Conference Session

Using Computers, Software, and Writing to Improve Mathematical Understanding

Collection

2012 ASEE Annual Conference & Exposition

Authors

N. Jean Hodges, Virginia Commonwealth University, Qatar

Tagged Divisions

Mathematics

to do so.One teaching strategy shown by researchers since the 1960s and 1970s to be an effective learningand thinking tool is writing. Writing enables the writer to capture otherwise random thoughts byplacing them on a writing surface where they become concrete and thus more readily examined andmanipulated. Consequently, writing should be an effective tool for enabling math students to retainthe mathematical principles being developed in the classroom as well as for aiding them to improvetheir critical thinking abilities needed for applying their mathematical understandings to problems ofthe modern world.By incorporating writing that emphasizes critical thinking into the math classroom, this study seeksan answer to two questions: (1) how can

Conference Session

Using Computers, Software, and Writing to Improve Mathematical Understanding

Collection

2012 ASEE Annual Conference & Exposition

Authors

John Schmeelk, Virginia Commonwealth University, Qatar

Tagged Divisions

Mathematics

AC 2012-2998: EDGE DETECTORS IN ENGINEERING AND MEDICALAPPLICATIONSDr. John Schmeelk, Virginia Commonwealth University, Qatar Page 25.489.1 c American Society for Engineering Education, 2012 Edge Detectors in Engineering and Medical ApplicationsAbstract Image edge detection is an integral component of image processing to enhance theclarity of edges and the type of edges. The current paper compares two methods forfinding the edges of an image. One method developed by the author is to define specialmatrices and applying them to the image using approximations for gradients

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

a project on first-order ordinary differential equations): The project described below is self-contained, meaning that you should be able to do it by carefully reading through it and using what you learned in class about first-order ordinary differential equations. A carefully written report is expected, which can be done in (legible) handwriting or typed with a text processor. You do not need to copy the problems into your report, but should clearly label to which problems your answers refer. Include the calculations that lead to your answers. Wherever appropriate, in particular if you are asked to state and justify an opinion, write your answers in full sentences and adequate English

Conference Session

Mathematics Division Technical Session 4

Collection

2015 ASEE Annual Conference & Exposition

Authors

Peter Goldsmith P.Eng., University of Calgary

Tagged Divisions

Mathematics

ua(D) = yb(D), (1)where u ∈ C∞ is the input signal, y ∈ C∞ is the output signal, a, b ∈ R[x] are real polynomials withb = 0, and D is the differential operator, applied in postfix notation. This defines a binary(input-output) relation R between u and y, and so we write it as uRy. This relation is obtainedfrom (1) as R = a(D)b(D)−1 , which is the (postfix) composition of two relations: the operatora(D) and the converse relation b(D)−1 . This rational relation 8 , also written as R = a(D)/b(D),represents the set of all (u, y) ∈ C∞2 satisfying (1).Like transfer functions, rational relations may be added, composed, and inverted (via theconverse) to model parallel, series, and feedback interconnections of

Conference Session

Issues and Answers in Mathematics Education

Collection

2011 ASEE Annual Conference & Exposition

Authors

Peter J. Sherman, Iowa State University

Tagged Divisions

Mathematics

traditional formative frameworkassociated with K-12 education, but rather, in relation to what one might deem, the positiveoutcome framework associated with students majoring in STEM areas at the university level.The motivation for this approach is based on an argument that, while university students inSTEM disciplines are considered as STEM education achievements, fundamental flaws in basicconceptual mathematical knowledge persist; flaws that if more aggressively addressed at the K-12 level could result in attracting more youth to pursue STEM interests. The argument is basedon personal anecdotal evidence associated with the author‟s experiences. Hence, it does not havea rigorous foundation. Nonetheless, it is an argument that will hopefully resonate

Conference Session

Computers and Software in Teaching Mathemathetics

Collection

2009 Annual Conference & Exposition

Authors

Ali Farahani, National University, San Diego

Tagged Divisions

Mathematics

and operations on sets are fundamental in discrete mathematics; Python has apowerful built in list type and set object that can easily be used to experiment with constructionof sets as well as operations on them. A list type in Python can be a heterogeneous collectionwhich can be modified. Often in a discrete mathematics course a set builder notation is used toconstruct a set. For example, the set of the first twenty even numbers using set builder notation isdenoted by S ? {x | x ? 2n;0 ∞ n ∞ 19} . In Python this set can easily be specified by S = [2*x for x in range(19)]The syntax is very intuitive and maps well to its counterpart in mathematics. Once a set a built, itis easy to index though its elements in a simple

