The Design of Educational Programs in System Dynamics at Worcester Polytechnic Institute (WPI) ^†

Abstract

Educational programs leading to degrees in system dynamics are rare and thus of critical importance to the future of the field of system dynamics. However, to a large extent such programs have not yet been made transparent to the system dynamics community as a whole. The present article describes the design and rationale for undergraduate and graduate programs at Worcester Polytechnic Institute (WPI). The goal of the article is to invite feedback from the system dynamics community about our specific programs as well as to facilitate wider discussion about the appropriate content, design, and pedagogy of degree programs and courses in system dynamics.

1. Introduction

System dynamics (SD) courses are taught at dozens of universities throughout the world. However, only a small number of institutions offer enough courses for complete degrees in system dynamics. In most cases, the system dynamics curriculum is part of a larger curriculum in a school of, for example, Business or Public Policy, and the primary means of educational delivery beyond a few introductory courses is research mentorship with individual system dynamics faculty. In a few cases, the system dynamics curriculum is part of a larger “system sciences” program that covers a wide variety of different modeling approaches. Those programs that offer substantial coursework in system dynamics (say, five courses or more) and a degree titled “System Dynamics” can be counted on one hand.

At the same time, there has long been interest within the system dynamics community in examining and understanding the nature and quality of university curricula in system dynamics. Certainly, the growth and well being of the field depends on the availability of high-quality education in system dynamics. Nearly twenty years ago, Barlas [1] argued that for system dynamics to be a successful discipline there need to be university educational programs that provide formal training. Not only such programs would teach the foundations of the system dynamics method, they would also ensure consistency in the interpretation of the skills and act as conduits for the latest developments in the field to be passed on to students.

However, various efforts over the years to develop curriculum guidelines have thus far not been successful. An alternative approach may be to encourage programs to voluntarily make available to others the design and rationale behind their programs, which would open them up to scrutiny and constructive criticism from peers. Thus far there has been little published literature in the system dynamics field describing the actual or recommended design, content, and pedagogy of system dynamics courses and programs (although, see, e.g., [1,2,3,4,5,6]).

The present authors believe that, given their rarity, university programs in system dynamics have a special responsibility to the field to make the content and design of their programs transparent. Thus, the purpose of the present article is to describe the development and design of degree programs in System Dynamics at Worcester Polytechnic Institute (WPI), as a way of encouraging the discussion of general issues of curriculum design. For example, how should programs in System Dynamics be structured and taught? What topics and in what sequence should be covered? What pedagogies should be emphasized? Is there a place for an undergraduate program or are graduate programs in system dynamics more appropriate? What topics beyond the field should a system dynamics student be familiar with (e.g., business, economics, psychology, mathematics)? This article does not answer all these questions, but we hope that the discussion will continue.

2. Attributes of University Courses

Based on the literature review and our own experience, we suggest that system dynamics courses can be characterized by several attributes, as shown in Table 1. These attributes form a convenient framework for course comparisons. We discuss some of the attributes of WPI courses in this article.

The ultimate goal of any system dynamics course—which can be part of a system dynamics program—is to teach students the system dynamics method so they can apply it to various situations. While there are many practitioners of system dynamics and courses have been taught for years, there is still no unequivocal set of skills identified and agreed upon by the system dynamics community as the skill core of the system dynamics method. Andersen and Richardson [2,7], who were two of the early authors to write about system dynamics curricula, emphasized that system dynamics training should methodically teach the seven stages of system dynamics modeling inquiry: problem recognition, system conceptualization, model representation, model behavior, model evaluation, policy analysis and model use. Richmond [8] groups various skills into the following sets: dynamic thinking, closed-loop thinking, generic thinking, structural thinking, operational thinking, continuum thinking and scientific thinking. Based on their experience at Delft University, Meyers et al. [5] add that communication and reporting, team and project work and academic reflection are also important skills for system dynamicists. As model development and use is an iterative process, there is a great deal of overlap and interaction between the modeling stages. The necessary skills of system dynamics can also be deduced from the content of textbooks on the subject, and there are several of them on the market.

Table 1. Attributes of a System Dynamics Course.

Skills Taught. What is exactly covered?

Target Audience. Is the course graduate, undergraduate or both? Or is it part of an executive education program?

Type Of Course. Is it a stand-alone course or is it part of a program?

Registration Requirement. Is it a mandatory or elective course?

Faculty. Do tenured/tenure-track, full time or part-time faculty teach it?

Difficulty Level. Is the course introductory or advanced?

Course Organization. Is it a dedicated system dynamics course or does the course include a system dynamics module?

Purpose. Is the purpose of the course to teach SD, or to teach something else using SD?

