directed.Despite instructors’ aspirations, students who have mastered the procedural tasks for a givenexam – and even those who have gained a deep understanding of the relevant concepts – stillmake errors when working out answers to exam questions. Different types of exams handle thesemistakes differently. For the purpose of this paper, common math exam types are categorizedinto three groups: 1) essay, 2) multiple choice, and 3) computer assisted. These types varyprimarily along parameters of a) scoring entity and b) partial credit. Exam type is often selectedalong these parameters for practical reasons such as class size and grading time required (seeCherkas and Roitberg [2]).The possibility for exams to be used as formative assessments exists. One well
evaluation when compared tothe APOS theory classification for quantitative classification. We invite other researchers to apply thetechniques that we used and introduced in this work to other empirical data sets for attaining measurableoutcomes.References[1] Asiala, M., Brown, A., DeVries, D. J., Dubinsky, E., Mathews, D., & Thomas K. (1997). A framework forresearch and curriculum development in undergraduate mathematics education. In J. Kaput, A. H. Schoenfeld,& E. Dubinsky (Eds.), Research in collegiate mathematics education II (p/. 1-32). Providence, RI: AmericanMathematical Society and Washington, DC: Mathematical Association of America. [2] Baker, B., Cooley, L., & Trigueros, M. (2000). A calculus graphing schema, Journal for
Paper ID #30878Towards creating motivationally supportive course structures forintroductory calculusDr. Paran Rebekah Norton, Clemson University Paran Norton is a lecturer in the School of Mathematical and Statistical Sciences at Clemson Univer- sity. She received her B.S. degree in Mathematics from the University of North Georgia in 2013, her M.S. degree in Mathematical Sciences from Clemson University in 2015, and her Ph.D. in Engineering and Science Education from Clemson University in 2020. She has taught introductory mathematics and statistics courses at Clemson University. Her primary research focuses on improving
Paper ID #22790Design of an International Bridge Program for Engineering CalculusDr. Sandra B Nite, Texas A&M University Sandra Nite, Ph.D., is a Research Scientist in the Department of Mathematics at Texas A&M University, where she has taught 10 different courses in mathematics and mathematics education. She has served on several committees in the mathematics department, including course development for teacher education in mathematics. Her research agenda includes engineering calculus success, including high school prepa- ration for college. Previously, she taught 8 additional courses at the college level and
similar hemispheric preference is to not stand too close to me with eye contact as she is explaining something because it can be uncomfortable at times. . . . maybe introducing some more materials and bring in examples and samples to class when explaining instead of just saying it orally would make a big difference to my learning. (B. Al-M.) Another student, who was visual and kinesthetic with a mixed-left preference, applied what she was learning about symmetry to the shape of a door, synthesized her new mathematical information with her existing knowledge of doors, and evaluated the outcome: I choose a shape of a door. Symmetrical, right side is a reflection of lift [sic] side. Axis of
related to that lesson or previous unit lessons. The Unit 2 Lesson6 Class Activity handout is shown in Appendix B. If the instructor felt that a specific student wasnot working productively during class, they could lower the class activity score for that day, andstudents were warned of this. The instructor had to warn a few students, but never had to alter aclass activity score.3.5 CALC-II-2TThree changes were made to CALC-II-2T: 1) the number of semester exams was reduced byalmost 50%, and 2) the instructor switched to an online system for administering RATs and 3) ateam component was added to the RATs.The number of semester exams was reduced because the instructor saw that each day most of thestudents were fully engaged with trying to
Engineering. 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 leadership, institutional change, engineering and STEM retention, and engineering, materials science, and mathematics education.Ms. Jocelyn B. S. Cullers, Boise State University Jocelyn B. S. Cullers is a Data Analyst at the Institute for STEM & Diversity Initiatives at Boise State University. c American Society for Engineering Education, 2017 Calculus Reform – Increasing STEM Retention and Post-Requisite Course Success While Closing the Retention Gap for Women and
