Maybe I’m just a mean old professor. Maybe. During a lab last week, I saw a group merrily going down the wrong path in their reasoning, and I said nothing.They were supposed to find the relationship between time and distance traveled for a ball rolling down a ramp, had carefully multiple data point and averaged at various distances, and had plotted them up on their graph. Only problem is they had only gathered data at relatively large distances (greater than a meter), so their data looked pretty linear, and were happily calculating the equation of the line that went through their points. I knew exactly what they were doing and that their result would give nonsense with regards to short distances/times, but I said nothing. Not yet.
Now, this is one of the SKyTeach classes for future math and science teachers, so there was a method to my madness. After all, it will only be in a few years that my current will need to be able to figure out errors made by their own students, so I figured it would be good practice to figure out their own. This is also the Research Methods class, where the whole point of the class is to learn how to figure things out by carrying out inquiries and not from some authority figure.The nominal goal of the activity we were doing—finding the acceleration of the ball—isn’t the real point.It was designing and carrying out an experiment, and experiments can be messing, with incorrect interpretations and all that. Furthermore, assuming a linear fit wasn’t such a bad idea; there is a whole branch of theoretical physics call perturbation theory that is all about trying to approximate non-linear relationships with linear relationships, since linear math is so much easier.
Yes, my students did figure things out. After getting their equation, I came over and asked them how far the ball would have traveled in a short period of time.They quickly realized that gave nonsense that the ball would have rolled up the ramp before rolling down, and I had only to point out they had not made any measurements at short distances for them to quickly be back taking more data. This time they got data that curved and realized that the curve had to go through the origin, resulting in a nice quadratic equation. The real result? Learning to make sense of the world for them selves. If we can produce teachers who can teach pre-college students to do that, that would really change instruction at the university.