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!

Spiiiiiiiiders

So there I am in the Pre-K, "just visiting" as they say on the Monopoly board, and the children are doing watercolors, and one child brings over her picture to show me.

"I painted a tabantula," she explains, her eyes as wide as a four-year-old's can get. Wider, if possible.

"A tabantula, huh?" I say. "Sounds mighty scary."

"It has eight legs," she says, and proceeds to count them, which she does very well (us Math Guys notice these kinds of things), and lo and behold, guess what, there ARE eight.

"Well, that's a good thing," I say, "because taban, I mean, taRANtulas are spiders, and spiders are supposed to have eight legs. Good for you for knowing that. I guess you're an expert on spiders."

She ignores this comment as the typical babbling of the Adult and points instead at a swirl of red paint. "That's the tabantula's head," she explains. "Do you want to know what that red is for?"

"Tell me," I say.

She leans in very close, stretches up, finds my ear, and stage whispers "IT'S BLOOD."

Can't wait for Halloween!

The whole nine yards; or, Dressed to the nines

If I'm timing this one correctly (and I'm probably not as the margin for error is not exactly huge), this post will be time-stamped

09 [month]
09 [day]
09 [year]
09 [hour]
09 [minute]

or

09/09/09 at 09:09

The nines have it!

[Edited to add: Ooh! Missed by ONE MINUTE. Oh well...I tried.]

SummerMath, Part 4: On the Road Again

If you're like most Americans, you and your children spend a lot of time on the road. There are plenty of ways for kids to pass the time on car trips, whether of 5 minutes or 500 miles. Several of them I'm quite sure you know:

Screaming "She's on MYYYY side!!!! Mom, make her get off of MYYYY side!"

Asking as often as possible, "Are we there yet?"

Threatening to throw up.

Singing vaguely risque songs like "The boys and girls are kissing in the D-R-A-K, D-R-A-K, D-R-A-K, Dark!"

Singing "George Washington Bridge." OH MY EARS QUICK RINSE THEM OUT WITH RUBBING ALCOHOL (George Washington Bridge, for those of you not in the know, repeats the lyrics "George Washington Bridge" again and again and again to an essentially unmelodic melody. My sister pulled this one on a 5-hour car ride between Chicago and La Crosse, Wisconsin, many years ago, and when she was finally told she could NO LONGER sing "George Washington Bridge" she said "Okay, then I will sing 'Adobe Bricks.' 'Adobe Bricks,' as it turns out, is 10 times worse. We eventually threw her out of the car)

But those days are over, for here is a list of WONDERFUL MATH ACTIVITIES that you can do in the car. (Assuming that your children can actually see out the windows.)

1. LICENSE PLATES. In New York State, most (not all) plates are of the form AAA 1111--three letters, then four numbers. Have kids hunt for license plates withe certain characteristics. Who can find one that has four even digits? Four odd digits? Four digits that are ascending (like 4689)? Descending (say, 8521)? Two digits that are the same? Three digits that are the same? If you're stuck at a stoplight, ask your child to add the four digits on the license plate of the vehicle in front of you--which two are best to add first? What shortcuts can your child find? (To add 6364, kids might start with 6+6=12, a "doubles fact," or with the "ten-friends" fact that 6+4=10.) Estimate by looking if the sum will be greater than or less than 20. Then check. Whoops, green light--better move on...

2. STOPLIGHTS. How many stoplights do you think there will be between here and the mall/camp/Grandma's house? Let's keep track. Will they mostly be green when we get to them, or red? You count the red ones, I'll count the green ones. Do you think it'll be about the same on the way back, or will it be different? Let's find out. For a route you drive frequently, choose a couple of lights and keep track of whether they're red or green over a period of 8-10 days. These are exercises in counting; they also ask kids to gather, use, and interpret data. More than half of the lights are green? Why do you think that might be?...That light where we cross Route 55 is almost always red when we get there--how come?