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

calculus,physics and chemistry. These are followed by the engineering science core courses that areintended to provide students with a foundation in fundamental principles needed for engineeringanalysis and the strong problem-solving skills required for upper-level courses that focus ondiscipline-specific material. Unfortunately, the engineering science core is often perceived bystudents as unrelated chunks of information that have unrelated problem-solving techniques andterminology [4].CAP provides a unifying framework for teaching the core engineering science courses. It doesthis by reframing the underlying physical principles using a common, consistent approach thatemphasizes the similarities between the material in different courses which is

Conference Session

Changing the Classroom Environment in Mathematics Education

Collection

2014 ASEE Annual Conference & Exposition

Authors

Rebecca Bourn, Tribeca Flashpoint Media Arts Academy; Sarah C. Baxter, University of South Carolina

Tagged Divisions

Mathematics

provides a structural framework that emphasizes real-worldapplication, encourages self-discovery and analysis, and teaches fundamental concepts, tools,and skills. It was originally designed for geotechnical engineering students. The designersunderstand that their discipline was as much art as science due to the many variable andunknown conditions [4] and no existence of one `right` answer. The theme of this paper is thatthis framework can also be used effectively to teach mathematics in a way that providesmotivation and context in conjunction with the rote practice of skills; offering a blend ofconstructivism and formalism.Background on EFFECTsThe goal of the EFFECTs framework is to formalize the theory-practice-revise problem solvingmethod in a

Conference Session

Integrating Math, Science, & Engineering

Collection

2006 Annual Conference & Exposition

Authors

Bruno Osorno, California State University-Northridge

Tagged Divisions

Mathematics

power system for a new mission. In the past he worked for several years as an electrical design engineer for a world wide chemical company. Currently he is a professor of Electrical and computer Engineering at California State University Northridge and lead faculty member in the Electric Power Systems graduate and undergraduate program. Page 11.1158.1© American Society for Engineering Education, 2006 Student Engagement through Mathematical Applications in Electrical Power SystemsAbstract- : Historically, electrical engineering students have been very proficient in

Conference Session

Students' Abilities and Attitudes

Collection

2010 Annual Conference & Exposition

Authors

Maria Terrell, Cornell University Math Dept.; Robert Terrell, Cornell University; Lisa Schneider, Cornell University

Tagged Divisions

Mathematics

based on the inter-correlations of the eleven items on the MAI). His estimate of reliability based on this methodyielded alpha = .77 which is lower than the range of .85 but is not alarmingly low given thebrevity of an 11 item scale like the MAI. We plan to modify the test by adding items andexplore the relationships between the items, to improve the reliability of the test.The next phase of test development is to write multiple choice versions of the questions andalternate forms of the exam. Distracters have been written by analyzing students’ responses tothe open ended questions on the pretest and posttest. We have also gathered information abouthow students responded to the questions through in depth interviews with 14 of the test

Conference Session

Mathematics Division Technical Session 3

Collection

2018 ASEE Annual Conference & Exposition

Authors

Campbell R Bego P.E., University of Louisville; Patricia A. Ralston, University of Louisville; Angela Thompson P.E., University of Louisville; Adrienne Parsons, University of Louisville; Gale J. Crush, University of Louisville, Speed Scientific School

Tagged Divisions

Mathematics

Paper ID #21341Flipping the Differential Equations Classroom: Changes Over TimeMs. Campbell R Bego P.E., University of Louisville Campbell Rightmyer Bego is currently pursuing a doctoral degree in Cognitive Science at the University of Louisville. She researches STEM learning with a focus on math learning and spatial representations. Ms. Bego is also assisting the Engineering Fundamentals Department in the Speed School in performing student retention research. She is particularly interested in interventions and teaching methods that allevi- ate working memory constraints and increase both learning retention and

Conference Session

Computers and Software in Teaching Mathmatics

Collection

2011 ASEE Annual Conference & Exposition

Authors

Micah Stickel, University of Toronto

Tagged Divisions

Mathematics

beeffective for increasing student engagement is to place these abstract concepts in a practicalcontext2,3,4,5. This way the students can experience the usefulness of these concepts and canrelate it to the other subjects which they are learning at the same time.With the ultimate goal of having students learn the fundamental mathematical concepts presentedin the initial years of the program, it is helpful to enable the student see and discover how thematerial is relevant to the rest of their engineering curriculum. This can provide an extraincentive for the student to engage with the material at hand. Since the vast majority of studentlearning happens outside of the lecture hall, it is important to create such experiences so thestudent is motivated to

