Conference Session

Computers and Software in Teaching Mathematics

Collection

2010 Annual Conference & Exposition

Authors

Zohra Manseur, SUNY Oswego; Adrian Ieta, SUNY Oswego; Rachid Manseur, SUNY-Oswego

Tagged Divisions

Mathematics

generalcurriculum that together constitute a complete degree program: 1. General education requirements – these courses provide a broad college education in the arts, humanities, social sciences, natural sciences, mathematics, and computer science. 2. Cognates – these are the courses in areas that provide essential preparation for the study of engineering. These consist of courses in mathematics, chemistry, biology, physics, and computer science. 3. Core – Core courses in engineering provide the education and training needed for the professional practice of engineering. 4. Electives – These are typically choice courses mostly in engineering or the cognate subjects that allow students to acquire deeper knowledge in a

Conference Session

Computers and Software in Teaching Mathmatics

Collection

2011 ASEE Annual Conference & Exposition

Authors

Cheri Shakiban, University of St. Thomas; Michael P. Hennessey, University of St. Thomas

Tagged Divisions

Mathematics

publication. In addition to teaching regular math courses, I also like to create and teach innovative courses such as ”Mathematical symmetry of Southern Spain” and ”Mathematics and Architecture of the Incas in Peru”, which I have taught as study abroad courses several times.Michael P. Hennessey, University of St. Thomas Michael P. Hennessey (Mike) joined the full-time faculty as an Assistant Professor fall semester 2000. He is an expert in machine design, computer-aided-engineering, and in the kinematics, dynamics, and control of mechanical systems, along with related areas of applied mathematics. Presently, he has published 41 technical papers (published or accepted), in journals (9), conferences (31), or magazines (1). In

Conference Session

Engineering Mathematical Potpourri

Collection

2011 ASEE Annual Conference & Exposition

Authors

John Schmeelk, Virginia Commonwealth University, Qatar

Tagged Divisions

Mathematics

ProcessingAbstract Image edge detection is an integral component of image processing to enhancethe clarity of edges and the type of edges. Issues regarding edge techniques wereintroduced in my 2008 paper on Transforms, Filters and Edge Detectors.15 The currentpaper provides a deeper analysis regarding image edge detection using matrices; partialderivatives; convolutions; and the software MATLAB 7.9.0 and the MATLAB ImageProcessing Toolbox 6.4. Edge detection has applications in all areas of research,including medical research6,16. For example, a patient can be diagnosed with ananeurysm by studying the shape of the edges in an angiogram. An angiogram is thevisual view of the blood vessels (see Figure 1-Vascular Web image). The previouspaper15 studied

Conference Session

Integrating Math Science and Engineering

Collection

2011 ASEE Annual Conference & Exposition

Authors

Po-Hung Liu, National Chin-Yi University of Technology; Ching Ching Lin, National Taipei University of Technology; Tung-Shyan Chen, National Chin-Yi University of Technology, Fundamental General Education Center; Chiu-Hsiung Liao, National Chin-Yi University of Technology, Fundamental General Education Center; Yen Tung Chung, National Chin-Yi University of Technology, Fundamental General Education Center; C. Lin, National Chin-Yi University of Technology, Taiwan R.O.C.; Ruey-Maw Chen, National Chin-Yi University of Technology

Tagged Divisions

Mathematics

-related courses werebetter than their counterparts in reformed Calculus I classes. Furthermore, 44% of reformedCalculus I students changed to traditional Calculus II programs and only 18% of traditionalCalculus I students shifted to reformed Calculus II. Baxter, Majumdar, and Smith[1] alsosurveyed reformed and traditional calculus students’achievement in the Math-ACT andfound that traditional Calculus I students’average grade was slightly higher than that in thereformed Calculus I, but only 52% of traditional Calculus I students passed the exam,significantly lower than reformed Calculus I students’passing rate of 64%. As for succeedingperformance, reformed Calculus I students surpassed the traditional students in Physics I andCalculus II, yet