Course Design. Is it project based, lecture, laboratory, case-studies, simulation games?

Delivery Method. Is it online, class-based or hybrid?

Length. Is it a semester, term, short workshop, or self-paced online course?

Academic Credit, full academic credit, continuing education credit, or none

Tuition, free to high

Table 1. Attributes of a System Dynamics Course.

Skills Taught. What is exactly covered?

Target Audience. Is the course graduate, undergraduate or both? Or is it part of an executive education program?

Type Of Course. Is it a stand-alone course or is it part of a program?

Registration Requirement. Is it a mandatory or elective course?

Faculty. Do tenured/tenure-track, full time or part-time faculty teach it?

Difficulty Level. Is the course introductory or advanced?

Course Organization. Is it a dedicated system dynamics course or does the course include a system dynamics module?

Purpose. Is the purpose of the course to teach SD, or to teach something else using SD?

Course Design. Is it project based, lecture, laboratory, case-studies, simulation games?

Delivery Method. Is it online, class-based or hybrid?

Length. Is it a semester, term, short workshop, or self-paced online course?

Academic Credit, full academic credit, continuing education credit, or none

Tuition, free to high

What is an appropriate audience for a system dynamics course or a program? Barlas [1] concludes that an “undergraduate stand-alone course dedicated exclusively to system dynamics… is least common, yet most important for the growth of the field”. He notes that only very few universities offer undergraduate courses in system dynamics and calls for more undergraduate education in system dynamics. A review of system dynamics courses in the U.S. reveals that most courses in system dynamics are still at the graduate level (see Appendix A). Massachusetts Institute of Technology (MIT) also offers system dynamics workshops as part of its executive education program.

The majority of available courses are stand-alone courses or they are part of a non-system dynamics program. For example, the Delft University of Technology lists two courses—Introduction to System Dynamics and Advanced System Dynamics—that are mandatory courses for one undergraduate program and one Master’s program, though these programs do not grant system dynamics degrees [5]. At Portland State University, system dynamics is taught as part of the graduate program in system science. System dynamics can also be incorporated into various application or modeling courses as a module. For example, Barlas [1] integrated a system dynamics module in a mathematical modeling course.

Unless a system dynamics course or program receives external funding, to be sustainable a university has to charge tuition to recover the course delivery cost. Thanks to government funding of the educational system, the University of Bergen in Norway offers a free online course on resource management. On the other hand, WPI currently charges $3,843 for a three-credit-hour graduate course, which is a typical tuition charge at a private American university. For anyone who does not require academic credit, WPI offers an audit registration option, which is half the regular tuition rate. A non-credit two-day class-based system dynamics course by isee systems costs $1200–1500 (see [9]). A five-day online workshop by Strategy Dynamics Ltd., a U.K. company, is £250, or about $400. A five-day executive education course at MIT is $8,100 (see [10]).

3. System Dynamics at WPI

System dynamics was established at WPI by Michael Radzicki, who began teaching a two-course undergraduate sequence in system dynamics in 1990. James Doyle was recruited in 1992 to teach group model building and judgment and decision making. By 1996 Khalid Saeed had joined WPI as Head of the Department of Social Science and Policy Studies, the department that administers WPI’s system dynamics programs. Soon thereafter, in 1998, Saeed, Doyle, and Radzicki established the world’s first Bachelor of Science degree program in System Dynamics at WPI [11]. Professor of Practice James M. Lyneis and Elise Axelrad joined the WPI system dynamics faculty in 2001, followed by Oleg Pavlov in 2002. In 2003 WPI began offering its first graduate courses in system dynamics. Some of these courses had previously been taught as distance learning courses at MIT, and several of the faculty involved in that program (Bob Eberlein, Andy Ford, Jim Hines, and Kim Warren) were brought in as adjunct faculty to keep the courses going. By 2004 nine graduate courses as well as a five-course graduate certificate program in system dynamics had been established. The first Ph.D. student in the interdisciplinary doctorate program in system dynamics, Shelly Friedman, graduated in 2005. In 2006 the M.S. program in System Dynamics was approved by the WPI Faculty and Trustees. The first four graduates of the M.S. program were awarded their degrees in May of 2007. Table 2 summarizes the development of system dynamics programs at WPI.

Table 2. History of System Dynamics at Worcester Polytechnic Institute (WPI).

1990	First SD courses
1998	B.S. degree program in SD
2003	First graduate SD courses
2004	Graduate certificate in SD
2005	First Ph.D. graduate
2006	M.S. degree program in SD
2007	First M.S. graduates

Table 2. History of System Dynamics at Worcester Polytechnic Institute (WPI).

