Holy Cow!

This post was begun in early November, 2010 and finished in late December.

I’m a smart person. I come from a smart family. I have always gotten clear messages from my family that intelligence and learning is valued. I was told by my mother that I could be anything or do anything I wanted to in life if I simply put my mind to it, and I believe that mostly. I enjoy challenges, brainteasers, puzzles and conundrums.  I like asking hard questions and fiddling around with possibilities.  I look for patterns and relationships in my world and love the big picture conversations that come my way.

BUT. . . . when I became a gifted teacher–or more accurately, a teacher of gifted students–I began to question just how smart I was.  My kids are so much smarter than me, and the parents of some of my students blow me away.  Just two examples:

I have a parent who is incredibly smart and he and I enjoy talking and sharing ideas and thoughts about his two very talented kids–and we always move on to big picture kinds of things, the world in general, education in particular, and lots of just general stuff that intrigues one or the other of us. The other day I was showing him a game we have done in math so he could play it with his son, and the minute I finished sharing the instructions, he said something that showed he had a deep understanding of the math behind this game intuitively and immediately. The quickness of his grasp of the big ideas and the depth of understanding in the minute details of the math was simply mind-blowing.  I sincerely was bowled over by the fact he got so quickly what I had taught and only come to through playing the game I had taught my kids.

Then, today, I was teaching divisibility rules to my 4th and 5th graders. I taught the rules for figuring out if a number was divisible by 2 and then by 3, and then showed them how easy it was to figure out whether a number was divisible by 6 from knowing the rules for 2 and 3. We then talked about how to tell if  number was divisible by 5 (it ends in  a 0 or 5) and  someone asked, what about 4?  I honestly drew a blank, so I told them I couldn’t remember and asked them to try to figure it out while I googled it. By the time I had done that and printed out a copy (so I could review the rest before tomorrow’s lesson), I had many kids with very reasonable hypotheses.  However, one kid had it down. . .she said (in words, with no lists, no drawings, no numbers written down) that in any 2 digit number if the first number was odd, then the ones place had to be a 2 or a 6, for the number to be divisible by 4.  Furthermore, if the 10’s digit was even, then the ones digit had to be 0, 4 or 8 for the number to be divisible by 4. (She’s 11.)

I had to write it down to see her pattern.  I chose to use a stem and leaf plot so the kids could begin to see real uses for it (It WILL be on the state test after all.) As I wrote it on the board for all to see, I realized the brilliance of her response. I realized she had seen a pattern in about as quick a moment as had the adult earlier in the day. Class was almost over, so we didn’t have time to talk about it much–but I left it up so we can tomorrow. The thing that really got me, though, was the fact that after school I called two of the three fifth grade teachers in to see her thinking and one didn’t get it, and the other was blown away–“Holy Cow!” were her exact words…

And “Holy Cow” is right…I have MANY students who think like that girl and that Dad…yet for the majority of their day they sit in  regular classroom and do exactly what everyone else does, being given the same directions. Yet the one that worries me is the teacher who didn’t even understand what the kid was doing and thinking. . .how can she recognize when the kid needs extension and some other work than the regular classroom work? This speaks to the need for gifted kids being in classrooms with teachers who have either had some support knowing how to work with gifted kids, or who are simply smart as heck themselves–because smart people can recognize the different kinds of thinking gifted kids do.

How do we restructure our classes, our schools, indeed, our very world so that the talents of our children do not get wasted?  How do we set up life experiences for all children so that they are constantly growing and thinking and being challenged instead of marking seat time until they can do what they want to do? How do I help my classroom teachers see the need for something else for children who learn faster than the speed of light, who think differently and who need more than marking seat time?

Holy Cow, we have a lot of work to do–the system as it exists doesn’t work for so many–so what will you do to change it where you are?

iPod Pilot Lesson- Station 2

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.
As I’m writing this blog, I’m realizing my questions are as much to probe their understanding as they are to get feedback for me on how well they’ve learned and how well I’ve taught what I think I have. I don’t know that the iPod added to THAT process, OR the process of practicing multiplication facts. What it did was it MOTIVATED them to practice.
If iPods will MOTIVATE kids to sit around and make up multiplication facts for each other, then they’re worth having in the classroom, as far as I am concerned. I haven’t found anything non-technologically they’ll stick with like that to practice simple facts.  Their other favorite way to practice is online games. . . and they can do that, too, on the iPods.
I believe devices like iPod Touches MOTIVATE today’s kids to work at school tasks they typically try to avoid, because of the novelty, the “coolness” of the tool, and in this case, the interactivity of this particular app!