Conference Session

Mathematics Division Technical Session 3

Collection

2016 ASEE Annual Conference & Exposition

Authors

Larry G. Richards, University of Virginia; Susan K. Donohue, University of Virginia

Tagged Divisions

Mathematics

Solar Car Figure 6: Pulling a Load with a Solar CarEach team prepares a summary sheet showing a sketch of their design, a bill of materials (theparts they used with the cost of each), the total cost of their design, and how much weight theircar was able to pull. After the competition, the entire class reflects on the results and discusseswhat worked and what did not.After completing this ETK, the students have learned about solar cells, motors, and tirematerials, but they have also learned about the engineering design process, and how to constructa vehicle to perform a task. They also learned how to measure the values of variables, theimportance of consistent procedures for making measurements, how to compute

Conference Session

Mathematics Division Technical Session 5: From Functions to Big Data–A Hands-on Challenge

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Emre Tokgoz, Quinnipiac University; Hasan Alp Tekalp; Elif Naz Tekalp; Berrak Seren Tekalp, Quinnipiac University

Tagged Divisions

Mathematics

research ([4]). Cooley, Trigueros and Baker reported results in 2007 ([5]) usingthematization of schema with the intent to expose those possible structures acquired at the most sophisticatedstages of schema development. Responses of research participants to a calculus graphing problem was analyzedin [2] by using APOS theory. The components of the APOS theory can be briefly explained as follows ([6]):  An action is a transformation of objects perceived by the as essentially external and as requiring, either individual explicitly or from memory, step-by-step instructions on how to perform the operation...  The individual reflects upon an action when the action is repeated and he or she can make an internal mental construction

Conference Session

Issues and Answers in Mathematics Education

Collection

2011 ASEE Annual Conference & Exposition

Authors

Peter J. Sherman, Iowa State University

Tagged Divisions

Mathematics

ideasmight contribute to improved motivation, one must still acknowledge that there are other largerreasons for the continuing decline of STEM education in the USA.Having taught university-level undergraduate and graduate courses in a wide variety of STEMtopics for over 30 years, this author has observed an equally disturbing decline in the relativeperformance of U.S. students in relation to students from other countries. This observation isoften reflected in the consistent and continued „dumbing down‟ of course concepts,acknowledged by many academics who have taught in STEM disciplines for any length of time.In view of this continued decline of competency among U.S. university graduates, it is notsurprising that more and more companies are looking

Conference Session

Mathematics Division Technical Session 1

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Rebecca Machen, University of Colorado Boulder; Wysheka Austin, Clemson University; Matthew K. Voigt, Clemson University

Tagged Topics

Diversity

Tagged Divisions

Mathematics

malintent, thatassociate people of color with negative concepts, even though most people self-report havingminimal to no bias (Greenwald et al., 1998). These unintentional beliefs, often referred to asracial microaggressions, communicate hostility toward people of color. Pierce (1974)conceptualized microaggressions as subtle, cumulative mini-assaults. Sue and colleagues (2007)define microaggressions as "brief and commonplace daily verbal, behavioral, or environmentalindignities, whether intentional or unintentional, that communicate hostile, derogatory, ornegative racial slights and insults toward persons of color" (p. 271). The current literatureexpands the definition of microaggressions to include "acts that reflect superiority, hostility

Collection

2016 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University

Tagged Divisions

Mathematics

memory, step-by-step instructions on how to perform theoperation...When an action is repeated and the individual reflects upon it, he or she can make an internalmental construction called a process which the individual can think of as performing the same kindof 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 atotality and realizes that transformations can act on it...A schema is an ... individuals collection of actions, processes, objects, and other schemas whichare linked by some general principles to form a framework in individual's mind... Baker, Cooley and Trigueros (2000) applied APOS theory to understand undergraduatestudents’ conceptual

Conference Session

Mathematics Division Technical Session 4

Collection

2016 ASEE Annual Conference & Exposition

Authors

Virgil U. Pierce, University of Texas, Rio Grande Valley; Javier Angel Kypuros, University of Texas, Rio Grande Valley; Shirley J. Mills, University of Texas, Rio Grande Valley