1990	First SD courses
1998	B.S. degree program in SD
2003	First graduate SD courses
2004	Graduate certificate in SD
2005	First Ph.D. graduate
2006	M.S. degree program in SD
2007	First M.S. graduates

4. Program Goals

The WPI System Dynamics teaching faculty has adopted the following mission statement for the university’s programs in system dynamics:

• System dynamics is a method for understanding and changing the behavior of systems. It centers around the development and use of formal computer models that:

  (1)

  Apply the accepted system dynamics theory of structure (endogenous behavior, positive and negative feedback loops, accumulations and delays, and representation of decision-making);

  (2)

  Are constructed following the scientific method (problem defined in terms of a reference mode of problem behavior, dynamic hypothesis as a theory of that behavior, formal computer model of the hypothesis, testing of the model/hypothesis against data, extensive analysis, and policy design); and

  (3)

  Use best practice tools and techniques (system dynamics software, units checking, standard formulations, generic models and building blocks, graphical functions, etc.).

• These three components collectively define rigorous system dynamics. Further, in real world applications:

  (4)

  Models should be developed so as to achieve client confidence and acceptance (using various approaches including “group model building”)

  (5)

  Model development must be taught in the context of the application field.

5. Program Design

WPI is the only institution in the U.S. that offers complete educational programs that lead to the B.S. in System Dynamics, Graduate Certificate, M.S., and Ph.D. degrees in System Dynamics (Figure 1). WPI currently offers 11 online semester-long graduate system dynamics courses (see [12]) that are also open to advanced undergraduate students. For the benefit of the undergraduate program, there are also two undergraduate class-based system dynamics courses and two project-based courses. System dynamics courses can be taken as an elective by WPI Economics majors. Additionally, system dynamics has been incorporated into various undergraduate economics courses.

The online program also acts as a hub that connects professionals and scientists with system dynamics experts, thus forming a community of practice. The interaction, which is important for building such a community of practice, is facilitated through WPI-sponsored online discussion boards, online sessions with instructors, and an active online group in LinkedIn called “WPI System Dynamics” which was established several years ago. The online LinkedIn group currently has 214 members at different levels of SD expertise.

The academic component of the online program is overseen by the Department of Social Science and Policy Studies. However, the administrative elements (enrollment, marketing, and online delivery) are managed by the Corporate and Professional Education (CPE) division at WPI, which has been an integral part of this university for nearly 30 years. All existing CPE programs are financially self-sufficient.

Below we provide more information on WPI programs. It should be noted that WPI follows separate academic schedules and uses different academic credit systems for its undergraduate and graduate programs. Undergraduate programs follow a term calendar, while graduate programs follow a semester calendar. Also, an undergraduate course is worth 1/3 unit. So the system dynamics requirement of 5/3 units means five undergraduate courses in system dynamics. A graduate course is counted as 3 credit hours. The Masters degree in SD requires 30 credit hours, or 10 graduate-level courses.

Figure 1. A Tiered Learning Levels view of skills and matching education programs in system dynamics at WPI. The courses, workshops and projects that are mentioned in the figure are on system dynamics.

Figure 1. A Tiered Learning Levels view of skills and matching education programs in system dynamics at WPI. The courses, workshops and projects that are mentioned in the figure are on system dynamics.

5.1. Bachelor of Science in System Dynamics

Table 3 and Table 4 explain the learning outcomes and distribution requirements for the Bachelor of Science in System Dynamics.

5.2. Master of Science Degree in System Dynamics

WPI’s M.S. program in system dynamics was the culmination of more than a decade of strategic planning and curriculum development on the part of several faculty. Students are required to complete 30 credit hours (10 courses). At least 21 of these credit hours (7 courses) must be in system dynamics. The remaining 9 credit hours may be taken in mathematics, management, economics, or additional system dynamics courses. Six of these 9 credit hours may also be supervised research. Table 5 shows course requirements for the M.S. in system dynamics (full course descriptions appear in Appendix B).

Table 3. Learning Outcomes of the System Dynamics Major.

1. Ability to recognize the dynamic patterns of behavior in real-world data. 2. Ability to formulate feedback hypotheses representing problems and understand the hypotheses’ logic. 3. Ability to translate feedback hypotheses into stock and flow models. 4. Ability to experiment with stock and flow models in order to establish their fidelity. 5. Ability to design experiments with a stock and flow model, implement them, and interpret their results, in order to arrive at effective solutions that address the defined problems of a system dynamics project. 6. Literacy in the technical aspects of problems in the student’s area of application. 7. Ability to communicate effectively the results of a system dynamics analysis in speech and writing.

