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

subjective feedbackon each targeted course to see the improvement in student learning and class engagement.ConclusionsTo summarize this ongoing project, we are developing new math learning modules and labsusing 3D gaming and virtual reality technologies to engage students and enhance their learningeffectiveness. With these learning modules, abstract and difficult mathematics concepts can besmoothly connected with engineering problems. It makes the math learning attractive and easy tounderstand. A phased implementation plan is followed to ensure the attainment of the projectgoals. Upon the completion of the project, we expect to have the following outcomes: (1) thevirtual reality learning environment and modules are applied to a number of mathematics

Conference Session

Students' Abilities and Attitudes

Collection

2010 Annual Conference & Exposition

Authors

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

Tagged Divisions

Mathematics

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

Conference Session

Students' Abilities and Attitudes

Collection

2010 Annual Conference & Exposition

Authors

Geoff Wright; Peter Rich, Brigham Young University; Keith Leatham, Brigham Young University

Tagged Divisions

Mathematics

teachers. The pre-serviceteachers supported the teacher in his effort to integrate the new curriculum into his existingcurriculum, and quickly learn the software and basics of programming. Involving the pre-servicetechnology and education majors had a secondary benefit, because it provided the pre-serviceteachers the opportunity to be involved in an actual real teaching environment where they werehelping develop curriculum, lesson plans, interacting with students, and so forth. During the pilottest the two classes were first given a mathematics pre-test that asked them questions aboutvariables, use of operators, functions, coordinates, and equations. The students were then taughtthe GUI (Graphical User Interface) of Flash, and by the second day of

Conference Session

Mathematics Division Technical Session 4

Collection

2013 ASEE Annual Conference & Exposition

Authors

Hassan Moore, University of Alabama, Birmingham

Tagged Divisions

Mathematics

components, like units and dimensional analysis, tying mathematics andengineering together. The course added more of an engineering appeal to the traditionalmultivariable calculus and differential equations material with the use of engineering-basedhomework problems, test questions, and projects. The projects typically tackle problems inmechanics, electrical systems, population dynamics, optimizations, etc. designed to address themajor focal areas of the course. This paper includes projects that tackle first-order ordinarydifferential equations (ODEs), second order ODEs, and multivariable calculus.IntroductionWith a year of planning between the School of Engineering and the Mathematics Department, anew four-hour course was developed to incorporate

Conference Session

Mathematics Division Technical Session 3

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Zeynep Akcay Ozkan, City University of New York, Queensborough Community College; Dona Boccio, City University of New York, Queensborough Community College ; Dugwon Seo, City University of New York, Queensborough Community College ; Sirin Budak, Univeristy of Wisconsin-Stevens Point

Tagged Divisions

Mathematics

and instructors have been largely dissatisfied with thismandatory change [9] and have expressed preference in face-to-face learning [10]. Deliveringthe course content to students in a virtual environment is not easy [5]. However, assessingstudent learning when teaching online is even more difficult and requires detailed planning [11].The existence of plentiful online resources makes it very difficult to assess student knowledge,especially for the current curriculum. Among the changes suggested to adapt to the new normal,revision of curriculum has been brought up [12]. In this article, we concentrate on students’improper use of smart phone applications which can solve mathematical problems. Our aim is tocontribute in restructuring College

Conference Session

Integrating Math, Science, and Engineering

Collection

2009 Annual Conference & Exposition

Authors

Hassan Moore, University of Alabama, Birmingham; Gregg Janowski, University of Alabama, Birmingham; Melinda Lalor, University of Alabama, Birmingham

Tagged Divisions

Mathematics

intent of the new course is to implement more project- and inquiry-based study in order tofoster deeper understanding of the fundamental theorems in multivariable calculus anddifferential equations. The new course (see Appendix A for content) was team taught by aProfessor from the Mathematics Department, Dr. Gunter Stolz, and an Assistant Professor fromwithin the School of Engineering, first author of this paper. Both instructors were involved inthe initial planning of the course and all phases in between, along with members from theMathematics Department and the School of Engineering. Thus, there was true collaboration inall aspects of the course. The need for calculus and differential equations reform withinengineering has been noted for quite

