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.

Are page numbers becoming obsolete? Check out how a Kindle app handles them

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Since I don't mind and actually kind of like to read (as well as listen to) books on my iPod Touch and I'm not going to spring for a Kindle (though the "experience of reading*" might be better) anytime soon, I discovered I can use an app for my Touch that will let me read books I buy on Amazon.com intended for a a Kindle Reader. At the moment I'm enjoying reading "The Science of Liberty" by Timothy Ferris. One problem I have is knowing what page I'm on. You see eBooks for Kindle do not keep track of location by page numbers but rather according to units dependent on bytes (1 unit = 16 bytes or 16 characters.) It really didn't matter that much as long as everything worked properly, but since electronic devices have a habit of causing trouble, so when I had to reinstall my operating system on the Touch I lost my location in the eBook. I knew what chapter I was in (because I printed out the TOC of the physical book from the Amazon website)  so I searched for the title and found my location that way. But what if I didn't know the name of the chapter or remember any key words on the page** that I was last reading?

This is a 4 unit location.
The final unit is at 8486.

I scratched my head and figured I could set up a function relating the number of units in the eBook with the total pages in the real book which is what I did. The accuracy was not great. Anyone one out there want to do another example and check the accuracy? Download any free Kindle book. Check out how many units long it is. Comapre that with the number of pages the physical book has. Let me know what you come up with. (I'm being purposely "less helpful" here to honor Dan Meyer who has coined the phrase in a teaching math context.)


*Positive attributes of reading on a handheld: All the usual suspects including: easier to carry and manipulate device; you can carry more books and articles than you probably can read in a life time etc. But also the most important one for me: I don't need a lamp to read at night since my wife can't sleep if there is any ambient light on. And so far the back lighting of the ipod touch doesn't bother her.

**Chronological pages on the screen depend on factors such as font size and the size of the screen. So the units used for the numbering system is based on the number of alphanumeric characters used in the book. So 1 unit in a Kindle eBook is 128 bytes or 16 characters (which include spaces and other punctuation.) My Science of Liberty ebook has 8486 units which means 8486 * 16 = 135,776 characters.

The Monty Hall problem revisited

This is one of my favorite problems because it always baffles me why its so hard to get to "know" the solution. Every time I come across and read it, it's like I'm seeing it for the first time.  Holding an intuitive notion of the solution always seems to elude me.

I came across it again today. This time on video explained by Keith Devlin who is a wonderful explainer.

http://www.stanford.edu/~kdevlin/Movies/MontyHall.mov

More about Keith, Monty Hall and why some math needs to be learned "top down" - at least according to Keith - coming soon.

Phantom Traffic Formula

Phantom Snarl?

Ever wonder why traffic snarls for no particular reason? Here's a mathematical explanation. (Formula below.)

Another math app added to the Apple Apps store

The Apple Apps store is starting to fill up with this kind of skills practice software. Since the only thing of interest for the kids is the game itself, there's not much learning going on here math-wise, unless you want kids to practice math facts they already know. But then, again, it's only a buck ninety-nine.

Tax Day Math