8. An understanding of basic concepts in software programming and management science. 9. An understanding of how to apply scientific principles in system dynamics modeling. 10. Ability to develop, organize, manage, and successfully conduct a significant system dynamics project. 11. Ability to locate and integrate valid and appropriate information from multiple fields and perspectives for use in systems dynamics models. 12. An understanding of the endogenous causes of societal problems. 13. An appreciation of the inter-connectedness between technology, society, and the environment. 14. Ability to form and work effectively in groups involving system dynamics modelers, appropriate domain experts, and stakeholders.

Source: WPI Undergraduate Catalog 2013–14.

Table 3. Learning Outcomes of the System Dynamics Major.

1. Ability to recognize the dynamic patterns of behavior in real-world data. 2. Ability to formulate feedback hypotheses representing problems and understand the hypotheses’ logic. 3. Ability to translate feedback hypotheses into stock and flow models. 4. Ability to experiment with stock and flow models in order to establish their fidelity. 5. Ability to design experiments with a stock and flow model, implement them, and interpret their results, in order to arrive at effective solutions that address the defined problems of a system dynamics project. 6. Literacy in the technical aspects of problems in the student’s area of application. 7. Ability to communicate effectively the results of a system dynamics analysis in speech and writing.

8. An understanding of basic concepts in software programming and management science. 9. An understanding of how to apply scientific principles in system dynamics modeling. 10. Ability to develop, organize, manage, and successfully conduct a significant system dynamics project. 11. Ability to locate and integrate valid and appropriate information from multiple fields and perspectives for use in systems dynamics models. 12. An understanding of the endogenous causes of societal problems. 13. An appreciation of the inter-connectedness between technology, society, and the environment. 14. Ability to form and work effectively in groups involving system dynamics modelers, appropriate domain experts, and stakeholders.

Source: WPI Undergraduate Catalog 2013–14.

Table 4. Program Distribution Requirements for the Bachelor’s Degree in System Dynamics.

The normal period of residency at WPI is 16 terms. In addition to the WPI requirements applicable to all students, completion of a minimum of 10 units of study is required in system dynamics, social science, basic science, and mathematics, and computer science as follows:
SYSTEM DYNAMICS	MINIMUM UNITS
REQUIREMENTS
1. System Dynamics (Note 1)	5/3
2. Other Social Science (Note 2)	5/3
3. Business (Note 3)	2/3
4. Mathematics/basic sciences/engineering (Note 4)	8/3
5. Computer Science (Note 5)	2/3
6. Application Area (Note 6)	5/3
7. MQP	1
NOTES:
1. Only social science courses with a “5” in the second digit of the course number count toward the system dynamics requirement.
2. Must include microeconomics or macroeconomics, cognitive or social psychology, and public policy.
3. Must include organizational science.
4. Must include differential and integral calculus, differential equations, and numerical or statistical analysis.
5. Courses on computer programming and programming languages are recommended.
6. This requirement is satisfied by a cohesive set of work from the fields of social science, management, science, mathematics, computer science, or engineering as specified in the curriculum the guidelines for system dynamics major.

Source: WPI Undergraduate Catalog 2013–14.

Table 4. Program Distribution Requirements for the Bachelor’s Degree in System Dynamics.

The normal period of residency at WPI is 16 terms. In addition to the WPI requirements applicable to all students, completion of a minimum of 10 units of study is required in system dynamics, social science, basic science, and mathematics, and computer science as follows:
SYSTEM DYNAMICS	MINIMUM UNITS
REQUIREMENTS
1. System Dynamics (Note 1)	5/3
2. Other Social Science (Note 2)	5/3
3. Business (Note 3)	2/3
4. Mathematics/basic sciences/engineering (Note 4)	8/3
5. Computer Science (Note 5)	2/3
6. Application Area (Note 6)	5/3
7. MQP	1
NOTES:
1. Only social science courses with a “5” in the second digit of the course number count toward the system dynamics requirement.
2. Must include microeconomics or macroeconomics, cognitive or social psychology, and public policy.
3. Must include organizational science.
4. Must include differential and integral calculus, differential equations, and numerical or statistical analysis.
5. Courses on computer programming and programming languages are recommended.
6. This requirement is satisfied by a cohesive set of work from the fields of social science, management, science, mathematics, computer science, or engineering as specified in the curriculum the guidelines for system dynamics major.

Source: WPI Undergraduate Catalog 2013–14.

Table 5. Course requirements for the M.S. in system dynamics.

