similar to the research question of Baker, Cooley, and Trigueros (2000).This question is analyzed qualitatively and quantitatively by using the triad classification in Action-Process-Object-Schema (APOS) theory. Mathematics graduate and undergraduate students succeeded the most among all theparticipants.Key words: APOS theory, Schema, Triad Classification, Functions, Derivative, Limit, Asymptote, Critical Points. Introduction Function concept is an important part of cumulative blocks of concepts in advanced levelmathematics and engineering courses. In these advanced courses, topics of single-variablecalculus, such as limits, derivatives, integrals, and power series, require function knowledge. Thefunction concept also requires knowledge of
raised above, but concerns still remain. First, adding acredit-bearing course to an existing engineering curriculum is difficult because there is littleroom for additional credits. Second, it is not uncommon for sections of the same calculus courseto differ in pace and in the order of concepts covered, making it difficult to align the companion Page 23.275.2course content with a given calculus course. Lastly, student performance in paired courses ishighly correlated; thus, paired courses put students at risk—poor performance in multiplecourses will impact students’ financial aid and/or academic status.J. Neubert et al.11 presented a low-cost
Paper ID #31635Applications of Linear Algebra applied to Big Data AnalyticsDr. Rajendran Swamidurai, Alabama State University Dr. Rajendran Swamidurai is an Associate Professor of Computer Science at Alabama State University. He received his BE in 1992 and ME in 1998 from the University of Madras, and PhD in Computer Science and Software Engineering from Auburn University in 2009. He is an IEEE senior Member.Dr. Cadavious M Jones, Dr. Cadavious M. Jones is an Associate Professor of Mathematics at Alabama State University. He received his BS in 2006 and MS in 2008 from Alabama State University, and PhD in Mathematics
Paper ID #6112Developing Mathematical Intuition by Building Estimation SkillsDr. Rebecca Bourn, Tribeca Flashpoint Media Arts Academy Dr. Bourn designed the math curriculum for the Core Studies Program at the Tribeca Flashpoint Media Arts Academy. She received her PhD in Applied Mathematics from the University of Virginia School of Engineering and Applied Science.Dr. Sarah C. Baxter, University of South Carolina Professor Baxter is an Associate Professor in the Department of Mechanical Engineering at the University of South Carolina. She received her PhD in Applied Mathematics from the University of Virginia School of
topic is covered as a separate section in College Algebra classes andnot a lot of time is allocated. We suggest to include a literal equation type of problem after eachfunction topic is covered.Suggestion 6. Accept and integrate use of smart phone apps for relevant problemsIt is essential for new generation learners to utilize digital tools to solve problems as technologycontinues to change and evolve. Qualification of professions in engineering and technologyfields nowadays demands fast adaptation to the new technology and the ability of using digitaltools to find relevant information and solve problems in addition to strong mathematicalbackground. An introduction to smart phone apps by the instructors could help students makeuse of these
courses, when context,application, and sometimes even notation can be quite different. This is often true forengineering students with respect to the Calculus sequence.In courses such as Calculus, concepts and solution methods are typically presented within amathematical context. While some students can recognize the underlying structure and themathematical construction, others have trouble identifying patterns or parallel thought structures,which makes it difficult for them to generalize the concept to a range of problem types. Forexample, students in an Introduction to Mathematical Statistics course were reported to claimthey do not know how to integrate a probability distribution over a region. The pre-requisite forthe course is Multivariable
in engineering curriculum: Students conceptions and performance. Journal of Engineering Education, 101(1): 138–162, 2012.[18] J. Hiebert and P. Lefevre. Conceptual and procedural knowledge in mathematics: An introductory analysis. Conceptual and procedural knowledge: The case of mathematics, pages 1–27, 1986.[19] J. R. Star. Reconceptualizing procedural knowledge. Journal of Research in Mathematics Education, 36: 404–411, 2005.[20] L. Filipsson, M. Cronhjort, and M. Weurlander. Can peer instruction in calculus improve students’ learning? Proceedings of the 9th international CDIO conference, 2013.[21] K. Chappell and K. Killpatrick. Effects of concept-based instruction on students’ conceptual and procedural knowledge
