Reflections of the TZSTeacher

On Thursday, May 21, 2009, ** Chris O’Neal ** brought a colleague from Fluvanna to observe my 3rd grade math students work with their iPods. The day before, I had discussed with my kids what they thought we should show and how the class should be organized.  I WISH I had videotaped that conversation, as it was simply amazing. However, I didn’t, so this is take 2, the description of Station 2.  (See previous post for description of station 1.)

In Station 2, the kids were to use the WhiteBoard app to drill each other.  They decided they wanted to show this to our visitors to show how the iPods could connect over WI-Fi. When we were establishing the boundaries for the problems, the initial rule suggested was “no plus less than 12.”  You can imagine the conversation that ensued over the meaning of that. . . it was a perfect reinforcement of my prior lessons on the need for precise language in describing mathematical situations, (though I chose not to mention that in this lesson.)  After we established what that meant, I wrote “No + <12″ on the board.  (I take every chance I can to reinforce the “greater than” and “less than” sign, as kids typically confuse those or don’t even name them, preferring instead to use the alligator trick.) Someone then suggested no multiplication over 100. I probed as to how many digits could they use, did that mean we couldn’t ask anything beyond 10 X 10, and the agreement became 1 digit by 2 digit problems up to 99 as the highest number, so I added that to our list.  I should have added n x nn, with n being 0-9 and nn=<100, to have that chance to reinforce a variable, the less than sign and algebraic thinking, but I didn’t think of it at the time. We stopped there, as I clearly got the impression they WANTED to practice multiplication facts, so I didn’t even address the other arithmetic operations.

Then I asked about checking correct answers. How were they to do that?  They decided that first, the person who developed the problem would also work it, and they would compare answers. THEN they would check it on a calculator–and they wanted a separate calculator, NOT the one on the iPod.  (I didn’t ask specifically why, but they wanted a separate one rather than move back and forth between apps on the iPod.)

When I went to this table, the problem they had created was 8 X 16. The kid working it, one of my best problem solvers, was doing something in his head , so I asked him to think out loud. He said he’d added 16 and 16 and gotten 32.  I had taught the strategy of “doubling and halving” where if you double one of the numbers, you can halve the other one and get the same answer (i.e., 4 X 32= 8 X 16), so I asked him what he was going to do to the 8 now. He stared at me blankly.  (HMMM. . .I may have taught it, but he, at least, didn’t get it–and neither did his partner, cause she didn’t jump at the chance to answer that one!) He then said, “128″ and I asked him how he got it.  He repeated that he had added 16 and 16 and gotten 32 and just kept adding. His partner volunteered, “I did it another way” so I asked how she did it.  She described adding 16 and 16 to get 32 and then 32 and 32 to get 64 and then 64 + 64 to get 128. I didn’t probe as to how hers was different from his, (I think she figured he was continuing to add 16s) and I just wanted them to move to another problem to practice more without me interfering. I left them using the calculator to check, but realized several things about my teaching from their work.

1. I had taught doubling and halving, but needed to work more with it.
2. NEITHER of them went to splitting the problem into smaller parts such as 8 X 10 and 8 X 6. I need to help them shore up the various strategies they use, so they don’t rely on the same one all of the time, and learn when to use which to be more efficient.
3. When I tried to suggest splitting the number, working 8X6 was not efficient for the boy, so he obviously didn’t know that fact. That tells me I need to work on fact mastery some more. This is a kid with an incredible memory, so I need to provide him some opps to practice the facts. Him not knowing that says I haven’t provided enough times to practice it.

On Thursday, May 21, 2009, ** Chris O’Neal ** brought a colleague from Fluvanna to observe my 3rd grade math students work with their iPods. The day before, I had discussed with my kids what they thought we should show and how the class should be organized.  I WISH I had videotaped that conversation, as it was simply amazing. However, I didn’t, so I’ll describe MY take on the observed lesson:

I had 6 students that day who were split into three groups of two, to move through three stations with about 10 minutes at each station. The kids had defined the stations the day before, but without clearly defined educational objectives. To begin the class, we did that together.

Station 1 was to play ** MetaSquares ** and “Think Like A Computer.”  One person would make a move on their iPod to make a square and the partner would mimic that move. The goals were to see if the computer worked the games the same way to block or win the game, and to try to figure out the computer’s strategy to determine how to beat it.

Station 2 was to connect the two iPods at that station through the** Whiteboard ** app and give each other problems–basically a drill station.  They wanted to show it, though, because it’s “cool” to connect their devices and draw on one and have it show up on the other.

Station 3 was to record the number of rolls it took to get 6 of a kind in ** Motion-X Dice**.  We had done this before, just collecting data and then looking at that data. Today’s twist was to predict how many rolls it would take and then calculate the variance between their prediction and the actual count.

When I was observing Station 1, “Think Like A Computer” the iPod did NOT make the same counter move on the student’s first move, so the kids had to decide what to do.  They decided to keep the “mimic the other person’s move” going.

Imagine their surprise when the iPod got the same score on both iPods on the same move, even though the iPod’s moves didn’t match.  Imagine their shock when it happened a second time.  The third time, one iPod made a combined square and thus got 9 points more. While both students won at the same time, with the same score, one iPod had the 9 more points.

In the follow up discussion, they decided that on level 1, (their current playing level), the iPod’s goal was simply to make squares, and not block the player, so that’s why they could a.) win and b.) the iPod’s scores were similar.  They hypothesized that on Level 2 (where the iPod begins blocking) that the device’s moves might be more similar since it would be blocking the exact same moves.  However, they didn’t have time to test out that theory.

I love that the kids’ perception is that they come to math class and “play on their iPods.” I love that they are dissecting and analyzing not only their strategies in their games, but also the algorithms of the device.  I enjoy hearing their hypotheses and questioning them, often causing cognitive dissonance (sometimes for me, too!) I love the AH-HAs they have as they work within the structure of the questions both they and I pose. I watched the surprise on Chris’  and his colleague’s faces when the students verbalized the explicit differences between levels 1 and 2 in the game. My kids were so much more specific in their understanding than a typical response of “the game gets harder as you go up in levels.” They clearly knew that in Level 1 the iPod was simply trying to make squares.  In Level 2, it begins to show awareness of the player’s moves and block them making a square.

I cannot wait to ask them how in the world a “computer” can forecast their moves AND have an intention to block that “only thought of in their own head” move. How can the computer know what they are thinking? How can it tell what they are planning to do? And, more importantly, how can they counteract that knowledge?

How can we teach students to think with logic and analysis intuitively?

I believe devices like iPod Touches and strategy games not only do so effectively, but are crucial to helping students learn to survive and THRIVE in the world in which they live!

Your thoughts?