1. Foundation courses, required courses (6 credits)
	SD 550 System Dynamics Foundation: Managing Complexity
	SD 551 Modeling and Experimental Analysis of Complex Problems
2. Methodological courses, two or three courses (6 to 9 credits) from the following courses:
	SD 552 System Dynamics for Insight
	SD 553 Model Analysis and Evaluation Techniques
	SD 554 Real World System Dynamics
	SD 556 Strategic Modeling and Business Dynamics
	SD 557 Latent Structures, Unintended Consequences, and Public Policy
3. Application courses, three or four courses (9 to12 credits) from the following courses:
	SD 560 Strategy Dynamics
	SD 561 Environmental Dynamics
	SD 562 Project Dynamics
	SD 565 Macroeconomic Dynamics
4. Electives, one to three courses (3 to 9 credits) from the following or additional courses from the previous lists:
	SD 590 Special Topics in System Dynamics (credit as specified)
	Graduate independent study courses in System Dynamics (credit as specified)
	MA 510/CS522 Numerical Methods
	MA 512 Numerical Differential Equations
	Approved graduate coursework in an application area (e.g., economics, psychology, management, engineering, or applied sciences)

Source: WPI Undergraduate Catalog 2013–14.

Table 5. Course requirements for the M.S. in system dynamics.

1. Foundation courses, required courses (6 credits)
	SD 550 System Dynamics Foundation: Managing Complexity
	SD 551 Modeling and Experimental Analysis of Complex Problems
2. Methodological courses, two or three courses (6 to 9 credits) from the following courses:
	SD 552 System Dynamics for Insight
	SD 553 Model Analysis and Evaluation Techniques
	SD 554 Real World System Dynamics
	SD 556 Strategic Modeling and Business Dynamics
	SD 557 Latent Structures, Unintended Consequences, and Public Policy
3. Application courses, three or four courses (9 to12 credits) from the following courses:
	SD 560 Strategy Dynamics
	SD 561 Environmental Dynamics
	SD 562 Project Dynamics
	SD 565 Macroeconomic Dynamics
4. Electives, one to three courses (3 to 9 credits) from the following or additional courses from the previous lists:
	SD 590 Special Topics in System Dynamics (credit as specified)
	Graduate independent study courses in System Dynamics (credit as specified)
	MA 510/CS522 Numerical Methods
	MA 512 Numerical Differential Equations
	Approved graduate coursework in an application area (e.g., economics, psychology, management, engineering, or applied sciences)

Source: WPI Undergraduate Catalog 2013–14.

SD550 serves as our basic introductory modeling course and is a prerequisite to all other courses in the program. SD551 serves as an advanced modeling course—it covers more advanced skills and more challenging and more open-ended modeling assignments. SD550 and SD551 serve as prerequisites for most of the advanced methodology courses.

Methodological courses, as opposed to application courses, develop important basic skills in greater detail than is possible in the introductory courses. SD552 is designed to build students’ modeling skills by increasing their ability to identify and adapt generic structures. SD553 covers basic topics in model evaluation and analysis, including use of subscripts, achieving and testing for robustness, use of numerical data, sensitivity analysis, and optimization/calibration of models. SD554 in many ways serves as a “capstone” course for the program. In this course students, under the direction of an experienced system dynamics consultant, work throughout the term on a consulting project in their own organization that they design and implement from start to finish.

Application courses are advanced topical courses that focus on the application of system dynamics in a particular domain of inquiry. Elective courses allow students the flexibility to take more system dynamics courses, explore new topics through one-on-one collaboration with a faculty member, improve their math skills, or develop expertise in an application area of system dynamics. Up to 6 credit hours can be Directed Research. This requirement allows students to undertake an optional Master’s Thesis.

5.3. Graduate Certificate in System Dynamics

A Graduate Certificate program requires 15 credit hours of graduate study (5 courses). Students take one or both of our Foundation Courses (SD550 and SD551), and complete the rest of the credits by taking a variety of methodological and application courses in system dynamics.

5.4. B.S./M.S. in System Dynamics

Undergraduate students can pursue a 5-year combined Bachelor’s/Master’s degree, in which the Bachelor’s degree is awarded in any major offered at WPI and the Masters degree is awarded in System Dynamics. For this program, WPI allows the double counting of up to four courses.

5.5. Interdisciplinary Master’s Degree in Systems Modeling

The departments of Mathematical Sciences and Social Science and Policy Studies offer an interdisciplinary Master’s degree in systems modeling. The program requires 30 credit hours (10 courses) in Mathematics, System Dynamics, and electives taught in engineering, science and management departments. Students entering the program must have a Bachelor’s degree, which is typically in science or engineering. Students complete 15 credit hours in system dynamics and 15 credit hours in mathematical modeling and an applications area (e.g., industrial engineering, management, infrastructure planning, telecommunications planning, and power systems). Up to 6 credit hours may be done as a supervised project which allows for an optional Master’s Thesis.

