Hi Kelly,

I guess my main point is this: I can use Newton’s 2nd law to create a single computational model that is good enough for modeling objects moving at constant velocity/balanced force, constant acceleration, and non-constant acceleration. Students can use this one computational tool to explore all of these ideas, and use it to model the movement of real objects moving around in front of them.

As you said, there is great value in the experience of taking data, but if the set-up does not work (for reasons unrelated to student assumptions or misuse of the equipment), it diverts resources away from the experience of digging in to the measurements students want to make and figuring out what these measurements mean. If the results match observations, this can be a good entry point for learning why. It’s also interesting because if a student asks if they could see acceleration vs. time data for an object in the model, I can simply make that an output. This is a lot easier than trying to locate/attach/troubleshoot an accelerometer just to be able to see what that data looks like.

As for the experimental set-up, I started on the air track because I was using fans that I attached to the air-track carts that weren’t strong enough to propel carts on a horizontal surface with friction. The problem with the data is definitely related to the ultrasonic sensors I am using (Vernier) – even for walking/generating graphs in the constant velocity model, the students needed a 2 ft. square piece of cardboard to avoid getting sudden spikes in the position vs. time data. The system was sensitive to ANY changes in the angle of the surface facing the sensor. I’ll see about posting pictures of the set-up and data if you are up for chatting about it.

It sounds like you just need help diagnosing what’s wrong with your equipment. So far, it sounds like the sensor isn’t seeing the object. Why are you using an air track? I’ve never seen anyone do that for the acceleration lab. Can you post a screenshot of what the data looks like and a photo of the setup?

Also, I’m not sure how your third point is satisfying. It still sounds to me like you’re programming a model, then using the program to find a pattern and build a model. Maybe I just don’t understand your point?

Hi Kelly,

I agree with you on the danger of hand waving-as-instructional-model, and it is lurking there in the back of my mind as a foil to the devil that tells me that Python makes it so I never need to do an actual lab again. (Eeek!) Here are the reasons I have come to terms with using this method for collecting data for an experiment:

• When I was working to set up the air track and ultrasonic sensors, I found that the data really was only correctly measuring distance vs. time during a very small portion of the overall movement of the cart. There was noise in almost every data set for position that was so jagged that the numerically differentiated velocity vs. time would have shown very little usable data. Whether this noise was because of an angle between the detector and the cart, vibration, or some other phenomenon, it was always there. I was staring at this data and picturing conversations with students that focused on analyzing the part of the graph that looks how they expect it to look. In other words, putting the model first and the data second — not at all the modeling instruction method. If they are going to observe velocity vs. time and look for a pattern, there needs to be a discernible pattern to the data to be found. Otherwise, that’s a very different kind of hand-waving.

  We shouldn’t need to tell our students to ignore large portions of data because they don’t seem to fit a model that they haven’t come up with themselves or don’t understand. Accepting that I was not able to generate the position vs. time data using this method, I knew the table of data generated through Python would at least give position and velocity data that students could analyze as they did for developing the constant velocity model and realize that this model was not appropriate in this situation. It was a short term solution that ended up working really well, hand waving/black box issues aside.

• My first Python and Geogebra models for the object were analytical models, and that did/does bother me a lot. It is just a set of data calculated through the presumption (hand-waving, sure) of constant acceleration. I was honest with the students about the fact that one program I gave them was a ‘constant velocity’ model, and that another one was a ‘constant acceleration’ model. These models were based on what they figured out looking at data though, not just an equation. Our time in class was spent taking the computer model and matching it to the data or information in a given situation. This requires the same set of skills as solving problems procedurally (as I have done in the past) or using a graph of velocity vs. time to do everything.
• My final point on this is the one that really lets me sleep at night. The free fall simulation is an ODE solver rather than a kinematics equation evaluated at different values of t (which is what my analytical model programs were). It simulates how an object would actually move through solving Newton’s 2nd law. Whether the computer is solving this ODE, or nature is (as it does when doing an actual experiment), the end result is the same – a set of answers to the question ‘where is it, how fast is it going, etc’ in the form of data. If students are to explore how something moves, and why it might move that way, they can do so in the classroom by throwing a ball in the air and taking data. When they leave my classroom, they can’t take data anymore. With the computer simulation, they can. They still have to analyze the data and look for patterns, but the difficulty of getting that table of data is significantly reduced.

I understand and have seen the problem that comes with calculator use. This is different though. The calculator is usually where we (and students) turn to get a single number as an answer. The computer instead generates a whole bunch of calculations based on an organizing premise, and students then have to analyze the results and really understand them to answer the questions we give them. I think the big piece I like is that for some students, a graph is a bit more of an abstraction than they really understand. A student might hear ‘graph’ and connect that to math, and that they don’t like math, and that the graph reminds them of all of the things they don’t like about math, and then that student has suddenly shut down answering the question. That’s a step in the wrong direction.

It’s inefficient, and ideally we want to push them to see why the graph is a better representation than a table of data. Still, I had one of my weaker students look at the position vs. time data and estimate when velocity was zero with seemingly little effort, while being unable to do so from a graph. That’s hard for me to ignore. If a table of results is concrete enough for my students to be able to answer these types of questions, that’s a good enough starting point for me.

I had that problem in a big way with my central force lab before. I did a better lab last year (not a simulation), and it was awesome (haven’t written it up yet). If it doesn’t seem a bit hand-wave-y to them, does that bother you? Shouldn’t it bother them?

Also, do you find that adding many layers of technology obscures the physics (sort of in a parallel way to your note about getting caught up in taking data might obscure it, though I’d have to disagree with the taking data part—taking data, even when it takes a while, can be awesome—when they really understand what they are doing and are invested in it, they start to see patterns as they go, and they get more and more eager to see what the graph will look like—that’s increasingly true as they become more skilled and experienced through the year)? I find that even using a calculator can make most of my students stop thinking. At least, they stop thinking about physics and defer to the mightier and more knowledgeable being—the calculator. If they were using the computer to do most of their physics work, it seems like that would be amplified quite a bit.

I don’t mean to sound really negative. Just some of the things I’ve been thinking about (in my own work) lately, and your post prompted some sharing of that musing.

I love his use of the robots – I’m convinced it is the absolute best way to teach the kinematic models. I’ve thought about doing this with LEGO robots, but I haven’t spent the time to address the limited resolution of the rotation sensors in the servo motors. His work deserves to be highlighted by everyone that sees it.

I’m happy with what the simulations have done (and will share more in a future post) about my next steps with the idea. That doesn’t change the fact that I’m really impressed with the robots and the videos he posted on his blog.