AC 2009-115: WRITING TECHNIQUES FOR IMPLEMENTINGPROJECT-DIRECTED MATHEMATICSJohn Schmeelk, Virginia Commonwealth University Qatar Branch John Schmeelk, Virginia Commonwealth University, Qatar Branch Campus Dr. John Schmeelk is a Professor of Mathematics at Virginia Commonwealth University, Doha Qatar Branch, where he is engaged in applied mathematics, generalized functions, image processing and educational pedagogy. He received his PhD from George Washington University in Washington, D.C. He was awarded many summer faculty grants to go to Fort Rucker, Alabama implementing procedures utilizing generalized functions. He has been an invited speaker to conferences in Australia
organization that manages Education City, among other projects. Initiallysupervised solely by Qatar Foundation, VCUQatar began in 1998 as Shaqab College of DesignArt, but in 2002 the school became an official branch campus of VCUR, began to operate morefully under its direction, and was officially renamed Virginia Commonwealth University inQatar.VCUQatar’s approximately 200 students come not only from Qatar but from all over the world.Regardless of their nationality, all must study in English because the country’s rulers recognizeEnglish as the lingua franca of global business.VCUQatar undergraduates may major in Fashion Design, Graphic Design, Interior Design, orPainting and Printmaking. The curriculum imposes specified Liberal Arts and Sciences (LAS
Paper ID #29726Qualitative and Quantitative Analysis of University Students’ Ability toRelate Calculus Knowledge to Function GraphsDr. Emre Tokgoz, Quinnipiac University Emre Tokgoz is currently the Director and an Assistant Professor of Industrial Engineering at Quinnipiac University. He completed a Ph.D. in Mathematics and another Ph.D. in Industrial and Systems Engineer- ing at the University of Oklahoma. His pedagogical research interest includes technology and calculus education of STEM majors. He worked on several IRB approved pedagogical studies to observe under- graduate and graduate mathematics and engineering
thecoursework required for their degree, there are also seminars offered which attempt to moreexplicitly connect the work and experiences of engineers to that of the K-12 mathematicsclassroom. There are five seminars offered over the course of the program and range in topic toinclude engineering, technology, curriculum, professional communities, and other aspects ofinterest to new teachers.This paper describes an activity used in one of these seminars to connect the Engineering DesignProcess to the content and process standards in the Common Core State Standards. In thissession, 10 engineering undergraduate students and 10 beginning mathematics teachersparticipating in the special program worked together to solve an engineering design challenge byusing
, our Department of Mathematics at The University of Tulsarelocated to newly renovated offices, and I had the task of emptying my office drawers andcabinets after twenty-eight years in the same office. I found all of my calculus notebooks that Ihad saved from the late 1960s, when I was an undergraduate and took my first calculus courses.After more than thirty years of teaching calculus, and in observance of my fiftieth anniversary ofhaving taken my first calculus course, I would like to share some of my experiences in learningand teaching calculus. As an undergraduate at Barnard College, I took a sequence of calculuscourses at Columbia University that was intended for physics and engineering majors. I nowteach in a mathematics department that
learning.Marion Usselman, Georgia Institute of Technology Marion Usselman, Georgia Institute of Technology Dr. Marion C. Usselman is a Senior Research Scientist at the Center for Education Integrating Science, Mathematics and Computing (CEISMC) at the Georgia Institute of Technology. Marion received her B.A. in biophysics from the University of California, San Diego, and her Ph.D. in biophysics from Johns Hopkins University. She focuses on K-12 educational reform, university-K-12 partnerships, and equity issues in education.Thomas Morley, Georgia Institute of Technology Thomas Morley, Georgia Institute of Technology Dr. Morley, is a CEISMC Professor of Mathematics at Georgia Tech
began to operate more fully under the direction of VCUR.Within the curriculum for design students in both VCUR and VCUQ, one general educationrequirement for all students is a contemporary mathematics course (MATH 131). Tailoring thiscourse to fit the unique needs and interests of VCUQ majors became a unique and excitingchallenge that gave rise to the authors’ 2006 study entitled, “Making Connections AmongCulture, Personality, and Content in Analytical Courses,” which was presented at the March2006 Conference of Middle Eastern Teachers of Science, Mathematics, and Computing in AbuDhabi.In their previous studies, the authors relied upon the work of Ricki Linksman, an expert inaccelerated learning who founded the National Reading Diagnostic
