Conference Session

Work-in-Progress Session: Exploring Learning and Development in Engineering Courses

Collection

2023 ASEE Annual Conference & Exposition

Authors

Elizabeth Ann Strehl, University of Michigan; Megan Ennis, University of Michigan; Aaron W. Johnson, University of Michigan; Corin L. Bowen, California State University, Los Angeles

Tagged Divisions

Educational Research and Methods Division (ERM)

Sustainability: The Challenge of Integrating Social and Ethical Issues into a Technical Course. 2018 ASEE Annual Conference & Exposition Proceedings, 30402. https://doi.org/10.18260/1-2--30402Accreditation Board for Engineering & Technology (ABET) (2021)“Criteria for Accrediting Engineering Programs, 2020 – 2021—ABET”. https://www.abet.org/accreditation/accreditation-criteria/criteria-foraccrediting-engineering-program s-2020-2021/Benham, A., Callas, M., Fotherby, R., Jones, M., Chadha, J., Dobbin, M., & Johnson, A. W. (2021). Developing and Implementing an Aerospace Macroethics Lesson in a Required Sophomore Course. 2021 IEEE Frontiers in Education Conference (FIE), 1–9. https://doi.org/10.1109

Collection

1997 Annual Conference

Authors

Robert P. Taylor; B.K. Hodge

NSF coalitions24 Curriculum emphasis and pressures25 Assessment and accountability26 MoneyFactor 2: ComputersThe dominant external influence on all aspects of engineering in the last half of this century hasbeen the ever-increasing capability and availability of computers. Mechanical engineering hasnot been an exception as the profession as well as ME educators have struggled to both ascertainwhat the computer can do for mechanical engineering and what the implications are for MEeducation. One only has to examine the proceedings of any engineering education conference tosense that struggle. The integration and use of computers in ME can be divided into at least threephases. Phase 1, the 1960’s and 1970’s

Conference Session

Multidisciplinary Design

Collection

2004 Annual Conference

Authors

Bullen Frank

to commence their degree program with explicit knowledge of the school’sexpectations for group work and laboratory practice and the experience to be able to achievethese expectations.Bibliography1. Dodd, D and Stoner, H. “Integrating design into an alternative engineering curriculum”. Proceedings of 14th Annual AAEE Conference, 29 Sept.-1 Oct. 2003. Page 9.415.92. Green, L.W. “Evaluating graduate engineers in industrial design”. Proceedings of 3rd UICEE Annual Conference on Engineering Education, 9-12 Feb. 2000. Proceedings of the 2004 American Society for Engineering Education Annual Conference & Exposition

Conference Session

Faculty Development Division Technical Session 1

Collection

2022 ASEE Annual Conference & Exposition

Authors

Darby Riley, Rowan University; Cayla Ritz, Rowan University; Cheryl Bodnar, Rowan University; Kaitlin Mallouk, Rowan University

) Dr. Cheryl Bodnar is an Associate Professor in the Experiential Engineering Education Department at Rowan University and is currently serving as the Provost’s Fellow for Student Success. Recently, the National Science Foundation (NSF) and the Kern Family Foundation have funded her research. Her research interests relate to the incorporation of active learning techniques such as game-based learning in undergraduate classes as well as integration of innovation and entrepreneurship into the engineering curriculum. In particular, she is interested in the impact that these tools can have on student perception of the classroom environment, motivation, and learning outcomes.Kaitlin Mallouk (Assistant Professor) Kaitlin

Conference Session

Embedded Computing

Collection

2005 Annual Conference

Authors

Eduardo Montanez; Andrew Mastronardi

many appliances that simplify our dailytasks. To the consumer, MCUs typically go unnoticed, but in industry they are very important.This paper stresses the importance of establishing a strong curriculum surrounding MCUs atvarious levels of engineering education. Most importantly, we must spark the student’s interestin MCUs in introductory engineering courses by introducing the subject in a very simple form.Students can be easily discouraged by the subject if they are initially drowned by complex MCUarchitectures and robust programming languages. Though these two topics are necessary tohave a full understanding of MCUs, students gain more interest in MCUs if they were first givena glimpse of an end application. This gives students a better

