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Proofs Without Words

So this year my IB Higher Level eleventh graders arrived with a full year of Precalculus which has made life a lot easier. I think we have been able to use some of this time to do more cool stuff, although we did get really bogged down doing vectors. Anyhow, I created this worksheet from Roger Nelsen's book Proof Without Words II and used it in my HL class last Friday. Most of the kids were able to figure out the proofs by themselves and the lesson went well.

Here is a screen shot of the first page of a worksheet I created around this idea.

Download The Proof Is In The Diagram - This is a Pages '09 file

Gator Golf

So I am reading, and enjoying Jeff Jarvis's very interesting What Would Google Do? and it has encouraged me to start blogging again. I am gonna try to follow the lead taken in a couple of the other edublogs and post some of my stuff to the net.

So here is a lesson I did this past week: Gator Golf

I love review games. I think I first heard of playing Gator Golf in the book Teaching for Dummies but I can never leave well enough alone so here is my twist on it.

Setup:

Divide the kids up into four teams -do this any way you see fit. Give each team a portable whiteboard to write down their final answers, along with scrap paper and golf pencils (obviously) to make notes if necessary. You will also need to get the Hasbro game Gator Golf. I also went to Home Depot and got some putting green carpet, and some tees and a putting glove at a golf store, you could probably make due without these but I love little details.

The Game

The game is played in multiple rounds

Round 1:

This round relies most heavily on the keynote. In round 1 there are 16 multiple choice questions (the questions I included are around trigonometry). When a question is revealed each team answers it on their whiteboard and then "locks in" the answer by flipping their board upside down. Once three of the four teams are locked in I cajole the last team into finishing as well. At this point the answers are revealed. The team in "control" reveals their answer first followed by the rest of the teams. If the team in control answers correctly they score a tee, if not, the next clockwise team has a chance to steal, etc. After each question is finished control passes to the next clockwise team around the room, the team in control is indicated by the location of the alligator in the slide deck.

Golf Round:

After the 16 questions are up I tally the tees that each team earned to determine each team's golf position. Sort of like in Hole In One on The Price Is Right (another post for another day) The team with the highest score gets to putt closest to the gator (but not too close). I usually wait until after the scores have been tallied to reveal the gator which always goes over very well. Prior to this just the green is on the floor and so the kids' curiosity is piqued. Everyone gets one putt, they score one point for hitting the gator at all, and three if the gator devours and spits out their ball. It is really important to allow the kids to have some fun golfing while also not getting so bogged down in the golfing part that no additional math gets done.

Round 2:

Each team gets a few minutes to peruse the longer form questions from the round two document (included in the zip file) then I have the teams in reverse order of score select a question (or two based on time) that they want control of. After this selection each team gets a few minutes to work together on their questions and write up solutions on the classrooms whiteboards (not the mini ones) for everyone else to see. If teams have extra time they can try to solve the questions their team did not select in hopes of stealing another teams questions. Once time is up I score each question, one putt per correct answer and we golf once more. This golfing round goes much more quickly since there are a maximum of 10 puts, probably much less.

Final Round:

If there is time, I will have teams wager part of their score on one final putt. To determine the grand champion.

I actually didn't give any of the teams any prizes for winning the golf game this year, just the glory of being champions. Candy would work fine but is not really necessary, I would certainly advise against giving any sort of bonus points as a prize.

Other Thoughts:

I hadn't played this game in a few years, since first gator had died, but I saw a new release of Gator Golf recently and picked up a copy. The game takes a bit of work to set up but always goes over very very well. I love tweaking rules and things so am always changing the games around to try to make them better. This time for example I had red tees and white tees mixed in my golf hat and when teams scored a point during round 1 they drew their tee out of the hat, red tees counted double. 

Whatever you do with the rules be sure to tell the kids what they are ahead of time and stick to them, kids go crazy when you change the rules in the middle of a game. Also during round one don't hesitate to stop the game and "go over" the tricky problems. This is a review game after all.

Files: This file includes the keynote slideshow I used for round one. Lately when I am making a slideshow for a game I create a Pages document with all the questions to begin with so I have included that document as well. I also included a copy of the Round 2 questions. The questions for this game are all about Trigonometry covering through trig equations but the game can easily be adapted for most other topics. More soon.

Gator Golf Zip (7.7mb)

The Netflix Contest

So  this New York Times Magazine article by Clive Thompson is the second I've read about the Netflix, algorithm contest, Wired magazine also wrote about the contest here last February. Here's a bit I particularly like from Clive's piece:

When someone makes a breakthrough, pretty soon every other team is aware of it and starts using it, too. Piotte and Chabbert soon learned the major mathematical tricks that had propelled the leading teams into the Top 10.
The first major breakthrough came less than a month into the competition. A team named Simon Funk vaulted from nowhere into the No. 4 position, improving upon Cinematch by 3.88 percent in one fell swoop. Its secret was a mathematical technique called singular value decomposition. It isn’t new; mathematicians have used it for years to make sense of prodigious chunks of information. But Netflix never thought to try it on movies.
Singular value decomposition works by uncovering “factors” that Netflix customers like or don’t like. Say, for example, that “Sleepless in Seattle” has been rated by 200,000 Netflix users. In one sense, this is just a huge list of numbers — user No. 452 gave it two stars; No. 985 gave it five stars; and so on. But you could also think of those ratings as individual reactions to various aspects of the movie. “Sleepless in Seattle” is a “chick flick,” a comedy, a star vehicle for Tom Hanks; each customer is reacting to how much — or how little — he or she likes “chick flicks,” comedies and Tom Hanks. Singular value decomposition takes the mass of Netflix data — 17,770 movies, ratings by 480,189 users — and automatically sorts the films.