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

to: ≠ Identify students with both the interest and academic qualifications to pursue advanced calculus while still in high school; ≠ Provide a pedagogically sound distance delivered program to these high school students; and, ≠ Track and support the students in the program to be sure that they were successful.The planning team identified a variety of issues that needed to be addressed, including: ≠ Admissions requirements, and student status for high school distance education students; ≠ Pedagogical requirements for effective mathematics instruction and student support, including help sessions; ≠ Technology infrastructure requirements and related costs; ≠ Available communication infrastructures including

Conference Session

Integrating Math, Science, & Engineering

Collection

2006 Annual Conference & Exposition

Authors

Leslie Keiser, University of Tulsa; William Hamill, University of Tulsa; Bryan Tapp, University of Tulsa; William Potter, University of Tulsa; Jerry McCoy, University of Tulsa; Peter LoPresti, University of Tulsa; Donna Farrior, University of Tulsa; Shirley Pomeranz, University of Tulsa

Tagged Divisions

Mathematics

semester freshmen.•Consider ILAP presentations or poster sessions as a change of pace and as a method ofdeveloping different modes of communication.•Strive for more visibility of current-semester student reports.•Consider extending the idea of ILAPs to high school students.Possible Pitfalls and Difficulties in Successfully Implementing ILAPsIn the process of generating ILAPs and implementing them in a classroom setting, weencountered a number of difficulties that hindered the success of the project. These difficultiesare described below in the hope that others who are interested in using ILAPs in their curriculamay avoid them through awareness of and planning for potential problems.Prepare Students for the Issue of Experimental ErrorThis problem

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

(at least) it took several courses to getcomfortable with probability and statistics to the point where I felt competent to apply it.” Theopening remarks should include a reminder of how the scientific method works, and that bothinduction and deduction are aided by statistical thinking and methodology. Then carefullyexplain why the course is required, or at least elective, in the various majors represented. Onecan refer to ABET general and program criteria, for instance discussing collection and analysisof data, planning and conducting experiments, engineering problem solving, and communicationof results/recommendations within ones organization or to customers—using the language ofprobability and statistics to professionally address the

Conference Session

The Use of Games and Unique Textbooks in Mathematics Education

Collection

2014 ASEE Annual Conference & Exposition

Authors

David Reeping, Ohio Northern University; Kenneth J. Reid, Ohio Northern University

Tagged Divisions

Mathematics

problems involving the engineering design process, criticaland creative thinking, and technology applications (such as JMP, Pspice, TI Calculator software,CAS) are planned for inclusion.The textbook offers an authentic opportunity to tie content to the Next Generation ScienceStandards and Common Core standards in Mathematics. Authentic examples provide a realisticcontext in, for example, "Defining and Delimiting Engineering Problems" (NGSS) and "Modelwith mathematics," from the Standards of Mathematical Practice in the Common Core,Mathematics standards 3,4.Reflection on Mathematics Textbooks Before DevelopmentTextbooks have been the common tools for communicating mathematics to students alongsidethe demonstration of practice problems on the board

Conference Session

Mathematics Division Technical Session 2

Collection

2015 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University

Tagged Divisions

Mathematics

15 questions were directly related to conceptual functionknowledge, with the rest of the questions related to concepts such as derivatives, integrals,power series, and programming preferences. Results regarding the questions that are notcovered in this paper are planned to be published elsewhere.Research Problem The question evaluated in this study is designed to observe participants’ ability todetermine the intervals of increase-decrease, convexity, critical points, horizontalasymptotes and vertical asymptotes of a quotient function to be able to graph it by using allthese properties. This problem aims to observe participants’ ability to calculate analyticalcalculus problems and their ability to reflect the obtained information on a

Conference Session

Mathematics Division Technical Session 1

Collection

2017 ASEE Annual Conference & Exposition

Authors

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

Tagged Divisions

Mathematics

is an interesting result of several reasonable decisions during the video creation, andwill be kept in mind for future recorded lectures. Additionally, a possible solution to this problemwould be to provide outlined notes that would help students who would like to stay engaged bywriting things down while maintaining the pace of the videos.Student feedback indicated a positive opinion of in-class activities as opposed to video lectures, asreported in previous studies [3], but it is not possible in this paper to separate the effects of one orthe other. In fact, the planned in-class problem-based activities would not be possible without thepre-recorded video lectures.ConclusionsResults from this study indicate that this initial implementation

