Here are the content objectives for the unit (from the Teacher Notes):
- Experimental design
- Build a qualitative model
- Identify and classify variables
- Make tentative qualitative predictions about the relationship between variables
- Data collection
- Select appropriate measuring devices
- Consider accuracy of measuring device and significant figures
- Maximize range of data
- Mathematical Modeling
- Learn to use Graphical Analysis software
- Develop linear relationships
- Relate mathematical and graphical expressions
- Validate pendulum model*
- Lab Report
- Present and defend interpretations
- Write a coherent report
Here's what we did in class:
The first discussion focused on a dowel, what we could measure about it and how we could make those measurements. (Note: measure, not calculate.) Once we had a good list, we moved on to what we could change, and what making those changes would affect from the list of things we could measure. It was a great way to introduce the idea of physical variables (though we never mentioned that we were talking about variables).
From this discussion, Bryan, our facilitator, picked two quantities we had stated were related (if we change the length, we change the mass) and asked if we thought we could find a relationship between the two. Everyone nodded and he asked us to explain how we would do that. There was a quick consensus that we would measure the length and mass for dowels of differing lengths. Then, with some quick questioning about the important parts of communicating our findings, Bryan set up the expectations for what our lab notebooks should look like. This laid the ground-work for presenting and defending our work.
So we moved into collecting, recording and analyzing the data. We had a lot of options for how we wanted to analyze our data. My group chose to use Excel. Others used Google Spreadsheets or their graphing calculators. We had Vernier's Logger Pro available to us, but I'm not sure anyone used it. I'm torn as to whether I would require my students to use Logger Pro, since that's what we'll be using to do video analysis and when we use our motion sensors, etc, or if I want to let them use whatever they're comfortable with. I'll check with our other math teachers, to see what they use with our girls when they introduce stats.
Once we had our data graphed, the linear fit was the clear choice. Bryan had told us which information from our lab notebook he wanted to see on our whiteboards, so we drew our predictive graph, our quantitative graph, our equation, and our qualitative observations.
When everyone was ready, we circled up for a discussion of our results. This is where we were introduce to the rules for discussion:
- Circle up - No one should see your back.
- Be respectful - No declarative statements. Ask questions.
- Listen before you talk.
- No hiding behind your board.
The highlight of our discussion for me was the analysis of the vertical intercept - most notably, the 5% rule. I've always struggled with deciding when you can neglect the y-intercept, and I think this rule is a fantastic one. If we suspect that our line of best fit should go through (0, 0) - that is, if it makes physical sense that when the independent variable is 0 that the dependent variable will also be 0, then we check to see if the y-intercept is less than 5% of our largest dependent value. If it is less than 5%, we can ignore it. If not, we have to consider it.
Once we wrapped up this first lab, we moved on to explore more relationships in the Lab-a-Palooza. We did 7 labs at once, investigating 7 different relationships. This let us practice the methods we'd started to use in the Dowel Rod lab, and allowed us to explore relations other than linear ones. Several of the labs still had linear relationships, but there were also quadratic and inverse relationships, and some had non-zero vertical intercepts. For each lab, 2 groups created a whiteboard. While we discussed some of the same issues as we did in the first lab, the highlight for me this time was the idea of choosing the fit that made sense. When looking at the Balance Beam lab, we had an argument between whether it should be an inverse fit or a quadratic fit. The arguments against the quadratic were what really caught my attention. First, a quadratic equation would have to eventually turn back upwards, meaning the object we were using to balance the beam would have to start moving away from the fulcrum again. (See how the discussion of what happens on the graph connects to what it would mean in the real world?) Second, a quadratic graph would have to intersect with the vertical axis at some point. That would mean that 0 mass would balance the beam at some (very large) distance from the fulcrum. Since both of these situations are untrue, the best choice is the inverse graph. It's a type of reasoning I have never seen my students use, but I'd sure like to!
This is where we wrapped up Unit 1. I could see breaking the 7 labs up into two sections, so we have more practice with these methods before moving on to Unit 2. Part of me actually wants to do 12 labs total, because I want students to see a few more inverse and quadratic relationships before we move on. But the rest of me says that probably isn't a great idea - we'd get bogged down doing lots of experiments whose content is meaningless at this point.*
I have spent time at the beginning of my courses talking about the types of relationships we'll see in the class and what they look like on the graphs. I also give an overview of how to interpret some of those features, but that part is brief because I want to have meaningful data to interpret. This unit is a much better version of what I do, because 1.) I won't be doing the talking and 2.) we'll have data that has physical meaning to interpret. We can practice interpretation of the data and the graphs right away. I'm excited for the beginning of physics now!
*I'm not sure how I feel about doing experiments now that will come up in later units. Why is validating the pendulum model important now? Isn't it enough to use this (and any others) in the appropriate units?