Paper ID #30800Lessons from a Lower Division Mathematics Co-Teaching SequenceDr. Charles Lam, California State University, Bakersfield Dr. Charles C.Y. Lam is a Professor in the Department of Mathematics. Dr. Lam received his Ph.D. in Combinatorics and Optimization from the University of Waterloo. His research areas are in cryptography, digital watermarking, and STEM education. He is the PI for the NSF IUSE grant (NSF-DUE 1430398) for STEM retention, and the co-PI for the NSF Federal Cyber Service grant (NSF-DUE1241636) to create models for information assurance education and outreach. He is currently the Project Director
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
undergraduate programs in the mathematical sciences in the Unites States: Fall 2010 CBMS survey. Retrieved from http://www.ams.org/profession/data/cbms-survey/cbms2010-Report.pdf 2. Mayes, R. (2004). Restructuring college algebra. International Journal of Technology in Mathematics Education, 11(2), 63–73. 3. Schunn, C. D., & Patchan, M. M. (2009). An evaluation of accelerated learning in the CMU open learning initiative course “logic & proofs” (Technical report). Pittsburgh, PA: Learning Research and Development Center. Retrieved from http://oli.cmu.edu/wpoli/wpcontent/uploads/2012/10/Schunn_2009_Evaluation_OLI_Logic_Proofs.pdf 4. Knewton. (n.d.). Knewton technology helped more
. Revista Latinoamericana de Investigación En Matemática Educativa, 12(3), 355– 382. 5. Noss, R., Hoyles, C., Mavrikis, M., Geraniou, E., Gutierrez-Santos, S., & Pearce, D. (2009). Broadening the sense of “dynamic”: A microworld to support students’ mathematical generalisation. ZDM—The International Journal on Mathematics Education, 41(4), 493–503. doi:10.1007/s11858-009-0182-8 6. Salinas, P., Quintero, E., & González-Mendívil, E. (2014). An environment to promote a visual learning of Calculus. In H. R. Arabnia, A. Bahrami, L. Deligiannidis, & G. Jandieri (Eds.), Proceedings of the International Conference on Frontiers in Education: Computer Science and Computer Engineering (pp. 425–429). Las
. APOS theory is initiated with Piaget’stheory of reflective abstraction [17] and got expanded to K16 mathematics education and RUME in recent years. Itwas applied in 1997 to mathematical topics for analyzing combined math knowledge of a student in a specificsubject [1]. Action, process, object, and schema are the mental structures proposed as a part of the APOS theory tofollow developmental stages of the learners. The main goal of this theory is to observe and categorize mentalstructures through observations of learners’ mental mechanisms; it is important to understand the totality ofknowledge and its’ reflection in applications.In the relevant APOS literature, learners’ conceptual view of the function was studied in [3] by relying on
and planning a new learningexperience by following the ideas of backward design [11].Phase 3. Design of the learning experienceBased on the inputs received from the previous stages and, most importantly, on her ownreflection, the mentored professor was supported in the design of a new learning experience thatfocused on the development of communication, modeling and problem solving competencies inmathematics. Since the Algebra and Functions course has not been redesigned yet to becompliant with competency-based education, for the case study we based on the mathematicalcompetencies proposed by OECD (Organisation for Economic Cooperation and Development) inits Programme for International Student Assessment (PISA) [12].The first step in the
and physical reasoning,” International Journal of Mathematical Education in Science and Technology, 11, no. 3, 1980, pp. 307–318. Page 23.352.11
. [5] D. E. Lee, G. Parker, M. E. Ward, R. A. Styron, and K. Shelley, “Katrina and the Schools of Mississippi: An Examination of Emergency and Disaster Preparedness,” J. Educ. Students Placed Risk, vol. 13, no. 2–3, pp. 318–334, 2008. [6] W. C. Chen, A. S. Huang, J. H. Chuang, C. C. Chiu, and H. S. Kuo, “Social and economic impact of school closure resulting from pandemic influenza A/H1N1,” J. Infect., vol. 62, no. 3, pp. 200–203, 2011. [7] D. J. D. Earn, D. He, M. B. Loeb, K. Fonseca, B. E. Lee, and J. Dushoff, “Effects of school closure on incidence of pandemic influenza in Alberta, Canada,” Ann. Intern. Med., vol. 156, no. 3, pp. 173–181, 2012
% over the past decade (from 244 in fall, 2006 to anenrollment of 433 in fall, 2015).With the increased demand for calculus instruction came several undesirable consequences.These included a lack of coherence between instructors in terms of content. Related to this was alack of agreement in terms of what exactly students were expected to be able to do by the end ofthe course. In fact, that topic – the learning outcomes of the course – had not been addressed;each instructor instead carried their own learning outcomes. In nearly all instances, theseoutcomes were not actually articulated into a statement such as, “By the end of this course(chapter, section, unit), students will be able to…,” but rather were internalized; each instructorhad their