Conference Session

Biomedical Engineering Division Poster Session

Collection

2022 ASEE Annual Conference & Exposition

Authors

Carly Eressy, University of Texas at Austin; Brittain Sobey, University of Texas at Austin; Margo Cousins, University of Texas at Austin

Cross in Studies in World Literature, with a concentration in Latin-American Studies, and a minor in Studio Art. Most recently, she worked as an Instructional Designer for the MD & MD-PhD programs at the University of Massachusetts Medical School in Worcester, Massachusetts. Her research interests include equity in education, technology integration, policy development and leadership & engagement.Margo Cousins Ms. Cousins has a MA in Higher, Adult, and Lifelong Education (HALE) from Michigan State University, and a BS in Biology from Washington State University. She has worked in engineering education as an academic advisor for more than 10 years. © American Society for Engineering

Conference Session

Meeting ABET Requirements

Collection

2007 Annual Conference & Exposition

Authors

Anne Spence, University of Maryland-Baltimore County; Liang Zhu, University of Maryland-Baltimore County

Tagged Divisions

Mechanical Engineering

quantitative value is obtainedindicating success in achieving the ABET outcomes. An example QuACO for the engineeringmathematics course is given in Table 5. Table 5. Sample QuACO for ENME303: Topics in Engineering MathematicsCourse Outcome Basis for AssessmentThe student will be able to solve linear algebraic equations One final exam problemnumericallyEach individual student will learn numerical methods to fit Three final exam problemcurves to data.Students will find roots of equations numerically. One final exam problemThe student will learn to evaluate integrals and One final exam problemdifferentials numerically.Students will solve differential equations numerically

Conference Session

K-12 & Pre-College Engineering Division: Evaluation: Impact of Curriculum for PreK-12 Engineering Education

Collection

2016 ASEE Annual Conference & Exposition

Authors

Amy Trauth, University of Delaware; Jenni Buckley, University of Delaware; Manuela Restrepo Parra, The Perry Initiative

Tagged Topics

Diversity

Tagged Divisions

Pre-College Engineering Education Division

analyzed. The most significant influence of the BMEC curriculum was its informativenature. Students overwhelmingly reported increased awareness of biomedicalengineering. We also saw a significant increase in the number of students that wantedto pursue careers in biomedical engineering. These findings demonstrate that informingstudents about engineering fields is an important first step in increasing the number ofstudents that pursue these fields. Results from Pilot implementation of BMEC, 13ReferencesBerland, L. K. (2011). Designing for STEM integration. Journal of Pre-College Engineering Education Research (J-PEER), 3(1), 23-31.Berland, L. K., Martin, T. H., Ko, P., Peacock, S. B., Rudolph, J. J

Conference Session

Bridging and Freshman Programs

Collection

2008 Annual Conference & Exposition

Authors

Wendy James, Oklahoma State University; Karen High, Oklahoma State University

Tagged Divisions

Mathematics

AC 2008-1277: FRESHMAN-LEVEL MATHEMATICS IN ENGINEERING: AREVIEW OF THE LITERATURE IN ENGINEERING EDUCATIONWendy James, Oklahoma State University Wendy James is a PhD student in the College of Education at Oklahoma State University. Currently she has a fellowship promoting collaboration between the College of Education and OSU's Electrical and Computer Engineering department on an NSF funded curriculum reform project called Engineering Students for the 21st Century. She has her M.S. in Teaching, Learning, and Leadership from OSU, and her B.B.S. in Mathematics Education from Hardin-Simmons University in Abilene, Texas. She has taught math and math education classes at both the high school and

Conference Session

Topics in Computing

Collection

2019 ASEE Annual Conference & Exposition

Authors

Alka R. Harriger, Purdue University; Suyash Agrawal, Purdue University; Arjun Shakdher, Purdue University

Tagged Topics

Diversity

Tagged Divisions

Computing and Information Technology

is essentialfor CT to be included as part of the K-12 curriculum. Furthermore, being able to employ a web-based tool that is a repository of peer reviewed questions that could be used to assess CT skills instudents should enhance the effectiveness of any curriculum incorporating CT [4]. Literatureshows that a number of solutions have been developed but lack standardization, require priorprogramming knowledge, or are too lengthy [5] [6].The tool described in this paper was designed to give users the ability to search for questionsbased on specific attributes. The questions can be rated by experts across the world for eachattribute of CT. The aggregate rating is available to users for each question.TECHFIT, an initiative to introduce and

Conference Session

Anything New in Dynamics?