Paper ID #15905Improving Performance in Trigonometry and Pre-Calculus by IncorporatingAdaptive Learning Technology into Blended Models on CampusJennifer B. Daines, Colorado Technical University Jennifer Daines received a B.S. in English from the U.S. Air Force Academy in 1998 and subsequently spent eight and a half years as a Personnel Officer in the Air Force, serving most of that time in the Air Force’s education and training command. In 2005, she went back to school, earning an M.A. in English from the University of Texas at San Antonio. In 2007, Jennifer separated from the Air Force and moved to Colorado Springs, where
, even though theseare rigorous courses for science, engineering, and mathematics majors, and most of the studentsare excellent).In the late 1960s, Columbia University had three distinct calculus sequences: Calculus SequenceA, supposedly the most computational and easiest; Calculus Sequence B, more theoretical andharder (primarily for engineers and physics majors); and Calculus Sequence C, for the mostinterested and talented students. As a physics major, I was in the calculus sequence B.In spite of (or maybe because of) the comments on my mathematics work, I eventually obtainedmy Ph.D. in mathematics. After a total of over thirty years of teaching calculus, and inobservance of my fiftieth year anniversary of having taken my first calculus course
Connecticut. Her educational research interests include retention, mathematics and materials science teaching and learning, first-year programs, accreditation, and faculty development.Ms. Jocelyn B. S. Cullers, Boise State University Jocelyn B. S. Cullers is a Data Analyst at the Institute for STEM & Diversity Initiatives at Boise State University. c American Society for Engineering Education, 2018 The Crux: Promoting Success in Calculus IIAbstractIn the 2013-14 school year, Boise State University (BSU) launched a major overhaul of CalculusI. The details of the reform, described elsewhere, involved both pedagogical and curricularchanges. In subsequent years, we developed several
- Type C Type E Options description posing Derivative Type A - Type F information: (rate of change) Function Type B Type D - (magnitude)For each of the seven Types of items, there is an extra feature that allows a new rating accordingto three types of contexts where the information has to be stated. It could be the real environmentof Motion Context (MC) that has been studied in class through SimCalc, or it could be anotherreal magnitude involved in Other Context (OC), or it
University and a master’s degree in journalism from the University of California at Berkeley.Cheryl Schrader, Boise State University Page 12.305.1 Cheryl B. Schrader is Dean of the College of Engineering and Professor of Electrical and Computer Engineering at Boise State University. Dean Schrader has an extensive record of publications and sponsored research in the systems, control and engineering education fields. She recently received the 2005 Presidential Award for Excellence in Science, Mathematics and© American Society for Engineering Education, 2007 Engineering Mentoring from the White House for
sectionsThe table below shows the final grade breakdown for the test section of Calculus I, as well asthe grade breakdown for all other Calculus I sections at SPSU taught by permanent facultymembers. (The restriction to full-time faculty members is due to a historical differencebetween course outcomes for permanent and adjunct faculty in our department.) The “OverallGPA” below attributes four points to students achieving an A, three points to those with a B,two points to those with a C, one point to those with a D, and none to those who withdrew orreceived an F. Test section (n=34) All other sections (n=208) Course grade Number of Percentage Number of Percentage students of
. Kato, O. Pfeiffer, E. Zorn, Pre-Freshmen Students Gearing up with Early Bird, Proceedings of the 2009 ASEE Annual Conference, ASEE6 http://www3.math.tu-berlin.de/OMB/7 https://www.tu9.de/8 http://en.wikipedia.org/wiki/Linux9 A. Heck: Introduction to Maple, 3rd ed., 2003, Springer, New York.10 Maple User Manual, Maplesoft, a division of Maple Waterloo Inc., 2011, www.maplesoft.com.11 L. Bernardin, P. Chin, P. DeMarco, K. O. Geddes, D. E. G. Hare, K. M. Heal, G. Labahn, J. P. May, J. McCarron, M. B. Monagan, D. Ohashi, S. M. Vorkoetter, Maple Programming Guide, Maplesoft, a division of Maple Waterloo Inc., 2011, www.maplesoft.com.12 D. E. Knuth, Computers & Typesetting, Volume A: The TeXbook, 1986, Addison
that faculty now faced students,many instructors feel their interaction with students during problem solving is vastly improved.From the student survey results, it was clear most students preferred faculty use of tablets andDyKnow to traditional chalkboard based lectures. Students and faculty both reported likingTablet PCs but there was insufficient data to support general conclusions about their impact onteaching and learning. An initial comparison of grades from the first year DyKnow and TabletPCs were used to the previous year showed the distribution of A and B grades to very similar.This is probably to be expected, as it would not be expect that measurable change in the moretalented students’ grades would occur. What instructors found
