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Although the idea of the long tail is mostly applied to business, I realized that there are also implications in education. Before I get to the educational aspects here is a brief description of the long tail.

The Short Head
If in 1990 you went into a B. Dalton bookstore you might have found 10,000 different book titles. (I’m guessing.) There were sections to appeal to most readers. (I could usually be found in the fantasy section.) Stocking these books costs the store money.

There are the actual rental costs of the store, the labor costs to stock the book, etc. There are also opportunity costs. If a book doesn’t sell it’s taking the spot of a different book that would sell. There is limited space in the store. So stores pay close attention to which books are selling and which are the most popular.

If you created a graph of the sales it might look like this:

The most popular books are on the left side. As you move to the right the books sales decrease. The area under the curve represents the total amount of sales for the store.

You can see that the stores make the most from the bestsellers. Some estimate that the top 20% of the titles make 80% of the store’s income. (That’s why you’ll see copies of some book about Harry Potter all over the store.)

You can also see that the right end of the graph gets cut off. This is because of the finite amount of space in the store. It is easy to see that if the store could stock more titles these titles would still sell. Barnes and Noble, and Borders have tried to capture some of this market by building their superstores that might be able to hold 100,000 different books. (I’m guessing again.)

This stretches out the right end of the sales graph. But there is still a finite amount of storage space.

Amazon and the Long Tail
The idea of the long tail came about when amazon came on the scene. Suddenly there was this business that doesn’t have the high overhead of a brick and mortar. They even have the option of waiting for an order before even printing the book. So there are little if any opportunity costs to store the books digitally. Suddenly it is profitable to have a million titles–or ten million titles.

Thus the long tail. The sales graph gets stretched along the x-axis. Although it’s not infinite, it is very large and growing rapidly.

The profits are still represented by the area under the curve. But suddenly the bestsellers are less important. Amazon makes as much money from the tail as from the head. So it is in Amazon’s best interest to help people find titles that interest them in the tail. That’s why they let people recommend books. That’s why they tell you “people that bought Harry Potter also bought….”

What about education?
I believe education is undergoing a similar transformation. In 1990 teachers tended to use the same textbooks, the same resources, and the same “best practices.” Textbook publishers had a monopoly. Teachers could expand their repertoire by attending conferences etc. But the number of resources was finite. There might have been a set of 20 or even 100 methods for teaching topic X.

With the arrival of the internet, especially web 2.0 technologies, we now have the potential to dramatically increase the instructional options. There are thousands of teachers coming up with unique ways of teaching various topics.

The problem is that all of these resources are hard to find. There might be a teacher in Pomona, CA with an incredible way to explain topic X. But the only people that benefit are his own students and anyone who stumbles onto his website–if he has one.

We could wait for some corporation to organize these resources. We would then have to pay for the information.
Or we could do it ourselves.

Stay tuned for details.

For more information
Check out Chris Anderson’s blog to learn more about The Long Tail. Pictures are created by Hay Kranen / PD and are available here.

The best feature of MathGuide is the ease of Navigation.  Links are clearly labeled and it is easy to find what you need from the menus.  It is the creation of Mark Karadimos a math teacher and administrator from Cicero, Illinois.

The first page I discovered allows you to create practice worksheets for your students.  You can select how many questions you would like and a worksheet is created.  Right now there are only worksheets available for three topics, factoring trinomials with and without a first term coefficient (other than 1), and solving a system of equations with 2 variables.

The most useful pages are the quiz-masters.  Each one allows students to practice very specific types of problems and get immediate feedback.  Most of the quiz-masters also have a page explaining how to do the problem.  I’m looking forward to sending my students online to practice.

There are also detailed rules for three classroom games:  baseball, football and Jeopardy.  The baseball game consists of breaking the class into teams of four and then answering questions.  When a team gets a question correct, they move so many bases based on the role of the dice.  When a team gets a question wrong the get so many outs also based on the role of the dice.

The detail of these rules makes me believe they are classroom tested.  You could use them “out of the box.”  You would need to come up with appropriate questions.  (Or have your students do so.)

Other promising resources include Math Projects and Puzzles and Games.

Mark continues to add new material–as recently as February.  I will be watching to see what else gets added.

While searching for math tutorials I stumbled across this very funny video.

Do you relate to any characters? In what way?

Despite the lame subtitle (Illuminating NCTM’s Vision for School Mathematics) Illuminations is a really great resource for math teachers of all levels.

