Conference Session

Applied Mathematics

Collection

2007 Annual Conference & Exposition

Authors

Johann Misterio, William Dickinson High School; Krshna Ravindra, Johns Hopkins University; Rene D Rivero, New Jersey Institute of Technology; Henry McCloud, New Jersey Institute of Technology; Levelle Burr-Alexander, New Jersey Institute of Technology; Nuggehalli Ravindra, New Jersey Institute of Technology

Tagged Divisions

Mathematics

of each leaf wasdetermined using the box-count method. Five trials were conducted using five plants. The meanfractal dimensions of each leaf was obtained and then analyzed by ANalysis Of VAriancebetween groups [ANOVA].I. IntroductionShapes have always been an important aspect in biological systems. Although usually ignored,shapes play a major role in description of functions of various organisms. Traditionally, theshapes of objects and organisms have been described using Euclidean geometry1. Euclideangeometry describes the basic, regular figures that are most familiar such as lines, squares, cubes,etc. Irrespective of the case, all these structures have dimensions that are positive integers (wholenumbers): 0 for a point, 1 for a line, 2 for

Conference Session

Mathematics in Transition

Collection

2007 Annual Conference & Exposition

Authors

Nirmala Gnanapragasam, Seattle University

Tagged Divisions

Mathematics

to developspeed in problem solving for certain contests.Based on the findings of the above research, the author developed a weekly lessonplan covering various contest topics, sample problems to work in class andassigned contest problems as homework. An example schedule for the first yearmath club students (typically fourth graders) is shown in Table 1. These topicscovered in a student’s first year of math club are reinforced every year withadditional topics and skills introduced in subsequent years till they completeelementary school in 6th grade. Some of these additional topics being,percentages, speed-time relationships, interpreting graphical data, areas andvolumes of various geometric shapes, Pythagoras’ theorem, symmetry and

Conference Session

Mathematics in Transition

Collection

2007 Annual Conference & Exposition

Authors

John Gardner, Boise State University; Pat Pyke, Boise State University; Marcia Belcheir, Boise State University; Cheryl Schrader, Boise State University

Tagged Divisions

Mathematics

impact in theengineering education community.Research MethodTwo studies are reported on this paper: 1) A backward-looking survey of successfulengineering students to see the level of mathematics at which they started college and 2)An analysis of factors correlated to student persistence. The first study began as aninformal attempt to assess the range of math preparedness among our students in an effortto help direct our program development efforts. The second was performed to test ahypothesis formed while carrying out the informal studies. As we will demonstrate, asignificant portion of our successful students began their college experience indevelopmental mathematics. We also found that attrition among students who began incalculus or came to

Conference Session

Mathematics in Transition

Collection

2007 Annual Conference & Exposition

Authors

Sandra Linder, Math Out of the Box; Donna Gunderson, Math Out of the Box/Clemson University

Tagged Divisions

Mathematics

mathematics curriculum impacts the instructional practicesof K-5 educators in a Title I school district. The purpose of this paper is to describe the changesin practice that occurred throughout the implementation process and to outline several strategiesthat aided teachers while making the transition from traditional to inquiry-based practitioners.introduction: According to the Building Engineering and Science Talent (BEST) report, “Twenty-fivepercent of our scientist and engineers will reach retirement age by 2010” (p. 1)1. The prevailingconcern that American students are not as prepared to meet the challenge of scientific innovationwhen compared to students in other nations has prompted a response from the federalgovernment. An abundance of

Conference Session

Integrating Mathematics, Science, and Engineering

Collection

2007 Annual Conference & Exposition

Authors

Jenna Carpenter, Louisiana Tech University

Tagged Divisions

Mathematics

lines, and graphs of functions (in this case, their growthcurves) with the data about the growth rate of the algae, their treatments of the algae sample,their calculated growth rates and other related concepts from the accompanying biology lecture Page 12.914.3course: 1. What does is mean for the growth rate to be large? 2. What does is mean for the growth rate to be small? 3. Can a growth rate be negative? Why or why not? What would the curve look like if these were so? 4. Can a growth rate be zero? Why or why not? What would the curve look like if this were so? 5. Looking at your graph for Control A, how are the growth

