Building Interdisciplinary Bridges between Undergraduate Courses

Abstract

The goal of this project was to help students make conceptual connections between traditional courses across disciplinary boundaries without a major overhaul of the individual courses or of the curriculum. We describe a collection of tools used in linking previously isolated disciplinary courses at WPI, and four models that illustrate their implementation. Qualitative results suggest that bridging can, but doesn’t always, improve student attitudes toward interdisciplinary work. Quantitative data show that bridging often improves academic performance in bridged courses.

I. Introduction

A Future Search conference on WPI’s freshman year identified several challenges for the first year program (Davis 1994). Perhaps the most important was that an overwhelming majority of students saw little relationship of introductory mathematics and science courses to one another or to their professional goals. Faculty see the same problem when students in a science or engineering course cannot apply basic mathematical methods covered in a calculus course. The students know mathematical concepts while they are in the mathematics building, but these are lost when they go across campus to physics or electrical engineering.

This problem is not unique to WPI. Many schools have put tremendous effort and resources into addressing exactly these problems. Some of these efforts have brought active learning into large-lecture introductory courses (Johnson and Johnson 1991; Felder and Brent 1994; Miller, Groccia, and Miller 2001). Many more recent initiatives have built and tested “integrated first year” programs (Al-Halou et al. 1998; Frair et al. 1997). For example, the IMPULSE project at the University of Massachusetts at Amherst (Pendergass et al. 1998) has achieved significant improvements in both retention in the engineering majors and student performance in the introductory courses. The Foundation Coalition (Frair et al. 1997) and the Integrated First Year Program at Drexel (Quinn 1993; Newdick 1994) are other notable examples. Almost all of the innovations described have reported impressive successes but all require very significant restructuring of programs. For example, in the IMPULSE project, a cohort of 48 students signs up for a single, 31-credit course that stretches over two semesters. In particular, such innovations require unusual cooperation between several different academic departments in order to succeed. In addition, all of these projects require a large group of truly committed faculty, with broad support from administration and often significant external funding.

A reform effort at WPI has been motivated by similar goals. However, we have chosen to focus on small, manageable changes to existing courses so that the changes will be simple to implement, flexible enough to be used in almost any discipline, and easy to sustain. In the traditional academic culture, individual courses are painstakingly optimized over many semesters of trial and error. Few faculty know how other courses in their own departments, let alone courses in other departments, are taught. In contrast, in a well-designed curriculum, different courses “cover” different material and concepts, but there are strong links between them. Courses should not overlap too much but neither should they be completely independent events. Our strategy was to change the way that both students and faculty think about courses so that, without significant extra effort or upheaval, students and faculty would more easily see the connections between previously isolated courses.

Our effort has been guided by some simple observations:

· Students take more than one course at a time, usually in several departments, and these courses often cover related concepts and use similar tools.

· Students rarely realize this.

· Faculty may realize this, but rarely take advantage of it.

Our approach to bridging makes use of the first of these observations, in order to overcome the last two. First we discuss our collection of bridging tools; then we present four bridging models that illustrate how the tools have been implemented in various bridging combinations.

II. The Toolbox

All of the tools described here were used in making small changes to existing courses at WPI. Some of the tools involve change in the way a course is organized or delivered. Most of the tools encourage students to carry important concepts across disciplinary boundaries. Most of the tools require some communication between the faculty teaching the courses. All of the tools are applicable to many different courses. No bridge used all of the available tools, and no single tool was used in every bridge.

A. Aligned Syllabi

Individual course syllabi can be rearranged so that related tools and concepts are introduced at the roughly the same time. For example, a calculus instructor can introduce basic mathematical properties of vectors just as the same concepts are being introduced in physics. On the other hand, it is downright damaging for the same faculty to introduce as “new” topics that have been covered recently in another course, especially if it is clear to the students that neither instructor knows anything about what the other has done.

B. Homework Excursions

Homework problems and examples can be taken directly from the disciplinary source. For example, the mathematics instructor can use plots and derivations directly from the current chemistry text. Homework problems for calculus can be assigned from the current physics text. A complementary strategy is to “send the students out” to find mathematical applications, instead of the instructor copying the problems and bringing them back to the disciplinary silo. For example, assigning students in a mathematics course to “bring back a function, dead or alive” from their chemistry or physics text encourages the students to “think calculus” while they are working in other texts.