I will probably share this with my students in the next few days. It reminds me not only that mathematics is cool, but perhaps most importantly that when folks find something interesting to do, they will learn the necessary mathematics (or other skill set) involved with both eagerness and pleasure. More soon.

World Class Potty Training

Scott' latest post on Dangerously Irrelevant is a great one:

Our middle school - arguably one of the state's finest - issues laminated punch cards to students at the beginning of each trimester. Each time a student needs to leave the classroom to go to the bathroom, visit her locker, etc., it costs one of the 12 punches.
Sorry, student, that it’s week 7 and you’re out of punches. No going to the bathroom for you.
Inhumane? Degrading? Illegal? What are your thoughts regarding this practice? Anyone else’s school doing this?
Oh, and did I mention that unused punches can be used for extra academic credit in some teachers’ classes?

This is, of course, completely ridiculous. These guys need to read Alfie Kohn's Beyond Discipline and then Seth Godin's Tribes.

I tell my students if they need to go somewhere (bathroom, locker, nurse, wherever) during class then they should just go.

If my class is as engaging as it should be nobody will even think about leaving (When is the last time I left a great movie to go to the bathroom?) And if students are leaving then I know there is a problem. 

This is really not that different from the whole laptop issue and students surfing facebook etc. during class.

What They Hate About Mumbai

So, living in the midst of this recent chaos in Mumbai has been strange. I talked to my family on Thanksgiving which was great and thanks to the wonders of the net was able to quickly get in touch with everyone else. 

It was just this morning that I was starting to feel a bit nervous about living in Mumbai, perspectives realigned when Paul read us Suketu Mehta's excellent piece "What They Hate About Mumbai" from today's New York Times.

Here's one great quote:

"I once asked a Muslim man living in a shack without indoor plumbing what kept him in the city. “Mumbai is a golden songbird,” he said. It flies quick and sly, and you’ll have to work hard to catch it, but if you do, a fabulous fortune will open up for you. The executives who congregated in the Taj Mahal hotel were chasing this golden songbird. The terrorists want to kill the songbird."

Imaginary Friends

So the cartoon blog xkcd.com is often hilarious and today's post is no exception.

Cube Cards v1.2

So, since I am presenting on the Rubik's Cube at the NESA conference in Bangkok later this week, I found some time to revise my cube cards. You can download version 1.2 here

Changes

• fixed a few spelling errors and rewrote text for clarity in a few spots
• reworked the layout of the cube diagrams on cards 5, 6, and 9
• corrected an error my mom spotted on card 5
• rearranged the pdf file so that they could conceivably be printed front to back

Incidentally, these cards along with everything else on this blog are published under the creative commons license, click on the CC Badge for more information. Feel free to edit the master files, remix, and rework anything as much as you want. If you come up with something clever I would love to see it. It would also be great if you could join the mix too, consider posting a great lesson or other activity you have developed for everyone to share.

Why You Need A Manual for Wikipedia

There is a great new article in the new issue of The New York Review of Books on Wikipedia (1), The article is also, ostensibly, a review of O'Reilly's new Wikipedia The Missing Manual Book. Its amazing to read about all the bureaucracy that has developed inside Wikipedia, how the site has evolved over time from a wild-west to an ordered system -a system so complex that you now need to buy a book if you want to fully participate in it.

(1) Wikipedia remains my go to site for quick, reliable information. On Friday for example after school we were reviewing for the IB Math HL exam when Akshay wanted to know exactly how many points he needed to pass the IB (this sort of plan, while initially very attractive I warned him, with personal experience from Calculus III, is generally not a good strategy for exam success). His instinct was to go to the IBO website where he searched in vain for the details for about 10 minutes. I launched wikipedia and found the answer almost immediately.

Who Owns The Organics?

So this is a cool chart showing who owns the big organic companies. Its from LawGeek via Good Magazine. It connects well with some of my favorite books lately including The Omnivore's Dilemma, In Defense of Food, What to Eat, and Animal, Vegetable, Miracle.

A New Math Study

So a new study is forthcoming from the government on the state of math education in the US. You can read an interesting article about it in the NY Times here. It suggests that common ground must be found between constructivist and more traditional direct instruction approaches. This is no surprise, I like to think I am pretty constructivist, but I still find myself at the board sometimes helping the students get their heads around what we have been learning or solidifying connections between the different areas of a topic we have been studying. My current batch of students are surprisingly eager to learn how to do everything by hand (1) so sometimes I will also get up front and show them how to do certain problems on their calculators and encourage them to try these approaches.
These math wars have been going on for a long time. I fondly remember my first year teaching at John Stark in NH. Right out of college and gung-ho I had all my kids write weekly math journals (2). The best outcome of this was a long dialog I had back and forth with one of my students, Matt Corsetti. Matt had found some articles from the California group Mathematically Correct on the internet and was wondering what was up since we were doing some of this "bad" stuff they talked about in our class. It was cool to discover how fruitful discussions could be with students. I find these conversations, whether about learning, the classroom environment, or whatever, keep me connected, inform my teaching, and improve my practice. This is something I try to do as much as possible now, even though I am not currently doing it through journals.

(1) This is probably because the IB has changed and now includes includes a non-calculator part so none of us are completely sure exactly what kinds of questions we need to be ready to do by hand.

(2) This, by the way, was not the most popular set of assignments I ever came up with and not one I would necessarily recommend for first year teachers -although now the lugging of journals could be done away with and kids could write blogs which teachers could evaluate painlessly with an RSS reader