5.6. Interdisciplinary Doctorate in System Dynamics

Social Science and Policy Studies collaborates with other departments to offer an interdisciplinary doctoral program in System Dynamics. Each program of study requires at least 60 credit hours of study and is adapted to the interests of the student and the interests of the participating faculty. A typical doctoral committee consists of three or more faculty members from participating departments.

6. Delivery Methods

Undergraduate system dynamics courses are delivered in the traditional classroom-based format. To allow for broader geographic reach, convenience and accessibility than class-based courses, WPI’s graduate courses in system dynamics are implemented exclusively in a distance learning format through WPI’s Division of Corporate and Professional Education (CPE). There are no classroom sections of the courses. They are delivered in an online asynchronous format through WPI’s web-based course delivery system, myWPI, powered by the Blackboard Learning Management System. Teaching courses online reduces the cost to students as they do not incur additional expenses for travel, lodging and meals as would be required for a residential course.

Graduate online courses are taught on the same semester schedule as WPI’s graduate classroom courses and students receive regular deadlines for completion of homework assignments and other tasks. The courses are just as challenging as classroom courses at WPI, often requiring 15–20 h per week of effort or more from students. Course lectures (as streaming video files) and supporting materials such as Power Point files are posted to myWPI. As in a classroom course, students receive detailed and timely feedback on their work. Faculty-student and student-student interaction takes place primarily via electronic discussion boards and email. WPI’s distance learning students are full members of the WPI community and have electronic access to all services available to on-campus students (e.g., library, bookstore, and technical help). Instructors can choose to record the lectures at their individual computers using commonly available video recording software such as Camtasia or tape lectures at the WPI’s Academic Technology Center (ATC).

Distance learning poses a unique set of challenges. The absence of face-to-face personal contact among students and faculty can potentially be a serious impediment to learning, especially for students who favor in person interactions. At WPI, we attempt to use technology to emulate the classroom experience. Below are a few solutions that we have adopted and which seem to be working well for us.

(1)

Talking head: Most of the lectures are recorded and professionally edited in a studio on campus in such a way that videos show not only slides and demonstrations of computer models but also the image of the instructor superimposed on top of the slides as the talking head.

(2)

Discussion board: Instructors may dedicate a sizable part of the grade to discourse on the discussion board. The discussion board tool is integrated with Blackboard. If the online discussions slow down, instructors may stimulate lackluster exchanges with challenging questions.

(3)

Synching the class: There is potentially a danger of losing class focus and the relevance of discussions to the syllabus of a course in the asynchronous format that we choose to follow in view of the many time zones involved and the fact that our students often need flexibility due to other commitments. We overcome this problem by not posting lessons all at once but revealing them according to a fixed schedule so students work on the same materials during the week assigned to a lesson. Assigning high penalties for late homework submissions also encourages students to observe the lesson schedule of a course. These measures greatly help create synchronism in our otherwise asynchronous classes.

(4)

Virtual office hours: Though not every instructor uses them, the option of virtual office hours is available with Adobe Connect, which is a video-conferencing tool integrated with Blackboard. Based on student course evaluations, certain types of students are particularly appreciative of the life interaction.

Since developing online materials is rather time consuming, frequently revising and updating courses remains a challenge. We have discovered that the best strategy for keeping the curricula current is to do revisions gradually rather than revamping an entire course all at once. From the program management perspective, counting time spent on course maintenance towards the faculty load creates strong incentives for the faculty to keep on-line courses vibrant and up-to-date.

7. Students

WPI is a technological university, but it recognizes the importance of the humanities, arts and social sciences in its undergraduate curriculum, and therefore all undergraduate students must complete two social science courses before they graduate. The system dynamics courses are open to all students in the university and since they are housed in the Department of Social Science and Policy Studies, any system dynamics course is counted towards the social science requirement. This helps with the enrollment in the undergraduate system dynamics courses.

The students enrolled in WPI’s graduate system dynamics programs are primarily mid-career professionals who enroll in courses part-time. They are not necessarily looking for a brand new career, but for the most part want to do their current job better by incorporating the tools and techniques of system dynamics. More than half of the students are above the age of 35. The students are widely geographically dispersed around the U.S. and the world, with only about 15% residing in WPI’s home state of Massachusetts. Our student body as a whole is already highly educated. Many students in graduate system dynamics courses have advanced degrees in other fields (e.g., M.B.A., M.D., M.S. in Engineering, Ph.D.). We also offer graduate SD courses which are taught on-site at various companies around New England as part of a corporate education program leading to the Certificate or the Master’s degree in Systems Engineering.

