Conference Session

First-Year Programs Division - Visualization and Mathematics

Collection

2018 ASEE Annual Conference & Exposition

Authors

Adetoun Oludara Yeaman, Virginia Tech; Diana Bairaktarova, Virginia Tech; Tamara Knott, Virginia Tech

Tagged Divisions

First-Year Programs, Mathematics

most ofthe mental processes students mentioned were exclusively happening in the mind, others wereuniquely different, for example drawing in air. In the case of John, his response reflects somesort of imagination or visualization (drawing from his own words), “I tried to visualize the partsbeing moved away from each other and what they would look like after they had moved apart.”Cindy on the other hand, took a more physical approach as indicated in her response, “Mystrategy for choosing the answer to each problem was drawing it out in the air with my hand andtrying to imagine myself looking down on it in order to figure it out.” Her approach involvedusing a physical process of drawing in the air to help her imagine what she expected to see in

Collection

2016 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University

Tagged Divisions

Mathematics

classification; Intra, Inter and Trans to investigate how first year calculusstudents construct the concept of chain rule. Their attempt to use the APOS theory resulted ininsufficiency by itself therefore they included the schema development idea of Piaget et al. (1989).Clark et al. (1997) used triad classification after realization of not being able to apply the APOStheory. Similar to Clark et al. (1997) APOS theory appears to be inappropriate for evaluating theresearch question in this work because students' responses didn't reflect a proper setting to applythe APOS theory; therefore, participating students' responses are analyzed by using the schemadevelopment idea. The Triad classification in this setting is as follows:• Intra Stage: Students

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

: modifying and extending thecourse objectives; assessing and appealing to students‟ super linksa; using various short papers asgauges of students‟ understanding and as concept reinforcements; assigning journal questions;estimating students‟ critical thinking skills; administering quizzes, tests, and projects; requiringreports and presentations by the Honors Students; and emphasizing writing as an instructionaltool. Course Objectives. The math professor and the writing center instructor firstcollaborated to develop course objectives reflecting the higher-level thinking and learning skillsdemanded by critical thinking. They stated such objectives for both the topics to be covered andfor critical thinking skills specifically. Both sets

Conference Session

Mathematics Division Technical Session 2

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Mary Katherine Watson, The Citadel; Tara Hornor, The Citadel; William J. Davis P.E., The Citadel; Simon Thomas Ghanat P.E., The Citadel

Tagged Divisions

Mathematics

research strategy enabled both statistical analysis ofparticipants’ quantitative ratings, as well as individual student’s rich personal reflections on theirown experiences and leadership development to be compared with other participants [20, 21].Our study adheres to an approved Institutional Review Board (IRB) protocol.Participant DemographicsOur first cohort of ExCEL scholars consisted of six male students, with two identifying asHispanic/Latino. Scholars varied in terms of their math preparedness, with two previouslycompleting Advanced Placement (AP) Calculus, one completing honors Calculus, and threecompleting Precalculus. Upon entry to The Citadel, scholars’ average score on a math placementexam was 66.7%, with scores ranging from 47.1% to

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

other essential topics with which students often struggle. Suchinteractions among students and peer mentors aid in improving student attitudes and their senseof belonging at the institution.Having Dr. Brooks attend the statics class as a student caused a great deal of reflection on Dr.McDonald’s part. It quickly became clear that many mathematical processes were only lightlytouched upon, in favor of dwelling on ‘this is how you work the problem’ discussions. Having amathematician in the audience makes one pay attention to how mathematics is presented andapplied. Engineers often take mathematical shortcuts without providing much in the way ofexplanation; this was quickly pointed out!One of the first opportunities that engineering students have

Conference Session

Mathematics Division Technical Session 4

Collection

2018 ASEE Annual Conference & Exposition

Authors

Eliza Gallagher, Clemson University; Christy Brown; D. Andrew Brown, Clemson University; Kristin Kelly Frady, Clemson University; Patrick Bass, The Citadel; Michael A. Matthews P.E., University of South Carolina; Thomas T Peters, South Carolina's Coalition for Mathematics & Science; Robert J. Rabb P.E., The Citadel; Ikhalfani Solan; Ronald W. Welch P.E., The Citadel; Anand K. Gramopadhye, Clemson University