Conference Session

Mathematics Division Technical Session 3

Collection

2015 ASEE Annual Conference & Exposition

Authors

Eliud Quintero, Tecnologico de Monterrey (ITESM); Patricia Salinas, Tecnologico de Monterrey (ITESM)

Tagged Topics

Diversity

Tagged Divisions

Mathematics

and integral are included in thefirst course, instead of the classic Differential Calculus course. The Fundamental Theorem ofCalculus has been adopted as an initial state, giving a strategy to accomplish the practice of Page 26.1556.2predicting values of a magnitude that is changing. This meaning allows the student to make senseof the concepts of derivative and integral (antiderivative) when dealing with the study of motionover a straight line2, 3, 4.We have been evaluating different software for learning goals, fitting this innovative approachfor Calculus. The need of a dynamic interaction between the user (student) and the tool(software

Conference Session

Integrating Math, Science and Engineering

Collection

2008 Annual Conference & Exposition

Authors

Hong Liu, Embry-Riddle Aeronautical University, Daytona Beach

Tagged Divisions

Mathematics

students to learn mathematics is to insert a small dose of applicationoriented modules into a traditional course.The performance objectives of MMM and the team projects are as follows: Page 13.939.31. Knowledge of using modeling methodology and processes to divide and conquer complicated problems2. Skills to use mathematical modeling tools to model an application incrementally3. Techniques to use graphics tools to present information intuitively4. Capability to combine mathematical analysis with numerical solutions to gain insight and justify answers to a problem5. Framework to write a mathematical paper6. Experience of working in teams and

Conference Session

Mathematics in Transition

Collection

2006 Annual Conference & Exposition

Authors

Bella Klass-Tsirulnikov, Sami Shamoon College of Engineering (formerly Negev Academic College of; Sharlene Katz, California State University-Northridge

Tagged Divisions

Mathematics

and processes to solve practical problems.Much of the gap between the sense of concrete and abstract in engineering lies in the poorscientific and mathematical background of engineering freshmen. The indispensable disciplinesof mathematics and physics, based on non-intuitive models, are sometimes inadequately treated Page 11.1263.2in the K-12 community.It is well-known that students with a solid background in mathematics and physics have a betterchance of succeeding in an engineering program. A study2 of predictive factors for success in anElectrical Engineering Fundamentals course, using the final course grade as the success metricfound that

Conference Session

Mathematics Division Technical Session 3: Diversity in Mathematics Education

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Kathleen Marie Fick, Methodist University; Denise H. Bauer, Methodist University

Tagged Divisions

Mathematics

differentiates the course from the traditionally taught MAT 1130Precalculus I course. The main differences include the added lab hour for the brief review of thefoundational and fundamental College Algebra concepts and the implementation of activities asboth group work and/or board work. These activities had students up, moving, conversing, andworking together to complete tasks within the classroom and lab. Figure 2 provides an exampleof the simple additional reading/writing questions attached to particular content quiz questions. Table 2: Pedagogical Differences of MAT 1130 Precalculus I and the newly created MAT 1125 Integrated Precalculus IMAT 1130: Precalculus MAT 1125: (NEW COURSE

Conference Session

Mathematics Division Technical Session 4: Assessing Success in Mathematics Education

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Daniel Raviv, Florida Atlantic University; Daniel Ryan Barb, Florida Atlantic University

Tagged Divisions

Mathematics

Paper ID #29078A Visual and Engaging Approach to Teaching and Learning the NormalDistributionDr. Daniel Raviv, Florida Atlantic University Dr. Raviv is a Professor of Computer & Electrical Engineering and Computer Science at Florida Atlantic University. In December 2009 he was named Assistant Provost for Innovation and Entrepreneurship. With more than 25 years of combined experience in the high-tech industry, government and academia Dr. Raviv developed fundamentally different approaches to ”out-of-the-box” thinking and a breakthrough methodology known as ”Eight Keys to Innovation.” He has been sharing his contributions

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

. Present J-Track – 3D from NASA’s website that tracks satellites in real-time as shown in Fig. 1.1. Fig. 1.1: Screen shot of NASA’s J-Track 3D 2. Pose part of the problem Ask: What do you think those dots are around the earth in the image? Have the students write down their answers. Explain to them that those dots are satellites that are being tracked in real-time on NASA’s website. Some seem closer to earth and some are farther, why do you think that is so? Is there any pattern to any of the sets of dots? Explain the term geosynchronous and ask if the picture shows satellites that exhibit that behavior. Ask: How far do you think are