Conference Session

Mathematics Division Technical Session 3

Collection

2019 ASEE Annual Conference & Exposition

Authors

Maizey Benner, Purdue University; Daniel M. Ferguson, Purdue University; Matthew W. Ohland, Purdue University; Behzad Beigpourian, Purdue University

Tagged Divisions

Mathematics

University in Iran, Tehran. He has been official Technical Teacher at Ministry of Education in Iran from 2007 to 2018, and received many certificate in education such as Educational Planning, Developing Research Report, and Understanding School Culture. During these years, he has taught construction courses in several technical schools. Mr. Beigpourian currently works in the CATME project, which is NSF funding project, on optimizing team- work skills and assessing the quality of Peer Evaluations. c American Society for Engineering Education, 2019 Analyzing Changes in the Individual Dimensions of a Behaviorally Anchored Scale for TeamworkAbstract

Conference Session

Mathematics Division Technical Session 3: Diversity in Mathematics Education

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Shuvra Das, University of Detroit Mercy; Kirstie A. Plantenberg, University of Detroit Mercy

Tagged Topics

Diversity

Tagged Divisions

Mathematics

acceleration. The electrical stuff is coming in now that I'm taking ELEE 2500. I actually plan to go over my notes because what we're doing in class definitely reminded me of things we did in ENGR 1234. Literally, all the math involved in ELEE right now, I can remember having done work like that in 1234. I didn't know anything about circuits then so it was gibberish to me, but now it clicks! Totally recommend keeping the class. I actually saw some homework my friend was working on for statics and it looked something similar to what we did in 1234. I'm definitely holding on to my notes for the next couple of semesters. • When I took ENGR 1234, the class was challenging because a lot of the material was new

Conference Session

Mathematics Division Technical Session 3

Collection

2013 ASEE Annual Conference & Exposition

Authors

Gregory Richard Baker, Ohio State University

Tagged Divisions

Mathematics

mathematical terms and then use theirproblem-solving skills to understand the consequences. Based on my experiences inteaching ordinary differential equations to engineering students, students see theirmathematical education as simply a vast collection of specific procedures. The questionraised here is whether better coordination of the content in first-year math and physicscourses could improve student ability to use math in subsequent engineering courses. Ifthis is so, then the mathematical content used in the physics course must be documentedbefore changes in the content in the math course can be planned. At the same time, thephysics course might benefit from a better illustration of important mathematicsconcepts, helping students to appreciate

Conference Session

Integrating Mathematics, Science, and Engineering

Collection

2010 Annual Conference & Exposition

Authors

Elton Graves, Rose-Hulman Institute of Technology

Tagged Divisions

Mathematics

to you. MA 336picks up where MA 222 leaves off with Fourier series. (Anybody who has passed MA 222(DEII) is well prepared for this course.) This is a very applied course. If you plan to take Heat Transfer, Thermodynamics, orE-Mag Fields this is a good prerequisite course as we will derive and show you how to solvethe partial differential equations that you will use in these courses. In this course we will discuss the solution to the heat equation (how heat dissipates in abar), the wave equation (how strings and drum heads vibrate) and the potential equation." The enrollment in the spring of 2002 was twenty-two students. Gee, maybe it’s a goodthing to advertise. It’s one thing to advertise, but it is another to have a course that

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

Moon.Fish frieze pattern at the Chan Chan Large walls at the Chan Chan complex Plan view of the Chan Chan complex, atcomplex (Tshudi Palace).21 (Temple del Arco Iris). least an 8th-order fractal of “nested Page 22.1046.13 rectangles.”4. Additional Noteworthy Student WorkAfter grading all of the student work, including their site journals, final papers, and collections ofsymmetry (excluding that from the internet), there are several noteworthy pieces of work worthsharing. In most cases, the work is tied directly to both visiting

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

department at Lamar University. Since joining Lamar in 1998, he has taught over 12 different courses including management, quality and economics. His research interests include six sigma, facility layout and risk management. Dr. Underdown is the academic advisor of the Industrial Technology academic program at Lamar. He has been a member of the Institute of Industrial Engineers since 1996. Dr. Underdown consults small businesses in the areas of strategic planning, process improvement, and lean manufacturing.Dr. Qin Qian, Lamar University Qin Qian EDUCATION Ph.D. Civil Engineering, University of Minnesota, Minneapolis, Feb., 2008 Dissertation: Solute exchange with sub-aqueous sediments: hydrodynamic interactions with