Tagged Topics

Diversity

Tagged Divisions

Mathematics

author(s) and do not necessarily reflect the views of the National Science Foundation.We also wish to acknowledge the assistance of the Institutional Research Officers at each campusin gathering the data used in this analysis.References [1] X. Chen and M. Soldner, STEM Attrition: College Students’ Paths Into and Out of STEM Fields (Statistical Analysis Report), ser. National Center for Educational Statistics (NCSE) Statistical Analysis Reports. U.S. Department of Education, 2013. [2] J. Levin and J. H. Wyckof, “Predictors of persistence and success in an engineering program,” NACADA Journal, vol. 15, no. 1, pp. 15–21, 1995. [3] J. Middleton, S. Krause, S. Maass, K. Beeley, J. Collofello, and R. Culbertson, “Early course and grade

Conference Session

Mathematics Division Technical Session 2

Collection

2015 ASEE Annual Conference & Exposition

Authors

Khalid El Gaidi, Royal Institute of Technology (KTH); Tomas Ekholm, Royal Institute of Technology (KTH)

Tagged Divisions

Mathematics

these examples, bearing in mind the initial differences in their programmingproficiency. Their use was still found stimulating.Rationale for the study – The context of mathematics in engineering educationDesigning engineering education with mathematics and physics in the first two years of theprogram is not a law of nature. 4 It can hardly be argued that abstract mathematics is taught in theinitial stages of programs for pedagogical reasons. Rather, such a design reflects a Tayloristicview of industrial production transferred to education where context-free bits and pieces aredispensed by specialists to be assembled to a coherent whole in the end. 5 Most engineeringteachers claim that they need to build on a ”solid” mathematics and science base

Conference Session

Mathematics Division Technical Session 3

Collection

2016 ASEE Annual Conference & Exposition

Authors

Doug Bullock, Boise State University; Kathrine E. Johnson; Janet Callahan, Boise State University

Tagged Topics

Diversity

Tagged Divisions

Mathematics

(3) face-to-face but taught in parallel with the online section. 600 500 400 300 Other 200 Reform 100 0Figure 2: Calculus I enrollment by semester.Total students “captured” by the reform project, as a percent of enrollment is shown in Figure 3.It appears to be stabilizing in the low to mid 70’s, which currently reflects the portion of calculusthat Boise State University has chosen to offer as honors, online, or face-to-face but parallel toonline. 100% 90% 80% 70% 60% 50% 40

Conference Session

Innovative Instruction Strategies in Calculus

Collection

2007 Annual Conference & Exposition

Authors

Jenna Carpenter, Louisiana Tech University; Ruth Ellen Hanna, Louisiana Tech University

Tagged Divisions

Mathematics

correlate well. Students are permitted to take the ACT multiple times and usetheir highest score for placement. Because our state implemented high-stakes standardizedtesting seven years ago in the public school system for 3rd through 12th grades, many students arenow approaching the ACT with a substantial amount of long-term training and practice in takingstandardized tests. Therefore, we wanted to investigate whether or not the Math ACT score isstill a sufficiently accurate method of placement into Calculus I. In a preliminary study, weexamined whether or not the Math ACT accurately reflects student preparedness for calculus.This study looks at student performance on the initial ALEKS assessment and total hours spentusing ALEKS during the term to

Conference Session

Mathematics Division Technical Session 1

Collection

2013 ASEE Annual Conference & Exposition

Authors

Patricia Salinas, ITESM; Eliud Quintero, ITESM

Tagged Divisions

Mathematics

technological platforms. Focus on the students and their learning, emphasis on collaborative work, use of didactic techniques, enhance of the process by the use of digital technologies and use of computers favoring active student participation are goals that guide her work. As a member of Tecnol´ogicos faculty several awards had been granted by the institution on the acknowledgment of her teaching performance and research activities related to analyze and reflect on the educational process. She coauthored several textbooks for the learning of Pre-College Mathematics and Calculus. Recently the Textbook Series of Ap- plied Calculus has been published by Cengage Learning offering an innovative approach to the teaching and

