Enabling divergent and convergent thinking in cross-disciplinary graduate students

By Gemma Jiang

Gemma Jiang (biography)

How can we enable graduate students to think in ways that open new possibilities, as well as to make good decisions based on diverse cross-disciplinary insights?

Here I describe how we have embedded 14 graduate students in a research team with nine faculty from four academic institutes, representing six disciplines (for simplicity only three disciplines – engineering, economics, and anthropology – are considered here). Our research addresses the circular economy. I have developed a three-step model (summarised in the figure below) to operationalize the “divergence-convergence diamond,” which is key to our teaching method.

The “divergence – convergence diamond” is widely used in design thinking. The divergent mode helps open new possibilities while the convergent mode helps evaluate what you have and make decisions. Both are important to cross-disciplinary collaboration. Divergence without convergence results in disjointed ideas without any impactful output, while convergence without divergence leads to “same old same old” ideas without a breakthrough.

The three steps in our teaching model are:

  1. Student meetings
  2. Three-minute pitch
  3. Convergence circles.
A three-step model to operationalize the “divergence-convergence” diamond (copyright Gemma Jiang)

Step 1. Divergence: Student Meetings

We have designed our bi-weekly student meetings to focus explicitly on fostering cross-disciplinary dialogues. Each meeting is facilitated to minimise structure and maximise creative ‘chaos’. We have two major types of meetings:

  • exploring the frontiers of research
  • topic ‘provocations.’

In meetings exploring the frontiers of research, each student is invited to pitch a research topic they would like to explore. The student team votes for one idea to focus on during the meeting, which is then examined through different disciplinary lenses. For example, in a recent meeting where the chosen topic was the social aspects of the circular economy, students from different disciplines shared their perspectives:

  • the anthropologist discussed professional identity and how the attachment to a fixed identity could trigger resistance to change;
  • engineers were primarily concerned about the technologies involved, and also brought up the importance of involving communities in developing and deploying technology from their past experiences;
  • the economist wondered how economic modelling could bring all the parts together.

In topic ‘provocation’ meetings, we invite students from one discipline as topic owners to start the meeting with a provocation on a topic and then foster cross-disciplinary interaction. For example, the economics student invited everybody to explore how the different disciplines could get involved in designing an experiment to test the feasibility of a “durability label” for products in the United States.

After the meetings, students have opportunities to continue to explore the ideas through collaborative writing and self-organized small groups.

When asked about their experience with these dialogue-driven meetings, one student said “These conversations are only possible because we have such a diverse team. We need to face circular economy as the complex system that it is. We can’t run away from the uncomfortable talks about our different worldviews.”

These activities enable students to “stretch” their divergent thinking through meeting themes, facilitation methods, writing initiatives and self-organized groups. Together they build a runway for deep thinking and cross-disciplinary exploration.

Step 2. Inflection: Three-Minute Pitch

Groups of students come together to pitch a research idea to the entire research team at the monthly whole team meeting. To qualify for a three-minute pitch, the idea has to be sponsored by at least three disciplines. This initiative facilitates not only the transition from divergence to convergence by clarifying potential research questions, but also the bottom-up dynamics by connecting students with faculty. In most cases, faculty advisors are invited to guide the development of pitch ideas and co-present the pitch with their students.

After the presentation, the pitching team receives coaching from the rest of the research team, followed by a participatory decision-making process to decide whether to move the pitch idea into a research project.

Step 3. Convergence: Convergence Circles

A convergence circle forms around pitch ideas that are chosen for research projects. Each convergence circle is a microcosm of the larger team with roles such as a process coach to help with the convergence process, academic advisors to provide subject matter expertise, and a circle captain to lead the team. In most cases, advanced graduate students are appointed to be circle captains, while faculty members experienced in cross-disciplinary collaboration volunteer to serve as process coaches.

We employ field-tested structures and processes to foster innovative thinking within such close-knit circles, such as liberating structures, design thinking, social labs, and agile methods. Outcomes of a convergence circle include scholarly outputs, such as peer-reviewed publications and conference proposals.


In my previous blog post, Three complexity principles for convergence research, I laid out three types of transformative containers. This post provides a practical model to operationalize one of them: the container for small, intensive transdisciplinary research teams and is especially useful in graduate student education.

Another application of the divergence-convergence diamond can be found in Carrie Kappel’s blog post Collaboration: From groan zone to growth zone.

For faculty readers: what has your experience been with teaching graduate students about divergence and convergence? What tools, methods or models have you found useful?