Paper ID #7891Robotics: Enhancing Pre-College Mathematics Learning with Real-worldExamplesDr. Ravi T. Shankar, Florida Atlantic University Dr. Ravi Shankar is a professor in the computer and electrical engineering and computer science (CEECS) department in the college of engineering and computer science (COECS) at Florida Atlantic University (FAU) at Boca Raton, Fla. He is the director of a college-wide center on systems integration. He has a Ph.D. from the University of Wisconsin, Madison, Wisc., and an M.B.A. from FAU. He is a registered Professional Engineer in the State of FL, a Senior member of IEEE, and a fellow of
as to whySTEM is important in today’s world through small examples of what already exists. This is doneas a step toward increasing the standing that the United States holds currently within the world’sSTEM community, which is low compared to other countries. This is partially due to a lack ofinterest that many American students have in STEM-related fields. To fix this, the STEM-relatedactivities that students perform in schools today need to incorporate what they do in theireveryday lives.1. Introduction: Math in Engineering and STEMThe first question to ask here is, "What is STEM?" STEM is an acronym for "Science,Technology, Engineering, and Mathematics." It is an educational curriculum dedicated to thesubjects stated in the name. The term
science to coordinating learning communities addressing mathematics curriculum as a persistent barrier impacting student success and retention in undergraduate STEM pro- grams. She is currently OI on a NSF DR K-12, Co-PI on a USDOE Title III Hispanic Serving Institution, internal evaluator on FAU’s NSF Advance early phase grant, and a member of the Advisory Board on the NSF STEM+C in Broward Schools and the NSF MSP at the University of Toledo.Dr. Ali Zilouchian, Florida Atlantic University Dr. Ali Zilouchian is currently the Associate Dean for Academic Affairs and a professor in the College of Engineering and Computer Science at Florida Atlantic University. He is also currently the Director of ”CAPTURE” program which
asbeing “trivial” – contributes no added proficiency in mathematics as they are merely algorithmicor procedural, the observations that can be made from the results of applying these “trivial”methods can assist to expand students’ knowledge in the basic property of numbers, which weargue actually enhances mathematical proficiency.Algorithmic procedures, though probably never used in any real application, can provide a solidbackground for a more advanced topic later. Calculus students are taught Riemann sums and canbe assigned problems to approximate an area under a curve (maybe by hand) prior to introducingthe concept of integrals. After learning how to compute integrals analytically, students maynever use Riemann sums to calculate areas under
(ST), which is why we propose to think how to include, in engineeringeducation, some of the abilities or skills from ST, and from the math education perspective. Thereport [2] explicitly mentions the work done by Senge [4] and motivated by this fact this paperaims to show the advantages and benefits of incorporating systems thinking in a math class. It ishoped that through this, it can be stated that the wealth of integrating the two seemingly disjointin two different disciplines (Systems Thinking and Mathematics). The present work shows theresults of the design of an innovative course of Differential Equations (DE), by means of usingmodeling and computer simulation, to have an active learning environment [4]. This course hasbeen taught for
the creative integration of STEAM into these videos, for years teachers havetold the band that they were showing these videos in the classroom and using them to inspirestudents. In partnership with the Playful Learning Lab at the University of St. Thomas, OK Gocreated an online resource for educators called OK Go Sandbox. Using OK Go’s music videos asinspiration, OK Go Sandbox creates new videos, activities, and challenges that can be integratedinto the K-12 classroom to teach a variety of STEAM concepts.Why Math? OK Go’s lead singer, Damian Kulash, has often spoken about the importance of math inthe creation of their music videos. While discussing “The One Moment” music video, he states,“The dance we were trying to choreograph, all
problem.7 Students’ difficulty in sketching the derivative graph of a function is observed by Ferrini-Mundy et al.9 In theirstudy, many students first tried to find an algebraic representation of the given function. Aspinwall et al.3 focusedthe research outcomes on a single student and concluded incorrect derivative images resulting in students’incorrect analytical reasoning. Graduate and senior undergraduate mathematics students’ weak rate of changeknowledge is observed to cause weak understanding of the integration concept by Thompson.16Participants and the General Procedure The participants of this qualitative and quantitative study are 17 senior undergraduate and graduate studentsmajoring in mathematics or engineering who were enrolled
