## Circles and Data

### September 3, 2010

So, as part of this whole *Inquiry* thing, I’ll be asking my students to do some data analysis. Nothing that ought to be too challenging, but some manipulations they may have never been asked to do. In the spirit of “education” and all that, I thought it might be prudent to actually **teach** them the methods I expect them to use. Revolutionary, right? I know…I think I might be on to something here 🙂

[As an aside, last week I had a student walk out of a different class because he “[doesn’t] like to have [his] time wasted” with the “tedious bullshit” of having to learn the software he’ll be using to take data for the rest of the semester. Students. Sheesh.]

We started with something I assumed everyone was already familiar with: circles. In groups of 4-6 the students measured the diameter and circumference of 7 circles. I showed them how to find the averages and manipulate data in Excel, and as a class we made a chart of Circumference vs. Radius. Unsurprisingly, we had a nice straight line! I explained how this means we have a proportional relationship between our variables, and we can begin to write the equation: C ∝ r. Now this is a good start, but we’d like to do better….insert a trendline, find the slope, no big surprises: it’s π! We can now write a real equation: C = πr. Ta Da!!!!

So that’s all well and good, but not all of our relationships are going to be linear… what do we do when our initial graph isn’t a straight line? Try squaring things. For our forced example, Area would be the next logical step. Unfortunately, we were running out of time to have the class measure the areas of the circles, so I fudged some data. I showed them a graph of A vs. r (hey! that line’s curvy!!!) and A vs. r^{2} (hey! that line’s straight!!!! Now we know that A ∝ r^{2}!). Again with the trendline, and Ta Da!!!! A = π r^{2}

So how’d it all turn out? I think it went OK. I have some figuring-out to do with the data-sharing problem. Google Docs doesn’t have a trendline function (not an easy one, anyway), and I can’t seem to set the correct permissions on our college’s shared Student drive to allow them to save changes to an Excel file. Irritating. I didn’t leave enough time to complete all the activities, and they were definitely antsy by the end. I had to remind them that class is not over until 8:50, so would they please sit back down at 8:45 and listen for the next five minutes? It was a reasonable introduction to Excel, I think, but overall it was less the student-directed activity I wanted it to be, and after the introductory measuring it felt primarily like a lecture in which they were following along on their own laptops instead of taking notes. If I do this again next year, I would allot at least two hours for the activity, and give them a cheat-sheet of Excel commands so that they could work more on their own, and I could circle through the class to help as needed.

But no one, as far as I could tell, left the room muttering “tedious bullshit” under their breath. That’s a win, right?