Conference Session

Engineering and Math Potpouri

Collection

2008 Annual Conference & Exposition

Authors

Jeffrey Fong, National Institute of Standards and Technology; James Filliben, National Institute of Standards and Technology; Alan Heckert, National Institute of Standards and Technology; Roland deWit, National Institute of Standards and Technology

Tagged Divisions

Mathematics

over many years by large teams, routinely deliver simulations without a global "guarantee" of correctness, and the users must devote considerable resources to plan and conduct ad-hoc numerical experiments before using the software with confidence. The fact that lessons learned during those ad-hoc experiments are seldom documented and calibrated with benchmarks gives rise to a trustworthy issue, i.e., different FEM software gives different results of simulations for the same mesh design and mathematical model of a specific physical

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

Dept. Head, D. Graham Copeland Professor of Civil Engineering and Director of Construction Engineering at The Citadel in Charleston, SC. His academic experience includes: trans- portation infrastructure planning and design, infrastructure resilience, traffic operations, highway safety, and geographic information systems. His research interests include: constructing spatial databases for better management of transportation infrastructure, improving transportation design, operation, safety and construction, understanding long-term effects of urban development patterns, and advancing active living within the built environment for improved public health. He teaches courses in interchange design, transportation

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

, commented “I really enjoyed thisclass, and [Calculus] has been my favorite series of classes here at WIU.” This student’scomment illustrates that he/she does not view mathematics as a ‘necessary evil’ dictated by adegree plan; rather, this student recognizes its worth and expresses his/her appreciation for thethree-semester sequence. Students also recognize the value of understanding the ‘why’ behindthe procedures for solving calculus problems. In the Calculus I course evaluations in the fall of2019, one student wrote, “She is always able to provide an explanation of why things in Calculusmust be done a certain way, which really helps to further my understanding.” By encouragingstudents to focus not only on the ‘how’ but also the ‘why’, they begin

Conference Session

Bridging the Gap and Freshman Programs

Collection

2009 Annual Conference & Exposition

Authors

Seung Youn Chyung, Boise State University; Janet Callahan, Boise State University; Doug Bullock, Boise State University; Kendra Bridges, Boise State University; Joanna Guild, Boise State University; Cheryl Schrader, Boise State University

Tagged Divisions

Mathematics

. Resource 12. Time and study Scheduling, planning, and management environment managing one’s study time, and strategies setting places to do class work. 13. Effort regulation Students’ ability to control their effort and attention in the face of distractions and uninteresting tasks. 14. Peer learning Dialoguing and collaborating with

Conference Session

Mathematics Division Technical Session 4

Collection

2017 ASEE Annual Conference & Exposition

Authors

Gavin Duffy, Ohio State University; Sheryl A. Sorby, Ohio State University; Austin Mack, Ohio State University; Brian Bowe, Dublin Institute of Technology

Tagged Topics

Diversity

Tagged Divisions

Mathematics

of the interventions they reviewed is a 1credit course that has been tried and tested over several years at Michigan TechnologicalUniversity (MTU) and emphasises mental transformation between 2 and 3 dimensionaldrawings in the style of isometric sketches, orthographic projections, coded plans andsectional drawings (Sorby, 2009). The course is attended by those who get a low score on aspatial test at orientation. It has been observed that completion of this course has led toimprovements not only in spatial test scores but also to grades in a wide variety of subjectssuch as fundamentals of engineering and pre-calculus (Sorby & Veurink, 2010). In addition,higher retention rates have been measured among those who enrol in the course with

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

progressively guide theparticipants in becoming more effective and independent learners through the application of self-regulated learning strategies (Zimmerman, 1990, 1995, 2002) integrated into the mentoringsessions, and (c) serving as student role models who can highlight how they addressed academicand social issues they encounter, identify what’s really necessary to complete a degree in arigorous domain such as engineering (e.g., persistence, autonomy, active learning), along withthe career potential in terms of what computer scientists and engineers really do, and some of thesupportive benefits offered by the university (See Figures 2-3-4). Our project plan usesevidenced-based mathematics learning initiatives (Bressoud, 2014; Klingbeil, et al

