Combining An Inquiry-Based Approach with Multiple Representations of Complex Systems
This is a pedagogical framework - or architecture - for doing collective inquiry on a central complex problem. The inquiry is inherently collaborative, team-based, and socially complex. The inquiry process is organic, flexible, adaptive and emergent - just like complex systems are. Students work with multiple representations that attempt to model, define, characterize, visualize and conceptualize key features and behaviors in the complex system under study. The inquiry process also mimics the process of real human inquiry into a complex problem. Thus, we think this inquiry framework is well aligned with the nature of the problems and systems being investigated.
- Students will be able to utilize multiple representations of complex systems. Here, a "representation" can be a model (computational, statistical, probabilistic...), a visualization, a data set, a concept map, a physical or kinesthetic analogy, etc. The use of the term representation here is meant to be broad.
- Students will be able to assess the value (pros and cons) of a representation for a complex system.
- Students will be able to synthesize different representations to explain a complex system.
Assessment of Learning Goals
Students will link evidence from multiple representations to explain a complex system or answer a question about a complex system. Formative assessment might involve presentations to one another about their representations (Learning Goals #1 and 2), while summative assessment could take the form of an essay or concept map (Learning Goal #3).
The Approach: An Inquiry-Based Teaching and Learning Cycle
Choose a Problem to Study
This can be chosen by the instructor of a course, or collaboratively by the students and instructor.
Pool Your Knowledge
As a class, work in discussion and other ways to collectively define:
- the nature of the problem
- what we (collectively) know
- what we need to know
Make initial concept diagrams of the relevant systems (flows, reservoirs, system parts, relationships, processes) that captures the collective knowledge of the group. During this process, be sure to address any naïve conceptions and misconceptions. This concept diagram will evolve!
Do the Research
Use your concept diagram to figure out how to break the problem down by investigative methods that could include:
- Computer modeling, using STELLA, NetLogo, EdGCM, Mathematica, or other software
- Exploring existing data sets and/or visualizations of them
- Researching the published scientific literature
- Physical modeling
Break into groups/teams with each team taking on one investigative method. Each team will gather and interpret data, as appropriate, keeping in mind that the ultimate goal is to inform the central question. The instructor needs to be ready to guide each team toward some productive pathways. Especially for students who are not used to open-ended inquiry, scheduling regular check-ins for each team with the instructor can forestall considerable frustration. What each team produces can be negotiated with instructor, but it needs to be shared with the class and instructor. Also, each team should be prepared to report their assumptions, the limitations and strengths of their approach, the outcomes (results, predictions, lessons learned...), new directions for inquiry, and questions raised.
Find an appropriate communication pedagogy by which to share information with rest of class. There are many ways to do this: poster session, group oral presentation, white papers that circulate and get discussed, etc. In the jigsaw method, you form new groups with at least one member from each of the original teams, and students are responsible for teaching each other what they've learned. Whatever approach you take, the goal is for every student to learn the results from every team.
Circle Back to the Problem
At this point, the class will be ready to formalize their newly developed conceptual understanding and connect it with established science knowledge and practices. You can use the class' initial concept diagram as a focal point for this conversation: have students add to and modify the diagram based on what they've learned. If appropriate, revisit your collective assumptions, knowledge base, knowledge gaps, etc...
Reflect on the Process of Inquiry
Spend some time as a class comparing and contrasting the various approaches that teams took and the representations of the system that they found or developed. What do these approaches and representations tell us, show us, or help us understand? Where do they fall short? What are their strengths and limitations? Which approaches and representations are most salient to the problem? Could we have addressed the problem without certain approaches or representations?
In short, what have we learned about how we are studying this problem? This is a very metacognitive stage. The goal is to reflect on the approaches and representations, and ultimately on the process of doing research (=inquiry). Instructors may find A Teacher's Guide to Relative Merits of Different Representations (Microsoft Word 29kB Apr20 10) helpful in guiding this discussion.
Define Further Inquiry
How you proceed at this stage depends on course context, time, and learning goals. It is up to the instructor to decide what will best serve the class. Some options for moving forward might include:
- Redefine teams and cycle through other approaches.
- Start a new aspect of the original problem (perhaps one of the questions raised by this cycle) or a brand new problem and direction for inquiry, with new groups. Use the same pedagogy, but revisit the various approaches and representations in the context of a new problem.
- Tackle a new problem, and pick up new approaches and representations.
- Invite interested students to work with you on a related research project during the coming semester, summer, or year.
Scaffold Student Independence
If you use an open-ended inquiry approach multiple times in a single course or a linear curriculum, consider guiding and facilitating students carefully the first cycle through (as in Guided Discovery Problems), and then passing increasing responsibility to students (coaching less) in later cycles (e.g. Investigative Case Studies). Giving increasing responsibility to students for their learning is empowering; watching them take on that responsibility is exciting.