I became interested in the determination of optimal engineering constraints in open-ended learning experiences when adapting a spaghetti bridge project, that I had previously taught online to elementary teachers, to middle and high school engineering students.

When I initially did not constrain the amount of pasta and glue, most students created very strong structures with large amounts of glue providing much of the structural support. This was especially true of middle school students and not as much for high school students, with one exception. When I previously taught this project to teachers, teachers also build traditional bridges with spaghetti trusses and used glue only to connect the beams. Let’s call this the minimal constraints case. See below for some middle school examples.

After I noticed that the bridges were basically indestructible and mostly made of glue, I decided to try and further constrain the problem to see if the results would be more in line with real bridges. When I constrained to 40 linguine and 2 glue sticks (and the addition of a rubric that included aesthetics and other considerations), the results were much more aesthetically pleasing and in line with actual bridges. Let’s call this the fixed constraints case. See below for minimally constrained (top) and fixed constraint bridge (bottom) from the same middle school team.

My next thought was to change from fixed constraints to a fixed cost where students could choose/buy materials based on what they had designed – so each piece of pasta has a value as well as each glue stick with the bridge required to support a certain amount of weight at the lowest cost. This makes the problem even more realistic in terms of providing cost based engineering constraints. High school students built a second spaghetti bridges under this fixed cost, variable materials case. Students built realistic bridges and furthermore were more “spare” than the fixed constraints middle school bridges, reflecting consideration of the cost constraint. See below for minimally constrained and fixed cost, variable materials bridges made by a high school student.

Here’s another example of a minimally constrained (bottom) and fixed cost, variable materials (top) bridges made by the same high school student.

Taking the fixed constraints case (but would also apply to fixed cost, variable materials case), we could theorize that as the constraints are made tighter, there would be a frustration point and the project would be too hard. Likewise, if the constraints were too lax, it would turn into the minimal constraints case. So I got to thinking about whether there was some optimal constraint that exists for engineering problems given to students. This is reminiscent of the notion of trade-offs in engineering.

I did a literature search of academic papers but could not find any previous research on this topic. I also consulted with two leading academics in the field, who reported they were unaware of any research on this topic. It would be interesting to try and set up some experiments to find the optimal constraints for different age students for this project. The research questions might be:

- What is the optimal constraints value in the fixed case that is not too strict (frustration) and not too lax (not realistic)?
- Should this differ for different students or teams to differentiate the project?
- At what age, should the most realistic fixed cost, variable materials case be used?
- What learning does or does not take place in each case and how does it differ?

I did capture some artifacts in my first go around on the project. The first was a question to high school students in their project documentation. Three students did not answer the question. Students reported that the more constrained bridge was harder to design and construct.

Question: compare and contrast the minimally constrained and fixed cost bridges both in terms of your engineering design process and the final result.

Student 1 (HC)

*The minimal constraints bridge I paid little attention to the amount of materials I was using. I just used as much as I wanted until I thought it was as sturdy I could make it in the time given for construction. I used the glue very liberally to make the connections as strong as possible. For the constrained bridge, I more thoroughly planned out my design for it to be as strong as possible using the least materials. Also I only used as much glue as I needed as to not run out of glue and have to buy another. *

Student 2 (LK)

*Between my two bridges the first one was stronger and could support more. This is because we could use as many resources as we wanted and the second bridge we had a limited amount of resources so it was harder because we had to be cost efficient. *

Student 3 (ML)

*Both followed a similar rectangle design. But, the unconstrained one used too much glue. The unconstrained one would easily succeed.*

In summary, I found that minimally constrained bridges didons not generally produce a realistic civil engineering experience. Younger students seemed less constrained by traditional notions of bridges and produced very creative, strong, glue heavy bridges while adults and high school students were less likely to do so. At this time, I am planning to use the fixed constraints case for middle school students and use the fixed cost, variable materials case for high school students. Further experiments are possible to further refine and answer the proposed research questions. I have four rotations per year of middle school students, which provides opportunities for further research and refinements.