Subject: Closed Loop Problems

Posted by Niall Palfreyman on 11/10/2009
In Reply To:Closed Loop Problems Posted by Tim Joy on 11/9/2009

Message:

Tim Joy schrieb:
> What is the first Closed Loop structure you present to your students?
>
> Tell a brief story that lets us in on your lesson and your students' process. Ultimately, how do they do?
>
My students are undergraduate biotechnology majors with a biology background from school, so that my first task with them is to get them up to speed in mathematics and physics. Their first closed loop is radioactivity (in physics), and population growth (in maths). They get these two fairly close together towards the end of their first semester.

I've tried using stock-and-flow diagrams in the first semester for these loops, however the real need for the diagrams only comes in their 4th semester, where we start looking at dynamical systems in general. The result was that the diagrams were kind of stuck in the middle of a sea of unrelated stuff, which meant they didn't really take them on board. I tried massaging the rest of the first semester material to do more with stock and flow diagrams, but it became awkward because the diagrams weren't really appropriate to the content, and I had to constantly explain aspects of the diagrams which weren't relevant to the aims of the course.

An example: SHM. I still use stock and flow diagrams to build a simulation of simple harmonic motion, but the students no longer see the diagram, but just study the behaviour of the model. The reason: the standard formulation of Newton's second law is F=ma, which is a second-order differential equation. In order to turn this into a 2-stock diagram I need to use the second law in the form F=dp/dt, which they find significantly harder to understand (or, which I find significantly harder to explain coherently). So since I'm already up to my eyeballs with content I find difficult to explain, I don't show them the diagram.

So the bottom line: My students see various examples of closed loops in their first semester, but I only formalise these as diagrams in their 4th semester. I must confess I feel a bit feeble as I say this, but that's the workplan I've come around to.

Best wishes,
Niall Palfreyman