Tagged Topics

Diversity

Tagged Divisions

Mathematics

at improving entering students’ college readinessand mathematics placement. The small scale intervention, A Bridge to Calculus, is intended toimprove students’ placement from College Algebra into Calculus 1. The target population forthis effort are students with high school experience in a Calculus course but whose performanceon placement exams does not reflect this experience. At our institution this is a significantnumber of students and the goal of the project is to develop methods to address and acceleratestudents in this category. The course design, to take advantage of the students’ prior experience,emphasizes practice and mastery using a modified emporium course design and the ALEKSsoftware1. This intervention runs as a summer course

Conference Session

Using Applications and Projects in Teaching Mathematics

Collection

2012 ASEE Annual Conference & Exposition

Authors

Gunter Bischof, Joanneum University of Applied Sciences, Graz, Austria; Christian Steinmann, Joanneum University of Applied Sciences, Graz, Austria

Tagged Divisions

Mathematics

Hours 30.03.2011 Kick-off meeting Explanation of the project and distribution of the tasks. 3 31.03.2011 Development of “RandDot” test routine Comprehension of the task; performance test 2.5 11.04.2011 Team meeting, clarification of tasks Implementation of a prototype 1 12.04.2011 Development of FHP1_simple Simple grid, reflection boundary conditions, 2 byte cell variable 3 13.04.2011 Development of FHP1_simple Real-time representation of particles 4 14.04.2011 2nd meeting with Dr. Bischof Lattice structure, FHP model, look-up table

Conference Session

Mathematics Division Technical Session 1

Collection

2017 ASEE Annual Conference & Exposition

Authors

Jeffrey Lloyd Hieb, University of Louisville; William B. Corley, University of Louisville; Jaqi C. McNeil, University of Louisville

Tagged Topics

Diversity

Tagged Divisions

Mathematics

negatively skewed.The CA scores were negatively skewed because they are the representation of the class activitiesthe students did in class. The authors corrected these violations by reflecting and square roottransforming the CA scores. The data was tested for normality after reflecting and transformingthe data, and the normality was met to run a regression analysis with the transformed data.CALC-IIICA scores in CALC-III violated the regression assumptions of normality and homoscedasticity.The CA scores were negatively skewed. To correct these violations, the CA scores were reflectedand square root transformed. Normality was met after transforming the data.CALC-II-2TFor this model, the original data for UL scores violated the regression assumption

Conference Session

Mathematics Division Technical Session 1

Collection

2015 ASEE Annual Conference & Exposition

Authors

Gunter Bischof, University of Applied Sciences Joanneum, Graz; Andreas Zwölfer, University of Applied Sciences Joanneum, Graz; Domagoj Rubeša, University of Applied Sciences Joanneum, Graz

Tagged Topics

Diversity

Tagged Divisions

Mathematics

Schuster1). Precollege characteristics - like high school grade pointaverages - as well as university entrance exams have, in general, turned out to be usefulpredictors of student retention.A prior investigation of the drop-out probability at the engineering department of ouruniversity (Andreeva-Moschen2) clearly showed that the university entry scores can be usedto identify groups of students at higher risk of failure. It also turned out that the probabilitydistribution for student drop-out depends on the type of high school the students graduatedfrom, namely secondary colleges of engineering or traditional high schools. Interestingly, theuniversity entry score distribution does not reflect any differences in this respect, which might

Conference Session

Mathematics Division Technical Session 4: Assessing Success in Mathematics Education

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Johannah L. Crandall, Washington State University; Kristin Lesseig, Washington State University

Tagged Divisions

Mathematics

strictly representative of all students in a given degreepath (i.e. mechanical engineering). However, because enrollment in differential equations is anearly universal requirement for those in engineering paths, and because the sample capturedstudents enrolled in differential equations at a cross-section of time-points in their degreetrajectories, the results are felt to be a fair reflection of the level of software exposure for 8multiple degree paths as they enter differential equations specifically, and upper-division mathcourses more generally.It is not possible to characterize the prior and current software exposure of students who did

