Paper ID #29062Addressing Math Readiness for Engineering and other STEM ProgramsDr. Kathleen Marie Fick, Methodist University Kathleen Fick is a Professor of Mathematics and her current research focuses on mathematics education and undergraduate curriculum, specifically the areas of 1) future educators’ mathematical understanding and preparation; 2) teachers’ mathematical content knowledge, understanding, and training; 3) the de- velopment of children’s algebraic and geometric understanding; 4) procedural versus conceptual error analysis; and 5) the use and understanding of manipulatives. Dr. Fick has been involved in
the prediction and modelling of insidious cyber-attack patterns on host network layers. She also actively involved in core computing courses teaching and project development since 1992 in universities and companies. c American Society for Engineering Education, 2020 Applications of Linear Algebra applied to Big Data Analytics1. IntroductionThe digital universe (the data we create and copy annually) is doubling every two years and willreach 44 zettabytes (44 trillion gigabytes) in 2020 [1]. The stored digital data volume has grownexponentially over the past few years [2, 3]. In 1986, only three exabytes of data existed and in2011 it went up to 300 exabytes [3], and at the end of 2020 it might
unusually large population of students who were homeschooledwhen they graduated from high school (about 1/5 of students university wide and 1/4 of studentscurrently enrolled in the School of Engineering and Computer Science). In this paper, I investigatethe retention rate and calculus readiness for homeschooled students entering the School ofEngineering and Computer Science as compared with their non-homeschooled peers.In this study, I hypothesized that homeschooled students might have a different likelihood tosucceed in engineering school compared to their non-homeschooled peers. The results of the datastudy support this hypothesis and suggest that homeschooled students are more likely than othersto succeed in engineering school, with retention in
Louisville, KY 40292 campbell.rightmyer@louisville.edu patricia.ralston@louisville.eduAbstractTraditional lecture style courses use class time to deliver new material to students and homework to provide practice.Flipped classrooms, on the other hand, provide new material outside of class and students are then givenopportunities to work actively on problems during class time. A flipped classroom design combines active,problem-based learning activities with direct instruction methods, and is seen by many as a teaching method thatresults in higher student satisfaction, greater retention of knowledge, and increased depth of knowledge [1] .The initial implementation of
Society for Engineering Education, 2018 Guided-Lecture Team Based Learning at Work: Teaching Differential Calculus to Part-time Engineering Students in Latin America.IntroductionThe United States Department of Education identified the so called “non-traditional student”, as astudent with at least one of the following characteristics: attends school part time, works full timeor is financially independent, among others [1]. In contrast, a student is called “traditional” whenthe student enrolls full time immediately after finishing high school, is financially dependent, anddoes not have a formal job during the academic year [2]. As reported by Hussar and Bailey, theenrollment of non-traditional
engineering.This paper focuses on introducing basic math concepts by linking them to daily experiencesusing relevant analogy-based examples, to be introduced prior to delving into purelymathematical explanations and proofs. The paper shows tangible physical explanations ofconcepts in calculus, specifically on topics such as: (a) Integration and differentiation. To explain these concepts, the paper uses several examplessuch as (1) relations between steering wheel angle of a car and the physical angle of the car inworld coordinates, (2) relations between water flow and its accumulation in a container, (3)elevator directional motion, and (4) energy and its temporal rate-of-change during running,walking, sitting, and sleeping. It also shows some unexpected
purpose of this paper is to recommend adapting new pedagogical methods to theaccepted topics in an introductory probability and statistics course for engineeringundergraduates—methods that better match the learning characteristics of Millennial students inour courses. In a nutshell, those characteristics may be summarized as: (1) They want relevanceto their major, and future engineering career; (2) They want rationale (for the textbook selected,and for specific course policies and assignments); (3) They revel in technology (to collect data,compute, communicate, and multi-task); (4) They want a relaxed, hands-on environment; (5)They prefer instructors who rotate among several classroom delivery methods.Considering the “Five R‟s” learning