Mailman and board chair Beth Kennedy for supporting thestudy. A special thank you to PedGames server administrator Hao Xu and to all of the PedGamesstudent programmers for their creativity, dedication and hard work.Bibliography1. Shaw, S., Boehm, Z., Penwala, H., and Kim, J., GameMath! Embedding Secondary Mathematics into a Game- Making Curriculum Proceedings of the American Society of Engineering Education, 2012.2. van der Meulen, R. and Rivera, J. (2013) Gartner press release. Online at http://www.gartner.com/newsroom/id/2614915.3. Moskal, B. and Skokan, C. (2007). An innovative approach for attracting students to computing: A comprehensive proposal. Online at http://www.nsf.gov/awardsearch
possibleoutcomes or combinations of a situation, and create and interpret graphs.Using Baseball Problems in Mathematics ClassesHome run trot--the batter’s eye a tapemeasuring the distance22There are many ways to incorporate baseball into mathematics. One could show how outfielderscatch a fly ball using the linear optical trajectory (LOT) model which received much nationalattention in 1995. This model uses equations to relate the motion of the fly ball to the motion of theoutfielder using a mathematical foundation. The LOT hypothesis determines “the strategy thefielder uses to catch a fly ball by following a path that will keep the optical trajectory projectionangle constant, this is equivalent to keeping the ratio (tan cx)/(tan B) constant.”23Merrimack
𝐹𝑦 𝐹𝑧 = (𝑟𝑦 𝐹𝑧 − 𝑟𝑧 𝐹𝑦 )i − (𝑟𝑥 𝐹𝑧 − 𝑟𝑧 𝐹𝑥 )j + (𝑅𝑥 𝐹𝑦 − 𝑟𝑦 𝐹𝑥 )k (3) Figure 1: The z-component of a force can be show to contribute to a rotation about y (a) and x (b) axes. This corresponds to the presence of Fz in the Mx and My terms of the formula in eqns. (3) and (4). Similarly, the component of the force in the y-direction contributes to a rotation about the z axes (c) and x axis, (not shown), and can be matched to the presence of Fy in the Mx and Mz components of the moment vector. = 𝑀𝑥 i + 𝑀𝑦 j_𝑀𝑧 k (4) (The x, y, z, coordinate unit vectors are
piezoelectrics, nanomanufacturing, optical measuring techniques, and intercultural design.Dr. Jeffery J. Leader, Rose-Hulman Institute of TechnologyMiss Jessa B. Ward, Rose-Hulman Institute of Technology Jessa Ward is a master’s student in the Biology and Biomedical Engineering Department at Rose-Hulman Institute of Technology. She is interested in biomechanics, prosthetics, and orthotics. More specifically, her thesis work is examining the biomechanics of Kinesio tape. c American Society for Engineering Education, 2018 Creating Laboratories to Aid Student Modeling Ability in Calculus IAbstractIn this paper we will report on the development and deployment of a laboratory sequence forCalculus 1 students
Ftotal = k f 2We find empirically that k ranges between 6 and 9 for the College of Engineering and Science atLouisiana Tech university for each year starting in 2000. Figure 1. shows the f-index for 2007-08, here k =6. Page 25.165.3 f-index for 2007-08 14 12Number of Students 10 8 6 4 2 0 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Paper ID #6492Tradeoffs in using Mathematica templates in an introductory numerical meth-ods courseDr. Shirley B. Pomeranz, University of Tulsa Shirley Pomeranz Associate Professor Mathematics Graduate Student Advisor Department of Mathemat- ics The University of Tulsa Research and Teaching Interests: Boundary Element Method and Finite Element Method, Numerical Methods, Engineering Applications of Mathematics, Applications of Mathematica, Women in Mathemat- ics Page 23.1258.1 c American Society
wherever you want, and orient the axes however you want;the value of a scalar remains the same.*If one desires, one can represent this invariance with an equation. Consider two orthonormalcoordinate bases, S and S , which differ by an arbitrary proper, rigid rotation, as shown inFigure 1(a). If a is the value of a certain scalar (such as your pen’s mass) in S, and a is the valueof the same scalar in S , then a = a. (1)This is the transformation rule for scalars under proper, rigid rotations. (a) (b) Figure 1. (a) Two orthonormal coordinate bases S = {ˆ ˆ3 } and S
1A). With development of the Technion Mathematics Web tutoringsystem the classes were reduced to one hour a week (Figure 1B). A. Lectures 4 h Classes 2 h B. Lectures 4 h Classes 1 h Web tutorials C. Lectures 4 h Classes 1 h Web tutorials Supplementary applications classes 1-2 h Figure 1. Multivariable Calculus outlines: A. Conventional; Page 11.779.4 B. Computerized; C. Applications integratedIn our study the course