Conference Session

Innovative Instruction Strategies in Calculus

Collection

2007 Annual Conference & Exposition

Authors

Elton Graves, Rose-Hulman Institute of Technology

Tagged Divisions

Mathematics

equations and modeling. Day Seventeen: Projectile motion, linear differential equations. Day Eighteen: Line integrals, work, and flux. Day Nineteen: Double integrals. Day Twenty: Centers of mass, moments of inertia. Day Twenty-one: Triple integrals. Day Twenty-two: Moments in space and change of coordinate systems. Day Twenty-three: Area of polar curves cylindrical coordinates. Page 12.1324.4 Day Twenty-four: Spherical coordinates. Day Twenty-five: Final exam.Weekly ScheduleIn order to cover all the material each day is tightly organized. The students are in classfrom 8:05 AM until 12:00 noon and from 1

Conference Session

Integrating Mathematics, Science, and Engineering

Collection

2007 Annual Conference & Exposition

Authors

Günter Bischof, Joanneum University of Applied Sciences, Department of Automotive Engineering,; Emilia Bratschitsch, Joanneum University of Applied Sciences, Department of Automotive; Annette Casey, Joanneum University of Applied Sciences, Department of Automotive Engineering,; Domagoj Rubesa, Joanneum University of Applied Sciences, Department of Automotive Engineering,

Tagged Divisions

Mathematics

increases the students’motivation. The outcome of some of these undergraduate projects has found application inindustry or has been published in professional journals.In this paper the idea of project based learning in engineering mathematics is exemplified onthe basis of students’ projects carried out in the third semester of their degree program.IntroductionIt seems that the critical issue in teaching mathematics to engineering students is to find theright balance between practical applications of mathematical methods and in-depthunderstanding 1. Project based learning has proved to be a particularly suitable method todemonstrate the need of mathematics in professional engineering. Students are confronted,complementary to their regular courses

Conference Session

Integrating Mathematics, Science, and Engineering

Collection

2007 Annual Conference & Exposition

Authors

Shane Palmquist, Western Kentucky University

Tagged Divisions

Mathematics

integrations, derivatives, and partial derivatives to solve problems. Some of thetheorems and methods with graphical notation and corresponding equations as applied to asimply supported beam with a distributed load are given in Table 1.. y w(x) x E, I L Figure 1. Simply Support Beam with a Distributed Load Page 12.1545.4 Table 1. Classical Structural Analysis Methods a

Conference Session

Innovative Instruction Strategies in Calculus

Collection

2007 Annual Conference & Exposition

Authors

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

Tagged Divisions

Mathematics

teamwork. Finally, we willoutline our plans for further investigation of questions raised as a result of teaching withinnovative activities designed to encourage teamwork and communication skills while allowingstudents to take a more active role in the learning of calculus.IntroductionTeamwork and communication skills are recognized as important outcomes in undergraduateengineering curricula. Accordingly, Criterion 3 of the ABET guidelines states that a student musthave an “ability to apply knowledge of mathematics,” an “ability to function on multi-disciplinaryteams,” and an “ability to communicate effectively.”1 In addition, the Committee on theUndergraduate Program in Mathematics (CUPM) of the Mathematical Association of America2004 Curriculum

Conference Session

Integrating Mathematics, Science, and Engineering

Collection

2007 Annual Conference & Exposition

Authors

John Quintanilla, University of North Texas; Nandika D'Souza, University of North Texas; Jianguo Liu, University of North Texas; Reza Mirshams, University of North Texas

