Conference Session

Use of Technology in Teaching Mathematics

Collection

2006 Annual Conference & Exposition

Authors

Arthur Snider, University of South Florida; Sami Kadamani, Hillsborough Community College

Tagged Divisions

Mathematics

. κ x 2 +κ y 2 ZThis example illustrates the straightforward extension of the procedure to three dimensions andthe transcendental equation that the Robin boundary condition invokes for the eigenvalues.Example 3. Steady state heat flow in a cylindrical sector with facial heat sources (homogenousLaplace equation in the three dimensions inside a partial cylinder, nonhomogenous Dirichletcondition on the top and one flat side, homogenous Dirichlet conditions on the bottom and thecurved wall, and a homogenous Neumann condition on the other flat side): 2∇ Ψ =0Ψ ( ρ ,θ , 0 ) = Ψ ( b,θ , z ) = 0,∂Ψ ( ρ , 0, z ) = 0, Ψ ( ρ , Θ, z ) = f θ = Θ ( z, ρ ) ,∂θΨ ( ρ , θ , Z ) = f z = Z (θ , ρ )The USFKAD solution:Ψ = Ψ1 + Ψ 2Ψ = ∑ κ z ∫ ∞0 d κ ρ : z sin

Conference Session

Mathematics Division Technical Session 3: Diversity in Mathematics Education

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Lee Singleton, Whatcom Community College; Eric Davishahl, Whatcom Community College; Todd Haskell, Western Washington University

Tagged Divisions

Mathematics

smaller. Knowing this, C has to be the biggest because of how far the region is from its axis of rotation. With C it is rotating around y=4, which will create the most overlap, which will make it smaller. A is the next smallest, rotating around x=2. That will make a cup 3 shape. The largest is B, rotating around y=-5. This will create the biggest range and will cover the most of the graph. Since A's shape involves a larger area when turned around x = 2, it gives the largest 2 volume. Since C has a larger radius than B, it has the larger volume making B the smallest volume. The size of the hole in the washer determines the area since the

Conference Session

Computers and Software in Teaching Mathemathetics

Collection

2009 Annual Conference & Exposition

Authors

Marilyn Reba, Clemson University

Tagged Divisions

Mathematics

-Centered Activities for Large-Enrollment University Physics (SCALE- UP)." Presented at the Sigma Xi Forum: "Reshaping Undergraduate Science and Page 14.781.6 Engineering Education: Tools for Better Learning", Minneapolis, MN (unpublished).2. Reba, M., and B. Weaver. (2007)"Tablet PC-Enabled Active Learning in Mathematics: A First Study." In Proceedings of the International Workshop on Pen-Based Learning Technologies (IEEE), 10-16.3. Bransford, J. D., and A. L. Brown. (1999). How People Learn: Brain, Mind, Experience, and School. National Academy of Sciences Press.4. Meyers, C., and T. B. Jones. (1993). Promoting Active

Conference Session

Using Applications and Projects in Teaching Mathematics

Collection

2012 ASEE Annual Conference & Exposition

Authors

Hassan Moore, University of Alabama, Birmingham

Tagged Divisions

Mathematics

should be able to complete the project with the material taught in class.Below are the primary course topics covered: I. First-Order Ordinary Differential Equations (ODEs) A. Basic Concepts, Modeling B. Initial Value Problems C. Direction Fields Page 25.1437.2 D. Existence and Uniqueness E. Separable ODEs F. Linear ODEs G. Applications II. Second-Order ODEs A. Homogeneous Linear ODEs with constant coefficients B. Free Oscillations C. Forced

Conference Session

Integrating Mathematics, Science, and Engineering

Collection

2010 Annual Conference & Exposition

Authors

Elton Graves, Rose-Hulman Institute of Technology

Tagged Divisions

Mathematics

and courses is ∞ 6 2π2t Ux, t = ∑ 2 ∫6x − x 2  sin nπx dx e − n 9 sin nπx . 3 6 6 n=1 0 For a lot of students the feeling is "Well, that’s nice, but so what?" We now use Mapleto calculate 6 72−2 + 2−1 n  B n = 2 ∫6x − x 2  sin nπx dx = − 3 6