There are 527 different lesson plans and 96 online activities you can do in class. Most of the online activities go with one of the lessons but you can always use them separately. When you narrow your search to grades 9-12, there are almost 70 lessons and over 60 online activities.

I have used several of the resources. My favorite lessons are: Successive Discounts is a great way to introduce the composition of functions by exploring which method is better: Applying a $5 off coupon before or after taking 25% off the price of a pair of jeans. Supply and Demand lets students determine the optimum price for merchandise by finding the equilibrium point for supply and demand. My favorite activity is the Fractal Tool which allows you to create various fractals on the screen. I use it to illustrate recursion.

Overall Illuminations is a great site. But it does have the same problem that most sites have. It can be hard to find what you need, or I’m just not using the right keywords. I have always ended up scrolling through the entire list of 70 lessons to find what interests me. If I needed to find something Sunday night to use on Monday morning, I wouldn’t look here.

If there were only some way for math teachers to collectively organize all of the resources on the internet. . .

Before telling my students they have to get to create videos for math class I decided to explore what is already available. So far I have discovered two types of videos on YouTube.

The easiest to find were the math tutorials. I have found 13 people creating them. I suspect there are well over 200 different tutorials. These would be a great review for individual students in class or as homework. They could also be useful in a classroom setting if you have a projector.

Although it was easy to find the collection of tutorials, its size makes it difficult to find a specific tutorial. So over the next few weeks I plan on bookmarking them in a way that is useful for myself and others.

I also found several videos which would be useful in the classroom to stimulate debate, help students visualize concepts, etc.

Here is an example which might help students understand probability.

Chances are I wouldn’t have thought to go looking for a video on probability. I just stumbled across it. If you’re looking for a specific video, these are easy to find. However, if you’re just looking for a video to help understand topic x, it might be more difficult.

I intend to remedy that. Stay tuned for details on my plan and how you can help.

The teachers at my school just finished the American Film Institute’s Screen Education training. This incredible program shows you how to teach basic filmmaking to your students. The main idea is that we now live in a visual culture and that students need to develop visual literacy as well as reading literacy.

In two days the teachers go through the same lessons which they will teach their students. We started filming and drawing storyboards the very first day. The second day involved more filming and editing of our final product. Our film can be seen here. (If the YouTube embed code works this time.)

We had so much fun that we wanted to implement it immediately in our classroom. So I started to think about how I might integrate filmmaking into math class…

I have some ideas. Before sharing them I would like to hear ideas from readers.

If you had access to camera equipment and computers, how would you utilize filmmaking in a math class?

The video in the previous post messed up the layout for my entire blog. I’ve tried a few things but this problem has challenged even my extensive skills with html and CSS.

So I am bringing in professionals (former students) to see what they can do.

It might take a few days to figure out. Until then you can always find my sidebar at the very bottom of the page.

Update:  My former students are so smart.  The problem seems to be fixed.

While looking for math videos on YouTube I stumbled across the following video. It pretty much needs no introduction.

To find out more about the history of the presentation and to participate in the discussion go to the Shift Happens Wiki.

It’s been an interesting week. Search for “Harry Potter and the Deathly Hallows” and you will see that Google has indexed (if that’s even the right word) 990,000 websites. I suspect that is some sort of a 5 day record. (If anyone at Google can confirm this please let me know.)

I am happy to report that my humble lens is at number 45!

The main thing I have done is post links to it from my other Harry Potter lenses and blogged about it. Squidoo seems to really help SEO. . .

Yesterday, there were zero websites about  “Harry Potter and the Deathly Hallows.”  Tomorrow there will be hundreds and in a week there will be thousands.

Right now every related website is “brand new” and has an “equal” chance to achieve good search engine results.  This presents the curious math teacher with an opportunity to see what it takes to get a web page on the top of a Google search.

So I created a website, appropriately titled, Harry Potter and the Deathly Hallows at Squidoo.  I’ve done a few things to help its SEO, which stands for search engine optimization…I think.  I have linked to it from my other Harry Potter lenses and at least two people have blogged about it.  (The other entry was written by Marti.)

Although traffic does not affect SEO, I have also told a number of friends and family and posted information on myspace and the Leaky Lounge.  (Traffic does help Squidoo’s internal LensRank.)

It will be interesting to see if these steps make any difference.  In the past posting at Squidoo has helped a lot with SEO.  Right now a Google search for “Harry Potter music” brings up my lens as the second site.

(Which is actually terrifying.)