Conference Session

Mathematics Division Technical Session 3

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Salvador Mayoral, California State University, Fullerton; Antoinette Sherrise Linton, California State University, Fullerton; Hassan Yousefi, California State University, Fullerton; Jidong Huang, California State University, Fullerton

Tagged Divisions

Mathematics

1 Percentage of students repeating lower-division Math and Physics CoursesFor students who pass their lower-division courses and continue pursuing a STEM field, thisdoes not often translate into success in math-intensive engineering courses. Figure 2 shows thepercent repetition rate for various lower and upper-division ECS courses. Many courses acrossECS consist of repetition rates above 20%. This alludes to students not retaining the materiallearned in their previous pre-requisite courses, and consequently, students continue to repeatcourses and extend their graduation date as reflected in the graduation trends in 4, 5, 6-yeargraduation rates, shown in Figure 3. Although the 4-year graduation rate has consistently stayedat 5% since 2009

Conference Session

Integrating Math, Science and Engineering

Collection

2008 Annual Conference & Exposition

Authors

Hong Liu, Embry-Riddle Aeronautical University, Daytona Beach

Tagged Divisions

Mathematics

1. 7. Methodology Project requirements and 1 The ninth week Honors 5, 6 assignment Stella tutorial 2 The 10th-11th week Honors 2, 3 Modeling systems and higher 2 The 11th week All 1, 4. 7. order equations Page 13.939.4 Final Presentation 2 End of the course Honors All objectivesTable 1In the first lecture on MMM, the deviations between models and application problems, and theerrors of numerical solutions are introduced. Students learn the basic concepts of validation andverification. Validation checks whether the model reflects the

Conference Session

Integrating Math, Science and Engineering

Collection

2008 Annual Conference & Exposition

Authors

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

Tagged Divisions

Mathematics

to changing technologies and constraints1. Ted Kennedy, a founder of BE&K, amajor engineering, construction corporation, emphasized the importance of these same problemsolving skills during his keynote address to the Engineering Council of Birmingham in 2007. Hestressed the importance of learning mathematics in an engineering context rather than inisolation, stating that applying mathematics to solve complex engineering problems is anessential, and often missing, skill for young engineers. These same expectations are reflected inthe engineering accreditation process which seeks to place engineering problem-solving anddesign earlier in curricula. Consequently, students must apply their mathematics and basicscience skills sooner within the

Conference Session

Integrating Math, Science, & Engineering

Collection

2006 Annual Conference & Exposition

Authors

Stephen Pennell, University of Massachusetts-Lowell; Peter Avitabile, University of Massachusetts-Lowell; John White, University of Massachusetts-Lowell

Tagged Divisions

Mathematics

material. As a result of this collaboration, the mathematician hasmodified his Engineering Differential Equations course to reflect more of the engineering pointof view. This paper describes these course modifications as well as the collaborative program andthe teaching modules being developed to implement it.Differential Equations Course ModificationsThe changes in the Engineering Differential Equations course discussed in this paper grew out ofa larger program designed to improve student motivation to learn basic STEM material and toimprove their retention of this material from one semester to the next. The main idea of thisprogram is to develop projects spanning several courses and several semesters. Two suchprojects have been developed to date

Conference Session

Improving the Mathematical Preparation of Students

Collection

2006 Annual Conference & Exposition

Authors

Shuki Aroshas, Technion-Israel Institute of Technology; Igor Verner, Technion-Israel Institute of Technology; Avi Berman, Technion - Israel Institute of Technology

Tagged Divisions

Mathematics

the experimental group vs. 25-35% in the control group.Typical student reflections to a question on the contribution of studying applications forunderstanding calculus concepts were as follows: "Through applications I grasped the complex calculus concepts". "The impact of a one-hour application session is the same as of a regular (two- hour) tutorial". "Sorry that applied problems were not given in the first Calculus course".The follow-up study using statistical and qualitative methods indicated that the groups whichstudied calculus with applications had significant advantage in the half-course and final examgrades. The students mentioned the high contribution of applications to understandingcalculus concepts and their

Conference Session

Mathematics Division Technical Session 1: Best Practices in Engineering Math Education