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

student and a condition attribute designates an attributeincluded in the student profile. In most cases where a decision needs to be reached, an additional Page 14.218.4attribute, decision attribute, is incorporated in the data set. A system that encapsulates all objects,condition attributes and decision attributes is called a decision system/table.Table 2 shows a part of the decision table used in this study. The attribute Performance is thedecision attribute which indicates if a student has received a passing (A, B, C) or a failing grade(D, F) in the course. Table 2. Decision Table

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

form 𝑦 = 𝑎 ∙ 𝑏 ! that could be used to describe thedata; (b) give an interpretation of the constants a and b in (a); (c) find the point in time when thevoltage across the capacitor was 0.05 V; (d) compute the average rate of change over threesubintervals, from t = 5 to t = 10 seconds, t = 20 to t = 25 seconds, and t = 40 to t = 45 secondsrespectively; and (e) write two or three sentences interpreting the negative average rate of changedata in (d). 2.0529 − 4.2245 t = 5 to t = 10 : = −0.43 v/s 10 − 5 .27252

Conference Session

Mathematics Division Technical Session 3

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Emre Tokgoz, Quinnipiac University; Elif Naz Tekalp; Hasan Alp Tekalp

Tagged Divisions

Mathematics

to solve related calculus problems [1,3,5,6,8-16]. The results of this work can help developing asuccessful teaching methodology of Taylor series after determining areas that can be used for improving learnersability to respond questions. The same research question is empirically evaluated in [19] to continue investigatingundergraduate STEM students’ ability to respond to the following set of power series questions:Q. In a few sentences legibly answer each of the following questions (a) through (d).a) Describe the difference, if any, that exists between ex and 1 + + ! !b) Describe the difference, if any, that exists between e1 + e1 + e1

Conference Session

Integrating Mathematics, Science, and Engineering

Collection

2007 Annual Conference & Exposition

Authors

Shane Palmquist, Western Kentucky University

Tagged Divisions

Mathematics

) + C3 x + C4 Page 12.1545.5 b) Moment Area Theorems Component Graphical Description Governing Equations M( x ) M(x ) M(x) from statics due to w(x)Moment, EI EI a bSlope angle, xa/b b where, a/b M a b a/b = Ð

Conference Session

First-Year Programs: Mathematics in the First Year

Collection

2019 ASEE Annual Conference & Exposition

Authors

Louis J. Everett, University of Texas, El Paso; Phillip Cornwell, Rose-Hulman Institute of Technology; Yirong Lin, The University of Texas, El Paso; Norman Love, University of Texas, El Paso

Tagged Divisions

First-Year Programs, Mathematics

properties. Any change in an extensiveproperty within the system can be accounted for by counting the amount of the extensive propertytransported across the system boundary and the amount generated or consumed inside the system[18].Given a generic extensive property B, e.g. mass or energy or momentum or charge or entropy, it ispossible to write a general accounting principle for any system. In its simplest form, the finitetime version of the accounting principle is very intuitive and can be written as: Amount of 𝐵 Amount of 𝐵 Amount of 𝐵 Amount of B Amount of 𝐵 Amount of 𝐵 inside inside transported transported generated consumed system − system = into system − out of

Conference Session

Applied Mathematics

Collection

2007 Annual Conference & Exposition

Authors

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

Tagged Divisions

Mathematics

, thusimplementing the autocatalytic process. A Matlab code ( a modified version of the code in [6]) for Ant algorithm for TSP is:function [] = antalgorithm()D = load('cityloc.txt'); % The file cityloc.txt is n x 3 matrix% Each row of cityloc has three elements. The second and third% elements representing the numerical coordinates (location) of the city%while the first element is the numerical name of the city starting from 1.Ncity = length(D); % number of cities on tourNants = Ncity; % number of ants=number of cities (each b(i) is taken as 1)% Cities are located at (xcity, ycity)x = [D(1,2)]; y = [D(1,3)];for i=2:Nants, xcity=D(i,2); x=[x xcity]; ycity=D(i,3); y=[y ycity]; end;% Calculate distance matrixfor i=1:Ncity-1, for j=i+1:Ncity,if i==j, dcity(i,j

Conference Session

Mathematics Division Technical Session 1

Collection

2019 ASEE Annual Conference & Exposition

Authors

Guisela Alejandra Illescas Ms, Universidad Galileo; Alberth E. Alvarado, Universidad Galileo; Jose Roberto Portillo, Universidad Galileo