V + (IroW - OroW)* t ø ø with S(t = 0) = S0 Figure 2. Example 2 of a diagram in Vensim for a tank of water mixed with salt; a related math model Page 26.302.9Session 2, Part C. Total Time: 90 minutes; time for this part C: 45 minutes. Week 14/16.The philosophy of Systems Dynamics is presented again in a new problem during the first 45minutes of the session. During this time, a mathematical model previously developed in class(week 3) is discussed. The model deals with the
This Have to do With Us?”:Teaching Statistics to Engineers,” Proceedings of the Sixth International Conference on Teaching Statistics (ICOTS6), Cape Town, South Africa, 2002. [Online]. Available: http://iase- web.org/documents/papers/icots6/5e1_wils.pdf . [Accessed May 20, 2017].[3] R. V. Hogg, et al., “Statistical Education for Engineers: An Initial Task Force Report,” The American Statistician, Vol. 39, pp. 168-175, 1985.[4] B.L. Joiner, “Transformation of American Style of Teaching Statistics,” Report 10, Center for Quality and Productivity Improvement, University of Wisconsin, Madison, WI, pp. 30-33, 1986.[5] B. Godfrey, “Future Directions in Statistics,” Report 10, Center for Quality and
placement. ALEKS (Assessment andLEarning in Knowledge Spaces) is a web-based tool that can be used to assess math proficiencyand skill level. All (or nearly all of) incoming freshmen and transfer students take the ALEKSplacement assessment online. It tests for courses below the level of calculus and for calculus-readiness. Transfer credits (including AP and IB credits) are used to determine readiness forcourses above Calculus I. Some students, especially international students, who may not havecredits but who are ready for higher-level courses, will take proficiency exams for course credit.The ASEE Mathematics Division has sponsored many conference sessions withpresentations/papers related to the use ALEKS. For example, a couple of topics are
enrollmenttook place. This is not ideal. As Mathematical Association of America (2010) recommends, it isbest to provide the placement before students enroll in courses. We hope to make thisimprovement in future years.Students were requested to register for the test via a Qualtrics Survey which collectedbackground information, including self-reported AP scores and dual enrollment credits. Studentscould select from 3 testing sessions per day, 5 days per week. They were requested to register fora test time during a particular week following their summer orientation session, but alternativeswere offered to those who needed or preferred to take the test during a different week.WeBWorK [5] was used for the actual online placement test. WeBWorK is an open
operation... • When an action is repeated and the individual reflects upon it, he or she can make an internal mental construction called a process which the individual can think of as performing the same kind of action, but no longer with the need of external stimuli... • An object is constructed from a process when the individual becomes aware of the process as a totality and realizes that transformations can act on it... • A schema is a ... individuals’ collection of actions, processes, objects, and other schemas which are linked by some general principles to form a framework in individual’s mind...In this theory, every concept can be constructed on different concepts and schemas. For example,if a researcher
Reality: Quantification and Western Society 1250 – 1600. Cambridge University Press, 1997. 2. Dantzig, T. and Mazur, J. Number: The Language of Science. Plume Books, January 30, 2007. 3. Donohue, S.K. and Richards, L.G. A Parent/Teacher ’s Guide to That’s How We Roll: Learning About Linear Motion and Underlying Concepts Using Engineering Design Activities, Virginia Middle School Engineering Education Initiative, University of Virginia, 2014. 4. Donohue, S.K. and Richards, L.G., “FIE 2015 Special Session – Movin’ Along: Investigating Motion and Mechanisms Using Engineering Design Activities,” Proceedings of the 2015 Frontiers in Engineering Conference. 5. Ferguson, E. S. Engineering and the Mind's Eye. MIT
Methodology and Statistics from the University of Virginia and is currently the Humana-Sherman-Germany Distinguished Professor at AU. He teachers courses in research methods and program evaluation. c American Society for Engineering Education, 2018 Infusion of Big Data Concepts Across the Undergraduate Computer Science Mathematics and Statistics Curriculum1. IntroductionStored digital data volume is growing exponentially [1]. Today, there are about 4.4 zettabytes (1zettabyte is equivalent to 1021 bytes) of data in the World and it is expected to be about 44zettabytes by 2020 [2, 3]. Society increasingly relies on such data to tell us things about theworld [1]. Recent advances in technology, such