C. Jargon control

Many students can recognize that the concepts in two different courses are similar but can’t take advantage of the connections because of the differences in terminology or notation. Faculty can help students overcome jargon barriers by using other notations when appropriate, or pointing out that the same concept is used in another class under a different name. Assigning homework from other texts can help reinforce jargon mastery, as can projects done in multidisciplinary teams, and visiting lecturers. It is not necessary that all classes use the same language and notation, because learning to deal with jargon is a valuable skill. It is necessary that differences in jargon be made explicit, so they can be tamed.

D. Guest Lectures

Let the expert present the topic or project supporting the connections. For example, a faculty member from Mechanical Engineering visited a Differential Equations class to introduce the resonance phenomenon in oscillating systems. The guest lecture took about one half of one class period and included a video that gave reality to the theory and provided the foundation for a project in the course. Later a mathematics instructor went into the mechanical engineering course to provide a brief review of the mathematics, in the same language in which the students first met the concept. The outside expert lends credibility to the bridging, thus emphasizing its importance.

E. Projects

Many courses at WPI include project work. In addition to providing excellent opportunities for students to explore some aspect of a course in greater depth than in standard homework, projects can focus on how the topics in one course are connected with other courses or disciplines. The connections can be between current courses or between the current course and the students’ majors. For example, students taking both the Vectors & Series calculus course and Chemistry worked on the mathematics related to equilibria and titrations as an application of numerical root finding techniques. Students simultaneously enrolled in Vectors & Series calculus and Computer Science I wrote programs in C++ to study the convergence of sequences and series in Calculus (one of the most difficult topics in the Calculus sequence). In Linear Algebra, Electrical and Computer Engineering students who were also taking the Signals course were asked to determine the feasibility of voiceprint security. (This project required competence in analyzing audio files based upon Fourier analysis, a linear algebra concept arising from orthogonal coordinate systems.) In many cases, the students formed teams based on major or interest, giving additional support to the bridging activity.

F. Labs

Labs can be redesigned so as to emphasize how a concept or method is applied in another discipline. For example, in Multivariate Calculus, students used Maple software to generate and study equipotential lines of electric fields due to an electric dipole. In the past in the corresponding physics course, Electricity and Magnetism, students had laboriously generated these by hand. The use of the mathematical software resulted in considerable time savings with correspondingly more effort put into understanding of the physics involved.

G. Registration Control

Our original conception of the bridging model was that a cohort of students would be simultaneously cross-enrolled in both courses of a bridged pair. However, it is impossible to achieve perfect cross-enrollment in a flexible curriculum like WPI’s. Depending on the particular courses, variants of this strategy have included the following.

After preregistration, all of those students who have registered for both course A and course B are segregated into a separate section of one or both courses. This strategy obviously requires considerable advance planning, and the cooperation of the scheduling staff.
Close to the start of a term, we advertise via email a bridged section of a multi-section course to pre-registrants and solicit voluntary changes into the bridged section. This strategy requires a very proactive campaign involving multiple individual contacts with each pre-enrolled student, but has been surprisingly successful.
Rather than trying to control which sections students enroll in, we plan bridging based on the population of students that we know from experience take certain courses in certain terms. Then we use bridging tools (such as multiple projects) that are flexible enough to accommodate a variety of students.

Because of WPI’s open course change policy, we have never achieved a perfect (“uncontaminated”) bridge. But the “mismatched” students seem not to be disadvantaged by the experience, and seem to profit from demonstrated applications even when they are in disciplines other than their own majors.

III. Bridging Models

In the past five years, more than 20 different courses at the freshman and sophomore levels involving more than 25 instructors and eight departments have participated in course bridging (Table 1). The following four selected examples illustrate how the tools have been combined in various bridging models.

A. Strong Bridge (made use of bridging tools A,B,C,D,E,G)

In this model, both courses are taught as self-contained sections, and almost all students in both courses are cross-enrolled in the two courses. This is close to a “team-taught” course, but the courses and instruction remain independent.

In one example of this model, an additional section of the Vectors & Series calculus course was created. All students enrolled in the introductory physics course Mechanics with Calculus were notified of its existence and purpose so that they could change sections. The new section met at exactly the same time as the original calculus section, making it possible for anyone to switch sections without time conflict. Thus all 56 students in the new calculus section were also in the physics course, and only five students in the physics course were not in the calculus course, having already taken it.

