Learning from the DVD...Player

Teachers of today can choose from a wide array of technologies to spice up their lessons and increase students' understanding. There's Powerpoint, of course, and calculators, smart boards and video cameras, wikis and spellcheckers, voice-to-text programs and DVDs, Excel spreadsheets and Activote systems, GPSes and, um, electric pencil sharpeners; the list goes on.

Most of these educational technologies get plenty of respect within the educational world. (Well, maybe not the pencil sharpeners.) Whole conferences are organized around these technologies and how they can help teachers do a better job of preparing students for the 21st century [Q: At what point will we start saying "preparing students for the 22nd century"?]. BUT there is one technology that is sadly overlooked. It is the Rodney Dangerfield of the educational technology world. I refer, of course, to the lowly DVD player. Not the DVD; the player.



"How did you know so quickly that 8 + 8 was 16?" I asked a first grade girl earlier this week. (If this question sounds familiar, it's probably because you read the previous entry in this blog.)

"Well," she said, "we have this DVD player at home and it has arrows. And if you want to speed through the movie it says 2, 4, 8, 16, 32, and then it goes back to 2 again. And I know that 2+2 is 4 and that 4+4 is 8, so 8+8 must be 16, and I guess that 16+16 would be 32. But then the pattern stops because it goes back to 2 and 32+32 is...something, but it isn't 2."

What can I say? Clearly, we should as a nation reduce our spending on old-boring-and-ineffective technologies such as computers, projectors, smart boards, and digital cameras, and load up classrooms instead with DVD players. Who's with me?

--Actually, this is a really good example of a child not only noticing but using math in everyday life. No one taught her that 8 + 8 was 16. She was struck by a sequence of numbers that appeared in her environment, and spent time and energy deciphering the pattern--learning, and evidently mastering, the fact that 8+8=16 along the way. This is the kind of thinking we always want to see in our students. As our report form puts it, one of our goals for children is that they "recognize and construct mathematics in daily life." It's lovely to see such a clear example.

That's All She (w)Rote

You have 8 cubes, I say.

The child, a first grader, nods happily. He's just counted them, accurately, and showed me how you could split them up so that we each had the same number (4 apiece, if you were curious), and answered several other questions about them as well.

What if you had 8 cubes and I had 8 cubes too? I ask. How many would we have in all?

This isn't necessarily an easy question for six-year-olds, and they vary in their approaches--also in the speed with which they answer. 28, says the boy, just as automatically as you please. There's no lack of confidence here. (Not a lot of accuracy, either, but hey, it's still early in the year.)

28? I ask, just to make sure.

28, he says. No. I mean, um, 34. Yeah, 34.

34, I repeat, resisting the temptation to ask, Regis-style, whether this is his final answer. And how did you know?

Oh, I didn't know, he says with a grin. I guessed.

Okay, I say, and go on to do a few more activities with him. I wrap up with a nice open-ended question: What else do you know about math that you'd like to tell me?

Well, he says eagerly, one thing I know is that 8 plus 8 is 16...

SMACK! goes my hand (metaphorically at least) against the side of my head.

This little anecdote nicely illustrates the difference between knowing a fact and KNOWING it. This boy knew that 8+8 was 16, but he didn't KNOW it--that is, while he could repeat it, he couldn't use that information in a real-life context. His verbal knowledge isn't yet supported by his conceptual understanding.

There's nothing wrong with learning some kinds of things by rote. Indeed, sometimes it's necessary. It's just that you have to be careful with kids and not automatically assume they KNOW everything they know....if you know (KNOW?) what I mean!