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Charles Lam, California State University, Bakersfield; Melissa Danforth, California State University, Bakersfield; Ronald Hughes, California State University, Bakersfield

Tagged Divisions

Mathematics

much more of a reflection upon me than the modules themselves. We get in aroutine and dropping something in is difficult for me. I would recommend that they prepareto drop those in.”In summary, both mathematics and STEM faculty members found value in the co-teachingexperience. The experience has created a cooperative culture between faculty members thathas led to benefits for both faculty members and students. In addition to gaining better insightinto each other’s disciplines, several faculty members remarked about how the model isadaptable to other situations.Student ObservationsIn interviews conducted by the external evaluator, students indicated they enjoyed the STEMprofessor coming into the classroom and giving them practical STEM problems

Conference Session

Improving the Mathematical Preparation of Students

Collection

2006 Annual Conference & Exposition

Authors

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

Tagged Divisions

Mathematics

accurate predictor of student success in Calculus I than the Math ACT or if it,together with the Math ACT, might be more reliable than the Math ACT data alone. In thispreliminary report, we focus on whether or not the Math ACT accurately reflects studentpreparedness for calculus.A Comparison of Math ACT Scores, ALEKS Initial Assessments and Course GradesOne measure of student preparedness and prerequisite knowledge in Math 240, our Calculus I, isthe student’s score on the initial ALEKS assessment. Students are asked to take their initialALEKS assessment during the first week of classes. Moreover, they are taking the assessment“cold”, that is, without reviewing or studying for the assessment. In the Fall Quarter, the

Conference Session

Students' Abilities and Attitudes

Collection

2011 ASEE Annual Conference & Exposition

Authors

Kendrick T. Aung, Lamar University

Tagged Divisions

Mathematics

. Based on these results, it may be concluded that the majority ofstudents believes the course materials are suitable and the course is valuable for theirgraduate studies. There is a drop in rating in 2009 but there are no significant differences Page 22.1371.8in the course content as well as how the course is conducted so there is no simpleexplanation to the rating differences.Lesson 3: It is imperative for the instructor to balance mathematical knowledge andapplication of mathematics in all aspects of the course delivery.Lesson 4: The tests and exams should reflect the importance of mathematical knowledgeand application of the knowledge in

Conference Session

The Transition from Secondary to College Mathematics

Collection

2012 ASEE Annual Conference & Exposition

Authors

Alex Feldman, Boise State University; Doug Bullock, Boise State University; Janet Callahan, Boise State University

Tagged Divisions

Mathematics

author(s) and do not necessarily reflect the views of the National ScienceFoundation.References1. http://www.aleks.com/2. Rueda, N.G. & Sokolowski, C. (2004). Mathematics Placement Test: Helping Students Succeed. TheMathematics Educator, 14 (2) (pp. 27-33).3. Cederberg, J. N. (1999). Administering a placement test: St. Olaf College. In B. Gold, S. Keith, & W. Marion(Eds.), Assessment practices in undergraduate mathematics (pp. 178−180). Washington, DC: MathematicsAssociation of America.4. Cohen, E., Friedlander, J., Kelemen-Lohnas, E., & Elmore, R. (1989). Approaches to predicting student success:Findings and recommendations from a study of California Community Colleges. Santa Barbara, CA: Chancellor’sOffice of the California

Conference Session

Mathematics Division Technical Session 2

Collection

2015 ASEE Annual Conference & Exposition

Authors

Doug Bullock, Boise State University; Janet Callahan, Boise State University; Susan E. Shadle Ph.D., Boise State University

Tagged Divisions

Mathematics

Page 26.355.4with a curriculum about enhancing teaching and learning and with frequent seminars andactivities that provide learning, development, the scholarship of teaching, and communitybuilding.”4, p. 8 As described in the literature, these groups generally draw faculty from multipledisciplines. The underlying logic of using an FLC to promote faculty change is that“undergraduate instruction will be changed by groups of instructors who support and sustaineach other’s interest, learning, and reflection on their teaching.”6 Indeed, studies have shown thatfaculty participation in FLCs increases interest in the teaching process, enhances understandingand influence of the scholarship of teaching and learning, increases reflective practice