mathematics placement test to all incoming first time full-time first yearstudents, except those with proof of advanced placement or transfer credits for calculus courses.Performance on this placement test determines students’ starting point in the calculus sequence.Students will either be placed in Calculus-I, which is the preferred scenario, or one of the twopre-calculus courses. Students that are placed in pre-calculus courses start 1-2 courses behind ascompared to those placed in Calculus-I. In addition, performance in the mathematics placementtest also drives placement in physics and chemistry. All this put together means that students thatdo not do well on the mathematics placement test are looking at 1-2 added semester(s) to theirgraduation
their major. A key detrimental factor contributing to this isthat a majority of the incoming first year students are considered to be underprepared inmathematics. Our university is exploring various options to help these students reach calculus Ias soon as possible. Pre-calculus summer boot camp is one of programs successfullyimplemented at our institution [1]. Other initiatives include: 1) developing sample placementtests for students to practice under the same environment as the original test, 2) making aplacement calculator for students to input the scores from the practice placement tests todetermine their likely mathematics placement, and 3) establishing a strong outreach to educatestudents about the impact of their mathematics placement
, and computer science;therefore observing responses of graduate and senior undergraduate students to Taylor series questions appears to be theinitial step for understanding students’ conceptual cognitive reasoning. These observations help to determine and develop asuccessful teaching methodology after weaknesses of the students are investigated. Pedagogical research on understandingmathematics and conceptual knowledge of physics majors’ power series was conducted in various studies ([1-10]); however,to the best of our knowledge, Taylor series knowledge of engineering majors was not investigated prior to this study. In thiswork, the ability of graduate and senior undergraduate engineering and mathematics majors responding to a set of
” (or, in the context of differentialforms, “1-forms”2) for stacks, “contravariant vector densities” for sheaves, and “covariantvector capacities” for thumbtacks.It cannot be the objective of introductory courses to teach that full menagerie. Nevertheless,the concept of co- and contravariance and dual bases strikes the authors as essential enough tobe embedded into the course content of undergraduate engineering mathematics. Dual basesemerge in a variety of contexts, reaching from solid state physics over continuum mechanicsto multiresolutional analysis.In solid state physics, for instance, one takes advantage of the fact that the atoms are arrangedin crystalline lattices. When considering waves propagating through such a lattice (x
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
rules, and I havedone so in three different undergraduate-level engineering courses: a sophomore-level dynamicscourse, a junior-level strength of materials course, and a senior-level advanced engineeringmathematics course. In this paper I discuss the methods I used to illustrate the geometricapproach in these courses, and report the results of end-of-semester surveys designed to assess mystudents’ cognitive and metacognitive understanding of tensors. Based on my experience, Iencourage other instructors to adopt the geometric approach in their own courses. By doing so, Ibelieve it is possible to remove some of the mystery surrounding tensors, making them moreaccessible, understandable, and perhaps even a little more interesting.1
bridge programs that addressed primarily the samemathematics content to support engineering calculus concepts and skills, we can see thepossibilities to adapt a program to different groups of students to achieve greater success. Thispaper describes the design, similarities, and differences of these programs along with quantitativedata results.IntroductionStruggles in mathematics knowledge and skills remain an issue for students in engineeringeverywhere [1]. One of the supports that many colleges have provided is a summer bridgeprogram. There are many variations on those programs [2] and reports of success [3], [4], [5], butrelatively little strong quantitative results [6]. Successful bridge programs generally utilize a lotof money, time, and
medicine,learning to read medical images requires the ability to understand cross-sections [1]. Wanzel,Hamstra, Anastakis, Matsumoto, & Cusimano, [2] also reported a correlation between medicalstudents’ scores in mental rotation and their performance on a surgical procedure, Z-plasty. Inengineering, higher abilities in cross-sectioning have been linked to better performance inMechanics of Materials courses [3]. Two categories of spatial reasoning, as defined by Linn andPetersen [4], are mental rotation and spatial visualization. Mental rotation involves the ability tomanipulate three-dimensional (3D) objects in one’s mind by rotation, and spatial visualizationinvolves the ability to manipulate three-dimensional (3D) objects in one’s mind
