b). Fourier coefficients from theoryn a b c n n n0 0 0 01 -1 0 12

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

, and boundary conditions Identify governing engineering principles Translate problem into equation(s) Teach mathematical tool(s) to solve equation(s) Determ ine if solution to Challenge is reasonable Defend approach and solutionFigure 1: Proposed Methodology for Discussions with Engineering Faculty. Page 13.72.9I. First-Order Ordinary Differential Equations (ODEs) A. Basic Concepts, Modeling B. Initial Value Problems C. Direction Fields D

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

literature? (Knows what’s been done before?) B. Backs claims with evidence from prior research or existing literature? 4: Backed by Literature B. Yes 3: Lacks some references A. 2: Supports

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

aspects beingidentical). In addition, the second group of Calculus I students were followed in Calculus II (stillutilizing textbook homework assignments and taught by Instructor A) and in Calculus III(utilizing WeBWorK assigned on a weekly basis for homework and taught by Instructor B).Louisiana Tech University is on a quarter calendar with semester hours. Terms are 10-weekslong and the maximum full-time student course load is 12 semester credit hours. The calculussequence consists of five three-semester hour courses. Calculus I consists of algebra andtrigonometry topics (approximately 2/3 of the course) and calculus topics (limits and conceptualdevelopment of derivative as a limit, up to but not including, the derivative rules). Calculus

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

AC 2008-1548: TEACHING DIFFERENTIAL EQUATIONS IN A DIVERSECLASSROOMTaskin Padir, Lake Superior State University Assistant Professor, School of Engineering and TechnologyKimberly O. Muller, Lake Superior State University Assistant Professor, School of Mathematics and Computer ScienceCollette Coullard, Lake Superior State University Professor, School of Mathematics and Computer Science Page 13.1157.1© American Society for Engineering Education, 2008 Teaching Differential Equations in a Diverse ClassroomAbstractA course on ordinary differential equations is included in the core of almost all undergraduateengineering programs. Therefore, it

Conference Session

Bridging and Freshman Programs

Collection

2008 Annual Conference & Exposition

Authors

Christopher Papadopoulos; John Reisel, University of Wisconsin - Milwaukee

Tagged Divisions

Mathematics

AC 2008-1623: DO STUDENTS IN SUMMER BRIDGE PROGRAMSSUCCESSFULLY IMPROVE MATH PLACEMENT AND PERSIST? AMETA-ANALYSIS.Chris Papadopoulos, University of Wisconsin - Milwaukee Chris Papadopoulos earned BS degrees in Civil Engineering and Mathematics from Carnegie Mellon University, and a PhD in Theoretical and Applied Mechanics, Cornell University. He previously served on the faculty of Engineering at the University of Wisconsin-Milwaukee, where he is currently a research associate, grant writer, lecturer, and director of educational programs. His research interests include biomechanics, nonlinear structural mechanics, computational mechanics, engineering education, and engineering ethics. He is

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

physical (modeling), mathematical (discretization),and computational (implementation) errors through the use of a rigorous statistical methodknown as the design of experiments (DOE). An introduction of the methodology is presented inthe form of five specific topics: (a) the fundamentals of DOE, (b) the assumptions of modelbuilding, (c) setting objectives for an experiment, (d) selecting process input variables (factors)and output responses, and (e) weighing the objectives of the virtual experiment versus thenumber of factors identified in order to arrive at a choice of an experimental design. The methodis then specialized for FEM applications by choosing a specific objective and a subclass ofexperimental designs known as the fractional factorial

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

learners based on observations of design students’ characteristicsand Linksman’s definitions of these super links. The second study set out to test that deductionby recording students’ super links after administering Linksman’s tests for determining learningstyle and brain hemispheric preferences (see Appendices A and B). The tests were given early inthe term shortly after introducing the course and its project-directed concept, and the results werediscussed with the students, who also received handouts of Linksman’s characterizations foreach of the learning styles and brain hemispheric preferences.Because Arabic art and architecture are strongly influenced by geometrical designs, MATH 131includes several chapters of the mathematical text6 that

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

scaffold proportional reasoning in young learners for the followingreasons. First, although similarity and analogy are not the same, Gentner and Markman (1997) 19suggest that the process of carrying out a comparison is the same in both cases, concluding thatsimilarity is like analogy involving a process of ”structural alignment and mapping betweenmental representations” (Gentner and Markman, 1997, p.45 19 ).Second, classical or conventional analogies take the form of A:B::C:D (English, 2004 20 ), wherethe A and B can be termed as the base or source, and C and D can be termed as the target(Gentner, Holyoak, & Kokinov, 2001 21 ). These analogies are basically proportional or relationalproblems (English 20 ; Gentner and Markman 19 ). In our