Collection

2008 Annual Conference & Exposition

Authors

Thomas Nordenholz, California Maritime Academy

Tagged Divisions

Mechanics

that generally grow with time (due to the time integration). An estimationof acceleration and angular velocity measurement errors can be made by calibrating theaccelerometer and rate gyro using simple homemade devices.After describing how these experiments can be set up and performed in general, this paper willdescribe a specific experiment done in the author’s junior mechanical engineering laboratorycourse. The rigid body object under study is a remote controlled car. The technique describedabove is used to find the position, velocity, orientation, and angular velocity of the car as afunction of time. Results of the measurements and data analysis are compared with observationsof the car’s motion viewed by a video camera. An examination of

Conference Session

Mechanical Engineering Division Technical Session 3

Collection

2018 ASEE Annual Conference & Exposition

Authors

Jessica Lofton, University of Evansville; Jared T. Fulcher, University of Evansville; Dick Blandford, University of Evansville

Tagged Topics

Diversity

Tagged Divisions

Mechanical Engineering

. Students in the BSME program complete a rigorous,project-based curriculum [7] designed to engage students in the engineering design-build-testprocess during all four years of undergraduate study. Program highlights include small classsizes, access to faculty, and an integrated study abroad option.The University of Evansville has implemented both admissions processes mentioned in theintroduction. Students entering the program directly from high school must meet admissioncriteria for ME Lower Division. After completing the required Lower Division courses with agrade of C- or better, students must apply for ME Upper Division status to complete the final twoyears of study.Lower DivisionLower Division is classified as the first two years of

Conference Session

Electrical and Computer Engineering Laboratories

Collection

2011 ASEE Annual Conference & Exposition

Authors

Mohammad N. Amin, National University; Ronald P. Uhlig, National University; Pradip Peter Dey, National University; Bhaskar Raj Sinha, National University

Tagged Divisions

Division Experimentation & Lab-Oriented Studies

lives and property, by designing a new fire detecting system using very low costelectronics, newly developed software, and existing wireless technologies. The system is capableof detecting fire at an early stage and helping to make an accurate plan to fight the wildfires in abetter way. The “Wildfire Detection and Monitoring System” capstone project dealt with a new design anddevelopment of a fire detecting system. In this capstone project, students integrated hardwareand software to develop an engineering product prototype to meet a pressing need3. They Page 22.344.2developed new software applications and used very low cost commercially

Conference Session

Computing and Information Technology Division Technical Session 4

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Stephany Coffman-Wolph, Ohio Northern University

Tagged Topics

Diversity

Tagged Divisions

Computing and Information Technology

coursetechniques to integrate these six skills into a more virtual learning experience using varioushands-on activities both individually and as a group. This paper shares techniques for faculty tobe more innovative as we live in the new "normal" with an increase in hybrid and online courses.Each activity is designed to not only cement a programming skill (or skills) but integrate EMskills with special attention to making connections between abstract programming concepts andthe real-world examples to help ground those concepts for all students and allow students tounleash their creativity. These techniques introduce (1) gamification, (2) students taking controlof their learning, and (3) encouragement of creativity which will hopefully spark their

Conference Session

Professional Issues in Ethics Education

Collection

2012 ASEE Annual Conference & Exposition

Authors

A. Dean Fontenot, Texas Tech University; Richard A. Burgess, National Institute for Engineering Ethics

Tagged Divisions

Engineering Ethics

currently works as a Research Associate and Deputy Director at the Murdough Center for Engineering Professionalism (MCEP) and National Institute for Engineering Ethics (NIEE) at Texas Tech University. He oversees the day to day operations of the center’s distance learning courses for both engineering students and practicing engineers. Additionally, he provides lectures on ethical theory and other topics in an on-campus engineering ethics course. Burgess was also a member of the Ethics in the Curriculum Task Force for Texas Tech’s Quality Enhancement Plan. The Quality Enhancement Plan was a crucial component of Texas Tech’s accreditation with the Southern Association of Colleges and Schools. A theme throughout these roles

Conference Session

Emerging Computing and Information Technologies I

Collection

2016 ASEE Annual Conference & Exposition

Authors

Afrin Naz, West Virginia University Inst. of Tech.

