Aligning the physical science midterm with the course

The midterm examination has, in the past, been an aggregation of the in-class quizzes and tests for the first half of the class. These quizzes and tests, however, have gradually been replaced by activities and content as the course has matured. This term midterm arrived with only a single quiz at the end of the first week having ever been given. The midterm as given spring 2019 was no longer aligned to anything the students had actually done.

The core of the course is now firmly structured around measurement and the language of mathematics to describe relationships between measurements, doing science. Engaging in research into simple physical systems. Content is encountered in the context of experiencing the phenomenon. In light of this, the midterm as written was no longer aligned to the course.

This term I decided to start from a blank sheet. The students would be provided with novel data, freshly gathered, and asked to analyze the data in a single 50 minute period. I wanted the exercise rooted solidly in the real world, so the data was gathered during the class period. I opted to use the swizzle rate versus velocity for a RipStik. This is reasonably linear up to about 3 m/s for me, and I could slip in a 0 Hz, 0 m/s point by using a constant state velocity hand waving argument. That is the argument that any given swizzle rate there is a constant continuous velocity for that rate after initial conditions settle out. For this to hold, I used a longer stretch to come up to speed prior to traversing the speed trap. I also extended the speed trap to 10 meters and shifted to using meters per second for velocity. I also measured the time and counted the swizzles until the final run.

Run start, headed west

I started the run slightly further to the west for a westbound run giving myself space to come up to a steady state velocity for a given swizzle frequency. This also helped me prep to time the run and count the swizzles.

Run end, 10 meters west

I carried my clipboard while making the runs, jotting down results on a scratch data sheet at the end of each run. I had to calculate the swizzle rate and velocity for each run: I was not looking to the students to figure out how to do this. The data alone would keep them busy.

RipStik Swizzle frequency versus velocity data

At the end of run four I knew I was near the point at which the relationship starts to flatten out, where decreasing amplitude offsets the increased swizzle rate and velocity levels off. The time was also 12:20 and I wanted the class to have time to write up their analysis.

As they had done in laboratory, and as scientists in this day and age often do, the students worked in teams. I required that the teams be pairs, two students. Solo was an option, but no student chose to work alone.

I had strongly suggested that the students form pairs such that at least one partner had Desmos. At the start of class I took role and recorded partnerships so I would know who was working with who, and to establish early on the separation of the partnership pairs.

The students would wind up working longer and harder on this midterm than on any prior midterm in the history of the course. None would finish by 12:50, and some pairs stayed until 2:00, working for 90 minutes on their analysis and write-up. Write up was by hand. Their work was framed by the following:

In the demonstration and data gathering phase you will gather data on the swizzle rate and velocity of the RipStik. You are to use this data to explore the relationship between the swizzle rate and velocity of the RipStik. Note that swizzle rate is in swizzles per second, velocity will be in meters per second. Show your data on this paper, make a hand sketch of the graph you make in Desmos. You should provide data based support for your discussion, analysis, and conclusions. Write up your work on this paper. Work alone or in pairs, put both names on the paper if working in a pair. Consider the following:

• What is the nature of the relationship between the swizzle rate and the velocity of the RipStik?
• How is the swizzle rate related to the velocity of the RipStik?
• What is the mathematical equation for the relationship between the swizzle rate and the velocity of the RipStik?

Write up your discussion, analysis, and conclusions using complete sentences. Explain your results. 

Preliminarily, the students appear to have well approached the problem and pushed through to a reasonable analysis. I would note that the data came out particularly well aligned with a linear model, which was as I hoped. I had worked hard to achieve a minimal swizzle low speed pass that is often missing from the statistics data. 

With attendance and partner selection occupying the first few minutes, only three runs were done by 12:20. And, as noted, students would take up to 90 minutes to work on their results. I was also pleasantly surprised to see the slope near one in mks units, this was not something I had previously stumbled into because in statistics class the software generates a y-intercept value. These points, however, suggest that in a steady state the existence of an apparent y-intercept might be spurious. Of course small sample sizes more easily lend themselves to spurious linear relationships. Still, there are hints in the data that below 3 Hz the data is well modeled by a linear with a zero or near zero intercept. 

The student pairs worked diligently and quite separately from each other, this was pleasantly surprising. They worked harder than students working solo on the traditional midterm in the course have. This caught me off guard. Perhaps the midterm was better aligned to the skill set I have helped them develop: they had the tools they needed to tackle the system and did so with some confidence. As note, a preliminary analysis suggests the students well tackled the system and found working mathematical models supported by the data, and then explained what they thought is happening. 

The only way to know for certain is to replicate...