Conference Session

Mathematics Division Technical Session 2

Collection

2018 ASEE Annual Conference & Exposition

Authors

Daniel Raviv, Florida Atlantic University

Tagged Divisions

Mathematics

Paper ID #22186Have You Seen an Integral? Visual, intuitive and Relevant Explanations ofBasic Engineering-related Mathematical ConceptsDr. Daniel Raviv, Florida Atlantic University Dr. Raviv is a Professor of Computer & Electrical Engineering and Computer Science at Florida Atlantic University. In December 2009 he was named Assistant Provost for Innovation and Entrepreneurship. With more than 25 years of combined experience in the high-tech industry, government and academia Dr. Raviv developed fundamentally different approaches to ”out-of-the-box” thinking and a breakthrough methodology known as ”Eight Keys to

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

varied from zero to 30.Begin with a system that is designed to recognize only two numerals (0 and 1). Apply each ofthe two inputs with varying numbers of pixel errors and observe the output. For each case varythe position of the pixel error. Students can use a calculator or existing software, or even write aprogram to repeat these calculations. Repeat the tests for systems that recognize more than twonumerals.Exercise 2 - Increasing the Character Set: Repeat the design performed in section V for more Page 12.1557.13than seven numerals. How many characters can the system recognize?Exercise 3 - ABC Character Recognition: Design a neural network 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

. “I learned a lot about how to teach math in a more understandable, hands-on way.Math was my weakest subject as a child and this program opened my eyes to how involved andeasy math can be. I learned a lot about patterns. The terms were words I had never associatedwith math.” Throughout this whole process, the facilitators of the workshops acted as guides,allowing teachers to construct their own meaning about what was required to implement theprogram effectively and providing questions to facilitate discussion. One teacher commented onthis reflection process on her questionnaire by writing, “I learned how helpful it is to getfeedback from others. It helps to communicate ideas that work and fail”.methodology: This paper describes a

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

over a subinterval and the average rate of change of thefunction over that subinterval. To meaningfully interpret the graph of a function that representstwo quantities that co-vary, students need to be able to simultaneously attend to and distinguishamong three quantities: the value of the output of a function, the change in the values of thefunction’s output over a subinterval, and the change in values of the input to the function.Reasoning about the latter two quantities is a foundational understanding for average rates ofchange in pre-calculus and instantaneous rates of change in calculus.An equally important educational objective for engineering students is the ability to interpret andcommunicate their mathematical reasoning about rates of

Conference Session

Mathematics Division Technical Session 1

Collection

2016 ASEE Annual Conference & Exposition

Authors

Rebecca Bourn, University of Wisconsin - Milwaukee; Sarah Baxter, University of St. Thomas

Tagged Divisions

Mathematics

challenging part of adopting the EFFECTs approximate the shape of the bell? approach for mathematics modules is to find a way to include an aspect of reflection. Visualization and demonstration are powerful tools, but a reflectioncomponent can help make students more aware of how they learn and when the learning is basedon internalizing the information, rather than memorizing. Because most of our students approachmathematics from the perspective of engineering, demonstrations have wide appeal, writing anessay does not. The approach that has been the easiest to implement so far has been short guideddiscussions, and greater transparency in explaining to the students

Conference Session

Mathematics Division Technical Session 2

Collection

2019 ASEE Annual Conference & Exposition

Authors

Scott W. Campbell, University of South Florida; Carlos A. Smith PhD, University of South Florida; Silvia M. Calderon, Universidad de Los Andes, Venezuela

Tagged Divisions

Mathematics

containing a fluid with mass Mf and heatcapacity Cf, initially at a temperature Tf(0). A value for the convective heat transfercoefficient h between the pellet and fluid is given. Students are asked to determine thetemperatures T of the pellet and Tf of the fluid as functions of time, ignoring any thermalinteractions between the cooling bath and surroundings. A diagram of the problem isshown in Figure 1a.Figure 1. Quenching of a pellet in a small bath (a) and in a large bath (b).Previously, students have been exposed to the fundamentals of heat transfer to a lumpedparameter system through the basic notion of conservation of energy (rate ofaccumulation of energy in the system = rate of energy entering – rate of energy leaving).In addition, they have

Conference Session

Mathematics Division Technical Session 2

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Blair J. McDonald P.E., Western Illinois University; Susan C. Brooks, Western Illinois University - Quad Cities

