Deceiving graphs

I was surprised find someone on the TED talk circuit use a classic example of graph distortion that advertisers like to use to make the growth of sales look bigger than it actually is. Here's how they do it. (I'm using Sketchpad to demonstrate it.)

Circle C is almost 16 times
bigger than circle A.

Since the money total in 2000 is double that of 1990 it makes sense to show visually this doubling effect. If you want to enhance it and make it more than just mere doubling then use a circle graph where doubling the diameter actually produces an area that is 4 times larger as I did in this Sketchpad sketch I made.

In the actual diagram used in the TED talk, the diagram was definitely not done to scale. The area of the largest coin is 7 times bigger than the smallest coin though the amount is only 5 times bigger. Not outrageous but still misleading.
Scenes #38 (11.22.10)

Be less helpful? It Depends

Dan Meyer writes about teachers being less helpful in the classroom. For me that depends on the situation. Knowing when to step back and let a student "flounder" a bit can be useful, but sometimes it can do more harm than good. A swimming analogy may not be appropriate, but it comes to mind. Here's what someone wrote about learning to swim: "Contrary to popular belief never throw your child in the water to help them learn to swim." Apparently in China parents aren't worried about this; it's very commonplace. Now learning math is not as life threatening as possible drowning might be but for many of our students who are not intrinsically motivated to learn math it could be a problem to be less helpful.  I'm sure Dan doesn't have in mind to let kids flounder. His concern is that there is too much hand-holding and dependence of students on teachers to tell them what to do most of the time. What we want is to have students become independent learners so they don't rely on the teachers to have to crack the whip all the time. A blend of both (nudges and standing back) by the teacher applied appropriately yields the best results.

A historical note:
Logo the programming, learning software environment that Seymour Papert championed in the 1980s and got such a splash from the media lost some its sparkle when too many teachers expected Logo to work its magic all by itself and were "less helpful."  Guidebooks were written to try to help with that, but that didn't allay the public perception that Logo doesn't work. Withholding help in a teaching sense is a skill that needs to be carefully applied.