Tuesday, November 17, 2015

Fill the Stairs, Redux

Last year we had an adventure in second grade with the game Fill the Stairs.

 I stole it from the Georgia Frameworks.  It became one of the most popular games in the grade level.
So when I saw that the second grade teachers had brought it back this year, I was delighted.  Turns out there are students who can compare numbers in traditional tasks like this:

...and correctly answer questions like this:

...who aren't always successful applying the skill in a different context:

 Same student as above.  The game is another way to assess number sense.

I knew the second grade teachers were working on having their students get better at constructing viable arguments and justifying their thinking, and had an idea about how to use the game to further that goal.  I ran the idea by Kristin, one of our second grade teachers, and she helped me come up with the following task:

 We wondered if any students would choose to use 42.  None did.
 Most kids had variations on similar answers.

 Even our "strugglers" managed to get something down.

My next thought was to have them actually play out a game, starting with the number 24 on the stair they selected, and then evaluate their choice.

 We asked them to trace over their 24 with a marker to ensure it would not be moved before they completed the game...
 ...and write their reflection on the back of the paper.

Next, a comment on the original post left by Joshua Greene inspired me to experiment with our first graders, some of whom are still working on counting and ordering numbers between 0 and 20:

 I modified the staircase to run from 1 to 20, and decided to use an icosahedral die.

I tested it out with one of my basic skills students:

 I gave her no hints or help of any kind.  I filled in my staircase first because she had limited her chances by placing 10 on the stair just below 20.

I was curious to know if she would learn from this experience, so I suggested we play another round:

 This time I provided her with a number tape that ran from 0 to 20.  The first number she rolled was a 1, which she placed on the stair directly above 0.

 She next rolled a 7, and then a 17.  Based on where she placed the numbers, I felt that she had learned from the previous game.
 Next came 6, followed by 10.  And she had a nice spot between 1 and 6 to place the 4.  After the experience, I knew the game was ready to be rolled out to the grade level.
Here are Joshua Greene's ideas:

A bunch of possible variations to play:
(1) each player has a different color to write their number and claim a stair. Player who claims more stairs is the winner.
(2) players have hands with more than 2 cards (5 is often a good number, reasonable amount of choice, but not too much) and get to choose which cards they play on their turn. Could be played head-to-head as in (1) or parallel
(3) different stairs have different point values and/or last stair claimed gets a bonus
(4) different stairs have multipliers that multiply the value entered (for kids who are ready to do some 2 digit by 1 digit multiplication)
(5) A 1-digit version with fewer than 10 steps with or without 0 and 9 already marked

And I'll add to his list: (6) a decimal version for the fourth and fifth graders.  Feel free to continue the list in the comments!

Saturday, November 7, 2015

Scenes From the Revolution

Here's a MTBoS story:
At TMC '15 this past summer, Lisa Henry told me that her high school students had a field day with a Which One Doesn't Belong task I had submitted:

 Credit also goes to my dad and his extensive collection of license plates.

Knowing that something I had created for elementary school students here in New Jersey sparked a positive experience for a class of high school students in Ohio gave me feelings of pride and empowerment, feelings that up until a few years ago I would never have associated with math.
Here's another MTBoS story: Mary Bourassa, a high school teacher in Ottawa, Ontario, once spent a winter break creating a website to house wonderful Which One Doesn't Belong tasks, tasks themselves inspired by the work of Christopher Danielson, a college teacher in Minnesota.  And no teacher has to pay any other teacher for the privilege of using the site or the tasks collected there.
Yet another MTBoS story:
Last week I brought one of Andrew Gael's Which One Doesn't Belong tasks to Nicole Rocha's first grade class:

The task provoked a lively class discussion, and Nicole was so excited she stayed in school until after 6 PM that evening working on one of her own.  Later that night she e-mailed me this picture:

 She used Andrew's as a template, and could hardly wait to use it with her class.  Now you can use it with yours.
One final story:
You all know our accomplished fifth grade teacher, Rich Whalen.  He created a 3-Act based on his own experience running last year's Chicago Marathon.  He regularly uses images from 101qs, another crowd-sourced MTBoS treasure trove, to spark interesting noticings and wonderings.  Several weeks ago, one of his students e-mailed him this picture:

 The student was at the mall one Saturday, saw this display, and thought his teacher might want to use it in class.  Of course he did!

His classmates came up with some great questions, including:
• How many cans did they use?
• Is it hollow or does it have volume?
• How heavy is it?
• How long did it take to make?
• How many bags are on the floor?
I'm not sure who was more excited: the student whose picture inspired his classmates, or Rich, who used his influence as a teacher to inspire one of his students.

Stories like these are being written every day.  They exemplify what Jo Boaler has called, "the mindset revolution", and what I like to think of as, "the MTBoS revolution."  It's a revolution against an order that believes some people are math people and others are not, an order that has sat by while generations of kids are made to feel humiliation and shame while their classmates look on in helpless silence.  I'm proud to be a foot soldier in that revolution, and it's less about arithmetic than it is about attitude and agency, less about rigor than it is about wonder, less about college and career than it is about collaboration and curiosity.    And in case you're wondering, it's personal.