Tagged Divisions

Computing & Information Technology

impact of computing on individuals, organizations,and society(h) Recognition of the need for and an ability to engage in continuing professional development(i) An ability to use current techniques, skills, and tools necessary for computing practice.(j) An ability to apply mathematical foundations, algorithmic principles, and computer science theory inthe modeling and design of computer-based systems in a way that demonstrates comprehension of thetradeoffs involved in design choices(k) An ability to apply design and development principles in the construction of softwaresystems of varying complexity Performance indicators are a means to focus on specific expectations of a program. Theyfacilitate the curriculum delivery strategies, and assessment

Conference Session

Implementing Transfer, Exchange, Research Programs and Professional Development; in Asia and Far East

Collection

2013 ASEE Annual Conference & Exposition

Authors

Scott I. Segalewitz, University of Dayton

Tagged Divisions

International

articulation be developed to transferstudents in two programs: Electronic Information Engineering at Shanghai Normal University toElectronic Engineering Technology at UD; and Mechanical Design, Manufacture & Automationat Shanghai Normal University to Manufacturing Engineering Technology at UD. Theagreement also indicated that “the two parties will negotiate the curriculum offered…”Early in the curriculum development process, faculty at UD shared course outcomes and syllabiwith their counterparts at Shanghai Normal University. A short time later, SHNU sent theircourse outlines, which in some cases, bore a very close resemblance in both content andnumbering, to the University of Dayton outlines. An initial articulation of courses from SHNU

Conference Session

New Trends in ECE Education II

Collection

2007 Annual Conference & Exposition

Authors

Min-Sung Koh, Eastern Washington University; Esteban Rodriguez-Marek, Eastern Washington University; Claudio Talarico, Eastern Washington University

Tagged Divisions

Electrical and Computer

pedagogical observation from the projects, further curriculum revision under developmentare explained in Section 3, namely, to tie Matlab programming skills with hardwareimplementation in DSP and/or FPGA boards. 2. GUI system designs using MatlabDigital signal processing is taught as a senior-level, 4-hour/week lecture, 2-hour/week laboratoryclass. The lab culminated in an intensive team-oriented class project. The projects wereproposed by the students to the instructor, who revised the project for appropriate content and sizeprior to approval. All specifications were chosen by students themselves, save for one criterion:the inclusion of a Matlab-based GUI system. Most of the students are seniors in EE, and morethan 60% of them had prior

Conference Session

Pre-College Engineering Education Division Poster Session

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Barbara Fagundes, Purdue University; Nrupaja Bhide, Purdue University ; Tamara J. Moore, Purdue University ; Kristina Maruyama Tank, Iowa State University of Science and Technology

Tagged Divisions

Pre-College Engineering Education

on low-cost makerspace programs in rural India with BAIF Development and Research Foundation.Prof. Tamara J. Moore, Purdue University Tamara J. Moore, Ph.D., is a Professor in the School of Engineering Education and the Interim Director of the INSPIRE Research Institute for Precollege Engineering at Purdue University. Dr. Moore’s research is centered on the integration of STEM concepts in K-12 and postsecondary classrooms in order to help students make connections among the STEM disciplines and achieve deep understanding. Her work focuses on defining STEM integration and investigating its power for student learning.Kristina Maruyama Tank, Iowa State University of Science and Technology Kristina M. Tank is an Associate

Conference Session

First Year and Cross-Disciplinary

Collection

ASEE Southeast Section Conference

Authors

George Prpich, University of Virginia; Natasha Smith, University of Virginia

Tagged Topics

Professional Engineering Education Papers

Paper ID #36599Sharing Best Practice in Safety Between Engineering DisciplinesDr. George Prpich, University of Virginia Professional Skills and Safety are my main pedagogical interests. I use the Chemical Engineering labora- tory to implement safety training to improve safety culture, and to adapt assessment methods to enhance development of students’ professional skills. I am an Assistant Professor of Chemical Engineering at the University of Virginia and I hold a B.Sc. (University of Saskatchewan) and Ph.D. in Chemical Engineering (Queen’s University). Complimenting my pedagogical research is an interest in bioprocess