Tagged Divisions

Mathematics

. (a) (b)Fig. 3. (a) Sample problems in a PSS worksheet, original version in Spanish (Problems taken or adapted from the course textbook [12], and [13]). (b) Translation to English. Fig. 4. Sample of a worksheet solution. This solution corresponds to Problem 2 in Figure 3. (a) (b) Fig. 5. (a) Sample problem in a Topic Quiz, original version in Spanish (problem taken from [13]). (b) Translation to English.3.3 MAPSIn this particular course, three mini-projects were carefully designed so that the

Conference Session

Mathematics Division Technical Session 4

Collection

2015 ASEE Annual Conference & Exposition

Authors

Virgil U. Pierce, University of Texas, Pan American; Javier Angel Kypuros, University of Texas, Pan American

Tagged Topics

Diversity

Tagged Divisions

Mathematics

students into a Calculus 1 course who would otherwise have started their firstsemester in a Pre-Calculus or College Algebra course. This is a significantly higher success ratethan has been found in other Pre-Calculus courses including other courses with an Emporium Page 26.1692.3model intervention. One possible reason for this is that the students are self selecting as moremathematically adept than their peers. Of those students, 16 enrolled in a Calculus 1 class in theFall semester and 10 of them successfully completed Calculus 1 with an A, B, or C. While this isan improvement in the passing rate over general Calculus 1 students, it is not

Collection

2016 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University

Tagged Divisions

Mathematics

(1989). In addition, Triad classification of the participants aredetermined to obtain the qualitative and quantitative results presented in this work.Key Words: Riemann integral, area, functions, concept image, concept definition, APOS theoryIntroductionAn important application of Riemann integral is determining the area between a single variablecontinuous function and the input axis. Given a continuous function f on the interval [a, b], thearea between the function and the input axis can be calculated by using the formula b Area = ∫ f ( x)dx aThis definition of area by using integral concept requires a well

Conference Session

Mathematics Division Technical Session 4

Collection

2013 ASEE Annual Conference & Exposition

Authors

Hassan Moore, University of Alabama, Birmingham

Tagged Divisions

Mathematics

. Below are the topics covered in the course: I. First-Order Ordinary Differential Equations (ODEs) A. Basic Concepts, Modeling B. Initial Value Problems C. Direction Fields D. Existence and Uniqueness E. Separable ODEs F. Linear ODEs G. Applications (primarily Biomedical, Mechanical, and Electrical) II. Second-Order Ordinary Differential Equations A. Homogeneous Linear ODEs with constant coefficients B. Free Oscillations C. Forced Oscillations D. Electrical/Mechanical Systems III. Multivariable Calculus A. Functions of Several Variables B. Partial Derivatives

Conference Session

The Transition from Secondary to College Mathematics

Collection

2012 ASEE Annual Conference & Exposition

Authors

Alex Feldman, Boise State University; Doug Bullock, Boise State University; Janet Callahan, Boise State University

Tagged Divisions

Mathematics

author(s) and do not necessarily reflect the views of the National ScienceFoundation.References1. http://www.aleks.com/2. Rueda, N.G. & Sokolowski, C. (2004). Mathematics Placement Test: Helping Students Succeed. TheMathematics Educator, 14 (2) (pp. 27-33).3. Cederberg, J. N. (1999). Administering a placement test: St. Olaf College. In B. Gold, S. Keith, & W. Marion(Eds.), Assessment practices in undergraduate mathematics (pp. 178−180). Washington, DC: MathematicsAssociation of America.4. Cohen, E., Friedlander, J., Kelemen-Lohnas, E., & Elmore, R. (1989). Approaches to predicting student success:Findings and recommendations from a study of California Community Colleges. Santa Barbara, CA: Chancellor’sOffice of the California

Conference Session

Mathematics Division Technical Session 1

Collection

2018 ASEE Annual Conference & Exposition

Authors

Nancy Romance, Florida Atlantic University; Ali Zilouchian, Florida Atlantic University; Michael Vitale, East Carolina University; Lisa Greenberg, Florida Atlantic University

Tagged Topics

Diversity

Tagged Divisions

Mathematics

gateway mathematics courses, (b) providing participants course-specific mentoringsupport offered by the University’s engineering majors for the same gateway courses, (c)working with math faculty across all three institutions by forming a learning community that isaddressing issues involving curricular coherence across the gateway courses which, in turn,provides an additional academic support for project participants who are enrolled in coursestaught by the faculty, and (d) refining the gateway mathematics courses with an emphasis oncore concepts, curricular coherence and curricular alignment that supports student conceptualunderstanding.Project InterventionGateway Mathematics Course Curricular RefinementThe mathematics partnership includes