Conference Session

Computers and Software in Teaching Mathmatics

Collection

2011 ASEE Annual Conference & Exposition

Authors

Lin Li, Prairie View A&M University; Yonggao Yang, Prairie View A&M University

Tagged Divisions

Mathematics

efficient in increasing studentengagement and supporting teachers’ instructional needs. The key strategy of the project is todevelop innovative math learning modules and use them to enhance students’ performance. Byapplying cutting-edge computer graphics and virtual reality technologies, these modules can: (1)make mathematics learning interesting while still retaining the underlying contents; (2) makeabstract and non-intuitive mathematics concepts “visible” and “touchable”, and thereby, easy tounderstand; and (3) bridge mathematics and engineering and motivate students to pursueengineering careers.The goal of the project is to ensure that students, especially freshmen and sophomores, canbenefit from the instructional strategies and develop a solid

Conference Session

Students' Abilities and Attitudes

Collection

2011 ASEE Annual Conference & Exposition

Authors

John R. Reisel, University of Wisconsin - Milwaukee; Leah Rineck; Marissa Jablonski, University of Wisconsin, Milwaukee; Ethan V Munson, University of Wisconsin, Milwaukee; Hossein Hosseini, University of Wisconsin, Milwaukee

Tagged Divisions

Mathematics

the students finish all the topics in their pie they are given a comprehensive assessment todetermine if they have retained all the items in their pie. The progress assessments mostly givequestions that the students have currently worked on, and some that they are ready to learn. Thecomprehensive assessments give questions on any topic in the pie from the most basic materialto the last item that they learned. If the student earns a 92% or better on this assessment they aremoved to the next course. The 92% is based on percent mastery of the entire course, not 92% ofthe questions correct on the assessment. If they do not get a 92% they relearn the topics they gotwrong, and try the comprehensive assessment again. Figure 1 shows an assessment

Conference Session

Issues and Answers in Mathematics Education

Collection

2011 ASEE Annual Conference & Exposition

Authors

Paul J. Kauffmann, East Carolina University; Sviatoslav Archava, East Carolina University; Ricky T. Castles, East Carolina University; Heather L. Ries, East Carolina University; Stephanie T. Sullivan, East Carolina University; Karen A. De Urquidi, East Carolina University

Tagged Divisions

Mathematics

students believe arethe issues which have the most impact and the interventions which would be most useful. Thispaper contributes to that area of the literature by presenting the results of a survey of 87engineering majors who took pre calculus. All had taken pre calculus within the past foursemesters and only 11% of the respondents had received a D or F grade. Specifically, the surveyexplored the research questions in Table 1. Table 1: Summary of Survey Research Questions 1. Do students believe they were placed in pre calculus appropriately? a. Is this substantiated by the correlation of the test score and the grade? 2. What is the role of high school preparation and how should this influence the course

Conference Session

Integrating Math Science and Engineering

Collection

2011 ASEE Annual Conference & Exposition

Authors

Murray Teitell, DeVry University, Long Beach, CA; William S. Sullivan, DeVry University, Long Beach

Tagged Divisions

Mathematics

describe theauthors’ approach to adding original derivation assignments to the curriculum of engineering andtechnology courses in order to ensure the genesis of this creative skill set at the undergraduatelevel. The goal is to develop in undergraduate students learning patterns that will facilitate theability to write for any system, a set of equations that describes the system. II. INTRODUCTIONMathematical modeling entails finding a series of steps that define all the relationships in asystem. An example of a system is an energy system, a power system, an electronic circuit, amanufacturing process or a cancer cell. Each of these systems is an ongoing subject formathematical modeling.1-4 Students can use a

Conference Session

Students' Abilities and Attitudes

Collection

2011 ASEE Annual Conference & Exposition

Authors

Kristi J Shryock, Texas A&M University; arun r srinivasa, Department of Mechanical Engineering, Texas A&M University; Jefferey E. Froyd, Texas A&M University

Tagged Divisions

Mathematics

theirspecific expectations for student mathematical knowledge and skills.After receiving sample problems from five faculty members, the questions were analyzed todevelop a set of learning outcomes that would reflect the knowledge and skills required to solvethe problems. There was significant overlap among the problems, with respect to the knowledgeand skills expected. The resulting set of mathematics topics for which engineering facultymembers expected student mastery are listed in Table 1. Table 1. First-year Mathematics Topics Determined by Engineering Faculty Members Projection Vector Components (2-D) Derivative (using Chain Rule) Second Derivative