from Auburn University in 2014. He is a contributor to the Australian Maths Trust, and member of the MASAMU international research group for mathematics.Dr. Carl Pettis Carl S. Pettis, Ph.D. Professor of Mathematics Department of Mathematics and Computer Science Al- abama State University Administrative role: Interim Associate Provost Office of Academic Affairs Alabama State UniversityDr. Uma Kannan Dr. Uma Kannan is Assistant Professor of Computer Information Systems in the College of Business Administration at Alabama State University, where she has taught since 2017. She received her Ph.D. degree in Cybersecurity from Auburn University in 2017. She specialized in Cybersecurity, particularly on
selected, an almostidentical window will be displayed, with the same 4 topics for users to choose. (a) Page 25.825.7 (b) Figure 4: Starting of the programIn the tutorial scene, if topic “Properties of Graphs” is chosen, first a window as shown in Fig. 5awill be seen. Here the users can learn how to find asymptotes and how to graph rationalfunctions. By clicking the “next” button, the module will randomly generate a rational function,graph it, and display the asymptotes, as shown in Fig. 5b. The same procedure applies to
making classes were interspersed with activities thatinvolved mathematics either directly, e.g., working on traditional math worksheets or playingmath games, or indirectly, e.g., creating games or participating in discussion activities.Students were given surveys to evaluate their a) interest in games, b) technological literacy, andc) math motivation and college plans. A pre-algebra readiness test was given from the suite ofstandardized tests developed by the Mathematics Diagnostic Testing Project (MDTP, 2010).Decisions about math integration were based on the results, and also on conversations withadministrators, in particular their concerns that every child be able to pass the California StateHigh School Exit Exam (CAHSEE) as soon as possible
equations for the different parts of the bottle can thenbe determined based on these values. The straight sections of the bottle can be assumed to followthe format of the equation r=rn where r is on the x-axis and rn is the value on the x-axis itself.The curved sections follow the format for a quadratic equation (which states y=ax2+bx+c). Theconstants a, b, and c of this equation can be determined based on at least three random points offof each curve assuming that the y-axis goes straight through the middle of the bottle. Theequations for each of these curves can then be used to determine the volume of each individualsection by rotating these curves around an axis (in this case, around the h-axis). This can be doneby using the integral seen in
class review/Q&A online Station #1 Station #2 online quiz quiz Three-station 10 min 10 min 40 min 40 min 40 min 10 min class review/Q&A online Station #1 Station #2 Station #3 online quiz (workshop) quizFigure 3. Class timeline (150 minutes)Learning Assistant Classroom SupportAn important part of the rotating station design was the availability of an undergraduate LearningAssistant (LA) provided by the University. Undergraduate students who qualify to become anLA have earned an A or B+ in the course they are an LA for, successfully
hisexperiences over the course of many years.3.1 Case Studies- In this section, results of a number of case studies related to the courses taughtduring the past two years are presented. Because each one typically entails support for more thanone of the hypotheses to be proposed in the next subsection, it was felt that by presenting thesestudies prior to the hypotheses, the reader might more naturally see how the hypotheses werearrived at.Case 1: Sets & Subsets- Let S be a set, or collection of two objects; specifically, S={ (0,1) ,(1,1)}, where the object (x,y) denotes the location of a point in the x-y plane. Define the subsetsA={(0,1)} and B={(1,1)}. Describe the set C A B , where the symbol denotes„intersection‟; that is, the objects that
" Proceedings of the American Society for Engineering Education Annual Conference and Exposition, Chicago, IL, 2006.[36] M. Allen and A. Kelley, "Emphasizing teamwork and communication skills in introductory calculus courses," Proceedings of the American Society for Engineering Education Annual Conference and Exposition, Honolulu, HI, 2007: https://peer.asee.org/2166.[37] A. Bernal, J. J. Leader, and J. B. Ward, "Creating laboratories to aid student modeling ability in Calculus I," Proceedings of the American Society for Engineering Education Annual Conference and Exposition, Salt Lake City, UT, 2018: https://peer.asee.org/30235.[38] J. D. Desjardins, E. Breazel, M. Reba, I. Viktorova, J. B. Matheny, and T. R. Khan