Because most of each class was cross-registered in the “partner” section, all course sessions could make use of bridging tools. In our particular case, the calculus professor made an active effort to bridge to the physics course, with the physics professor as a less active partner. Although this situation was not ideal, it was nevertheless surprisingly effective. The two instructors had several meetings during the summer, reviewing each other’s texts and syllabi. The calculus professor aligned his syllabus as much as possible with that of the partner physics course, so that concepts that were needed in physics next week would be covered in calculus this week. Specifically, vector algebra and calculus were introduced at the start of the calculus course because they would be needed by students throughout the physics course. The calculus instructor used the standard physics notation for coordinate systems (the “i-j-k” system) and ignored the different notation used in the calculus book. He also assigned some homework out of the physics textbook, and in general made a regular effort to convey to students a concern and support for their success in the physics course. Finally, the weekly calculus laboratories, which used the Maple computer algebra system, dealt with physics examples such as kinetic and potential energy, vector functions, improper integrals and potential energy, and orbital data and Kepler’s Laws.

B. Bridging Achieved through Separate Conferences (made use of bridging tools b,c,d,e,g)

Creating a new course or section for bridging purposes may be very difficult or impossible. A less intrusive approach is useful when a large course contains a subset of students who can be bridged to another course. The lecture portion of one or both courses remains the same, perhaps being generic due to diverse needs, but individual conference sections can be tailored to the needs of a particular bridging partner course. This model was used for two years in a bridge between Physics (a course on Oscillations, Waves & Optics) and Electrical Engineering (an introductory course entitled Fundamentals of Electrical and Computer Engineering), where not all students in the physics course were electrical engineering (EE) majors and where the EE faculty were less active partners (Pierson et al., 2001).

In one term, enrollment in the physics course was 67 students and enrollment in the electrical engineering course was 84 students. Of these, 15 EE majors were concurrently enrolled in both courses. Cross-enrolled EE students were isolated into a single physics section in which linkages between the two disciplines were encouraged through discussion and a guest lecture by the EE professor. Examples, demonstrations, a project, and homework problems were selected and designed to connect and interrelate the topics and content of the two courses. Differences in notation between physics and electrical engineering were explicitly pointed out. In the second year of the bridge, all students in the physics course were required to do a project related to one of three majors: EE, Mechanical Engineering, and Biology (Pierson et al., 2001).

C. Distributed Bridging (made use of bridging tools c,e)

In this model, neither lecture nor conference relies on cross-registration between specific courses. The lecture and conferences serve all students in the course, covering the material that the department syllabus requires, presenting concepts, and reviewing skills and techniques. However, all students are assigned projects, where the bridging work is accomplished without perturbing the fundamental course. We have offered multiple projects at a given time, allowing bridges to be made simultaneously to multiple courses or multiple majors.

Students in Linear Algebra chose weekly projects based on their majors. For a class of 105 students, this resulted in projects for Mechanical Engineering, Electrical Engineering, Physics, Civil Engineering, Biology, and Industrial Engineering majors. The goal of the project was to tie material from the math course to courses and needs in the students’ majors, regardless of when those courses might be taken or when the needs might exist. For example, linear transformations were tied to LaPlace transforms for Electrical Engineering majors and Fourier Transforms for Physics majors. Industrial Engineering majors studied linear programming and optimization. Civil Engineering students used linear algebra as it related to truss analysis. Mechanical Engineering students used diagonalization to study mechanical vibrations. Biology majors used the Leslie Population model to study the spread of HIV in the human population and to consider the effects of a hypothetical vaccine. Particulars of the projects are available (Goulet, 2000).

D. Asynchronous Bridging (made use of bridging tools c, f)

Another approach to the logistical problems presented by requiring cross-registration in two courses for successful bridging is to identify sequences of courses that students in a particular major typically take, and then to bridge between successive courses rather than between concurrent courses. This approach has been tested in a bridge between General Chemistry I and II and Introduction to Material Science. Two instructors, one from engineering and one from chemistry, collaborated on the preparation of augmented instructional materials for two laboratories in each of the chemistry courses. These “bridged labs” were used in the spring semester, when engineering and computer science majors greatly outnumber life science majors in the general chemistry courses. The intent was to help students see the relevance of chemistry concepts in terms of tangible material properties and in applications familiar from their everyday experiences. Simple changes that were made included rewriting the goals of the lab to emphasize that engineering applications would be considered, and replacing references to “scientists” with “engineers and scientists”. In the labs themselves, examples of important engineering materials and properties were used to convey concepts such as density, covalent bonds, graphing, and crystal structure—all topics that were the foci of existing labs. For example, in the bridged density lab, density was emphasized as a key material property to consider when weight reduction is a design goal, and students measured and compared the densities of steel, aluminum, titanium, and copper using both a pycnometer and a digital caliper to measure sample volume. (Previously, the terminology “mass-volume relationship” rather than “density” had been used, and students had measured sample volume using only a pycnometer.) In the bridged covalent molecules lab, engineering plastics were used as examples (previously primarily halides and sulfides had been addressed) and students modeled a kevlar molecule instead of an amino acid. Wherever possible, examples of commercial products incorporating advanced materials were on display in the laboratory.