Conference Session

Mathematics Division Technical Session 3

Collection

2019 ASEE Annual Conference & Exposition

Authors

Daniel Raviv, Florida Atlantic University

Tagged Divisions

Mathematics

therefore we use discrete valuesthat can help in developing good intuition for the different rules.The paper details many examples, among them:(a) Chain Rule:--Inflating a balloon: Change in the volume of a constantly inflated (or deflated) balloon dependson the change in its radius which changes as a function of time.(b) Product Rule:--Delivering apples: An agricultural plant delivers apples on a daily basis. The apples are packedin a fixed number of boxes with of a fixed number of apples in each box. The company is tryingto calculate the change in the total number of apples if it changes both the number of boxes andthe number of apples in each box. A specific numerical and visual example shows how tocalculate this change and how it is

Conference Session

Integrating Math, Science, & Engineering

Collection

2006 Annual Conference & Exposition

Authors

Leslie Keiser, University of Tulsa; William Hamill, University of Tulsa; Bryan Tapp, University of Tulsa; William Potter, University of Tulsa; Jerry McCoy, University of Tulsa; Peter LoPresti, University of Tulsa; Donna Farrior, University of Tulsa; Shirley Pomeranz, University of Tulsa

Tagged Divisions

Mathematics

6 . L e a rn in g a s m e m o r iz in g in ta c t L e a r n i n g a s c o n s tr u c t i n g a n d u n d e r s t a n d i n g k n o w le d g e I V . U s e f u ln e ss o f M a th e m a tic s F a ll: 5 .3 4 S p r in g : 4 .7 1 7 . M a th e m a tic s a s a s c h o o l s u b je c t w ith M a th e m a tic s a s a u s e fu l e n d e a v o r little v a lu e in e v e ry d a y life o r fu tu re w o rkFor example, with respect to Dimension 1: The Nature of Mathematical Knowledge -Composition of Mathematical Knowledge, a response of 1 indicates that a student feels thatmathematical knowledge

Collection

2016 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University

Tagged Divisions

Mathematics

responses. Participants are asked tocalculate the definite integral of the function f(x) = x2 on the interval [1, 2] by using the limitdefinition of Riemann integral. Missing conceptual knowledge of the participants in calculus areobserved when they were incapable of determining the solution to the problem.Key Words: Riemann integral, functions, derivative, triad classification, APOS theory.IntroductionRiemann integral is an important concept in calculus that is often used by engineering andmathematics majors during their undergraduate and graduate studies. Given a continuous functionf on an interval [a, b], the Riemann integral (for definite integral) of f on the given interval can bedetermined by using the limit of sums

Conference Session

Issues and Solutions in Mathematics Education

Collection

2010 Annual Conference & Exposition

Authors

Andrew Grossfield, Vaughn College of Aeronautics

Tagged Divisions

Mathematics

the equation so that the unknown appears only once and is isolated on one side ofthe equation. The rules for changing the forms of the conditions without changing the values ofthe unknowns are well known. If a = b and c = d, then a + c = b + d, ac = bd,a - c = b - d, and if c and d ∫ 0 then a/c = b/d. In addition, identities can be used to changethe forms of expressions.I have no fixed order for performing the form changing manipulations. I examine each equationin order to select a course of action, which will bring me closest to obtaining the solution.Acquiring the ability to follow fluently the mathematical calculations by either a professor or atext will require some practice on the part of the student but the strategy should always be

Conference Session

Mathematics Division Technical Session 1

Collection

2013 ASEE Annual Conference & Exposition

Authors

Catherine Matos, Clayton State University; Tamara Pearson, Clayton State University

Tagged Divisions

Mathematics

Page 23.720.5semesters. Student performance shows a significant increase (z = 1.898, P =0.029) in theproportion of students passing the class (grade of A, B or C) from Fall 2010 to Fall 2012. In bothcourses, Maple was used in class, while Camtasia recordings and posted class notes were addedfor the 2012 class. Use of Maple was more extensive in the 2012 class. The P value gives theprobability of obtaining a difference in sample proportions that is at least as large as what wasactually obtained, if there is actually no difference in the population proportions. P-values below0.05 are generally regarded as strong evidence of a difference in population proportions. The z-score value gives the number of standard deviations away from 0 (no

