Supermarkets marketing strategies 101: How to pull the wool over the shopper's eyes

Notice Dial's effort to conceal the  

decrease in the amount by using a 
taller, thinner container.

Another gem from Dan Meyer's repertoire of great lesson ideas. Here's what this particular "lesson" offers.

• The context for the lesson makes for a great story. Your supermarket is out to hoodwink you!

• The math is intrinsic to the context of the problem. The only way to understand the supermarket's strategy trickery is to do the math. Kids will actually want to understand how unit pricing works. This is what I mean by learning the math from the "inside out." That is, the math is embedded in a context that encourages real, non-scripted learning.

• Dan does not offer you a specific plan of action, but rather helpful guidelines. He gives you resources to work with and makes them accessible via download.

• The ideas for the lesson are developed collaboratively online with other math teachers.

• Dan credits his sources.

• Dan ships* his product. 

*An expression coined by Seth Godin that mean you get your idea/project out there so that others can take of advantage of it.
Shipping is fraught with risk and danger. - Seth Godin

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

Add caption

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

Doing homework 2.0

Link to story

Different...

Marketing Done Different
Friday, April 09, 2010
Consumer marketing expert and Harvard Business School professor Youngme Moon talks about how companies can stand out in a saturated market and how she's practicing what she preaches in selling her new book: Different: Escaping the Competitive Herd.



Source: Brian Lehrer Show 4/9/10

Math 2.0? I don't think so...

According to the students at Lincoln Middle School the Mathtrain.TV video (below) demonstrates Math 2.0 in action. Watch the video and see if you can tell me what my problem with it is.



Hint: This is Math 1.0 using Web 2.0 tools. What's missing? (See What is Math 2.0?)
Tweet me at @climeguy with your comment.

Noon Day Project - My measurement - part 2

Here's how I measured the sun angle for the Noon Day project.

• I set up a meter stick perpendicular to the ground with the help of a metal bookend.
• I checked the Internet for the approximate time of local noon (when the sun is highest in the sky). Sunrise was at 7:00am and sunset at 7:06pm. I found the midpoint between those times which was 1:03pm.
• I set up my station at about 12:45 and then watched and recorded the lengths of the shadow every 5 minutes using a piece of chalk as the time approached local noon. (The length was getting shorter and the shadow was moving west to east.)
• After I put down my mark I also took a photo of the shadow and stick from as close to ground as I could.
• I continued till 1:15 when I noticed that the shadow was now getting slighter longer and more easterly in direction.
• I used the photo where the shadow appeared to be at its shortest which was 1:03 EDT and copied an pasted it in Geometer's Sketchpad.
• The Sketchpad tools allowed me to make the sketch with the details that you see in the picture including the sun angle which is formed by the sun's ray and the meter stick. (The image size of the meter stick was 6.7 cm.)
• Next I'm going to post this summary on the CIESE Noon project page. (My School Name is: CLIME)

This is part 2. See previous post for part 1.

Windy News

The Big Tree Take Down

The wind brought it down to its present position. How would you bring it to the ground without further damage?

Here's what the experts did.

I do wonder why the chain saw guy stopped cutting it and was told to saw it elsewhere. I was too busy filming and didn’t think to ask.

I was looking for math in their solution to the problem. But what I learned is that if you have the right tools and the know how to use them properly the job becomes a “no brainer.”

There obviously is a lot of science here. Any suggestions as to how the science might inform the math?

Noon Day project begins this week - March 8, 2010

The Goal of the Noon Day Project is to have students measure the circumference of the earth using a method that was first used by Eratosthenes over 2000 years ago. Students at various sites around the world will measure shadows cast by a meter stick and compare their results. From this data students will be able to calculate the circumference of the earth.

Watch as Carl Sagan describes some of the background surrounding Eratosthenes' experiment in this 6 1/2 minute video.

Follow me on Twitter (Hashtag #noonday) As I recreate the experiment that Eratosthenes did. I hope to my measurements on March 17 weather permitting.
There is some good background material on the measurement at the Noon Day project site hosted by the CIESE (Center for Innovation in Engineering & Science Education) - Stevens Institute of Technology in Hoboken, NJ.

Get real "Do Nows" to kick start your math class

"Do Now" classroom openers are all the rage these days (i.e. Everday Math). Why not reach out of the box and do one that's timely for the day you do them? Today is the day (3/1/10) after the Olympics closed and by the latest count the USA, Germany and Canada were the biggest winners.

What if we wanted to give a gold medal to the country that "won" the Olympics how would you decide? One way might be to assign 3 points for each gold medal won, 2 for the silver and 1 for the bronze. (This is similar to how they determine standings in the National Hockey League.) Who would be the winner? Would Canada's 14 gold medals compensate for their lower total of medals than the USA? (See a Google Spreadsheet with the results.) Feel free to edit it! Help me turn this "do now" into an activity worth exploring.

WCYDWT defined?

Blog entry - 2/13/10 updated 3/1/10

Two Excellent Entries For The WCYDWT Course Catalog

February 9th, 2010 by Dan Meyer

Kate Nowak:

Here’s what basically has to happen to make a successful WCYDWT lesson:

1. Lighting strikes (you observe something).
2. You recognize that lightning has struck (you say “holy *&^%”).
3. You investigate by building layers of abstraction on your observation.
4. You realize that that particular abstraction fits in your curriculum.
5. You strip away all those layers to a core question interesting to a 15 year old, who (I’m sorry and draw whatever conclusions you will about me or my school system) are the least interested people on the planet.
6. You rebuild the abstraction in a way that will support the questions you successfully predict they will ask.
7. You make attractive keynote slides out of it.
8. You extend your original abstraction to questions that they will want to pursue to enhance their understanding.

This is a pioneer profile of a WCYDWT activity. The education world will never be the same once this becomes mainstream. Why? Because it encourages teachers to break out of the mold and be creative in "lesson planning" whether its in the box (brick & mortar school) or out in the virtual world probably a combination of both.

In one of Amazon's user reviews of Seth Godin's latest book "Linchpin: Are you Indispensible?" the reviewer writes:

Linchpin is a most unusual, well-organized, concise book about what it takes to become indispensable in the workplace - whether you work for someone else (at any level) or are self-employed. It's about how business has rapidly changed and how treating employees like factory workers (or doing your job like one) doesn't work any longer. We must make choices and take action to "chart our own paths" and add value that others do not. We cannot wait for a boss or a job description to tell us what to do, rather we must just take the initiative ourselves. Only then can we become indispensable "linchpins," rather than replaceable "cogs."

(This is a key to educators becoming "life long learners".)

Get ready, get set, go Educon 2.2 with a math spin (I hope)

So here I am ready to do Educon 2.2. Since the event is in Philly and I'm at home I got my tweetdeck set up to view tweets that I follow along with tweets that contain #educon and #noneducon in their message. Let the circus begin....

I'm back from my first go at it. Lasted about 45 minutes. What did I make of it so far? I'm reminded of what computers were said to do most of the time: GIGO - garbage in, garbage out. It wasn't really that bad. A #educon tweet told me about an interview the writer did with Seth Godin and that transcripted in her blog. His views on education. Interesting. I followed my mind drift and clicked on an intervew Seth gave on his quidoo.com website as I was being bombarded by a cacophony of tweet flashes every few seconds or so it seemed. There's something fun about this blitz of info. Nothing about math. but then retrieving relevant stuff is like catching the proverbial needle in the haystack. There has got to be a better way. The show begins tomorrow. This time I will be ready for Math!

PS - I missed the virtual feed of the panel discussion at Franklin Institute. I wonder if it actually happened.