Tagged Divisions

Mathematics

that students areoften required to show in their solutions is minimal. For full credit, high school students areaccustomed to simply writing their answers down in a list. In college-level math, science, andengineering courses, they quickly learn that showing their work is not just encouraged, it isrequired! Some students have never had to show any work, and they really don’t know how. Inpractice, just knowing how to find the answer is not enough. Presenting and defending a solutionrequires that the solution be supported with dialogue explaining what was done and why it wasdone. Students cannot create that dialogue without looking beyond the equations. They have tounderstand the model and the mathematics in order to explain it, and without an

Conference Session

Mathematics Division Technical Session 4: Assessing Success in Mathematics Education

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Danielle Marie Fredette, Cedarville University

Tagged Topics

Diversity

Tagged Divisions

Mathematics

Placement TestingCedarville University’s engineering program began in 1990 and has grown steadily since, nowwith over 300 students, six majors, and 24 full time faculty members. The programs areaccredited by the Accreditation Board for Engineering and Technology (ABET), though at thetime of this writing accreditation for two new programs is pending.The School of Engineering works very hard to advise each new and prospective student toward asuccessful academic trajectory, and student preparedness in math is perhaps the most significantand measurable indicator we have to help us toward that goal. The Science and Math Departmentoffers an internal placement test for incoming freshmen called the calculus readiness exam. Thetest is given to any incoming

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

, which must provide the basis for the Fundamentals of Computational Fluid Dynamics(CFD). A complete review of all fluid flow equations by the CV methods together withnecessary principles of statics and dynamics is conducted in the first two weeks of the Fluids IIcourse. This solves the preparedness check for our dual degree students who choose CFD as theirterminal elective. The traditional MS students take the sequence of Ideal Flows, ConvectivePhenomena and CFD in their thermal-fluids concentration before thesis work.Sample resultsHere we used a 10-step approach to reach the terminal CFD course in our program. Somesamples were reported before [6], [19]. The newly organized small steps not only providecoherence but have built-in motivational

Conference Session

Mathematics Division Technical Session 4

Collection

2018 ASEE Annual Conference & Exposition

Authors

Gianluca Guadagni, University of Virginia; Hui Ma, University of Virginia; Lindsay Wheeler, University of Virginia

Tagged Topics

Diversity

Tagged Divisions

Mathematics

research studyexplored the impact of the Teaching Methods course for UTAs and demonstrates the success ofour program. A discussion of the program and preliminary outcomes are discussed in this paper.IntroductionUndergraduate Teaching Assistants [UTAs] provide a fundamental support to our educationalmission. We started to employ them, as an experiment, in 2014 in a Differential Equationscourse, and we have reported about the details in [1a]. After few years many more courses in ourEngineering school, and Applied Mathematics (APMA) courses in particular, have introducedUTAs in their class activities. The project of this effort has grown substantially to become astable feature of our program. Students who enroll in our APMA courses know that in

Conference Session

Mathematics Division Technical Session 2: Poster Presentations

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Anibal Sosa, Universidad Icesi, Colombia; Norha M. Villegas, Universidad Icesi, Colombia; Stephanie Celis Gallego, Universidad Icesi, Colombia; Diego Antonio Bohórquez, Universidad Icesi, Colombia

Tagged Divisions

Mathematics

Paper ID #28781On the effectiveness of designing didactical situations targeting Rˆn toteach the concept of subspace in linear algebraDr. Anibal Sosa, Universidad Icesi Mathematician with a PhD in Computational Sciences from UTEP, and works as an Assistant Professor for the Dept. of Information Technology and Communications at Universidad Icesi (Colombia).Dr. Norha M. Villegas, Universidad Icesi, Colombia Norha M- Villegas is an Associate Professor in the Department of Information and Communication Tech- nologies, Director of the Software Systems Engineering Bachelor Program at Universidad Icesi, Cali, Colombia, an Adjunct

Conference Session

Mathematics Division Technical Session 1

Collection

2017 ASEE Annual Conference & Exposition

Authors

Campbell Rightmyer Bego, University of Louisville; Patricia A. Ralston, University of Louisville; Il Young Barrow, University of Louisville

Tagged Divisions

Mathematics

facilitate ongoing research on retention. Ms. Bego is a registered professional mechanical engineer in New York State.Dr. Patricia A. Ralston, University of Louisville Dr. Patricia A. S. Ralston is Professor and Chair of the Department of Engineering Fundamentals at the University of Louisville. She received her B.S., MEng, and PhD degrees in chemical engineering from the University of Louisville. Dr. Ralston teaches undergraduate engineering mathematics and is currently involved in educational research on the effective use of technology in engineering education, the incorpo- ration of critical thinking in undergraduate engineering education, and retention of engineering students. She leads a research group whose