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

Each CourseFaculty were divided into three math focus groups (leaving College Algebra for the end) wherethey specifically addressed main learning outcomes for the course, the core ideas upon whicheach course is grounded, and the supporting concepts that make up the core idea(s). Thisapproach builds upon a theoretical framework resulting from the work of numerous groups (i.e.,Mathematical Association of America - [MAA]) and individuals, such as Bransford et al., (2000)who, in his National Research Council commissioned book, How People Learn, providedrecommendations based on extensive work addressing learning and teaching in mathematics.Guiding their discussions were a series of questions such as (a) does the course outline reflect thedesired

Conference Session

Mathematics in Transition

Collection

2007 Annual Conference & Exposition

Authors

Anne McClain, University of Alabama-Birmingham; Dale Feldman, University of Alabama-Birmingham; Lee Meadows, University of Alabama Birmingham

Tagged Divisions

Mathematics

Science Partnership conference onchallenging courses and curricula and the five strands of teaching for math proficiency (from theNational Research Council report, Adding It Up [4]), GBMP has arrived at a definition ofchallenging courses and curricula. For GBMP, there are four key aspects of challenging coursesand curricula: ‚ Deepening Knowledge of Important Mathematical Ideas ‚ Productive Disposition ‚ Inquiry and Reflection ‚ CommunicationDeepening knowledge of important mathematical ideas includes developing conceptualunderstanding, procedural fluency, and strategic competence. A productive disposition includesdeveloping a willingness to persist in working on mathematical problems and developingconfidence in one’s own ability

Conference Session

Innovative Instructional Strategies and Curricula

Collection

2010 Annual Conference & Exposition

Authors

Robert Homolka, Kansas State University, Salina; Greg Stephens, Kansas State University, Salina

Tagged Divisions

Mathematics

Washington; DawnWilliams, Howard University; and Ken Yasuhara, University of Washington conducted aresearch project supported by the National Science Foundation to explore storytelling inengineering education. They found storytelling can provide an important instructional method forengineering educators and they encourage taking storytelling research forward so others canbuild on their ideas. “Simply put- our stories matter—and storytelling provides a vehicle forscholarly discourse that makes explicit knowledge, promotes reflective practice, and providesentry points into a community of practice.”28Storytelling is also now being applied in the business, industrial, and corporate world bymanagers and human relations specialists for employee training

Conference Session

First-Year Programs: Mathematics in the First Year

Collection

2019 ASEE Annual Conference & Exposition

Authors

Mary Katherine Watson, The Citadel; Simon Thomas Ghanat P.E., The Citadel; Timothy Aaron Wood, The Citadel; William J. Davis P.E., The Citadel; Kevin C. Bower, The Citadel

Tagged Divisions

First-Year Programs, Mathematics

. computer lab work and group exercises [25].Table 3. Description of categories within the Assessment Methods theme. Description Example Student reflections Students are asked to report A five-point scale was used to on their perceptions of the ask students about the course innovation(s), impacts of an engineering typically using Likert scales professor visiting precalculus and/or open response courses [17]. questions. Pre

Conference Session

Integrating Mathematics, Science, and Engineering

Collection

2007 Annual Conference & Exposition

Authors

Jenna Carpenter, Louisiana Tech University

Tagged Divisions

Mathematics

on pre- and post-test performance of integrated sectionsonly (collected during the process of course revision as a formative evaluation) shows thegreatest improvement in laboratory safety skills, with data on mastery of course content varyingfrom discipline to discipline. While this likely reflects the fact the differing rates ofimplementation of the course revisions in each of the disciplines during the time frame this datawas collected, differences in use of graduate teaching assistants in the labs and the varyingdegree of training they receive also may be contributing to this behavior. Data collected thisyear, after full implementation of content revision, should provide a clearer picture of studentperformance.ConclusionTraditionally

Conference Session

Mathematics Division Technical Session 2

Collection

2013 ASEE Annual Conference & Exposition

Authors

Jamiiru Luttamaguzi, Elizabeth City State University; Ka'Ren Ladoris Byrd; Akbar M. Eslami, Elizabeth City State University; Ehsan O Sheybani, Virginia State University; Giti Javidi, Virginia State University