IV. Outcomes

The outcomes we hoped for fell into two broad categories: attitudes toward the value and relevance of linkage of knowledge across disciplines, and learning in both disciplines.

A. Attitudes

If attitudes toward interdisciplinary work improved, especially in a large service course, that could constitute success, because improved cross-disciplinary thinking could be expected to improve motivation and make teaching easier and is likely to ultimately improve learning. In many bridged courses, our only attitudinal data is subjective in nature. In general, instructors reported more interest and participation on the part of the students in bridged courses. Goulet observed qualitative attitudinal changes among his Linear Algebra students that he describes as “close to overwhelming”. He observed that the “educational quality” of his conversations with students was elevated from “what score they needed on what exam to get a B in the course” to “how the material in the course relates to their other course(s) and major”.

Where pre- and post- attitude surveys were conducted, results were encouraging. In the Waves & Oscillations-Introduction to Electrical Engineering bridge the attitudes of the bridged group toward interdisciplinary work were considerably but not significantly higher than those of the control group at both the beginning and end of the course (Pierson et al., 2001). And while the ratings of both the control and bridged groups declined over the course of the term, the ratings of the control group fell considerably (though not significantly) more than those of the bridged group. We suspect that the ratings declined from beginning to end partly because Pierson built high expectations of the bridged course in order to recruit students, and partly because the last third of the course (immediately preceding the survey) was not bridged due to topic mismatch between the two courses. Therefore the students may have felt that their high expectations were not met. In the Chemistry-Materials Science bridge, while students’ attitudes about chemistry were not affected by bridging, particular aspects of the students’ lab experience were enhanced to a statistically significant degree regardless of laboratory or course instructor. Specifically, students in the bridged group reported learning more from the density lab, and viewed the covalent molecules lab as having more practical importance, than did non-bridge students. Additional benefits were achieved for some but not all instructors.

Overall, attitude changes in bridged courses were at best significantly positive, but some were positive but not significant, some were nonexistent (no change detected), one (described above) was negative or counterintuitive, and some were not measured. Confounding variables seemed to include the particular instructor, students’ heightened expectations of bridged courses, and overall attitudes toward the course.

B. Performance

In most bridges involving mathematics courses, significantly better performance was noted in the mathematics course, in the form of lower failure rates and higher course grades (Goulet, 2000; unpublished data). In a series of Calculus (Differential and Integral)-Physics (Mechanics and Electricity & Magnetism) bridges involving first semester freshmen, course grades in both math and physics were significantly higher in the bridged group compared with a control group of students. In the Vectors & Series-Mechanics with Calculus and Vectors & Series-Computer Science I bridges, exam scores on bridged material improved significantly in the physics and computer science courses (unpublished data).

In two years of experience with the Waves & Oscillations-Introduction to Electrical Engineering bridge, better performance was evident on specific exams in the physics course and on the relevant material in the EE course; however, neither of these differences reached statistical significance (Pierson et al., 2001). Specifically, it was on exams targeted by the bridge treatment that bridged students’ scores exceeded control students’ scores by the greatest number of points. On the exams where no bridged material was covered, no measurable differences between the bridge and control groups were noted, reinforcing the idea that bridging makes a difference in performance. Indeed, our assessment as well as student comments suggest that bridging is exerting a small but systematic effect that would be detectable with increased sample size or with more sensitive measurement techniques.

In general, we observed performance improvements in most bridged courses, although they did not always reach statistical significance.

V. Conclusions

We began with the intent of fostering links between naturally compatible courses. This required some significant cultural changes, mainly having to do with interdisciplinary communication. Faculty looked at each other’s textbooks and syllabi (in some cases, syllabi were posted on the Web). Instructors from different departments discussed the relationship between their courses. Although bridging could have been accomplished without it, one especially motivated instructor sat in on the entire partner course in order to see it from the perspective of his students. The word “bridge” took on special meaning and became part of the local jargon. Students debated whether they should sign up for bridge sections or ordinary sections. Faculty collected data and discussed whether valid controls could be found. In short, there was a qualitative change in communication in all portions of the community.