majors and these include: 1. “cramsorption learning”, where students listen to professors lecturing and then regurgitate the formulas to solve problems in a test, 2. concepts that are not learned through experience but by sitting in a lecture hall, 3. lower grades because of hard courses and hence not qualifying to enter the engineering major, 4. entry level salaries in engineering being lower than other majors such as business, and 5. coursework has a higher difficultly level compared to other majors.So, coupled with the above reasons for dropping out or switching majors and having a small poolof potential students to begin with, it is imperative that state universities increase their retentionrate for greater use
tensors? Or, in mathematical language, how are tensors defined? 2 On this matter,the scientific community is divided into two camps. Many 3–8 understand tensors as things with acertain number of components (measured with respect to a given coordinate basis), whichtransform in a given way under certain coordinate transformations. We will refer to this as thecomponent approach. Others 1,9,10 understand tensors not as sets of components, but as singularobjects with certain geometric properties. This is known as the geometric approach, because itimbues tensors with inherent geometric meaning via the concepts of “space” and “direction.”Historically, these two viewpoints went head-to-head during the mathematical formulation ofrelativity theory, and
externalinstructions. Cognitive development starts with the elementary “applications” as the actions that turn intoprocesses when the learner manages to operate correlated variations. Process turns into object when new actionscan be applied with the existing process. Schema is “more or less coherent collection of objects along with actionswhich the subject can perform on them” ([3]).Pedagogical research on APOS theory applications of functions’ series expansion is limited in the literature([1]). The only research overlap on APOS theory and infinite series concepts’ is the report that describes athree-semester calculus course developed at Purdue University with support from the U.S. National ScienceFoundation. The design of the course was based on APOS theory
topics covered ingrades 5-10, and most, but not all, students were expected to have some level of familiaritywith the topics covered in grades 11-13. Vectors is introduced in the introductory physicscourse, but is not covered in Norwegian high schools, so the students were not expected to befamiliar with these four problems prior to Science I.Table 2: Overview of problems in the mathematics test. Category Type of problem Number of Grade level problems introduced Basic mathematics Numeracy 3 5-10 (15 problems) Measuring 2 Reading tables 2
Cohorts program and other strategies can be implementedat relatively low cost to support the success of the Algebra II students.A Different Approach to Enhance the Success of the Algebra II StudentsTraditionally, students with ACT-MATH sub-score of 19 to 23 and who are placed into AlgebraII in their first semester in college are considered to be under-prepared in science, technology,engineering and mathematics (STEM) studies, and their success as measured by second-yearretention to STEM has been low. [In fall 2015, the ACT-MATH sub-score was revised to 20 to24 for Algebra II.] Summer Bridge2, 3, 4 and Peer5, 6, 7 and Alumni Mentor8 programs have beenimplemented by many engineering schools to support the success of this student population.These
Santiago has been a technical engineer, manager, and executive with more than 26 years of leadership positions in technical program management, acquisition development and operation research support while in the United States Air Force. He currently has over 15 years of teaching experience at the university level and taught over 40 different courses in electrical engineering, systems engineering, physics and mathematics. He has over 30 published papers and/or technical presentations while spear- heading over 40 international scientific and engineering conferences/workshops as a steering committee member while assigned in Europe. Professor Santiago has experience in many engineering disciplines and missions including