walls, 1986-1987; and the United States Air Force Summer Faculty Research Award, Edwards Air Force Base, California, to work on experimental and theoretical analysis of the fracture behavior of a composite solid rocket propellant, Summer 1989. He holds current membership in professional organizations the American Society of Mechanical Engineers and the American Society for Engineering Education. He has been awarded travel grants to present a research paper at the Fourth International Congress of Biorheology, Jikei University, Tokyo, Japan; expenses covered in part by an invited lecture travel grant from the In- ternational Congress of Biorheology and in part by a Purdue XL International Travel Grant, 1981; the
Paper ID #16578Longitudinal Success of Calculus I ReformDr. Doug Bullock, Boise State University Doug Bullock is an Associate Professor of Mathematics at Boise State University. His educational re- search interests include impacts of pedagogy on STEM student success and retention.Dr. Kathrine E. JohnsonDr. Janet Callahan, Boise State University Janet Callahan is Chair of Materials Science and Engineering at Boise State University. Dr. Callahan received her Ph.D. in Materials Science, M.S. in Metallurgy, and B.S. in Chemical Engineering from the University of Connecticut. Her educational research interests include freshman
AC 2011-51: EVALUATION OF THE IMPACTS OF MATH COURSE PLACE-MENT IMPROVEMENT ACHIEVED THROUGH A SUMMER BRIDGEPROGRAMJohn R. Reisel, University of Wisconsin - Milwaukee John R. Reisel is an Associate Professor of Mechanical Engineering at the University of Wisconsin- Milwaukee (UWM.) He serves as Associate Director of the Center for Alternative Fuels, and co-Director of the Energy Conversion Efficiency Lab. In addition to research into engineering education, his research efforts focus on combustion and energy utilization. Dr. Reisel was a 2005 recipient of the UWM Dis- tinguished Undergraduate Teaching Award, the 2000 UWM-College of Engineering and Applied Science Outstanding Teaching Award, and a 1998 recipient of
the 2001 ASEE Annual Conference. Page 12.1557.143. Buechler, Dale. "Mathematical Background versus Success in Electrical Engineering," Proceedings of the 2004 ASEE Annual Conference.4. Carpenter, Jenna; and Schroeder, Bernd S. W. "Mathematical Support for an Integrated Engineering Curriculum", Proceedings of the 1999 ASEE Annual Conference.5. Buechler, Dale, and Papadopoulus, Chris. "Initial Results from a Math Centered Engineering Applications Course", Proceedings of the 2006 ASEE Annual Conference.6. Douglas Josh, Iversen Eric, and Kaliyandurg Chitra. "Engineering in the K-12 Classroom: an Analysis of
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
curriculum for design students in both VCUR and VCUQ, one general educationrequirement for all students is a contemporary mathematics course (MATH 131). Tailoring thiscourse to fit the unique needs and interests of VCUQ majors became a unique and excitingchallenge that gave rise to the authors’ 2006 study entitled, “Making Connections AmongCulture, Personality, and Content in Analytical Courses,” which was presented at the March Page 12.1199.22006 Conference of Middle Eastern Teachers of Science, Mathematics, and Computing.In their previous study, the authors relied upon the work of Ricki Linksman, an expert inaccelerated learning who founded the
, curriculum theorists, instructional researchers, and specialists in testing and assessment led by Lorin Anderson, one of Bloom‟s former students, published an updated version of Bloom’s Taxonomy. The revised version modified terminology, structure, and emphasis of the original taxonomy (see Figure 1) to provide “ „a clear
student success in introductory college calculus courses, and her research interests include students’ mathematics identity development, active learning environments in mathematics classes, and increasing student motivation in mathematics.Dr. Karen A High, Clemson University Dr. Karen High holds an academic appointment in the Engineering Science and Education department and joint appointments in the Chemical and Biomolecular Engineering department as well as the Envi- ronmental Engineering and Earth Sciences department. Prior to this Dr. Karen was at Oklahoma State University where she was a professor for 24 years and served as the Director of Student Services as well as the Women in Engineering Coordinator. She
Paper ID #21246Conceptual Power Series Knowledge of STEM MajorsDr. Emre Tokgoz, Quinnipiac University Emre Tokgoz is currently the Director and an Assistant Professor of Industrial Engineering at Quinnipiac University. He completed a Ph.D. in Mathematics and another Ph.D. in Industrial and Systems Engineer- ing at the University of Oklahoma. His pedagogical research interest includes technology and calculus education of STEM majors. He worked on several IRB approved pedagogical studies to observe under- graduate and graduate mathematics and engineering students’ calculus and technology knowledge since 2011. His other