Friday, February 18, 2011

Reason #792 I Love Mathematics

Is 80 degrees twice as warm as 40 degrees?  Discuss...

Ok, so obviously I wouldn't be posting this if there weren't some subtlety to this question.  I will say that three days ago I was pretty confident in my initial answer to this question.

Monday, February 14, 2011

Tracking Study

Probably most appropriate for twitter, but I'm still holding out on that end...

At the Escape from the Textbook conference I attended last Saturday, Jo Boaler referenced a large scale study in England on tracking.  A cursory search came up empty so I came here to let someone else do the work of finding it.  Ok, ok, not really.  Actually, I was hoping someone familiar with the study could point me in the right direction.


Thursday, February 10, 2011

Escape from the Textbook Conference

On Saturday I'm attending what I hope to be a great conference at The Urban School of San Francisco: Escape from the Textbook with speakers Jo Boaler (What's Math Got to Do With It), Paul Zeitz (The Art and Craft of Problem Solving), and me (too many books to name). Ok, I'm not really one of the speakers but I will be leading an afternoon workshop that I am calling Habits of Mind: From Student-Posed Problems to Assessment. 

Here's the plan:
We will complete a high speed version of a project where students create, explore, and generalize visual counting patterns (pile patterns for example). Sprinkled in will be discussions of how mathematical habits of mind (aka problem solving, aka mathematical practice) can be developed and assessed. Come prepared to do some math. 
Basically, we're going to start with

and go from there...

Here's the current draft of my powerpoint (zzzz) presentation.  I've never done this before (mostly because I've never been finished mostly finished putting together a presentation this far in advance). Obviously, there are lots of pieces that need to be filled in (I kind of hate powerpoints that don't have pieces that need to be filled in) but I'm hoping that I can get some feedback beforehand, send participants here during, and continue the conversation afterwards.

Here are some additional resources related to the workshop.

Supposedly there will be attempts to stream the conference for those of you that fail to scalp tickets between now and then.  We'll see how well this works, but stop by if you have some time (9-3PST).

Monday, February 7, 2011

Teaching via Games: The Introduction

I like games.  Board games, video games, sports, Bear/Ninja/Cowboy, you name it.  I've even managed to get to a place where I even enjoy games when I lose.  I and dad are so proud.  When I moved to California, one of my best craigslist furniture finds was a nice big coffee table that opens up to reveal a not-so-secret compartment.  Mine's filled with board games.  Below are some of the most recent games I've played and/or added to the bowels of the coffee table.  

There are lots of games that are explicitly and implicitly mathematical.  Some a great and some are terrible.

Math Mama Writes has introduced me to some of the great ones.  Math for Love has a great post cautioning us that any game labeled as a "fun math game" is like calling something you would ingest a food product--typically not a good sign.
If your goal is to teach and you just slap the word “fun” on at the end, you end up with garbage. On the other hand, if you’re focused on making a game that’s really good, well, then it is fun. Of course, whether it has any educational value is pretty dubious.
I've played mathy games for many years.  There are hundreds (never mind the hundreds more using nothing more than a deck of cards).  Here are 20 (and please add your own favorites in the comments):
I find these games to be fun first, and mathematical second.  I use some of these in my classroom and a few to complement or inspire content.  For example, there are some great counting questions that can be asked about Set:

How many cards are in the deck? 
How many sets are in the deck?
What's the greatest number of cards you can have without a set?

I've used Mastermind lessons as a tool to develop the concept of proof with middle schoolers.  Backgammon is a great game to practice probability.  

Overall, though, many of these games present challenges in the classroom: they take too long to play or teach the rules, they require too much set up, they can only be played by a limited number of people, students can play without actually trying to implement any thoughtful strategy, and the big one: it is challenging to convince kids (and schools and parents) that playing these games is not just an extra, froofy, free time activity and a break from doing "real" math.  True, becoming better at chess will most likely not help you become better with fractions, but I've begun to think about how these above games could help develop mathematical thinking and habits of mind.