For student readers: what worked in enabling you to conduct cross-disciplinary research both divergently and convergently? Are there particular tools, methods or models that you would recommend?


Funding for this research was provided by the U. S. National Science Foundation Award, ID: 1934824, GCR: Collaborative Research: Convergence Around the Circular Economy.

Biography: Gemma Jiang PhD is the founding director of the Organizational Innovation Lab in the Swanson School of Engineering and the founding host of the Pitt u.lab hub at the University of Pittsburgh in the USA. She applies complexity leadership theory, social network analysis, and a suite of facilitation methods to enable transdisciplinary teams to converge upon solutions for challenges of societal importance.

24 thoughts on “Enabling divergent and convergent thinking in cross-disciplinary graduate students”

  1. Thank you Gemma and others for these posts and for contributing to this conversation. These teaching methods, as described, contribute to the field of education in BIG ways and can be applied in primary and secondary school as well as graduate studies. Thank you again for sharing. As Paul mentioned, I too am interested in hearing how these various projects develop over the next 6-12 months (PhD student at the University of Alberta, Canada, studying career integrated learning and interdisciplinary competencies in school communities).

    • Thank you for your interest, Colleen. Good luck applying the methods in your context. I would love to hear your stories as well.

  2. While my instinct reaction to the notion of diamond cycles was decisively positive, the Double Diamond (British Design Council) workflow representation includes a couple of essentials missing here. With one proviso of course, the ideals framing my observations are those of a design process, as opposed to brainstorming style workshops, I doubt that introducing a ‘pitch’ formalism makes up for that difference.

    First, progression through two distinct sets of divergent and convergent phases; provides a more explicit guide of actual activities. And second, accounting for the transition between two distinct stages of work (rendered as diamonds) seems to be more constructive that the proposed inflection point of pitching proposals.

    At the point of transition, the all important ‘problem definition’, captured in the first diamond, moves into the development domain, generally implying new roles and corresponding abstractions entering the collaborative space. Absence of explicit emphases on this translation or mapping from ‘doing the right thing’ (problem definition) to ‘doing things right’ could prove to be a serious drawback.

  3. Hi Gemma, thanks very much for sharing this model and your experience of using it. It is a very practical approach to how to get interdisciplinary groups of students to work on problems. I was just wondering whether, after convergence, the students took their ideas for research projects and further developed them into funded projects, papers, conferences, etc? Best wishes, Paul

    • Thank you, Paul. Great question. Our expected outcomes are exactly what you described–funded projects, papers, conferences. We are moving nicely along the trajectory, and it takes time, as we all know!

      • Thanks Gemma for your reply. Great to hear that the outcomes have a lifetime after the process – this should really cement and deepen the interdisciplinary collaborations. I would be interested in hearing how these various projects develop over the next 6-12 months.

        • Yes, absolutely. I would love to follow up on this. One quick follow up I can already give is that we are listing one of our pitch ideas, ‘material passport’, as one of our ’emergent projects’ that were not described in our original proposal, as we seek further funding for this project.

  4. Dear Gemma,

    Great to see a colleague at Pitt also working on this topic! I wondered how you attend to issues of power, particularly when race/ethnicity and gender are correlated with status at Pitt.


    • Hi, Chris, what a delightful surprise to connect with a fellow Pitt friend! Apparently we are doing similar things but plugged into very different networks. We should connect.

      I love your question about race and gender. Could you clarify if this question is for this NSF project specifically, or for Pitt in general? Only about half the researchers and students on this project are from Pitt, and we have three collaborating universities. So the dynamics are different…

      • Let’s just pick gender for now, but a similar story could be told for race/ethnicity. In every discipline, the higher up the food chain you go, the more male dominated it becomes (true everywhere and at Pitt in engineering). So, when students are female and faculty are male, how do you disrupt the double power dynamic? Is it worse in heavily male-dominated departments (ECE, MechE vs. ChemE and IE).

        And then there is the intersection of gender and ethnicity/race/culture, mansplaining, in my experience is pretty common in engineering students (at least at the undergrad level, according to recent studies at Pitt). When students are coming from more male-dominant cultures (common in engineering grad students), does this amplify the challenge in getting full and equitable participation in convergence and divergence phases?

        I’m also curious about power by ‘dominant’ discipline for a project. In my experience, each project has a primary discipline (e.g., it is more BioE than MechE or more ECE than IE). Does the likelihood of gender differences that are confounded by discipline disciplines complicate either divergence or convergence phases?

        Too many questions here, so I’d be more than happy with an answer to any of them!

