Conference Session

Mathematics Division Technical Session 3

Collection

2016 ASEE Annual Conference & Exposition

Authors

Edmund Tsang, Western Michigan University; Kenneth David Domingue, Western Michigan University ; Sarah Gray Hagen, Western Michigan University; Rebecca A. Scheffers, Western Michigan University; Lenore Yaeger; Katherine Fox, Western Michigan University

Tagged Divisions

Mathematics

courses a semester).Another enhancement to CEAS-EXEP Cohort in Fall 2014 was adding the textbook, StudyingEngineering: A Road Map to a Rewarding Career by Raymond B. Landis13, to give the studentdevelopment aspect of FYE 2100 an engineering focus. We searched the internet for used copiesof Studying Engineering, which can sometimes be obtained for much less than $10 (sometimesas low as $3 or $4), and provide the textbook free of charge to students in the CEAS-EXEPCohort. We collect the textbooks at the end of the semester to use again the following year.FYE 2100 is a university-wide transition course for first-year students that was begun in Fall2005. It is listed in the university’s undergraduate catalog as “a two-credit hour course [that]gives

Conference Session

Issues and Solutions in Mathematics Education

Collection

2010 Annual Conference & Exposition

Authors

Andrew Grossfield, Vaughn College of Aeronautics

Tagged Divisions

Mathematics

AC 2010-387: TECHNICAL ENROLLMENTS AND MATHEMATICALPEDAGOGYAndrew Grossfield, Vaughn College of Aeronautics Throughout his career, Dr. Grossfield combined an interest in engineering design and mathematics. He earned a BSEE at the City College of New York. During the early sixties, he obtained an M.S. degree in mathematics part time while designing circuitry full time in the aerospace/avionics industry. As a Graduate Associate, pursuing a doctoral degree at the University of Arizona, he was uniquely positioned as both a calculus teacher and as a student taking courses in applied mathematics. He prepared and attended lectures, concurrently, which developed his acute sensitivity to differences

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

effortsto mitigate the dropout of non-traditional students enrolled in engineering degrees by designing acalculus course taking into account important characteristics of the non-traditional students.In Universidad Galileo, Guatemala, most of the non-traditional students who are enrolled inengineering degrees take courses with schedules specially designed for those persons who are notable to pursue a career as a full-time student. Hereafter, we will refer to this subset ofnon-traditional students simply as ”part-time students”. Our experience with the first calculuscourse offered to part-time students is very similar to the scenario described in the previousparagraph, namely that many dropout or fail. Hence, in recent years, Universidad Galileo has

Conference Session

Students' Abilities and Attitudes

Collection

2011 ASEE Annual Conference & Exposition

Authors

Andrew G Bennett, Kansas State University; Todd Moore; Xuan Hien Nguyen, Kansas State University

Tagged Divisions

Mathematics

American Society for Engineering Education, 2011 A longitudinal study on students' development and transfer of the concept of integrationAbstract: We present results from the first two years of a project investigating how engineeringstudents develop problem solving skills through their academic career. The project consists of alongitudinal study as well as cross-sectional studies in multiple courses in mathematics, physicsand engineering. In this article, we focus on the transfer of knowledge from mathematics tophysics courses. We track how students' understanding of function and integration evolves asthey progress through the Calculus courses using individual semi-structured interviews. Moststudents develop a

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

electricalengineering. The broad goals of the collaborative are to increase representation of Hispanics orlow-income students in computer science careers, provide necessary course-specific academicsupport especially for gateway mathematics courses and introductory computer science coursesacross all three institutions.Project leadership is provided by a research-intensive university that has experienced a rapidincrease in the number of Hispanic and low income minority students who either are directlyenrolled at the university or who transfer from the two-local state colleges The two feeder statecolleges have more than 100,000 students whose demographics are represented as follows: 65%Hispanic, African-American, low income, or first time in college. Both state

Conference Session

Issues and Answers in Mathematics Education

Collection

2011 ASEE Annual Conference & Exposition

Authors

Amelito G. Enriquez, Canada College

Tagged Divisions

Mathematics

disadvantaged students interested in pursuing careers inSTEM fields. Among the strategies developed for this project is the Summer Math Jam – atwo-week intensive mathematics program designed to improve students’ preparation forcollege-level math courses. This paper summarizes the results of the implementation of theMath Jam and its one-week version, the Mini-Math Jam, over the last two years.2. Incoming Student Interest and Level of Preparation for EngineeringCañada College is a member of the California Community College System, and is one of threecolleges in the San Mateo County Community College District (SMCCCD). It is one of onlytwo federally-designated Hispanic Serving Institutions in the San Francisco Bay Area. TheCollege opened in 1968, and is