Tagged Divisions

Mathematics

effective aperture area of the antenna, and  is the wavelength of the mean frequency ofinterest. Both TB and Fn are functions of direction. Accurate antenna temperatures are obtained bymodifying the step sizes while getting faster results. The rate of convergence in numericalintegration can be slowed down or even reversed due to a singularity at the boundary of theregion of integration in the integrand function or data.II. MethodologyThe recent development in computational capabilities, along with increased software reliability,made the numerical method and simulation approach more favorable. Examples of radiationpatterns can be used to evaluate the integrals that reflect different kinds of antennas, such astraditional versus a focused antenna

Conference Session

Issues and Solutions in Mathematics Education

Collection

2010 Annual Conference & Exposition

Authors

Gisela Gomes, Universidade Presbiteriana Mackenzie; Janete Bolite Frant, Universidade Bandeirante; Arthur Powell, Rutgers University

Tagged Divisions

Mathematics

mathematicians,engineers, industry professionals and educationalists interested in reflecting on themathematics used by engineers that could help them to address new technologicalrealities and societal challenges in a more complex and globalized world. The conferencefocused on the links among mathematics, engineering, and society and proposed to be apermanent forum to discuss the pedagogical aspects of mathematics in engineeringcurriculum and to reevaluate the mathematics education of engineering students. It is therefore appropriate to investigate further the educational background ofengineers, both in terms of mathematical knowledge acquired in engineering courses andits application in professional activities. Such investigations will

Conference Session

Using Applications and Projects in Teaching Mathematics

Collection

2012 ASEE Annual Conference & Exposition

Authors

Julie Gainsburg, California State University, Northridge

Tagged Divisions

Mathematics

the mandatory language fordesign and analysis, and mathematical proof the industry standard for final justification. In thislast point there is some overlap between the perspectives of engineers and JPFs: Both sometimesused formal mathematics for post hoc justifications of solutions obtained by other means.The epistemological aspect of skeptical reverence recalls the broader concept advanced by Kingand Kitchener (1994)32 of reflective judgment. Mainly applied to college students, reflectivejudgment is the endpoint of a developmental continuum corresponding to the recognition of thecomplexity and uncertainty of real-world problems, an awareness of the need to interpretknowledge in the context in which it was constructed (and revise it in light

Conference Session

Mathematics Division Technical Session 2

Collection

2017 ASEE Annual Conference & Exposition

Authors

Hui Ma, University of Virginia; Gianluca Guadagni, University of Virginia; Stacie N. Pisano, University of Virginia, School of Engineering and Applied Science; Bernard Fulgham, University of Virginia; Monika Abramenko, University of Virginia; Diana D Morris, University of Virginia

Tagged Divisions

Mathematics

Engaging Student’s Perspective (ESP) was conducted at the mid-semester point. It wasfacilitated by a trained teaching consultant, who is a professor from the school of education atour institution. ESP asked students to reflect on what helped and hindered their learning, andadditionally solicited their suggestions for improvement.Question 1: Are the common gaps identified for advanced students being addressed by thiscourse?The five topics identified by the instructor team includes: Newton’s Method, IntegrationTechniques (including partial fractions), Simpson’s Rule, Applications of Integration, and Taylorseries and Taylor polynomial applications. There were two topics that over 60% of studentsmentioned that they had little or no knowledge of; the

Conference Session

Mathematics Division Technical Session 3

Collection

2018 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University

Tagged Divisions

Mathematics

! ! ! !function centered around x=1 and x=2 respectively. Some of the participating students respond by thinking thatthe “difference” stated in the question is the mathematical difference.Written responses of research participants 1, 4, 8, 13, 14, 16, and 17 given in Figures 3-9 reflected themathematical difference between the given two series approximations. During the interviews the participants wereshown Equation (1) given in Section 1 when f(x) = ex. Participants 1, 4, and 14 could not remember the locationaldifference between the two Taylor series approximations given in the question whereas participants 8, 16, and 17were able recognize the locational difference between the two terms and explain how they differ in center.Participant 13 tried to