Conference Session

Students' Abilities and Attitudes

Collection

2010 Annual Conference & Exposition

Authors

Chih Hsien Huang, MingChi University of Technology

Tagged Divisions

Mathematics

AC 2010-725: AN INVESTIGATION OF ENGINEERING STUDENTS' ATTITUDESTOWARD CALCULUS IN TAIWANChih Hsien Huang, MingChi University of Technology Page 15.168.1© American Society for Engineering Education, 2010 An Investigation of Engineering Students' Attitudes toward Calculus in TaiwanAbstractThe purpose of this study was to investigate engineering students in Taiwan to (1) assess theirattitudes toward calculus, (2) determine the difference in attitudes scores between males andfemales and (3) assess the relationship between students, attitudes toward calculus and theircalculus achievement. Attitude was measured in cognitive, affective, and

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

: (1) Development of the first draft of the MAI, (2) Pilot testing the MAI,and (3) Preliminary analysis of the pilot test data.To develop the MAI, faculty of second- and third-year engineering courses were surveyed abouthow key concepts and techniques from single variable differential and integral calculus are usedin intermediate-level engineering courses. Based on their feedback, as well as feedback fromadvanced undergraduate engineering students, an initial set of test items was developed. Theresulting MAI consists of five open-ended questions with eleven sub-questions. The test isdesigned to be administered during one hour in paper-and-pencil format.The MAI was administered during the first week of the Fall 2009 semester as a pre-test to

Conference Session

Issues and Solutions in Mathematics Education

Collection

2010 Annual Conference & Exposition

Authors

Dianne Raubenheimer, North Carolina State University; Hatice Ozturk, North Carolina State University; Alina Duca, NCSU

Tagged Divisions

Mathematics

performance, pre-requisiteknowledge and skills. Page 15.239.2IntroductionThe mathematics knowledge and skills gap encountered by undergraduate engineering studentswhen they enter engineering courses requiring the use of mathematics abilities which weretaught in the three semester calculus sequence has been well documented 1, 2, 3. However, there is'widespread agreement among academics and practicing engineers that a good grounding inmathematics is essential for engineers' 4. The challenge facing the engineering instructor is howto bring all students up to mathematical mastery level as quickly as possible at appropriate pointsduring the semester when

Conference Session

Issues and Solutions in Mathematics Education

Collection

2010 Annual Conference & Exposition

Authors

Andrew Grossfield, Vaughn College of Aeronautics

Tagged Divisions

Mathematics

: variable, limit, polynomial, inverse function and function.Students embarking on a study of algebra must confront the word variable, usually defined as aletter representing a member of a set. In a study of rectangles, the length, width, area andperimeter, all belong to the set of positive real numbers. Can an area be added to a length? Canthe students be blamed for being confused?Variables are symbols representing measureable properties of systems. The concept is anotational device for writing the laws of these systems. Consider the set of rectangles as oursystem to study. The laws are relationships of the system, in this case: 1) The area of any rectangle is the product of its length and width and 2) the perimeter is twice the sum of

Conference Session

Issues and Solutions in Mathematics Education

Collection

2010 Annual Conference & Exposition

Authors

Andrew Grossfield, Vaughn College of Aeronautics

Tagged Divisions

Mathematics

to use if the table is not too long and the desired values of theindependent variable are listed. A table description of the function A = ρ R2 is shown inTable 1. 2 R A=ρR 0 0 1 A= ρ= 3.14159 2 A = 4 ρ = 12.56637 3 A = 9 ρ = 28.27433 4 A = 16 ρ = 50.26548 5 A = 25 ρ = 78.53982 6 A = 36 ρ = 113.09734Table 1Another format for describing functions is called a