Conference Session

Pedagogical Issues in Manufacturing Education

Collection

2008 Annual Conference & Exposition

Authors

Jahangir Ansari, Virginia State University; Amir Javaheri, Virginia State University; Stephen S. Tompkins, Virgina State University; Keith Williamson, Virginia State University

Tagged Divisions

Manufacturing

AC 2008-2236: OUTCOME ASSESSMENT PROCESS IN A MANUFACTURINGENGINEERING PROGRAMJahangir Ansari, Virginia State University Jahangir Ansari is an Associate Professor of Manufacturing Engineering in the Department of Engineering and Technology at Virginia State University. He received his M.S. degree in Mechanical Engineering in 1979 and Ph. D. degree in Mechanical Design and Production Engineering in 1983 both from Seoul National University. He joined the faculty at VSU in 2002. He has over 18 years of industrial experience in different areas including shipbuilding and cement plant industries. His research interests include Structural Vibration, FEM, CAD/CAM/CNC, and Computer Integrated

Conference Session

Manufacturing Curricula for the Year 2015 and Beyond

Collection

2009 Annual Conference & Exposition

Authors

Venkitaswamy Raju, State University of New York-Farmingdale

Tagged Divisions

Manufacturing

) State University of New York – Farmingdale, NY 11735Abstract:The project leading to this paper was carried out as part of SME’s efforts to prepare themanufacturing curricula for the year 2015 and beyond. In doing so, it considered the roleof manufacturing in the global economy, the factors affecting the scope of manufacturing,and the current efforts to revitalize manufacturing in the various parts of the world. Itthen reviewed the curricular models proposed to address the needs of the manufacturingindustry. As an extension of the analysis, recommendations were made on the key aspectsof a manufacturing curriculum with an emphasis on innovation and entrepreneurship.Further, the recommendations included the creation of a flexible degree program

Conference Session

NSF Grantees Poster Session

Collection

2006 Annual Conference & Exposition

Authors

Stephanie Farrell, Rowan University; Mariano Savelski, Rowan University; Robert Hesketh, Rowan University; C. Stewart Slater, Rowan University

Tagged Divisions

Division Experimentation & Lab-Oriented Studies

chemical engineering students are rarely exposed to drugdelivery through their coursework. To provide students with the skills directly relevant to theevolving needs of the pharmaceutical industry, this we have developed and integrated applieddrug delivery coursework and experiments throughout the Rowan Engineering curriculum.To design and produce a new drug delivery system, an engineer must fully understand the drugand material properties and the processing variables that affect the release of the drug from thesystem. This requires a solid grasp of the fundamentals of mass transfer, reaction kinetics,thermodynamics and transport phenomena. He or she must also be skilled in characterizationtechniques and physical property testing of the delivery

Conference Session

Special Session: Impacts of Service in Engineering

Collection

2010 Annual Conference & Exposition

Authors

Linda Barrington, University of Massachusetts, Lowell; John Duffy, University of Massachusetts Lowell

Tagged Divisions

Educational Research and Methods

can doin the process of providing useful services to community groups. Embedding S-L projects inrequired courses sends a message that service is part of what engineers do as professionals. Inother words, it is a given that service is part of the curriculum and part of the profession.Interviews with students and faculty who have participated in such projects have independentlyidentified this aspect of S-L (Burack, Duffy, Melchior, & Morgan, 2008) (West, theseproceedings, 2010). For example, solving community problems was discussed with student’soften emphatically stating, “That is the role of an engineer!”    One faculty member even said, “It[service-learning] will change the way we think about engineering. It adds an additionaldimension

Conference Session

K-12 & Pre-College Engineering Division Poster Session: Works in Progress

Collection

2016 ASEE Annual Conference & Exposition

Authors

Bradley Bowen, North Dakota State University

Tagged Divisions

Pre-College Engineering Education Division

. (Poster Presentation).16. Bowen, B. (2014). K-12 Teachers in Industry: Teaching Transformed through Authentic Work Experience. Annual Proceedings of the American Society for Engineering Education, Seattle, WA. (Poster Presentation). Appendix A End of School-Year Survey (Also considered pre-survey for current cohort)1. When designing lessons, it is important for you to:  Teach formal problem solving techniques  Show the importance of my subject in everyday life  Integrate my course curriculum with other subjects  Encourage students to explore alternative methods for solving problems*  Incorporate "real-life" examples of my subject  Incorporate 21st century