conditions. We defined three distinctperiods that correspond with when the departmental policy changes were implemented. Theseperiods are Traditional Methods (2002-2005), SCALE-UP (2006-2013), and Return toTraditional (2014-2015), which are defined in more detail below.Traditional Methods (2002-2005)Traditional lecture was the pedagogical approach used during this time. Additional componentsof instruction and assessment for this period are described in Table 1 below.Table 1. Overview of Traditional Methods period course policies Textbook Homework Exam Format Grading Policy(2002) Calculus 4thEdition (Stewart Four exams- 60%2001) Variety of
retained in STEM in the academic year immediately subsequent to their enrollment in Calculus I? Q4: What, if any, is the difference in STEM retention rate between students who experience R-Calc versus those who experience N-Calc? Q5: What, if any, effect does R-Calc have on retention rates for URM, Women, Pell- eligible students? Q6: What, if any, effect does R-Calc have on pass rates in post-requisite courses?Questions 1 and 3 are answered with descriptive statistics. The remaining questions ask whethera metric applied to students taking R-Calc differs from the same metric applied to students takingN-Calc. In all cases the metric is a simple proportion (pass rate or retention rate) so all of thesequestions are
mathematics courses to engineering students. He is also very interested in the effects of small learning communities on learner motivation, commitment and strategies. Email: Isolan@scsu.eduDr. Ronald W. Welch P.E., The Citadel Ron Welch (P.E.) received his B.S. degree in Engineering Mechanics from the United States Military Academy in 1982. He received his M.S. and Ph.D. degrees in Civil Engineering from the University of Illinois, Champaign-Urbana in 1990 and 1999, respectively. He became the Dean of Engineering at The Citadel on 1 July 2011. Prior to his current position, he was the Department Head of Civil Engineering at The University of Texas at Tyler from Jan 2007 to June 2011 as well as served in the Corps of
-Fields-With-Applications/Mandrekar-Gawarecki/9781498707817 Gawarecki L., Mandrekar V. (2011) ”Stochastic Differential Equations in Infinite Dimensions with Appli- cations to Stochastic Partial Differential Equations” Springer. http://www.springerlink.com/content/u040lr/#section=823672&page Gawarecki, L.; Mandrekar, V. (2010) ”On the existence of weak variational solutions to stochastic dif- ferential equations”, Commun. Stoch. Anal. 4, no. 1, 1–20. Gawarecki, L.; Mandrekar, V., Rajeev, B. (2009) ”The monotonicity inequality for linear tial differential equations”, Infinite Dimensional Analysis, Quantum Probability and Related Topics, 3 Vol. 12, No. 4 , 1–17. Gawarecki, L.; Mandrekar, V. Rajeev, B. (2008) ”Linear
severalreports [1], [2], [3], on Calculus curriculum renewal across the first two years in college. Theleading trends are clustered in three areas: • Calculus re-sequencing [4], [5] • Active learning methods [2], [6], [7], [8] • Applications from Engineering & Sciences [9], [10], [11], [12].Based on these suggestions, our goal is to create three “Engineering Math” tracks, each tailoredto different skill levels. The hope is that careful customization will enable all students tocomplete the calculus sequence (including both single-variable and multivariable) in twosemesters. These tracks are named Core Engineering Math I and II, Engineering Math I and II,and Honors Engineering Math I and II.The Honors track was launched in 2016-2017, and
representation of the problem. For simple problems with few forces/moments astudent may be able to write down the equations with ease. However, as the number of forcesincreases the cognitive load [1] on the student increases making it difficult to setup the equationsdirectly from the problem description. To help remedy this, an intermediate step (or additionalrepresentation) is often taken where a free body diagram (FBD) is drawn showing the forcesand/or moments which act on a body. Literature has suggested that the use of multiplerepresentations helps develop problem solving skills for students [2,3]. Formally a FBD isa schematic representation of a particle or rigid body that is isolated from its surroundings anduses vectors to represent external
modern technologyappropriately to take advantage of the speed and power of calculation but not impede conceptualunderstanding and learning. As technology continues to change, it is important that engineersretain the conceptual understanding so they can adapt to new tools and still solve futureengineering problems. It is hoped that through this literature review, good practices for properlyusing technology to supplement and improve mathematics education in undergraduateengineering can be compared and expanded upon.IntroductionThe mathematics ability of undergraduate engineering students has seemingly declined over thedecades [1, 2]. Due in part to the increased role of technology in their studies as well as theincreased focus on application of
