http://i.imgur.com/cgNzM.jpg

My kids thought the entire rectangle represented the 76 Billion, thinking that the 25 Billion should have been one-third, not one-fourth, of the rectangle.

Josh: But I think it almost ironic (well maybe totally ironic) we put all this energy into dissecting the graphs in this talk.

Granted. It seems there’s no shortage of places to have the policy debate, though.

Josh: Maybe I am in the wrong profession (is it a profession? I feel like a sparring partner).

Yeah, my sympathies. Seriously. Just as often as I find myself missing the classroom work, I think to myself, “Man, what a mess.”

We cut nearly three weeks from the school year because of budget shortfall. The curriculum did not get cut. Class sizes skyrocketed. When(if) things turn around, we will not be compensated for the heaps of work and stress we have endured.
Maybe I am in the wrong profession (is it a profession? I feel like a sparring partner).

I noticed the rectangular graphs that compares Available Resources ($76 Billion) to Budget Shortfall ($25 Billion), a ratio of 3.04:1.

I measured the rectangles of having respective areas of 561,267 pixels and 140,450 pixels, which gives a ratio of 4:1. At first glance it appears the ratios are incorrect.

However, I because the rectangles are overlayed, I wondered if I was looking at it wrong. If $76 Billion + $25 Billion is the total resources needed, then each rectangle represents their respective portion of those resources (those available and those lacking). In this case, the comparison would be ($76 Billion + $25 Billion) / $25 Billion which does give a ratio of 4:1.

Did your students find something different?

http://mgoblog.com/sites/mgoblog.com/files/Tressel_12A0A/image.png

There is another graph in his talk that caused my kids fits. It was the rectangular graph early in the talk. This led me to the same questions you posed. I wondered if the data presented in the rectangular graph was presented in a pie chart instead, would the kids still misread it?

If circles, the RADIUS of the larger circle should be ~144 times the radius of the smaller circle.

Since it was only about 32 times the radius, it actually represents an AREA that is about 20 times too small.

If it’s spheres, then the larger one is a bit too large, as the desired ratio is about 1:27.5

I would argue that at first look, circles would represent area. Unless the design of it hints towards a sphere. My example above had a shaded gradient on the circle which might make it look more like a sphere, so that is something I would remove to make it more accurate.

In the subsequent discussion folks in about equal parts argued: 1) that diameter of a circle is an OK way to show the data and 2) that area should have been used accurately.

I have to say that, as the instructor, I disagree with point 1 in favor of point two. This, leads me to my question:

If you see a circle, what do you think of first? It’s area? Diameter? Equivalent spherical volume?

I think human nature needs to be understood when viewing something like this. Only then can we pick the right representation.

What about LINES for linear comparisons? Rectangles for area comparisons? And shoeboxes for volumetric comparisons? The “anisotropy” of the dimensions may force us to see the relevant metric (volume, area, length).

???