Hey!

Surely you have not stumbled upon this blog, but if you have my blogging has moved. I'm blogging about math and teaching at crispymath.com. I plan to move over some of the best math content from this site as well. Thanks for visiting!

Hey!

Surely you have not stumbled upon this blog, but if you have my blogging has moved. I'm blogging about math and teaching at crispymath.com. I plan to move over some of the best math content from this site as well. Thanks for visiting!

Just finished a busy weekend with another great ASB Unplugged 1:1 technology conference. I attended both Scot(t)'s workshops on Friday and Saturday and got a lot out of both of them. It was especially fun to try to make connections between the things they were talking about and what I am currently doing in my classes and what I can be doing.

Scott McCloud shared a thought provoking video he made on Bloom's Taxonomy which you can view here:

He also suggested what I think would be a great activity to do at school. Take your entire department and have them collect all the things they assign students to do for a week. Then at the end of the week, divide them all into bins for where they are on bloom's pyramid. Discuss. Would probably be insightful I think.

Thoughtful, new article in the New York Times this weekend about Wikipedia, comparing the site to a city. I'm looking forward to getting a copy of Andrew Lih's book which inspired this. Here's a quote:

"The greater the foot traffic, the safer the neighborhood. Thus, oddly enough, the more popular, even controversial, an article is, the more likely it is to be accurate and free of vandalism. It is the obscure articles — the dead-end streets and industrial districts, if you will — where more mayhem can be committed. It takes longer for errors or even malice to be noticed and rooted out."

When I tell my student's in my facetious voice (which if you know me does not sound particularly facetious) "not to trust Wikipedia since anyone can edit it" I often have some good discussions. Although more folks at school I think are finally beginning to see the great site's merits. More soon.

So I discovered this nice article about the German board game "Settlers of Catan" when I got my current issue of Wired magazine this week. So I went and found the link online. Its hard (I guess it shouldn't be) to believe that people are just discovering Settlers. Anyhow the game is great fun and keeps everyone well involved until the end, for this reason alone it’s a million times better than Risk or Monopoly. My only complaints about Settler's are that luck is a bit of a factor more than it should be, and that the robber can be infuriating, otherwise it’s a blast and really engages whomever is playing. Lately I've been playing a lot of Power Grid and Agricola, but gonna pull out Settler's today (and win!)

If you are completely unfamiliar with "German" board games like these be sure to check out Board Game Geek. The best gaming web site around, I've even tagged a few of my games there with some comments but haven't gone too crazy. More soon.

So today must be a day to write about the newspaper business. Here is another good post from another favorite author, Clay Shirky.

It makes increasingly less sense even to talk about a publishing industry, because the core problem publishing solves — the incredible difficulty, complexity, and expense of making something available to the public — has stopped being a problem....

...When someone demands to know how we are going to replace newspapers, they are really demanding to be told that we are not living through a revolution. They are demanding to be told that old systems won’t break before new systems are in place. They are demanding to be told that ancient social bargains aren’t in peril, that core institutions will be spared, that new methods of spreading information will improve previous practice rather than upending it. They are demanding to be lied to....

Last year Clay Shirky wrote Here Comes Everybody a book about how online collaboration has changed different areas of society. One of my favorite examples of this is Consumerist.com now owned by Consumer Reports.

So the newspapers it seems are going to die (and from what I have been reading lately perhaps a shorter than expected death) but in this new piece Steven Johnson (a favorite writer) argues that perhaps the future isn't so bleak for news in general

"What’s more: the ecosystem of political news also included information coming directly from the candidates. Think about the Philadelphia race speech, arguably one of the two or three most important events in the whole campaign.

Eight millionpeople watched it on YouTube alone. Now, what would have happened to that speech had it been delivered in 1992?"

You can read the rest here. I can completely identify with Steven when he talks about stalking the college bookstore to get the new copy of MacWorld. I used to spend Sunday mornings beside the radio so I could record American Top 40 and know which songs were popular. (And this data was 2 weeks old by the time it aired) Now I can click on the Mediabase website and get accurate chart information updated hourly. I definitely feel much more in touch with the news I want to read more than ever before. Living in India today is a completely different experience than living in Morocco when I was in high school, much because of the access I have to news and other information on the internet. Its amazing. More soon.

So I just discovered tonight that Phillips Exeter has all of their homegrown math texts in downloadable PDF form on their website. I downloaded them all and have been really enjoying them. Great reading and lots of stuff I can use. It was hard to head off for my dinner plans. More soon.

Here is the link: Exeter Web Site

So Tedd Herr and Ken Johnson's Crossing The River with Dogs from Key Curriculum Press is definitely one of my favorite math text books ever. I first learned about the book when I was still a student at Keene State where one of my methods classmates was using in a ninth grade class she was in. The book is designed for a problem solving course and I was lucky enough to be able to adopt it for use at John Stark. We don't (yet) have a problem solving course at ASB, but I still use the book whenever possible. The text has an enormous selection of well written problems adaptable for any math class. We have been studying mathematical induction in my Math HL class and so I decided to use the milk lovers problem from the text and extend it into an induction problem for my students.

*Tree, Polly, Manas, and Sahil loved milk. They convinced their older brother, Ankit, who did all the shopping, to buy them each their own gallon of milk because they each liked it so much. They all put their names on their full gallons. It happened that on this day they were all really thirsty and each took ten drinks according to a different system.
Tree started by drinking half of the milk in her container. Then she drank one-third of what was left. Then she drank one-fourth of what was left, then one-fifth, and so on.
Polly started by drinking one-eleventh of her milk, then one-tenth of what was left, and so on.
Manas started by drinking one-half of his milk, then two-thirds of what was left, then three fourths of what was left, then four-fifths, and so on.
Sahil started by drinking one-half of his milk, then one-half of what was left, then one half of what was left, and so on.
To do:
After each had taken ten drinks, how much milk remained in each container?
Write a formula for the amount of milk left in each container after n drinks if they had continued drinking in the patterns originally indicated.
Prove these formulas using induction or other methods.
In what order do the 4 finish their milk? Discuss.
*Here is the pages document this problem I created for my students. They are going to use it for a "practice" IA.

Download Milk Lovers Pages '09 Files

So for years I used Proof By Induction, but never really understood why it worked. This frustrated me, and so I set out to discover the “proof” for proof by induction. I searched far and wide in all my textbooks and just kept finding the domino analogy to justify the three steps. Sure the analogy is cute but to me it never seemed like a proof. So after looking up induction in nearly every book I have, I found a decent explanation in Paul Foerster's Precalculus. He uses Proof By Contradiction to develop induction and the method is both clear and logical. Unfortunately this great induction lesson has been relegated to an appendix in the book with no exercises at all (particularly unfortunate since Foerster's claim to fame is his problem sets). Anyhow I used it to create a lesson, along with problems, that I have attached below:
Here is the Pages '09 File: Induction 1.pages

So the first proof without words lesson went so well that I devised a follow-up. The original proof is from *Proof Without Words* by Roger Nelsen. In some ways I like this one even more because my students often find the initial statement with the inverse trig functions to be completely baffling. It is also nice because it makes the kids dig out some of their geometry skills to justify the necessary angle measurements.
Here is the Pages '09 File:
The Proof Is In The Diagram 2.pages

I'm a math teacher living in Bombay. I blog at crispymath.com or find me on twitter.

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