exit the discipline [1]. Important factors in student attrition from STEM disciplinesinclude: 1) instructional experiences such as first-year Mathematics courses and facultyexpectations [1][2] and 2) individual self-efficacy, epistemologies, and goal orientations [2][3].In order to enhance student cognitive and affective outcomes and retain students in STEMdisciplines, undergraduates have been used as Learning Assistants (LAs), course UTAs, and labUTAs with positive results [4][5][6]. For example, UTAs used in an inquiry-based generalchemistry laboratory context have similar student content knowledge gains as GTAs in the sameposition [5]. As another example, in a large-enrollment introductory physics course, studentshave significantly higher
assessment tools to measure the effects ofthe project on students’ grades and retention. The toolkit includes: (1) pass rate and GPA inCalculus I, (2) longitudinal analysis of pass rates and GPA in subsequent courses, (3) impact ofCalculus I on retention in STEM and retention at BSU, (4) all of the above comparing students inreformed Calculus vs traditional Calculus, (5) all of the above for underrepresented minorities,women, or other demographic subsets. While these tools were originally developed to study theCalculus I project, they are available for studying the effects of other courses on studentacademic performance and retention.In this paper, we briefly describe a rebuild of Calculus II, overhauled in the 2015-16 school yearfollowing the same
, Mathematics & Statistics Department2 1 Edwardsville, IL 62026AbstractThis Evidence-based practice complete paper describes the experiences with a holisticMathematics Enrichment Sessions, Freshmen Mentoring, Mathematics Tutoring and newFreshmen Engineering course that are implemented during the last five years at Southern IllinoisUniversity Edwardsville as part of our NSF STEP project. The mathematics Enrichment Session(ES) idea, which is a combination of the best aspects of Supplemental Instruction idea andPeerLed Team Learning methods, can be an effective way of supporting students in their firstyear of studies. The implementation of the peer-mentoring program that was
thatappear in the summation of functions’ power series expansion. Applications of derivative and integralmathematical operations to power series of functions have important real-life applications such ascalculating the noise differentiation of wave lengths and observing the area between the wave length andinput information by integrating the function as a part of the Fourier analysis. Several other results onstudents majoring in mathematics and physics power series’ knowledge was conducted in various studies([1-9]). Pedagogical research on engineering majors’ understanding of how to apply mathematicaloperations to series expansion of functions received hardly any attention from researchers ([10]). In thiswork, the emphasis is given to engineering
for the text:communicate essential mathematics effectively, represent the engineering professionauthentically with appropriate application problems, and provide support to the student to ensuresuccessful learning experience.Finding a Foundation for a Textbook to Authentically Incorporate EngineeringThe desired content and structure of the book was informed by an advisory board of teachersthrough three guiding questions 1. At the time of the initial survey, teachers representing 10different schools across 2 states offered to assist in this effort. The first round of questions wasdeveloped by the investigators to create some idea for the target for this project in terms ofcontent and market. The teachers were sent the following questions:1
. Figure 4: Examples of long divisionThe virtue of teaching students to perform the quotient of two integers using long divisionsbecomes more apparent especially when discussing the parity of numbers, i.e. whether a giveninteger is odd or even. Instructors can demonstrate to students that the parity of an integer can bedetermined using long divisions where the remainder will be zero when even numbers aredivided by 2 (in other words, even numbers are completely divisible by 2), and the remainderwill be 1 (or non-zero) when odd numbers are divided by 2.Students can also learn that all even numbers are multiples of 2 and that odd numbers are nevermultiples of 2. However, the concept of remainders from long divisions can be applied intocomputer
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
. Gainen and Willemsen [1] assert that calculus provides thefoundation for future engineering courses. Without a good foundation in calculus, engineeringmajors will have difficulty in applying the knowledge in their junior or senior level courses.Many aspects of engineering require an application of calculus such as: design of storm drainand open channel systems; calculation of forces in complex configurations of structuralelements; analysis of beams (i.e., shear forces, bending moment, deflection, stress distribution);analysis of structure relating to seismic design; design of a pump based on flow rate and head;calculations of bearing capacity, lateral earth pressure, and shear strength of soil; computation ofearthquake induced slope