Conference Session

Techniques in Improving Mathematics Education in STEM Curricula

Collection

2012 ASEE Annual Conference & Exposition

Authors

Jennifer Vandenbussche, Southern Polytechnic State University; Christina R. Scherrer, Southern Polytechnic State University

Tagged Divisions

Mathematics

exposureto the material to solve the problems. Since College Algebra students are at the beginning oftheir mathematical careers, it is not surprising that they lack the mathematical sophisticationneeded to teach themselves the material using only the textbook.The workshop students appeared to avoid the dip in mathematical confidence experienced bythe students in the traditional section. Whereas students in the traditional section agreedsignificantly more with the statements “It scares me to have to take mathematics” and“Mathematics is harder for me than for most persons” at the end of the semester than beginningof the semester, the workshop students had no statistically significant change in their agreementwith these statements. This lends mild

Conference Session

Techniques in Improving Mathematics Education in STEM Curricula

Collection

2012 ASEE Annual Conference & Exposition

Authors

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

Tagged Divisions

Mathematics

skills and teachstudents during their first year in college how to practice independent problem solving methods.This procedure requires deep thought, time, discussion and risk taking; these are all skillsbeneficial for careers in engineering and computer science. For this reason, peer mentors do nothave solution manuals. The peer mentors act as facilitators who work with students to solve Page 25.188.3problems methodically while encouraging critical thinking, as opposed to supplying answers toquestions. Learning problem solving skills in a group will inevitably raise the confidence levelsof the students early in their college career. These

Conference Session

Integrating Mathematics, Science, and Engineering

Collection

2010 Annual Conference & Exposition

Authors

John Heublein, Kansas State University, Salina; Kenneth Barnard, Kansas State University, Salina

Tagged Divisions

Mathematics

lead to understandingthe relevancy and importance of a solid background in mathematics. Moreover, this knowledgeis necessary for aviation students to attain success in their aviation careers. The researchersdesire to create a learning environment and meaningful course for the students. They not onlywant to teach the content of the courses to be understandable and meaningful, but also enhancethe ability of the students to develop and process the current information to formulate new ideas,concepts, and use in subsequent courses. “Learning is not just a process of taking in newinformation, ideas, and skills, but the new material is reconstructed by the mind.”9   By engagingand motivating the students, they will not only attain academic success

Conference Session

Mathematics in Transition

Collection

2007 Annual Conference & Exposition

Authors

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

Tagged Divisions

Mathematics

test these assumptions. We have found that more than 30% of oursuccessful students (those who earn bachelors degrees) began their college career at theeighth or tenth grade algebra level. Even more significantly, we found that the gradeearned in their first college level mathematics class was significantly correlated towhether or not they persisted in engineering while the level at which they beganmathematics study at the university was not. These results, if they prove to berepresentative, have significant implication for policy, admissions standards and programdevelopment to improve retention in engineering schools.IntroductionNearly every discussion about recruitment and retention of students in engineeringinvolves, or focuses on

Conference Session

Integrating Math, Science, & Engineering

Collection

2006 Annual Conference & Exposition

Authors

Bruno Osorno, California State University-Northridge

Tagged Divisions

Mathematics

the writing center, counseling center, student health center, library, and career center. Page 11.1158.614. I feel good about myself and about my situation, and I am confident about my ability to succeed academically. 15. Taking quizzes every week has forced me to reconsider my academic approach to my classes by adjusting and/or including some of the questions 1 through 14 into my every day schedule of activities 16. If you ranked question 15 please, indicated below what questions 1 through 14 have you added or adjusted this semester to help you do better in this course.1 2 3 4 5 6 7 8

Conference Session

Mathematics Division Technical Session 2

Collection

2019 ASEE Annual Conference & Exposition

Authors

Cathy Poliak, University of Houston

Tagged Topics

Diversity

Tagged Divisions

Mathematics

Paper ID #25877The Use of Technology in Statistics CoursesDr. Cathy Poliak, University of Houston I have been teaching undergraduate statistics for over 20 years. As an instructor of statistics it is my goal to develop and encourage students’ statistical skills for use in other courses and their careers. Ph.D.: North- ern Illinois University, 2007 , Mathematics with concentration in Statistics Masters: Akron University, 1996, Statistics Bachelors: Mount Vernon University, 1991, Mathematics c American Society for Engineering Education, 2019The Use of Technology in Statistics CoursesAbstractA