Conference Session

Engineering Mathematical Potpourri

Collection

2011 ASEE Annual Conference & Exposition

Authors

Jean Hodges, Virginia Commonwealth University, Qatar

Tagged Divisions

Mathematics

key article in this work was Janet Emig‟s “Writingas a Mode of Learning,” that claimed “writing is neurophysiologically integrative, connective,active, and available for immediate visual review,” 5 characteristics that make it an effectivelearning tool. The work of writing researchers James Britton and his colleagues stressed the Page 22.86.4distinct power of writing to help the writer organize and express experience. They explained thatto express an experience, the writer first must capture it, investigate it, and then reflect uponhis/her ideas about it. This process was found to enhance students‟ learning6. This findingreiterates

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

. Whenever numerical answers are required, find the exact values using a calculator. A certain amount of collaboration is acceptable in doing this project, but reports must be written individually. Thus, when writing your report, make sure that it is clearly different from reports of others and reflects your own thoughts for solving the problems. Reports that are virtually identical to others will not receive credit.In project 1, students are asked to use their knowledge of solving first-order ordinary differentialequations to tackle basic ideas in rocket science through the examination of the Jules Vernecatapult idea and single-stage rockets. The second project explores ideas in mechanicalvibrations with the concept of

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

college, so we can more easilyimplement evidence-based practices with potential to improve retention, of which there are several.Recently, we have focused on implementing formative assessment, which has been shown to improveretention of at-risk students and under-represented minorities [3], [4]. This paper presents and reflects onthe implementation of formative assessment in our Calculus I course for engineering students.Theoretical Framework: Formative assessmentFormative assessment is an instructional technique in which teachers quickly assess students during oroutside class for minimal reward/penalty, with emphasis on improving learning. Formative assessmenthelps both students and teachers to identify knowledge gaps and misconceptions, and

Conference Session

Mathematics Division Technical Session 3: Diversity in Mathematics Education

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

John Kerrigan, Rutgers University; Lydia Prendergast, Rutgers University; Jillian A.S. Mellen, Rutgers University; Geraldine L. Cochran; Antonio D. Silva

Tagged Topics

Diversity

Tagged Divisions

Mathematics

Calculus II course? To answer this research question, twelve semi-structuredinterviews [22] were conducted during the last week of class with a focus on gaining a deeperunderstanding of students’ experiences in the flipped classroom. The research team adaptedquestions from a previous study on students’ self-efficacy in calculus [23]. Students names wereneither provided nor were known to the interviewer. Each interview was 10-20 minutes long andallowed students to reflect on their self-efficacy in mathematics (see Appendix B). Examples ofinterview questions included, “How do you rate your confidence in math now? Why?” and“What could make you feel more comfortable about math?” [23]. All interviews were audiorecorded using a digital recorder

Conference Session

Innovative Instructional Strategies

Collection

2008 Annual Conference & Exposition

Authors

Martha Allen, Georgia College & State University; Amy Kelley, Georgia College & State University

Tagged Divisions

Mathematics

away from theory. In developing the modified lecture with activities format, the authors triedto choose assignments and divide class time to reflect the needs of the students. Currently, themodified lecture with activities format contains elements of traditional lecture, IBL and PBL. Page 13.284.7The authors are continually seeking ways to improve the modified lecture with activities format.The challenge for improvement rests in the desired outcomes for this particular linear algebracourse. The pre-engineering majors need computational skills as well as the ability to know whento apply linear algebra techniques. In essence, linear algebra

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

) motivating students in the applications of themathematical concepts that reflect realistic problems in their prospective engineering careers, 2)integrating these complicated applications into the tight schedule of engineering courses, 3)leveraging the overwhelming complexity so that the students are not intimidated, and 4)compensating for the lack of physical models required in most engineering applications Theauthors considered these challenges in the development of modules and agreed that a frameworkfor module development was required. The authors began preliminary research to develop sucha framework centered on the concept of abstraction.The authors began by exploring resources developed by other colleagues, reviewing the existingdigital library