Some students in graduate courses are researchers who see the systems thinking paradigm coupled with the power of system dynamics modeling as the intellectual and methodological foundation of their desire to extend beyond the limited modes of inquiry of traditional disciplines. Established researchers may take a course to acquaint themselves with the system dynamics methodology and its applications. Some of our students are researchers who already have a good understanding of traditional fields of inquiry but might need to acquire only sufficient understanding of system dynamics to draw new ideas and methodology into their work. After taking one or two courses, while maintaining a foothold in their traditional first disciplines, these researches are able to understand system dynamics sufficiently to communicate and collaborate with expert modelers.

Enrollment in system dynamics courses at WPI is shown in Table 6. It should be noted that in addition to our primary population of part-time M.S. students, a small number of B.S./M.S. and interdisciplinary Ph.D. students also register for graduate online courses.

Table 6. Enrollment in System Dynamics Courses at WPI.

	Undergraduate		Graduate
Academic year	Sections	Enrollment	Sections	Enrollment
1998–99	2	12	N.A.	N.A.
1999–00	5	119	N.A.	N.A.
2000–01	5	141	N.A.	N.A.
2001–02	5	71	N.A.	N.A.
2002–03	3	78	N.A.	N.A.
2003–04	5	95	8	99
2004–05	4	107	10	91
2005–06	4	86	7	97
2006–07	3	93	10	101
2007–08	5	109	8	107
2008–09	3	87	9	91
2009–10	3	65	14	117
2010–11	2	42	12	85
2011–12	3	55	9	70
2012–13	2	64	11	76

Table 6. Enrollment in System Dynamics Courses at WPI.

	Undergraduate		Graduate
Academic year	Sections	Enrollment	Sections	Enrollment
1998–99	2	12	N.A.	N.A.
1999–00	5	119	N.A.	N.A.
2000–01	5	141	N.A.	N.A.
2001–02	5	71	N.A.	N.A.
2002–03	3	78	N.A.	N.A.
2003–04	5	95	8	99
2004–05	4	107	10	91
2005–06	4	86	7	97
2006–07	3	93	10	101
2007–08	5	109	8	107
2008–09	3	87	9	91
2009–10	3	65	14	117
2010–11	2	42	12	85
2011–12	3	55	9	70
2012–13	2	64	11	76

8. Faculty

There are currently three full-time tenured faculty in Social Science and Policy Studies at WPI who teach in the system dynamics programs. In addition, there are six adjunct faculty who regularly teach online courses. WPI has been fortunate in being able to draw on the talents of system dynamics experts from around the world for its programs. Collectively, the system dynamics teaching faculty bring a wealth of experience and expertise to the program, and include three winners of the Jay Forrester Award as well as five past Presidents of the International System Dynamics Society. The list of faculty and their research interests appear in Appendix C.

9. Course Design

The System Dynamics courses at WPI emphasize building modeling skills through homework assignments that receive prompt and detailed feedback from the instructor. Variations in approach and emphasis are encouraged in the belief that students benefit from learning why and how diverse faculty may approach a given problem or topic differently. In all of our modeling courses students gain hands-on experience with reference modes, hypothesis formulation using causal and stock-flow diagrams, equation-writing, and model analysis. We believe that lasting, generalizable learning is best obtained by returning to the same topics again and again, with different instructors, in different courses, while studying different problem domains. Our goal is to turn students into experienced modelers who, upon graduation, will be able to manage a modeling project in a real organization from start to finish.

Table 7. System Dynamics skills taught in SD550.

System Dynamics as a theory of behavior	Scientific modeling process	Tools and tricks
Policy Resistance/Unintended Consequences Fundamental Behavior Patterns Causes of dynamic behavior: feedback and accumulation Basic Archetypes (success to successful, limits, fixes that fail, shifting burden) First-order positive systems (analytical solution, rate-level graph, doubling time) First-order negative systems (analytical, rate/level, half-lives) Draining processes, Goal-gap Exponential average First-order system with inflow and outflow (all linear) S-shaped Growth (carrying capacity) Overshoot and Collapse (resource depletion) Growth feedbacks from Sterman Ch. 10 Product Diffusion Model Epidemic (SI and SIR) Stock Management with 3-stock delay Material Delays (1st, 3rd, 6th, pipeline) Second-order systems and oscillations (role of minor and major loops)	System Dynamics “Standard Method”: conceptualization (problem definition, dynamic hypothesis), formulation (model construction, testing, validation), use (testing and understanding, policy design) Conceptualization exercise— Peer-to-Peer Modeling and policy design exercise—Tragedy of Commons/Fishbanks (formulation including carrying capacity, graphical function, first-order stock control, analysis of each loop's parameter sensitivity, policy design focused on info from system and when action needs to be taken) Material delays exercise (relative peaks of inflows, outflows, stock; equilibrium; distribution relative to average) A business case exercise	Vensim Causal-loop diagramming (basics and conventions, link/loop polarities, etc.) Problems with CLDs Stock-flow diagrams (as means of building models) Graphical integration Calculating equilibrium and setting up model in equilibrium using equations Units checking Graphical Functions (normalization, etc.) First-order stock control Test inputs (step, pulse, cycle, ramp, exponential, noise) Sensitivity testing Loop knockout

Table 7. System Dynamics skills taught in SD550.