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

2016 ASEE Annual Conference & Exposition

Authors

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

Tagged Divisions

Mathematics

- ing his MAT as part of Boston University’s STEEP program which gives students the ability to earn an engineering BA and MAT in 5 years. Michael is also a member of BU’s varsity cross country and track and field teams and volunteers an after-school program for Boston Public School students. A native of Boston, Michael would like to return to the Boston Public Schools as a Math/STEM teacher after completion of the STEEP program.Dr. Gretchen Fougere, Boston University Dr. Fougere has split her career thus far in industrial and academic research and product development, management, and STEM education. At Boston University, she leads and has founded several nationally impactful technology and engineering programs that

Conference Session

Use of Technology in Teaching Mathematics

Collection

2006 Annual Conference & Exposition

Authors

Paul Wlodkowski, Maine Maritime Academy

Tagged Divisions

Mathematics

Maritime Academy. Studentsappreciate its highly visual interface and nimble facility with engineering unit display andconversion. Its application is carried beyond the numerical methods course and into coreengineering classes, e.g. strength of materials, fluid mechanics, and engineering testlaboratories. As the case study has shown, MATHCAD enables students to reinforcetheir knowledge of the underlying mathematics behind the numerical method. With aversatile combination of graphical display, symbolic processing, and user-definedcomputer programs, MATHCAD augments the student’s experience base which is a vitalcomponent for their future careers in solving complex engineering problems.References1 C. Domnisoru, “Using MATHCAD in Teaching Power

Conference Session

Mathematics Division Technical Session 2

Collection

2013 ASEE Annual Conference & Exposition

Authors

Jamiiru Luttamaguzi, Elizabeth City State University; Ka'Ren Ladoris Byrd; Akbar M. Eslami, Elizabeth City State University; Ehsan O Sheybani, Virginia State University; Giti Javidi, Virginia State University

Tagged Divisions

Mathematics

Paper ID #6229Case Study: Numerical Convergence Study on Simulated Spaceborne Mi-crowave Radiometer Measurements of EarthDr. Jamiiru Luttamaguzi, Elizabeth City State University Dr. Jamiiru Luttamaguzi is an Assistant Professor in Elizabeth City State University. His main research interest is in Optimal Control Theory. Most of his professional career has been spent teaching graduate and undergraduate math courses. He has supervised students in the McNair Internship program and the ECSU- NAM Summer Research Computational Science-Scientific Visualization programs. He graduated with a PhD is MAthematics and MS in

Conference Session

Bridging the Gap and Freshman Programs

Collection

2009 Annual Conference & Exposition

Authors

Nelson Baker, Georgia Institute of Technology; Marion Usselman, Georgia Institute of Technology; Thomas Morley, Georgia Institute of Technology; Rick Clark, Georgia Institute of Technology

Tagged Divisions

Mathematics

Recruiting, Preparation, and CommunicationEffective communication with potential students about the Distance Calculus program is anessential component to a successful experience. The communication must start early, continuethroughout the program, and provide the students with accurate and timely information. Studentsshould hear as early as possible in their high school career about the course requirements in orderto ensure that they have the proper qualifications for eligibility. Ideally, this communicationshould begin in the 9th grade so that students can plot a path that allows them to complete APCalculus by their junior year. Potential students also need to make sure they have taken the SATor ACT and the AP Exam in time for admission into the

Conference Session

Mathematics Division Technical Session 3

Collection

2018 ASEE Annual Conference & Exposition

Authors

Robert G. Batson P.E., University of Alabama

Tagged Topics

Diversity

Tagged Divisions

Mathematics

purpose of this paper is to recommend adapting new pedagogical methods to theaccepted topics in an introductory probability and statistics course for engineeringundergraduates—methods that better match the learning characteristics of Millennial students inour courses. In a nutshell, those characteristics may be summarized as: (1) They want relevanceto their major, and future engineering career; (2) They want rationale (for the textbook selected,and for specific course policies and assignments); (3) They revel in technology (to collect data,compute, communicate, and multi-task); (4) They want a relaxed, hands-on environment; (5)They prefer instructors who rotate among several classroom delivery methods.Considering the “Five R‟s” learning

Conference Session

Mathematics Division Technical Session 3

Collection

2018 ASEE Annual Conference & Exposition

Authors

Guenter Bischof, Joanneum University of Applied Sciences; Benjamin Edelbauer, Joanneum University of Applied Sciences

Tagged Topics

Diversity

Tagged Divisions

Mathematics

Paper ID #21766Coordinate Transforms and Dual Bases: a Teaching Aid for UndergraduateEngineering Students ¨Dr. Gunter Bischof, Joanneum University of Applied Sciences Throughout his career, Dr. G¨unter Bischof has combined his interest in science and engineering appli- cation. He studied physics at the University of Vienna, Austria, and acquired industry experience as development engineer at Siemens Corporation. Currently he teaches Engineering Mathematics at Joan- neum University of Applied Sciences. His research interests focus on automotive engineering, materials physics, and on engineering education.Benjamin Edelbauer