Conference Session

Innovative Instructional Strategies and Curricula

Collection

2010 Annual Conference & Exposition

Authors

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

Tagged Divisions

Mathematics

teaching of MATH 131 at VCUQatar.This study, the fifth in a series examining ways to motivate learning of contemporary mathamong VCUQatar’s design students, summarizes the preceding studies and extracts from themobservations and recommendations that may be adapted to transform other analytical coursesinto culturally-appropriate studies.The Evolution of MATH 131The Journey. Year 1 (2005-2006, “Making Connections Among Culture, Personality, and ContentIn Analytical Courses”).3 MATH 131 at VCUQatar began with a textbook, graphic calculator,white board, and markers. Several lectures delivered each textbook topic. VCUQatar was afemale-only institution of mostly Qataris, who were difficult to motivate into studying andunderstanding the math

Conference Session

Approaches to Mathematics Curriculum to Include Projects and Technologies

Collection

2014 ASEE Annual Conference & Exposition

Authors

Gunter Bischof, Joanneum University of Applied Sciences; Annette Casey B.A., University of Applied Sciences FH JOANNEUM, Graz, Austria; Emilia Andreeva-Moschen, Bombardier Transportation Austria GmbH

Tagged Divisions

Mathematics

applies to lattice-gas models, which must be run at moderateMach numbers to remain incompressible, and to avoid spurious high-order nonlinear terms.The behavior of a viscous incompressible fluid is governed by the simplified Navier-Stokesequation, which can be written as ∂v 1 + ( v ⋅ ∇) v = − ∇p + ν ∆v ∂t ρ (1)and by the continuity equation (under the assumption of incompressibility): ∇⋅ v = 0, (2)where v is the flow velocity, p the pressure, ρ the constant mass density, and ν the kinematicviscosity4. The

Conference Session

The Use of Games and Unique Textbooks in Mathematics Education

Collection

2014 ASEE Annual Conference & Exposition

Authors

Adrian J. Lee, Central Illinois Technology and Education Research Institute; Sheldon H. Jacobson, University of Illinois, Urbana-Champaign; William A. Cragoe, Sacred Heart-Griffin High School

Tagged Divisions

Mathematics

highschool probability and statistics, and when delivered in the days prior to tournament tip-off, thecurriculum provides an excellent opportunity to inspire students into addressing real worldproblems through mathematical analysis.I. Introduction Commonly referred to as “March Madness”, the NCAA men’s basketball tournament fuelsthree weeks of excitement (and anguish) nationwide as fans root for their favorite collegiateteams to advance through each stage of the competition. Following a committee selectionprocess and set of four initial play-in games, sixty four teams – seeded 1 through 16 in fourseparate regions – participate in a single elimination tournament format to determine who will becrowned national champion. The structure of such a

Conference Session

Changing the Classroom Environment in Mathematics Education

Collection

2014 ASEE Annual Conference & Exposition

Authors

Robert Talbert, Grand Valley State University

Tagged Divisions

Mathematics

. Page 24.1233.1 c American Society for Engineering Education, 2014 The inverted classroom in introductory calculus: Best practices and potential benefits for the preparation of engineersWhat is the inverted classroom?Higher education has for many years organized its curricula and instruction around aninstructional design model that should be instantly recognizable to most readers. This modelinvolves three phases for each unit that is taught: 1. The instructor decides what concepts and topics should be covered in the unit and articulates a collection of learning objectives that will eventually be assessed. 2. The instructor uses class time to present information on the main

Conference Session

Mathematics Division Technical Session 4

Collection

2013 ASEE Annual Conference & Exposition

Authors

Murray Teitell, DeVry University, Long Beach; William S. Sullivan, DeVry University, Long Beach

Tagged Divisions

Mathematics

success,preparedness, and overall achievement of the outcomes of their degree program.Introduction Metrics are used to make measurements about performance in order to evaluate andcompare.1 They are widely used in sports to compare the performance of athletes in a game (e.g.batting averages and slugging average).2 Likewise, Metrics are used to compare the performanceof a task. 3 Software metrics are applied to measure the efficiency of the software/algorithm bymeasuring parameters such as speed and storage use.4, 5 A simple metric can measure how long ittakes to perform a task in actual time or man-hours (quantity), the number of resources required(quantity) and the quality of the outcome. A metric therefore usually measures quantity and