Tagged Divisions

Mathematics

quasiequilibrium process by integrating W = ∫ Vi V 1.3 dV . • The endpoints of a beam of length L under a load tend to move closer together by a slight amount because of the deflection. This displacement, called the curvature L 1 shortening, is given by λ = ∫ [v' ( x)] dx, where the deflection curve of the beam 2 20 4δ

Conference Session

Mathematics in Transition

Collection

2007 Annual Conference & Exposition

Authors

Janet Callahan; Joe Guarino, Boise State University; Seung Youn Chyung, Boise State University; John Gardner, Boise State University; Amy Moll, Boise State University; Pat Pyke, Boise State University; Cheryl Schrader, Boise State University

Tagged Divisions

Mathematics

State University is 64%for engineering students, and 63% overall.1 This is low when compared with the nationalaverage2 of all four-year institutions, 69% and provides strong motivation for investigating waysto increase freshman success.This study focuses on helping students succeed in Precalculus, a 5-credit mathematics course, inwhich 84 first-semester engineering students were enrolled in fall 2006 (19% of the incomingfreshmen engineering class). An additional 37 engineering students classified as non-freshmenalso enrolled in Precalculus (transfer students, repeat takers, etc.). These 121 engineeringstudents were enrolled in ten sections of Precalculus which had an average enrollment of 33students per section, with engineering students thus

Conference Session

Project and Model-Based Mathematics

Collection

2007 Annual Conference & Exposition

Authors

Dennis Berkey, Worcester Polytechnic Institute; Bogdan Vernescu, Worcester Polytechnic Institute

Tagged Divisions

Mathematics

AC 2007-2014: A MODEL FOR VERTICAL INTEGRATION OF REAL-WORLDPROBLEMS IN MATHEMATICSDennis Berkey, Worcester Polytechnic Institute Dennis Berkey became the fifteenth president of Worcester Polytechnic Institute on July 1, 2004. Prior to that he had served as Provost and Dean of Arts and Sciences at Boston University where he had joined the faculty in 1974. His undergraduate and graduate degrees are in mathematics (B.A., Muskingum College; Ph.D., University of Cincinnati) and his published research is in applied mathematics and optimal control theory. He is an accomplished teacher, having won Boston University’s highest teaching award, and is the author of two calculus textbooks

Conference Session

Mathematics in Transition

Collection

2007 Annual Conference & Exposition

Authors

Anne McClain, University of Alabama-Birmingham; Dale Feldman, University of Alabama-Birmingham; Lee Meadows, University of Alabama Birmingham

Tagged Divisions

Mathematics

-based learning curricula modeled after the NationalCouncil of Teachers of Mathematics, Principles and Standards for School Mathematics throughcontent and pedagogical preparation of future teachers, the professional development ofpracticing teachers, and the placement of interns in classrooms that model exemplary practices[1]. Page 12.617.2The engineering faculty contribution to the partnership lies in the connection of mathematics toreal world applications and to users of mathematics within this framework of an inquiry-basedmiddle school mathematics classroom. In developing these connections, the engineering facultyhope to provide middle

Conference Session

Innovative Instruction Strategies in Calculus

Collection

2007 Annual Conference & Exposition

Authors

Jenna Carpenter, Louisiana Tech University; Ruth Ellen Hanna, Louisiana Tech University

Tagged Divisions

Mathematics

is, students with higher Math ACT scores spendslightly less time using ALEKS. This could be caused by a lower perceived need for assistanceamong students with higher Math ACT scores.BackgroundFive years ago the Mathematics Program at Louisiana Tech University began using a web-basedtutorial program marketed by McGraw-Hill entitled ALEKS (Assessment and LEarning inKnowledge Spaces)1 in an effort to provide a more effective mathematics tutoring program forour students. The goals were to 1) increase student retention and success in freshman andsophomore-level mathematics courses (such as calculus, which all engineering majors take), and2) increase the willingness of students to utilize the available tutorial services. Note that “studentsuccess

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