Buggy data was analyzed and results were displayed on the whiteboards below using our standard four quadrant board system. (As described in the bouncy ball post)
We are still perfecting our abilities to effectively communicate via white board but I would say they did a nice job over all.
Now, down to the nitty gritty: I/we planned our investigation very carefully how should we go about making some sense of all of this data.
Commence board meeting.
First, I sugguest that we sort the boards into some arbitrarily choosen groups, they decide that graph shape is the most obvious way to group them. Thus, we get three groups; two boards in each group.
*positive slope, 0 y-int.
*negative slope, 0 y-int.
*negative slope, + y-int.
Students are asked to explain how the slight differences we planned have accounted for all of this different data. They immediately identify that groups cars had different speeds and each grroup has a different slope so angle of the line represents how fast the buggy goes. Okay, that’s the easy part for anyone who’s made it through algebra II. But I make them go further, “What about your data supports this claim? One group catches on that the units on their slope are cm/s, a unit of speed. Hooray. They have made a claim and supported it with their data; I am so proud. They definately are not wrong but it is time to tear them down a little. After careful inspection of a few more boards I point out that not everyone’s slope has units of cm/s. I see at least two s/cm; what about those? Students easily decipher data collection technique as our culprit for inverse slopes. Thus begins the “Independent vs. Dependent” variable discussion. They all know the convention of independent variable goes on the horizontal axis and have obeyed it.
What good is a convention that even when followed gives us “backwards” data. Who’s version of slope is superior/inferior? It takes them a really long time; nobody wants to say that the others are wrong. Finally, someone suggests that we are used to speed measurements given in units for distance per unit time like mph or m/s. Why do you suppose speeds are reported this way on road signs and on speedometers? Again, a long pause for thinking; eventually there is mention that time/unit distance seems illogical and is immensely less intuitive than the distance/unit time. So we have finally concluded that the superiority lies in the usefulness/interpret-ability of the slope. Neither group is wrong; both slopes tell us the same info but one is just easier to interpret that the other. I indicate that this could be a useful footnote to add to our axes labeling convention. Normally, we can place independent on the x-axis and dependent on the y-axis; but before we do that we should take a moment to consider which version of the slope seems to be a more intuitive interpretation of the data. If I had guided them in their data collection techniques everyone would have gotten data in the same way, produce graphs with the same axes, and had the same units on their slope; we’d have missed out on a very important discussion and decision making process.
We spend the next 10 minutes piecing together the significance of their y-intercepts and the signs on their slopes. Students leave with a good idea of how things need to be done in physics class.