System Dynamics as a theory of behavior	Scientific modeling process	Tools and tricks
Policy Resistance/Unintended Consequences Fundamental Behavior Patterns Causes of dynamic behavior: feedback and accumulation Basic Archetypes (success to successful, limits, fixes that fail, shifting burden) First-order positive systems (analytical solution, rate-level graph, doubling time) First-order negative systems (analytical, rate/level, half-lives) Draining processes, Goal-gap Exponential average First-order system with inflow and outflow (all linear) S-shaped Growth (carrying capacity) Overshoot and Collapse (resource depletion) Growth feedbacks from Sterman Ch. 10 Product Diffusion Model Epidemic (SI and SIR) Stock Management with 3-stock delay Material Delays (1st, 3rd, 6th, pipeline) Second-order systems and oscillations (role of minor and major loops)	System Dynamics “Standard Method”: conceptualization (problem definition, dynamic hypothesis), formulation (model construction, testing, validation), use (testing and understanding, policy design) Conceptualization exercise— Peer-to-Peer Modeling and policy design exercise—Tragedy of Commons/Fishbanks (formulation including carrying capacity, graphical function, first-order stock control, analysis of each loop's parameter sensitivity, policy design focused on info from system and when action needs to be taken) Material delays exercise (relative peaks of inflows, outflows, stock; equilibrium; distribution relative to average) A business case exercise	Vensim Causal-loop diagramming (basics and conventions, link/loop polarities, etc.) Problems with CLDs Stock-flow diagrams (as means of building models) Graphical integration Calculating equilibrium and setting up model in equilibrium using equations Units checking Graphical Functions (normalization, etc.) First-order stock control Test inputs (step, pulse, cycle, ramp, exponential, noise) Sensitivity testing Loop knockout

Rather than focus on the topics a course covers, when we design (and redesign) courses, we place more emphasis on skill achievement. Each lecture, assignment, or activity is considered in relation to the general “skill” categories described in our mission statement. These “skill grids” help instructors plan their courses and help them keep track of what other instructors are doing. They also allow us a high-level view of the entire program, which helps us assess the amount of overlap and redundancy across courses (while keeping in mind that a certain degree of redundancy is desirable) as well as to identify important omissions in our program.

Table 7 provides an example of a skill grid for our introductory course, SD550. It constitutes a statement of what we think is important to include in an introductory system dynamics course, with an emphasis on skills taught in various goal categories versus the traditional linear format of a course syllabus. This list of topics is comparable to the list in an introductory system dynamics course described in Barlas [1].

10. Conclusion

In this article we have tried to give an overview, in some detail, of the design and rationale for our degree programs in system dynamics. We hope that by sharing this information about our program, we will obtain feedback from the system dynamics community about what we are doing wrong and perhaps, occasionally, feedback on what we are doing right. We also hope to encourage the field of system dynamics to more fully and collectively address the question of what a graduate of a system dynamics program should know and be able to do and how best to achieve those goals. In addition, we hope that by sharing our experience, other universities will be encouraged to travel down the long and difficult path of turning a few system dynamics courses into a substantial degree program.

While the usual discussion about online education revolves around the quality of online courses, creating and managing online programs brings forth a host of issues that are typically not of serious concern in class-based instruction. For distance education to work, the university must be able and willing commit significant additional resources besides the instructor’s time to such programs. Creating an online program requires facilities and staff for videotaping and editing lectures as well as handling email and phone communication with students. Such a mundane task as registering for a course might suddenly turn into an ordeal and a flurry of frantic emails when students have to figure out the registration process remotely. Therefore, it is essential for an online program to have dedicated, patient and well-trained staff who can provide administrative support to the program on a day-to-day basis.

This article is not a comprehensive review of program design. We did not address resource requirements and the financial side of running a program. We did not cover many agency issues. For example, we did not discuss how to convince university administration of the viability of a program and how to reach an agreement with them about cost and revenue sharing. Also, we did not cover the issues of student and faculty recruitment in the context of managing instructional capacity in the competitive marketplace that higher education has become.