Conference Session

Mathematics Division Technical Session 2

Collection

2018 ASEE Annual Conference & Exposition

Authors

Daniel Raviv, Florida Atlantic University

Tagged Divisions

Mathematics

principally designed for a learner-centered e-based environment, making it ready for largescale dissemination. Examples of calculus concepts that the author and his team plan to developand integrate include: (a) games, (b) puzzles and teasers, (c) animations, (d) visual and intuitivedaily-experiences-based examples, (e) movies and short video clips, (f) demonstrations, (g)hands-on activities (including those based on virtual reality and augmented reality), (h) teamingand communication exercises, (i) small-scale inquiry-based research, (j) presentations, and peer-based teaching/learning, (k) visual click-based e-book, (l) community and social engagement,and (m) challenges beyond the basics.2 Calculus ExamplesThe following is a set of examples for

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

., Eng., & Math. (STEM) Health Science Transportation, Distribution & LogisticsThe selection of career cluster is non-binding, but allows for systematic development ofindividualized graduation plans (IGPs) based on career interests. The IGPs primarily affectrecommendations for course electives; all sixteen career clusters have identical recommendationsfor the four-year sequence of mathematics courses, as shown in Table 2. Table 2 Mathematics course recommendations for high school graduation in South Carolina. Grade 9 Grade 10 Grade 11 Grade 12 Algebra 1 Geometry Algebra 2 Precalculus or

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

to which universitythey should collaborate with for their innovation project, relevance of a university tothe project should be put into priority over its research capacity (or its reputation).3.2.2. The University’s Game. A university, in order to maximize its payoff, need tolink to the correct firm (or innovation project) that allows the university to exploitits research capacity and support for students the most. The available variables for auniversity to plan the utilization of its research capacity are: (1) A firm’s investmentfor its innovation project M ; (2) The intensity of university’s engagement to theinnovation project β.Claim 4. The increase of the investment M in an innovation project increases theuniversity’s payoff ΠU from the

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

. Faculty perceptions seem to begenerally positive from the Calculus I reform1 and we will continue to monitor this. We willcontinue to rigorously analyze student performance by looking at course grade performance andpost-requisite course performance. We plan to also begin to monitor student performance incertain engineering courses for which Calculus I or II are prerequisites (Statics and Dynamics).AcknowledgmentsThis material is based upon work supported by the National Science Foundation under GrantNos. DUE-0856815 (Idaho STEP), DUE-0963659 (I^3), and DUE-1347830 (WIDER). Anyopinions, findings, and conclusions or recommendations expressed in this material are those ofthe author(s) and do not necessarily reflect the views of the National Science

Conference Session

Mathematics Division Technical Session 2

Collection

2017 ASEE Annual Conference & Exposition

Authors

Guo Zheng Yew, Texas Tech University; Aimee Cloutier, Texas Tech University; Stephen Michael Morse, Michigan Technological University; Audra N. Morse, Texas Tech University

Tagged Divisions

Mathematics

advance a student’s cognitive ability to analyze and evaluate a problem, not merely tomemorize a method and apply it blindly to any problem of a particular topic.Building Fundamental Understanding of Mathematics Through ProofsMathematical concepts are grounded on established mathematical logic, axioms and proofs. Theprescriptive method of teaching mathematics often omits proofs, although axioms may beemphasized. Many engineering instructors who may also cover mathematical topics omit proofsso that they can stay on schedule with the material that they have planned to cover over thesemester, and also focus on the application of formulas and equations to specific problems. Someinstructors also believe that examples and applications will suffice to

Conference Session

Mathematics Division Technical Session 3: Diversity in Mathematics Education

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Lee Singleton, Whatcom Community College; Eric Davishahl, Whatcom Community College; Todd Haskell, Western Washington University

Tagged Divisions

Mathematics

time frame allotted each day was a challenge, with activitiesusually taking longer than planned. As the activities are refined, the time estimates for eachactivity are becoming more accurate, and tend to fit well into the 50 minute time periods. Forlonger class sessions, multiple activities could be used together.Time always seems to be a big factor when deciding whether or not to try an intervention. Thesame amount of time was spent on each topic for classes using models vs. non-models since eachcourse went through similar activity sheets. Active learning can take a little more time than justlectures. For example, four days were spent on volumes of revolution using activity sheets (withmodels or electronic visuals), versus three days