Throughout the day, I’ve seen and been a part of a great discussion about how to do the Modeling Buggy Lab. For those not familiar, think classic algebra problem with 2 trains. After screaming, “I hated that problem!” Ask yourself what did you dislike about it? Probably the fact that it had no context. This is where modeling steps in.
Here’s the set up, you show the class a motorized car that moves at constant speed. And, through socratic questioning, lead them to realize that the position and elapsed time are related. You then ask them to determine the “graphical and mathematical” relationship between position and elapsed time (or clock reading). You leave it up to the students to figure out how to find those relationships.
If you try this, your students might come up with one of these two solutions, (A) set up fixed distances and measure the time to travel those distances, or (B) place marks at distances for fixed values of time (place a piece of tape where the car is at 1 sec, 2 sec, …)
This is where are tweebate begins. Since the “convention” is to plot the independent variable on the horizontal axis, the two different means of collecting data would produce two different plots. Option A, since the student set up fixed distances, that would be the independent variable. Thus elapsed time (clock reading) would be on the vertical axis and distance traveled (or more specifically position) on the horizontal. Option B would yield the opposite.
Our debate was whether or not we should let this happen. Also discussed was the above was ok, but to just tell them to all plot time on the horizontal axis.
So here’s my two cents:
What I love about the modeling curriculum is that we (teachers) are trying to foster discussion, which in the end should induce critical thinking skills. So to me, let the students measure it how they think they should. Let them graph it how they think they should. As they all come together in the “Board Meeting,” where they share their results, as the teacher try to help them draw out the important conclusion. Did the two methods produce different results? Did both methods produce a straight line? What does that say about the relationship between position and time for the buggy? Assuming the buggies go at the same speed, how do the slopes compare? If some have a slope that has units of m/s and some have s/m, lead them to generate the algebraic equation for the line. Have one group rearrange their equation