Conference Session

Integrating Math, Science, and Engineering

Collection

2009 Annual Conference & Exposition

Authors

Eduardo Chappa, Texas A&M International University; Terutake Abe, Texas A&M International University; Fethi Belkhouche, Texas A&M International University; Rohitha Goonatilake, Texas A&M International University; Qingwen Ni, Texas A&M International University; Rafic Bachnak, Texas A&M International University

Tagged Divisions

Mathematics

Page 14.773.2Engineering and other disciplines explicitly.The process of revising the Mission and Vision statements itself was short. It took about two meetings intwo weeks, and a few e-mail exchanges, for faculty to agree on their new job description. TheAssessment Committee started the process by modifying the document to include all disciplines in thedepartment. Most faculty did not feel comfortable in modifying the document past that, because they feltthat the current Mission and Vision Statements already reflected well the current activities in theDepartment. The activities, as listed in the Mission statement, are very generic, and therefore are easy forfaculty to agree on.Developing Program OutcomesDuring the spring semester of 2008

Conference Session

Innovative Instructional Strategies

Collection

2009 Annual Conference & Exposition

Authors

Josue Njock-Libii, Indiana University-Purdue University, Fort Wayne

Tagged Divisions

Mathematics

ofthe motion at hand. Our experiments suggest that this is due to the fact that the coefficient ofviscous damping is a dynamic variable rather than a fixed parameter that solely reflects theinteraction among the viscosity of the fluid, the geometry of the oscillating mass and its surfacecondition.Finally, in addition to their use to check the validity of the solution of the differential equationshown in Eq.(1), the data included in this paper (Table 2) could also be used in class byinstructors to demonstrate the process of fitting an exponential function to experimental data as apractical use of natural logarithms in physics and engineering.References 1. Lalanne, Michel, and Guy Ferraris, Rotordynamics Prediction in Engineering

Conference Session

Mathematics in Transition

Collection

2006 Annual Conference & Exposition

Authors

Dale Buechler, University of Wisconsin-Milwaukee; Christopher Papadopoulos

Tagged Divisions

Mathematics

necessarily reflect the views of the National Science Foundation.References1 D.N. Buechler, C.M. Papadopoulos, T.R. Johnson, E.S. Key, “Development of a targeted engineering applicationcourse to improve retention,” Proceedings of the 2005 ASEE Annual Conference, Portland, OR, June, 2005.2 University of Texas at Austin and GE Foundation, “Water Rockets: First Derivatives, Building and UsingClinometers,” 2004. Located at:www.engr.utexas.edu/aim/curriculum/files/AIM_Calc_2004/Rockets_T_BuildingClinometer.doc3 Wisconsin Dept. of Transportation Page 11.765.11

Conference Session

Use of Technology in Teaching Mathematics

Collection

2006 Annual Conference & Exposition

Authors

Peter Avitabile, University of Massachusetts-Lowell; Jeffrey Hodgkins, University of Massachusetts-Lowell; Tracy Van Zandt, University of Massachusetts-Lowell

Tagged Divisions

Mathematics

STEM Material Critical for Solving Dynamic Systems Problems”. Any opinions, findings,and conclusions or recommendations expressed in this material are those of the authors and donot necessarily reflect the views of the National Science Foundation The authors are gratefulfor the support obtained from NSF to further engineering education. Page 11.771.11VII Bibliography1 Higley,K.A., Marianno,C.M., “Making Engineering Education Fun”, Journal of Engineering Education, Vol 90, No. 1, pp105-107, January 20012 Davis,B.G., “Tools for Teaching”, Jossey-Bass Publishers, San Francisco, 1993, p100.3 Piaget,J., “To Understand is to Invent

Conference Session

Mathematics Division Technical Session 1

Collection

2017 ASEE Annual Conference & Exposition

Authors

Gianluca Guadagni, University of Virginia; Bernard Fulgham, University of Virginia