3. VROOM, VROOM. On a 4-lane highway, have kids count the cars you pass and the cars that pass you. Make this an exercise in counting forwards and backwards: start with a score of 10, add one for every car you pass, subtract one for every car that passes you. Or, start with 50 or even 100. Try not to give in to your children's pleadings to do whatever it takes to avoid being passed by that in-your-face Oldsmobile or to overtake that weirdly painted appliance truck. Does it matter who's driving?...why yes, yes, it might. (And can we correlate that with speeding tickets received? Why yes, yes, we can...)

4. NUMBERS ON SIGNS. There are lots of these running around the roads: speed limits, mileage markers, route numbers, distances to upcoming cities. We call Route 376 "route three-seventy-six," but what's its "proper" name? (Three hundred seventy-six. Yes, I know it isn't *really* a number, because it doesn't indicate three hundred seventy-six of anything...) Who can find a two-digit number on a road sign? A three-digit number? An odd number? The sign tells how many miles to Montreal and how many to Buffalo. Which is further away from us right now? How do you know?

5. MENTAL ARITHMETIC. We're at milepost 27--look, there's the sign. What milepost will we pass in five miles? Ten miles? (Careful--are we driving towards milepost 0 or away from it?) How many more miles till milepost 40? (See above.) The sign says Albany is 65 miles away. Our speed is, guess what, 65 miles per hour. About how long till we're in Albany? (Only use easy numbers for this kind of question!) The car can be a good place to go over basic facts as well: "7 + 2." "9!" "Tell me two ways to make 10." "Um--"

6. MAPS and DIRECTIONS. Have children direct you to a location they've visited many times before. Ask them to tell you where to go straight and where to turn, and whether you should go left or right when you turn. Obviously, don't break any traffic laws--you are still the captain of the ship! As for maps: Print out a map showing your route to a (relatively) nearby place. Go over the map with your child before you leave. Have your child hold the map and try to track your position along the route as you drive. Try using a road map for longer distances: Find a long thick blue line with a shield and the number 84. That's the road we're on now. We're heading west...which way is west? Can you find a city called Middletown? Excellent--we're just a little bit west of that right now. What's the next town you see? Some third and fourth graders can become quite good at navigating. Just be sure that the "road" they're having you follow isn't just a marmalade stain on the map (this happened once to Paddington Brown and his family, I believe).

As always, these are ideas, nothing more; you can come up with others yourself. Be sure not to push too hard. REPEAT: BE SURE NOT TO PUSH TOO HARD. If you find you're suddenly more invested in these activities than the kids are, cut the games short and do something else: talk, sing, tell jokes, look at scenery. But if people start yelling about siblings being on theirrrrr side, it helps to have games like find-a-license-plate-with-4-odd-digits in your back pocket; and if you can find the right combination of math activities for the car ride on any given day, you will NEVER EVER EVER have to put up with anybody singing George Washington Bridge, and that will make any hardship worthwhile.

My Heart's in the Heartland

A cool map for you geography geeks out there:


http://strangemaps.wordpress.com/2009/07/27/402-homeland-is-where-the-heartland-is/#comments

Note that some of the sizes are a bit off. Also, something seems to have happened to Dutchess County. STILL!

More Rabbit News

--> NEWS FLASH <--

THE MATH GUY'S RABBIT CAN MULTIPLY!!!!

(Technically, this is NOT the Math Guy's rabbit. It belongs to his daughter, who purchased it from a pet store a couple of years ago and then hid it in the garage for three days while she worked up the nerve to tell us what she'd done. However, now that she's away at school, guess who does the bulk of caretaking for Miss Rabbit? --That's right.)

Anyway. The other day I was communing with the rabbit and asked it a question, offhandedly:

"Rabbit!" I said. "What is 3 x 5?"

And darned if she didn't woffle her nose 15 times.

"Remarkable!" I said. "And, Rabbit, what is 2 x 4?"

I counted eight woffles.

"Such a mathematical rabbit!" I crowed, and took her through several more examples: 6 x 2, 4 x 4, and 2 x 10. Woffle, woffle, woffle, and she was right on the money EVERY TIME.

My family seems suspicious of her awesome abilities. They seem to believe that I am cheating or perhaps misinterpreting her responses, but I swear she woffles the correct number of times. Anyhow, who cares what they say. I'm considering taking her on the talk show circuit--your thoughts?