secondary science and mathematics classrooms. Her education includes a B.S. in Bioengineering from the University of Vermont, and M.S. and Ph.D. in Bioengineering from Clemson University.Dr. Geoff Potvin, Florida International University c American Society for Engineering Education, 2016 The Use of Case Studies in Preparing First-Year Mathematics Graduate Teaching AssistantsIntroductionIn 2000, 7.2% of all students enrolled in regular stream Calculus I in the United States weretaught by mathematics graduate students who served as instructors of record and had sole orprimary responsibility for all course activities 20 . By 2005, that number had grown to 10.7% 21 .The 2010 data
struggles that was observed at Wright State andother universities prior to the adoption of the Wright State model. In 2015 an internal study wasconducted to address this problem of student retention in engineering. The report [6] stronglyrecommended that we adopt the Wright State Model. In Fall 2016 the course IntroductoryMathematics for Engineering Applications (ENGR1234) was first offered. Subsequently, it hasbeen offered both in Fall and Winter semesters the first two years and only in Fall after that. Twoof the four engineering programs (Mechanical and Civil) made this class a requirement in theircurriculum but two other programs didn’t. Students entering Electrical engineering or Roboticsprograms were sometimes placed in this class if the
contact hours and active learning strategies will require buy-in from allthose involved.Transition to New StructureMeasures we could employ to assist in making this transition would include: 1) initiate a bi-weekly or monthly (at the minimum) informal interdepartmental pedagogy and best practicessharing session, 2) employ the current SI – Supplemental Instructor tutoring service to the MAT1125 and MAT 1130 courses, and 3) encourage fellow faculty to take advantage of the TLC –Teaching and Learning Center workshops provided through our institution. SI – SupplementalInstructor tutoring is currently being used in the introductory level mathematics courses. SI is atutoring program where a current student, who can provide tutoring in the topic area
% 23% Slightly20% 13% Disagree 8% 5% 3%10% 3% 0% 0% 0% 0% 3% 3% 0% Somewhat0% Disagree The activities helped me clarify The models helped me The "Concept Check" questions the material on volumes of internalize
and Composite Functions 1.5 Basic Trigonometry 2. Factoring and Solving Equations and Inequalities 2.1 Factoring 2.2 Solving Equations and Inequalities 2.3 Basic Trigonometry 3. Algebraic Fractions, Exponents, and Radicals 3.1 Algebraic Fractions 3.2 Exponents and Radicals 3.3 Basic Trigonometry 4. Trigonometry 4.1 The Unit Circle 4.2 Right Triangle Trigonometry 4.3 Trigonometric Identities 4.4 Solving Trigonometric EquationsRegular online tutoring sessions were required for all students. This feature is unique toonline bridge programs10. In cohorts of about 20 students each, they were assigned a tutorwith whom they met for 36 hours during the program. Hiring capable tutors, preferable withhigh
a complete understanding ofgoverning differential equations and boundary conditions. Linking the undergraduatemathematical base requires reviewing some concepts first seen in high school. The next sectionpresents specific topics that assist understanding formulation and problem solving in this course.Connectivity – Step 2After identifying the technical topics presented in figure 3 it is clear that the review focuses onboth control volume analysis and differential equations. The relevant physical concepts link thefollowing mathematical topics with our approach (Fig. 4). The analytical methods requiremathematical concepts of Taylor series, line, surface and volume integrals, sign conventions ofsurfaces and stresses, review of directional
Curriculum," Journal of Engineering Education, vol. 93, no. 3, pp. 253-257, 2004.[3] C. McLoughlin and B. Loch, "Building cognitive bridges in Mathematics: Exploring the role of screencasting in scaffolding flexible learning and engagement," in Show me the Learning. Proceedings ASCILITE 2016 Adelaide, ASCILITE 33rd International Conference of Innovation, Practice and Research in the Use of Educational Technologies in Tertiary Education 2016, Adelaide, Australia, November 27-30, 2016, S. Barker, S. Dawson, A. Pardo, C. Colvin, Eds. pp. 412-420.[4] M. Anastasakis, C. L. Robinson, and S. Lerman, "Links between students’ goals and their choice of educational resources in undergraduate mathematics
Paper ID #5702Vertical assessment of math competency among freshmen and sophomore en-gineering studentsDr. Kendrick T. Aung, Lamar University KENDRICK AUNG is a professor in the Department of Mechanical Engineering at Lamar University. He received his Ph.D. degree in Aerospace Engineering from University of Michigan in 1996. He is an active member of ASEE, ASME, SAE, AIAA and Combustion Institute. He has published over 70 technical papers and presented several papers at national and international conferences.Dr. Ryan Underdown, Lamar University Dr. Underdown is an Associate Professor in the Industrial Engineering