Implementation of these modifications required more planning than faculty are used to doing. For example, getting department head approval for a specific interested faculty member to teach a specific bridged section, and then communicating with the person in charge of scheduling courses and rooms so as to construct cross-enrolled bridge sections, must be done several months in advance.

Five years of bridging experience have resulted in these conclusions about the components of a successful bridging effort. Fundamental is the willingness on the part of the instructor to consider new approaches and the broader needs of his or her students. Generation of an environment that demonstrates to students a sincere interest in their broader educational success, empowers students to make decisions about their own education, and encourages them to develop a professional identity, is a major contributor. Communication between instructors and with students is essential. As with all good teaching, clarity of goals is important. Finally, bridging efforts must always be guided by the effort to achieve “contextual learning”—putting the concepts that the student is learning in one course into the terms of another course.

After several years of working with these projects, the longer term issues of sustainability and institutionalization became clearer. Many indications are positive. Because the work was on sound educational footing, and initial efforts yielded positive data that were communicated through talks and workshops, bridging gained campus wide credibility. (Publicity is important here.) Various members of the administration, having seen the benefits of bridging, can now be counted upon to help with the logistical issues. Many of the educational outcomes identified by accrediting bodies such as the Accreditation Board for Engineering and Technology (ABET) and the New England Association of Schools and Colleges (NEASC) identify learning goals that focus on students’ abilities to apply the tools developed in one course in another, a focus that is very much in concert with the bridge philosophy and that has helped to foster acceptance.

Nevertheless, challenges remain. We emphasize that bridging consists of changes that are easy to implement and easy to sustain, but our own experience shows that it is still not easy to sell the program to many colleagues. Perhaps as a byproduct of an educational system that hallows disciplinary silos and individual faculty members’ academic freedom, it was initially surprisingly difficult to get faculty from different disciplines to talk with each other about the substance of their courses. Issues of appropriate rewards for young, tenure-track faculty who must take time from disciplinary research if they wish to work on such educational projects are just beginning to be dealt with. A subtle but substantial change in the culture of the academy is either a necessary condition for the success of these programs, or perhaps an outcome that will follow a bridging program.

Acknowledgements

Funding was provided by the National Science Foundation Institution-Wide Reform program under award DUE-9653707 and by the Davis Educational Foundation. Additional support was provided by the WPI Provost’s Office. The opinions expressed here are those of the authors and not necessarily those of the supporting agencies.

References

Al-Halou, N., N. Bilgutay, C. Corleto, J. Demel, R. Felder, K. Frair, J. Froyd, M. Hoit, J. Morgan and D. Wells. 1998. “First-year integrated curricula across engineering education coalitions”. Proceedings, 1998 frontiers in education conference. IEEE.

Davis, P. 1994. Report of the future search conference on the first year (June). Worcester Polytechnic Institute, Worcester.

Felder, R. and R. Brent. 1994. “Cooperative learning in technical courses: procedures, pitfalls, and payoffs”. ERIC Document Reproduction Service, ED377038.

Frair, K., D. Cordes, M. Cronan, D. Evans, and J. Froyd. 1997. “The foundation coalition—looking toward the future,” Proceedings of the 1997 Frontiers in Education Conference, http://fie.engrng.pitt.edu/fie98/ (accessed 08/01/01).

Goulet, J. MA2071 Linear Algebra Syllabus, http://www.wpi.edu/~goulet/ma2071/syll.htm (accessed 08/01/01).

Johnson, D., and R. Johnson. 1991. Active learning: cooperation in the college classroom. Interaction Book Company.

Miller, J. E., J. E. Groccia, and M. Miller. 2001. Student assisted teaching: a guide to faculty-student teamwork. Anker.

Newdick, R. 1994. E⁴: The Drexel Curriculum. October Engineering science and education Journal 5, no. 3(October):223-8.

Pendergass, N., J. Laoulache, J. Dowd, and R. Kowalczyk. 1998. “Efficient development and implementation of an integrated first-year engineering curriculum,” Proceedings of the 1998 Frontiers in Education Conference, http://fie.engrng.pitt.edu/fie98/ (accessed 08/01/01).

Quinn, R., 1993. “Drexel’s E⁴ Program: A different professional experience for engineering students and faculty”. Journal of Engineering Education 82,

no. 4 (October).