        • Very thoughtful questions here, Chris. In terms of gender, we have 4 female co-pi and 4 male co-pi; 9 female students, and 5 male students. The gender dynamics is overall balanced, in my view. In terms of disciplines, we have 3 social science co-pi and 5 engineering co-pi; 3 social science students and 11 engineering students. Apparently the engineers are in the majority, but given the emphasis of our grant on convergence, our social scientists are quite respected and sought after. of course, not all the power dynamics is as healthy, but I do not feel comfortable to discuss it here in protection of identity.

          • Ok, sounds like you have built a uniquely healthy microcosm that will be challenging to scale! I also had positive experiences with collaborating engineers in the School of Engineering. When my collaborators left and I had to quickly take substitutes, the experience was less positive. 😉

            • That is the point, Chris, complexity is highly contextual. There are general principles we could abide by, but how it works out with each team configuration is so context specific–no principles can encompass all the human complexities.

              • I am worried about statements like “no principles can encompass all the human complexities”. It seems to deny the engineering or science of teamwork. I think it is on us to theorize, design for, and test approaches which are robust across more and less desirable starting conditions.

  5. Hi Gemma, very nice application of the divergence-convergence diamond to cross-disciplinary research and graduate training as described in your article! I like how you’ve operationalized the diamond through the student brainstorming meetings, three-minute pitches, and convergence circles. On the divergence side of the diamond, a strategy that we’ve used to foster the development of creative ideas among members of cross-disciplinary teams is the “idea tree” exercise as described in this earlier i2i blog article: https://i2insights.org/2019/03/12/idea-tree-brainstorming-tool/. Please let us know if you have occasion to try it out with your faculty-student research teams. I look forward to learning more about your research. All best, Dan

    • Hi, Dan, thank you for the comment, and for sharing your idea tree exercise. I just read your post, and really appreciated the ease of applying this method. It reminded me of the Round Robin method I learned in design thinking. Here is a post to learn more: https://www.mindtools.com/pages/article/round-robin-brainstorming.htm

      I am curious how you adapted the idea tree exercise for virtual environment. Did you use Mural as a platform?

      I use a method called 1-2-4-all, one of the liberating structures, to facilitate our divergence process.

  6. Dear Dr. Gemma Jiang.

    Thanks for your interesting insights. I, as a PhD student, agree with your concept and think that especially ‘provocation” meetings or other comparable spaces are needed to trigger cross-disciplinary approaches. During my studies as a Masters student and now as a PhD student at ETH (in Zurich Switzerland), I realized that especially the method “drawing a rich picture” helped me and my colleagues to first get the overall picture. All experts from the different fields were thereby able to put their puzzle part on the picture. Afterwards, we were able to jointly define a research question.

    However, I would have one question for you. Is this concept only applicable to cross-disciplinary research or also transdisciplinary research? Have you made any experiences with that?

    Thanks again and best wishes,

    • Hi, Irina, I appreciate your comments. I also really enjoyed reading your post on your experience with transdisciplinary research in the winter school (https://i2insights.org/2020/10/06/students-on-transdisciplinary-learning/)

      Yes, I use the word cross-disciplinary to refer to a wide range of research: inter-, multi-, disciplinary, and convergence research in a more US context. The common thread is bringing coherence to an otherwise fragmented system by bringing people together who are otherwise isolated. I believe this model is definitely applicable, esp. the divergence phase. We need to make room for our differences before hurrying to convergence, otherwise those unrecognized differences will becoming tension and resistance.

        • Dear Gemma,

          thanks a lot for this well-presented post. I wish I had had the possibility to follow a similar “onboarding” to cross-disciplinary research during my studies. It is great to see how you make an effort to integrate students into your groups’ work.

          The question that it sparked in me goes into a similar direction as Irina’s above, so I like to follow up here. I also feel that the setup you described in the post would work very well for multi- and interdisciplinary projects. Including non-academic actors would most likely make things way more complex, both logistically, but also process-wise, since you then need to invest even more time in finding a common language, boundary objects etc.

          Learning the relevant competences to lead such processes is crucial for students who like to work in transdisciplinary settings. At the same time, I would assume that most higher education institutions don’t yet provide spaces to develop these competences. So it might be worthwhile to explore whether the process outlined above could be adapted to transdisciplinary projects, and which changes would need to be made.

          (This is more a comment than a question.)


          • It would be very useful exploration, Jan. As you so wisely pointed out, adding non-academic actors would add additional layer of complexity, and all complexity is contextual, so further exploration case by case is definitely needed.


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