Conference Session

Mathematics Division Technical Session 1: Best Practices in Engineering Math Education

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Nathaniel Rossi, Arizona State University; Adam R. Carberry, Arizona State University; Scott Adamson, Chandler-Gilbert Community College

Tagged Topics

Diversity

Tagged Divisions

Mathematics

currently use active learning techniques andproblem-solving tasks in their classrooms. Instructors were asked to describe the process theyuse for creating tasks. The strategies described by the instructors were analyzed and grouped intoemergent themes. These themes are discussed in this paper and will ultimately be compiled into aguide made for instructors on how to create good problem-solving tasks for mathematics andengineering courses that heavily use mathematics. The goal is to enhance mathematics educationthroughout an entire post-secondary program to better prepare all students for their degreeprograms and careers, particularly in engineering.BackgroundThere are a variety of strategies for incorporating active learning into the classroom

Conference Session

Computers and Software in Teaching Mathematics

Collection

2010 Annual Conference & Exposition

Authors

Cynthia Young, University of Central Florida; Michael Georgiopoulos, University of Central Florida; Tace Crouse, University of Central Florida; Alvaro Islas, University of Central Florida; Scott Hagen, University of Central Florida; Cherie Geiger, University of Central Florida; Melissa Dagley-Falls, University of Central Florida; Patricia Ramsey, University of Central Florida; Patrice Lancey, University of Central Florida

Tagged Divisions

Mathematics

Research, evaluator for an NSF CAREER Grant, and Coordinator of Assessment for the "EXCEL-UCF-STEP Pathways to STEM: From Promise to Prominence" grant for two years.Cherie Geiger, University of Central Florida Cherie Geiger is an Associate Professor in the Department of Chemistry in the UCF College of Sciences and a Co-PI of the NSF-funded S-STEM program at UCF entitled the "Young Entrepreneur and Scholar(YES) Scholarship Program" as well as the NSF-funded STEP program entitled "EXCEL:UCF-STEP Pathways to STEM: From Promise to Prominence." Dr. Geiger's research interests are in the areas of developing novel materials and technologies for use in environmental remediation and degradation

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

beginning their post-secondary school journey. Manystudents are finishing their high school career in an Advanced Functions or Algebra IImathematics course.Methodist University began an Engineering Program in 2016 with no changes in the requiredmathematics sequence. As at other universities, if an engineering student (or any STEM student)is not prepared to start in Calculus their first semester, he/she must begin in the appropriate lowermathematics course according to their ACT or SAT math score. Even though a more formalmathematics placement mechanism would be preferable, Methodist University does not have theresources to implement a placement mechanism at this time. Thus, ACT or SAT math scoreshave been used. Furthermore, as a small, private

Conference Session

Mathematics Division Technical Session 1

Collection

2016 ASEE Annual Conference & Exposition

Authors

Jing Zhang, Virginia State University; Yongjin Lu, Virginia State University ; Zhifu Xie, Virginia State University; Dawit Haile, Virginia State University; Keith Williamson, Virginia State University

Tagged Divisions

Mathematics

Engineering and Mechanical Engineering Technology. Before starting his career in academia, Williamson served as a naval architect and electronics engineer for the Department of the Navy and received the Civilian Service Medal for his efforts during the first Gulf War. Dr. Williamson’s teaching, research, and publication interests span a range of topics including trans- port phenomena, metallurgy, thermomechanical stir processing, and university-K12 partnerships. He is a strong advocate for information technology literacy within public schools, He is the past Secretary and current member of the Board of Directors for the Commonwealth Center for Advanced Manufacturing (CCAM) which is a public-private partnership between

Conference Session

Innovative Instructional Strategies and Curricula

Collection

2010 Annual Conference & Exposition

Authors

Robert Homolka, Kansas State University, Salina; Greg Stephens, Kansas State University, Salina

Tagged Divisions

Mathematics

tournaments and the College World Series two times andat the professional level (National League) a couple of times. Throughout this lengthy career, Igathered numerous stories to share (See Appendix A). Here are three abbreviated sample storiesused: 1. The pitching coach at WSU, while objecting to my strike zone, kicked dirt on the entire plate. He proceeded to uncover a two inch space down the middle of the plate and commented that was my strike zone! What percentage of the plate did he uncover? 2. While umpiring a major league game, Davey Johnson the manager of Cincinnati, questioned why a pitch was not called a strike which would have resulted in strike three. The batter hit the next pitch for a home