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

taken from theinteractive worksheets illustrating these three kinds of examples. • Example (basic computation): 1. Find x and y so that the following two matrices are equal.     2 x−4 2 6 A = 3 0  and B = y − 1 0 7 0 7 0 • Example (application of theory): 1. Plot a triangle in R2 with vertices F = (x1 , y1 ), U = (x3 , y3 ) and N = (x2 , y2 ) where x1 , x3 , x2 are all positive and x1 ≤ x3 ≤ x2 . 2. Find a formula for the area of this triangle by using trapezoids. Recall that the area of a trapezoid is half the distance between 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

Page 13.550.9The third null hypothesis was: There are no strong relationships between students’ self-regulativebehaviors (the total time spent and the level of Math skills mastered while using ALEKS) and thedegree of improved knowledge in Precalculus. To test the hypothesis, we analyzed the total time(measured in hours) students spent with ALEKS and the level of Math skills they mastered inALEKS obtained from the experimental group (section 1 and section 2). See Table 6.Table 6. Descriptive Statistics for Total Time Spent and Mastery Level Achieved in ALEKS. Total Time Spent b Math Skills MasteredSection 1 M 115.69 88.07(N = 41)a

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

the geosynchronous satellites from earth’s surface? Have the students write down their ideas and reasons for their beliefs. 3. Present the problem to be solved. a. Explain: Period, orbital period, and rotational period with the help of students acting as satellites around you, the teacher. Then explain that geosynchronous satellites are satellites whose orbital period around the Earth matches Earth’s rotational period. b. Ask: Why doesn't a geosynchronous satellite drift off into space? Or why doesn't it crash into the earth? Help them understand about forces especially gravitational and centripetal forces and then show what happens when the

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

real-world implementation. The simple integrationI = ∫ e cos x dxcannot be analytically integrated while it can be numerically readily integrated given the limitof integration [a, b] = [1,3] , say, using, for example, the Simpson’s 1/3 closed quadratureformula.Golden ratio ϕ in nature, artfacts, and architecture The Greek mathematicians Pythagoras(about 582 BC−507 BC) and Euclid (about 330 BC−275 BC), the Italian mathematicianFibonacci (about 1175 −1250), also known as Leonardo of Pisa, the German Lutheranmathematician J. Kepler (1571−1630), the British mathematical physicist R. Penrose (1931)are just a few names over the past 25 centuries, who have spent countless hours over thissimple yet amazing number, the golden ratio and its properties

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

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

AC 2008-2703: EARLY BIRD - TEACH MATHEMATICS BEFORE PROBLEMSARISESabina Jeschke, University of Stuttgart After receiving her M.Sc. in Physics at the Berlin University of Technology in 1997, graduating with distinction, Sabina Jeschke worked as an assistant teacher at the department for mathematics and natural sciences and earned her doctorate in 2004. Holding a scholarship from the German National Academic Foundation, she spent several months of research at the NASA in Moffet Field, CA. In 2000 and 2001, S. Jeschke worked as an instructor at the GaTech (Georgia Institute of Technology, Atlanta). Since 2005, Sabina Jeschke has been associate professor for "New Media in Mathematics and

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

AC 2008-1697: MATHEMATICS SKILLS ASSESSMENT AND TRAINING INFRESHMAN ENGINEERING COURSESPhillip Mlsna, Northern Arizona University Dr. Phillip Mlsna is an Associate Professor in the Department of Electrical and Computer Engineering at Northern Arizona University. His research interests are primarily in image processing, image analysis, computer vision, and engineering education. He has extensive industry experience as a computer hardware design engineer.Janet McShane, Northern Arizona University Dr. Janet McShane is Chair of the Department of Mathematics and Statistics at Northern Arizona University. Her research interests are primarily in group theory, commutative algebra and

Conference Session

Integrating Math, Science and Engineering

Collection

2008 Annual Conference & Exposition

Authors

Hong Liu, Embry-Riddle Aeronautical University, Daytona Beach

Tagged Divisions

Mathematics

Course Option within an Ordinary Mathematics Course for Undergraduate students in Engineering MajorsAbstractIn order to attract talented students, many selective small universities have established honorsprograms in recent years 10,13 . However, because it is difficult for those small universities toschedule enough honors program students to fill all the seats of a regular-sized class, it is oftentoo costly to offer sufficient honors courses for students in an honors program alone. A costeffective solution to this problem is to allow students who are not in the honors program to takeany seats that may remain after the honors students have registered. An alternative is to offer anhonors course option in a regular non-honors course by

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

education for some students. Of interest is the role of two-year colleges in thepreparation of such engineering students. This study looks at the relative success (GPA andretention) of 297 engineering students who took mathematics coursework at one of the system’sthirteen two-year colleges and then transferred to one of the three universities within the systemthat have multiple ABET accredited engineering programs. Over half of these students wereinitially placed at a level of pre-calculus or below. The success of these students is compared tolike groupings of engineering students who went directly to one of the three system engineeringschools. This study will look at the relative success of students as a function of initial mathplacement. In