Conference Session

Mathematics Division Technical Session 2

Collection

2013 ASEE Annual Conference & Exposition

Authors

Shirley B. Pomeranz, University of Tulsa

Tagged Divisions

Mathematics

Conference Session

Mathematics Division Technical Session 4

Collection

2013 ASEE Annual Conference & Exposition

Authors

Hassan Moore, University of Alabama, Birmingham

Tagged Divisions

Mathematics

at the University of Alabama at Birmingham, co-authoring the textbook used in the course. As a National Director with the Mathematics Division of ASEE, he works tirelessly to grow and develop the STEM workforce in the Cen- tral Alabama area. Dr. Moore teaches (1) Engineering Mathematics and (2) Engineering Computation using MATLAB at UAB. Work Background / Experience: He interned at UNC/Chapel Hill, Argonne National Laboratory (Atomic Physics Division), and Entergy Corporation in Transmission and Distribution, and then Standards. He then began serving as a high school physics teacher for three (3) years where his students would inspire him to continue his education. Upon completing his doctoral studies, Dr

Conference Session

Mathematics Division Technical Session 4

Collection

2013 ASEE Annual Conference & Exposition

Authors

Kendrick T. Aung, Lamar University; Ryan Underdown, Lamar University; Qin Qian, Lamar University

Tagged Divisions

Mathematics

/2003 – 05/2003), University of Minnesota, Department of Geology and Geophysics • Research/Teaching Assistant (07/1998 – 02/2000), Nanjing University, Department of Earth Science, China • Construction Engineer and Geotechnical En- gineer (06/1994 – 06/1998) Nanjing Construction Company, China PUBLICATIONS Book Chapter Sediment pollution, Handbook of Hydrology, 2012 Journal paper 1. Qian, Q., Voller, V. and Stefan, H., 2010, Can the ”dispersion tensor model” for solute exchange in the sediment bed of a stream or lake be simplified? Advances in Water Resources 33 (2010) 1542–1550. DOI:10.1016/j.advwatres.2010.09.001 2. Qian, Q., Voller, V. and Stefan, H., 2009, Mod- eling of vertical solute dispersion in a sediment

Conference Session

Mathematics Division Technical Session 4

Collection

2015 ASEE Annual Conference & Exposition

Authors

Peter Goldsmith P.Eng., University of Calgary

Tagged Divisions

Mathematics

setting of abstract algebra, the theory is presentedhere in a less general but more accessible manner. We also introduce some new concepts andconstructs that increase its utility and pedagogical value. These include relation diagrams (thecounterpart of traditional block diagrams) and impedance relations. Examples illustrateapplications of the theory and its potential benefits for engineering education.1 IntroductionEngineers use problem solving to invent, design, build, and improve structures, machines,devices, systems materials, and processes. Thus, a central goal of engineering education is todevelop the problem solving abilities of students. Since mathematics is the basis for modeling,reasoning, and communicating solutions of technical

Collection

2016 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University

Tagged Divisions

Mathematics

either enrolled or recentlycompleted (i.e. 1 week after the course completion) a Numerical Methods or Analysis course at alarge Midwest university during a particular semester in the United States. Each participant wasasked to complete a questionnaire consisting of calculus concept questions and interviewed forfurther investigation of the written responses to the questionnaire. The research question isdesigned to understand students’ ability to apply Riemann’s limit-sum definition to calculate thedefinite integral of a specific function. Qualitative (participants’ interview responses) andquantitative (statistics used after applying APOS theory) results are presented in this work by usingthe written questionnaire and video recorded interview

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

benefits we aim to show are improved engineering readiness, reduced time-to-graduation,and improved performance in gatekeeper courses. In this report we show the results of the firstcohort, which did improve the Calculus placement for most students and were significantly moresuccessful at doing so than a traditional Pre-Calculus class, although the subsequentimprovement in performance in the Calculus 1 course was not statistically significant.KeywordsMathematics Placement, Emporium Models.IntroductionThe University of Texas – Pan American is a minority serving institution in Texas. The studentpopulation is predominantly made up of students from the local region, which includes two of