Conference Session

Mathematics Division Technical Session 2: Poster Presentations

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Daniel Raviv, Florida Atlantic University

Tagged Topics

Diversity

Tagged Divisions

Mathematics

littleattention to connecting the concept to reality. The paper focuses on two sets of examples: 1. Examples that are unrelated to time. These include (a) discontinuity in space, forexample water levels at different sides of the locks in Panama Canal, sharp change in elevationof sidewalks (known as curbs), length of unused paper towel or toilet paper, change in brightnesslevel from light to shadow and between intensity level of pixels in a digital image, (b) numericaldisplays, such as an abrupt change in the numerical display of an elevator’s floor, change indigital display of radio frequencies, (c) switch-based devices such as light switches, (d) audiofrequencies, such as audio frequencies of piano keys, and (e) cartoon-based and non

Conference Session

Engineering and Mathematics Potpourri

Collection

2009 Annual Conference & Exposition

Authors

Andrew Grossfield, Vaughn College of Aeronautics

Tagged Divisions

Mathematics

AC 2009-700: VISUAL ANALYSIS AND THE COMPOSITION OF FUNCTIONSAndrew Grossfield, Vaughn College of Aeronautics Throughout his career Dr. Grossfield has combined an interest in engineering design and mathematics. He studied Electrical Engineering at the City College of New York, graduating with a BSEE. During the sixties, he attended the NYU Courant Institute at night, obtaining an M.S. degree in mathematics, while designing circuitry full time during the day for aerospace/avionics companies. He earned his doctorate studying Continuum Mechanics under the direction of L. M. Milne-Thomson, CBE at The University of Arizona. He is a member of ASEE, IEEE, and MAA. Grossfield@IEEE.org is his email

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

Mathematics Division Technical Session 3

Collection

2016 ASEE Annual Conference & Exposition

Authors

James E. Lewis, University of Louisville; Gerold Willing, University of Louisville; Thomas D. Rockaway, University of Louisville

Tagged Divisions

Mathematics

Paper ID #15737Peer-Led Team Learning in an Introductory Calculus CourseDr. James E. Lewis, University of Louisville James E. Lewis, Ph.D. is an Assistant Professor in the Department of Engineering Fundamentals in the J. B. Speed School of Engineering at the University of Louisville. His research interests include paral- lel and distributed computer systems, cryptography, engineering education, undergraduate retention and technology (Tablet PCs) used in the classroom.Dr. Gerold Willing, University of Louisville Gerold (Jerry) A. Willing is an Associate Professor in the Chemical Engineering Department at the Uni

Conference Session

Mathematics Division Technical Session 2

Collection

2018 ASEE Annual Conference & Exposition

Authors

Jose Roberto Portillo, Universidad Galileo; Alberth E Alvarado, Universidad Galileo; Jorge Samayoa Ranero, Universidad Galileo

Tagged Topics

Diversity

Tagged Divisions

Mathematics

Differential Calculus) offered for part-time students during the first semester of 2017.This section was comprised of 15 students from different specializations within engineering and itis offered in a suitable schedule (during evenings) for part-time students.GL - TBLIn order to implement the GL-TBL, we created groups of five students which we formed takinginto account the following characteristics: a. Academic profile (measured using a diagnostic test [14]) b. Gender c. Age d. Years of enrollment in the university (some students may have been held back in the course)In GL-TBL, group formation is crucial. This methodology requires that the students workinteractively, with a common goal: to learn while helping other students in their

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

Mathematics Division Technical Session 1

Collection

2018 ASEE Annual Conference & Exposition

Authors

Amitabha Ghosh, Rochester Institute of Technology (COE)

Tagged Topics

Diversity

Tagged Divisions

Mathematics

compound angles (e.g., how sin (A+B) may be used to yield sin 2A or, sin 3A)4. Clearly establish the understanding of a well-posed problem using a lumped, differential orintegral approach.4. Sketch a tiny volume and write conservation laws using first order approximations, then showthe transition to differential equations including dividing by the volume before limits. As anexample, each term of Navier-Stokes equation for incompressible flows expresses force per unitvolume. Continue with simplifications to various applications in two and three dimensions.5. Discuss concepts in creation of a boundary condition by using a stretched CV.6. Thoroughly review dimensional analysis for algebraic and differential equations.7. Discuss regimes of fluid flows