Tagged Divisions

Mathematics

explain mathematical concepts improved greatly; - Different kind of understanding was required to teach a subject than to be in a class; - Students were asking challenging questions forcing the PLs to think deeply about the material.But also they gained/had - More confidence in their knowledge and skills related to course content, which reflected in other advanced courses they were taking while being PLs; - The opportunity to peer behind the curtain: find out what is means to teach “it has helped me foster a new appreciation for the work professors put in outside of class to prepare lecture and grade assignments”; - More creativity and engagement: a PL created a video on a topic that several students had

Conference Session

Mathematics Division Technical Session 4

Collection

2017 ASEE Annual Conference & Exposition

Authors

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

Tagged Divisions

Mathematics

second. There are also differences between causes of attrition in the firstyear versus in the long-term. Students who continue into the second year of engineering school aremuch less likely to leave engineering, despite any difficult courses they may face. Both retentionand repetition are therefore important when reviewing student progress through a multiple-semester math sequence to get reflections on the engineering program as a whole. This analysiscan identify problem areas to address more specifically. At this engineering school, attrition is a particularly high during and after the secondsemester. This is the same for the students who start on-track in the math sequence, takingEngineering Analysis I, and for those who must take the

Conference Session

Mathematics Division Technical Session 1

Collection

2019 ASEE Annual Conference & Exposition

Authors

Rebecca George, University of Houston

Tagged Topics

Diversity

Tagged Divisions

Mathematics

then move to modify place-ment exams, curriculum, faculty attitudes, or pedagogy training as needed.Math PlacementAlthough many universities use SAT, ACT, or some other standardized placement exam todetermine if students will be successful in certain math courses, it has been reported thatthese scores under-predict the grades for female students [1]. In their article, Kessel and Linn[1] claim that college admissions officers may be missing talented females if they are relyingheavily on ACT and SAT scores. Their article points out that “females report spending moretime reflecting on similarities among problems, organizing and linking their ideas, and review-ing material” and because of this, they tend to be less able to demonstrate speed and

Conference Session

Mathematics Division Technical Session 4

Collection

2015 ASEE Annual Conference & Exposition

Authors

Judith A Komar, Colorado Technical University; Tonya Troka, Colorado Technical University

Tagged Divisions

Mathematics

completed by Schunn and Patchan3 and Knewton.4 This paper willinclude one specific university’s approach to revising college algebra using multipleinterventions including AL technology delivered using Intellipath™ within its online courses.This research includes work that began in the fall of 2012 (October term), and the resultspresented reflect 13 terms (each term equals one five-and-a-half-week session, two sessions in aquarter, eight total terms per year, equaling four quarters) of data (2,000 students). The results ofthis CTU’s approach to college algebra indicate many improvements including a reduction instudent failure and withdraw rates. Student success in college algebra has been a concern for educators for many years. In2002

Conference Session

Mathematics Division Technical Session 1

Collection

2018 ASEE Annual Conference & Exposition

Authors

Lynn Albers, Campbell University

Tagged Divisions

Mathematics

improvement.The author is not certain why the average in 2016 was so low however, the loss of half ofthe students from the fall to the spring semester might indicate that their were manystudents who were undecided and therefore, uncommitted.In 2017, we hired a teaching assistant who held a minimum of five office hours per week.This student had taken the course in 2016 and had performed very well. The 2017students related well to him and found him extremely helpful as reflected in the increasefrom 3.3 to 4.3 on question five.MATLAB was well received until the chapter and assignment on functions. Only one ortwo students from the 2017 class had prior programming experience so learning theconcept of a function, calling a function, and returning results to

Conference Session

Use of Technology in Teaching Mathematics

Collection

2006 Annual Conference & Exposition

Authors

Melinda Z. Kalainoff, U.S. Military Academy; Dawn E. Riegner, U.S. Military Academy; Matthew Deloia, U.S. Military Academy; Russ Lachance, U.S. Military Academy; Andrew Biaglow, U.S. Military Academy