Conference Session

Objectives, Assessment, and Methods for Teaching Technological Literacy

Collection

2011 ASEE Annual Conference & Exposition

Authors

Steve Macho, Buffalo State College; Su Wang, China National Institute for Educational Research

Tagged Divisions

Technological and Engineering Literacy/Philosophy of Engineering

institutions in China. The Buffalo State College Center for China Studiescelebrated its ten-year anniversary this past fall (2010). Additionally, Buffalo State Collegehouses a Technology Education program and several Engineering Technology programs.Workshop Goals and Objectives The workshop goals were developed collaboratively among CNIER staff and BuffaloState College faculty. Research was conducted by reviewing CNIER Future Engineers materials,Chinese news stories on education, and conducting many interviews. The common over-archingtheme was to promote technological literacy in an integrated fashion that is not specific to anyexisting curriculum, e.g., not a portion of the science or math curriculum. The workshop goals were to

Conference Session

NSF Grantees: K-12 Session 1

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Elizabeth Cady, National Academy of Engineering; Greg Pearson, National Academy of Engineering

Tagged Topics

NSF Grantees Poster Session

.) with the National Academy of Engineering (NAE) in Washington, D.C. Greg served as the responsible staff officer for the NSF-funded project ”Educator Capacity Building in K-12 Engineering Education,” published in 2019. Status, Role, and Needs of Engineering Technology Education in the United States.” He previously was the study director for the NSF-funded project that resulted in the 2014 report, STEM Integration in K-12 Education: Status, Prospects, and an Agenda for Research. He was the study director for the project that resulted in publication of Standards for K-12 Engineering Education? (2010) and Engineering in K-12 Education: Understanding the Status and Im- proving the Prospects (2009), an analysis of efforts

Conference Session

Electrical and Computer Division Poster Session

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Selahattin Sayil, Lamar University

Tagged Divisions

Electrical and Computer

IEEE and serves as an Associate Editor for International Journal of Electronics American c Society for Engineering Education, 2021 Enhancing Student Learning via Hardware in HomeworkI. Introduction:An important problem that has come up over the years in some engineering programs is the lossof laboratory experiences in favor of more theoretical emphasis in upper division courses. InElectrical Engineering (EE) curriculums, the majority of programs now include laboratory workonly in introductory courses such as circuits and logic design [1]-[3]. Advanced courses such asElectronics II, Communications, and others have lost their labs due to the curriculum changesand the

Collection

1999 Annual Conference

Authors

David P. Heddle; Robert F. Hodson; David C. Doughty

available solely through ALNs. For example, Web-4M is very effective ina hybrid class that not only meets in a traditional, time-bound classroom but also requires thestudents to take part in a given amount of on-line synchronous discussions, problem-solvingsessions, group homework, or to view presentations. A key component of making these newteaching paradigms work effectively is a tightly integrated distance education delivery system thatallows for storage and retrieval of materials presented in a synchronous forum, thusaccommodating absenteeism and providing a means for student review. The following sections willdiscuss some of the features of Web-4M, explain how the synchronous and asynchronous tools areintegrated and give an example of how

Conference Session

Engineering Physics & Physics Division Technical Session 2

Collection

2017 ASEE Annual Conference & Exposition

Authors

Robert A. Ross, University of Detroit Mercy; E. Prasad Venugopal, University of Detroit Mercy; Meghann Norah Murray; Gary P. Hillebrand, University of Detroit Mercy; Matthew Gonderinger, University of Detroit Mercy, Wayne State University

Tagged Topics

Diversity

Tagged Divisions

Engineering Physics & Physics

Treasurer of the Detroit Local Section of the American Chemical Society.Prof. Gary P. Hillebrand, University of Detroit Mercy Lecturer in Physics at the University of Detroit Mercy since 2008, following 30 years in automotive product development at Ford and GM.Dr. Matthew Gonderinger, University of Detroit Mercy, Wayne State University c American Society for Engineering Education, 2017 Gender Effects in a General Physics Laboratory AssessmentIntroductionTwenty years ago the second-semester general physics laboratory courses at the University ofDetroit Mercy adopted an active-learning curriculum based on the work of both Arnold Arons1and Lillian