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

, engineers will need something that cannot be described in a single word. In involves dynamism, agility, resilience, and flexibility. […] Encompassed in this theme is the imperative for engineers to be lifelong learners. They will need this not only because technology will change quickly but also because the career trajectories of engineers will take on many more directions – directions that include different parts of the world and different types of challenges and that engage different types of people and objectives. Hence, to be individually/personally successful, the engineer of 2020 will learn continuously throughout his or her career, not just about engineering but also about history, politics, business, and so forth

Conference Session

Mathematics Division Technical Session 1

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Patricia A. Ralston, University of Louisville; Campbell R. Bego, University of Louisville

Tagged Topics

Diversity

Tagged Divisions

Mathematics

assessment. Dibbs’ manuscript was interesting; she studied 8students who were required to repeat calculus at the beginning of their STEM careers, and whoexperienced formative feedback the second time. Through interviews, Dibbs found that participantsidentified three primary reasons for their success the second time around: (1) processing their initialfailure, (2) having a better instructor, and (3) participating in formative assessments. In her analysis, shefound that formative assessment is what caused the cognitive and behavioral engagement benefits. Thesestudents later succeeded in STEM, with 6 eventually receiving a math major or minor.In summary, effective use of formative assessment has the potential to high-information feedback thathelps

Conference Session

Mathematics Division Technical Session 2

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Emre Tokgoz, Quinnipiac University; Samantha Eddi Scarpinella , Quinnipiac University; Michael Giannone, Quinnipiac University

Tagged Divisions

Mathematics

East Hartford, CT as well as Crash Safety located in East Hampton, CT. Both of these experiences has helped him strengthen his knowledge in data analytics and optimization. One of Michael’s biggest interests in Ergonomics and Human Factors which he plans to purse later in his career. American c Society for Engineering Education, 2021 Analysis of STEM Students’ Ability to Respond Algebra, Derivative, and Limit Questions for Graphing a Function 1 Emre Tokgöz, 1Samantha Scarpinella, 1Michael Giannone 1 Emre.Tokgoz@qu.edu, 1 Samantha.Scarpinella@qu.edu

Conference Session

Mathematics Division Technical Session 3

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Salvador Mayoral, California State University, Fullerton; Antoinette Sherrise Linton, California State University, Fullerton; Hassan Yousefi, California State University, Fullerton; Jidong Huang, California State University, Fullerton

Tagged Divisions

Mathematics

of lower-division and upper-division courses taken by Engineering and Computer Science (ECS) studentsat California State University, Fullerton (CSUF) demonstrates an achievement gap betweenstudents. The achievement gap begins in the lower-division math and physics courses, which areprerequisites for engineering courses. Figure 1 below presents a box and whiskers plot of therepetition rate between Fall-2014 to Fall-2016 for six lower-division courses. An "×" indicatesthe three-year average. Calculus I and Calculus II yielded the highest values with averagerepetition rates of 36% and 45%, respectively. Repetition of these courses will delay students'graduation and potentially discourage first-year students from pursuing STEM careers. Figure

Conference Session

Mathematics in Transition

Collection

2007 Annual Conference & Exposition

Authors

Nirmala Gnanapragasam, Seattle University

Tagged Divisions

Mathematics

, state, national and international level. The process of establishing the club,development of a work schedule, various math competitions available toWashington State elementary school students and their levels of difficulty, andchallenges, rewards and lessons learned through the past seven years aredescribed. By getting involved in such programs engineers have an opportunityto teach students the art of problem solving along with team building, leadershipand negotiating skills, keeping schedules and meeting deadlines which areimportant skills for an engineering career. This is also a great opportunity tobuild a positive image of engineers among K-12 students and to attract girls toengineering.IntroductionThe Trends in International Mathematics

Conference Session

Innovative Instructional Strategies

Collection

2008 Annual Conference & Exposition

Authors

Taskin Padir, Lake Superior State University; Kimberly O. Muller, Lake Superior State University; Collette Coullard, Lake Superior State University

Tagged Divisions

Mathematics

methods for solvingdifferential equations. The paper will exemplify the student work and discuss the effectiveness ofour methodology.IntroductionTeaching mathematics in a classroom filled with students from various science and engineeringmajors poses challenges to the instructor. It seems that even though the students appreciate theimportance of studying mathematics for their professional careers, they don’t show the samelevels of interest. Many students view the mathematics courses as part of their degreerequirements only and perform with low levels of motivation in the classroom. The instructor’schallenge then becomes to build the bridge from the abstract mathematical concepts to practicalapplications of the theory. The key to success is to