Tagged Divisions

Mathematics

after only one examination. The statistical differences areinsignificant in most cases. We are encouraged by the fact that none of the sectionsappears to be lower than their peers. Future results that show additional graded events asa function of time will be very informative. We also place a considerable amount ofimportance on student attitudes as reflected in Table 1. The follow-up survey, to beadministered at the end of the semester, will tell us a great deal about whether we are ableto improve student attitudes toward use of technology.Question ResponsePlease rank the following in terms of your preference for solvingproblems. Pencil and paper

Conference Session

Mathematics Division Technical Session 3

Collection

2013 ASEE Annual Conference & Exposition

Authors

Kathleen A Harper, The Ohio State University; Gregory Richard Baker, Ohio State University; Deborah M. Grzybowski, The Ohio State University

Tagged Divisions

Mathematics

task group to frame the problem.SampleThe survey was developed and distributed using the college’s on-line Qualtrix system. All of thecollege’s approximately 275 departmental teaching faculty (professors, clinical faculty, andlecturers) were requested to take the survey. These instructors are distributed over 11instructional units. The survey was available for approximately 3 weeks near the end of theautumn 2012 semester. Two reminders were sent during this time. The resulting response ratewas 77 (28%), and the responses reflect a fairly representative sample of departments and jobtitles.Tables 1 and 2 depict the distributions of the sample with respect to department and job title

Conference Session

The Use of Games and Unique Textbooks in Mathematics Education

Collection

2014 ASEE Annual Conference & Exposition

Authors

Erin Shaw, University of Southern California; Jihie Kim, University of Southern California; Zinan Xing, University of Southern California

Tagged Divisions

Mathematics

game (a platform game). In 2012,the program was piloted at a second school site, as part of a media arts class, and did notincorporate the math exercises. As interest in teaching the program as a media arts courseincreased, we were faced with how to “teach” mathematics in the absence of a credentialed mathteacher. To this end, we have begun to rely less on standards-based math practice and more onassessing computational thinking and mathematical reasoning skills that are reflected in thegame-making activities.AcknowledgementsThis study was supported by a National Science Foundation Creative IT grant (#1002901). Theauthors wish to thank Leadership in Entertainment and Media Arts (LEMA) High School teacherRajeev Talwani, principal Roberta

Conference Session

Mathematics Division Technical Session 1

Collection

2013 ASEE Annual Conference & Exposition

Authors

Jenna Tague, Ohio State University; Jennifer Czocher, Ohio State University; Gregory Richard Baker, Ohio State University; Amanda Roble, Ohio State University

Tagged Divisions

Mathematics

formore procedural examples rather than only the conceptual ones given during class.The differences in lecture execution (Figure 4) can be traced to technology issues. At times, wehad trouble with internet connectivity or microphone issues. For example, in weeks associatedwith surveys 5 and 10, we had both of these issues. Beyond connectivity and hardware issues,the transactional cost for setting up the technology at the beginning of each class was large. Evenwhen we were able to save the necessary technology settings to the university computer, 3programs needed to be started, a microphone needed to be attached, and files off a jump driveneeded to be downloaded. We continue to troubleshoot and reflect on if our technology choices

Conference Session

Mathematics Division Technical Session 4

Collection

2013 ASEE Annual Conference & Exposition

Authors

Jennifer Vandenbussche, Southern Polytechnic State University; William George Griffiths IV, Southern Polytechnic State University; Christina R Scherrer, Southern Polytechnic State University

Tagged Divisions

Mathematics

a small step toward filling thisgap. Over 600 E/ET students were surveyed in order to understand what key factors theyperceive as preventing them from completing their mathematics homework, and what policiesare effective in encouraging a high completion rate. Although we acknowledge that thestudents’ perspective may not always reflect reality, we do believe that the results provide aguide to inform future research in the area.MethodsApproximately halfway through fall semester 2011, we surveyed undergraduates at ouruniversity in mathematics courses ranging from College Algebra to Calculus III, asking them Page 23.111.3questions about their