In the summer of 2011, I attended a Modeling Workshop. It was an intense two week (~90 hours) course designed to introduce us to an interactive method of teaching known as Modeling. The basic idea of Modeling is this:
- Each unit starts with an experiment. Students collect data and learn how to properly represent and interpret that data.
- Students use the experimental data to construct a physical or mathematical model. For example, a student studying springs might realize that there is a linear relationship between the force applied to a spring and the amount it stretches by, which leads the student to develop an equation as a mathematical model of the relationship. A student studying atomic bonds might realize that the properties of bonds are similar to the properties of springs, so he or she develops a physical model of an atomic bond as balls connected by a spring. This is typically followed up by a presentation of results on portable whiteboards (a topic for another post), and the students are asked to come to a consensus on a model that explains their observations.
- Students apply the model they created to new situations and evaluate its applicability.
It was an awesome workshop, and it radically changed the way that I teach (by the way, there are Modeling Workshops for other subjects as well). We were even given a set of materials and a course plan that we could use in our classes. The only problem for me was that those materials were designed for high school physics, not calculus-based college physics.
In the following year of teaching, I used whiteboards and interactive methods of teaching, but I didn’t exactly follow the Modeling learning cycle as described above.
This summer I decided to spend some time redesigning the course so that I could incorporate more of the Modeling method. The example lab that I described in a previous post was my first attempt at this, and I recently did this lab with my students. The lab consisted of taking electric field strength and distance data from a simulation, then plotting that data and using it to create a mathematical model for electric field strength. After the lab was over, I went back to my office to plan the next day’s lesson. At first, I just copy-and-pasted the lesson that I used when I last taught the course; the lesson involved using a gravitational analogy as a means of deriving the relationship between electric field strength and distance. I was pretty happy with how that lesson went last time, as the students got to start with something that was comfortable to them and create something new from it. Having the students derive it also meant that they didn’t just have to watch me do it. Lesson done…time for lunch!
Later that day I realized something: we had already derived the relationship between electric field and distance in the lab! Sure, the gravitational analogy is cool and all, but why waste time doing a derivation when the empirical results had already done that for us in the lab? Creating the model in the lab had actually saved us a bunch of time…time that I will gladly use on more interesting things in the future.
It makes so much sense when I think about it now. We generally use regular class time to develop our physical and/or mathematical models, then use lab time to “prove” that those ideas were correct. In addition to other reasons I dislike those kinds of labs, they are not a valuable use of time. Using lab time to develop those very same models, though, means that we don’t need to spend regular class time on them. Instead, we can use our regular class time to practice using the concepts that they have learned.
The trick now is to see if I can come up with modeling-style labs for the other chapters we need to cover.