Pierson, S. W., S. T. Gurland, and V. Crawford, "Improving the effectiveness of introductory physics service courses: bridging to engineering courses,'' http://www.wpi.edu/Academics/Depts/Physics/News/Talks/Pierson/bridge.html (accessed 08/26/01).

Table 1. Relationships between bridged courses

	Inrto Bio Macromol¹	Computer Science I²	Inorganic Chem III³	Mechanics⁴	Mechanics w/ Calc⁵	E & M⁶	E & M w/ Calc⁷	Dynamics⁸	Materials⁹	Intro EE¹⁰	Signals¹¹
Diff Calculus¹²				P®P
Integral Calculus¹³						P®P
Vectors & Series¹⁴		P¬P	P®P		F®P
Multivar Calculus¹⁵							F¬P
Diff Equations¹⁶								P®P
Linear Algebra¹⁷		P®P									P¬P
Molec. & Struct¹⁸	P®P
Inorganic III/IV¹⁹									P®P
Osc & Waves²⁰										P®P

The first letter in each cell refers to the row course, and the second refers to the column course. P (partial) indicates that a subset of the class population participated in bridging with the partner course while an F (full) indicates that all of the students were involved. Arrows indicate the direction of flow of applicable skills and concepts. For example, in the Vectors & Series-Mechanics bridge, the entire Vectors & Series section (F) was also enrolled in the Mechanics course, but the Mechanics course contained students not in the Vectors & Series course (P). Material in the Vectors & Series course was adjusted to complement the Mechanics course, but material in the Mechanics course was not modified (one way arrows, ®). In contrast, in the Multivariate Calculus-E & M w/ Calculus bridge, material from the E & M course was imported into the Multivariate Calculus course and vice versa (two way arrows, ¬ ). Examples discussed as bridging models in section III are shown in bold face type.

Key to course title (discipline): (All courses listed or freshman and sophomore level.)

¹Introduction to Biological Macromolecules (Biology)

²Computer Science I (Computer Science)

³Inorganic Chemistry III (Chemistry)

⁴Mechanics (Physics)

⁵Mechanics with Calculus (Physics)

⁶Electricity and Magnetism (Physics)

⁷Electricity and Magnetism with Calculus (Physics)

⁸Dynamics (Engineering Science)

⁹Introduction to Materials Science (Engineering Science)

¹⁰Introduction to Electrical Engineering (Electrical and Computer Engineering)

¹¹Signal and System Analysis (Electrical Engineering)

¹²Differential Calculus (Mathematical Sciences)

¹³Integral Calculus (Mathematical Sciences)

¹⁴Vectors and Series (Mathematical Sciences)

¹⁵Multivariate Calculus (Mathematical Sciences)

¹⁶Differential Equations (Mathematical Sciences)

¹⁷Linear Algebra (Mathematical Sciences)

¹⁸Molecularity and Structure (Chemistry)

¹⁹Inorganic Chemistry III and IV (Chemistry)

²⁰Oscillations and Waves (Physics)

333 Ravenswood Ave.

Menlo Park CA 94025

Phone 650-859-2000

Fax: 650-326-5512

Abstract

I. Introduction

II. The Toolbox

III. Bridging Models

A. Strong Bridge (made use of bridging tools A,B,C,D,E,G)

B. Bridging Achieved through Separate Conferences (made use of bridging tools b,c,d,e,g)

C. Distributed Bridging (made use of bridging tools c,e)

D. Asynchronous Bridging (made use of bridging tools c, f)

IV. Outcomes

References

Materials⁹

P®P

P®P

P¬P

P®P

F®P

P®P

P®P

P®P

P®P

P®P

333 Ravenswood Ave.

Menlo Park CA 94025

Phone 650-859-2000

Fax: 650-326-5512

Abstract

I. Introduction

II. The Toolbox

III. Bridging Models

A. Strong Bridge (made use of bridging tools A,B,C,D,E,G)

B. Bridging Achieved through Separate Conferences (made use of bridging tools b,c,d,e,g)

C. Distributed Bridging (made use of bridging tools c,e)

D. Asynchronous Bridging (made use of bridging tools c, f)

IV. Outcomes

References

Materials9

P®­P

P®­P

P¬­P

P®­P

F®­P

P®­P

P®­P

P®­P

P®­P

P®­P

Materials⁹

P®P

P®P

P¬P

P®P

F®P

P®P

P®P

P®P

P®P

P®P