Conference Session

Mathematics Division Technical Session 3

Collection

2015 ASEE Annual Conference & Exposition

Authors

Seunghyun Chun, California Baptist University

Tagged Topics

Diversity

Tagged Divisions

Mathematics

strong science, technology, engineering, and math (STEM) workforce is essential and critical in advancing the economy and society of the future. But the U.S continues to trail the world in math and science. And also the number of U.S students pursuing a STEM career or educating is decreasing as mentioned in [1] – [3]. A change in the way math is taught and presented in the classroom is urgently needed. Instructors need to be able to engage the students in learning by communicating that the study of mathematics and its objective is not to study math for math sake but to be able to apply it as a tool to solve the world’s complex and essential problems. The topic of sustainable energy is no longer a topic reserved for scientists and

Conference Session

Mathematics Division Technical Session 2

Collection

2015 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University

Tagged Divisions

Mathematics

iscategorized as inter-level. Students’ trans-level triad classification is based on their abilityto answer the question correctly in the entire domain. Page 26.213.6 The Question The following question is designed to observe participants’ ability to transform analgebraic function from to its geometric/graphical representation by calculating the relatedlimit and derivative questions. A2G Problem: Please draw the graph of f ( x) = xx+1 at (e) below by finding and applyingeach of the following information if they are applicable.a) Vertical and horizontal asymptotes of f(x) and limiting values of f(x) at the vertical asymptotes if there exists any

Conference Session

Mathematics Division Technical Session 2

Collection

2016 ASEE Annual Conference & Exposition

Authors

Muteb M. Alqahtani, Rutgers University; Arthur Belford Powell, Rutgers University

Tagged Divisions

Mathematics

Arthur B. Powell Rutgers University Rutgers University muteb.alqahtani@gse.rutgers.edu powellab@andromeda.rutgers.eduDynamic geometry environments can support learning of geometry through meditating learners’activity. To understand how dynamic geometry environment mediate the activity of mathematicsteachers, we used Rabardel’s categories of instrument mediations in an instrument-mediatedactivity [1, 2]. We analyzed the discursive and inscriptive interactions of 4 mathematics teacherswho worked for 15 weeks in a team to construct geometric figures and solve open-endedgeometrical problems in a collaborative, dynamic geometry environment. In addition

Conference Session

Mathematics Division Technical Session 2

Collection

2016 ASEE Annual Conference & Exposition

Authors

Aaron Brakoniecki, Boston University; Michael Ward, Boston University; Gretchen Fougere, Boston University

Tagged Divisions

Mathematics

learn in their mathematics classrooms. In addition to these grade-levelcontent standards, there were also standards of mathematical practice that cut across grade levels(See Table 1). These standards described mathematical habits of mind, which are important forcritical consumers of mathematics content.MP1 - Make sense of problems and persevere in solving themMP2 - Reason abstractly and quantitativelyMP3 - Construct viable arguments and critique the reasoning of othersMP4 - Model with mathematicsMP5 - Use appropriate tools strategicallyMP6 - Attend to precisionMP7 - Look for and make use of structureMP8 - Look for and express regularity in repeated reasoning Table 1 – Standards for Mathematical Practice (NGA, 2010)What becomes

Conference Session

Mathematics Division Technical Session 4

Collection

2016 ASEE Annual Conference & Exposition

Authors

Virgil U. Pierce, University of Texas, Rio Grande Valley; Javier Angel Kypuros, University of Texas, Rio Grande Valley; Shirley J. Mills, University of Texas, Rio Grande Valley

Tagged Topics

Diversity

Tagged Divisions

Mathematics

at improving entering students’ college readinessand mathematics placement. The small scale intervention, A Bridge to Calculus, is intended toimprove students’ placement from College Algebra into Calculus 1. The target population forthis effort are students with high school experience in a Calculus course but whose performanceon placement exams does not reflect this experience. At our institution this is a significantnumber of students and the goal of the project is to develop methods to address and acceleratestudents in this category. The course design, to take advantage of the students’ prior experience,emphasizes practice and mastery using a modified emporium course design and the ALEKSsoftware1. This intervention runs as a summer course