I think @WBahn will get a kick out of this one. Here is a question from my 4th grader's homework today: I miss the days when teachers were educated in something more than just, um, education.
[POUND-HEAD-AGAINST-WALL] [/POUND-HEAD-AGAINST-WALL] Come to senses and [REPEAT - 100 times] [POUND-TEACHER'S-HEAD-AGAINST-WALL] Which is the greater number, 86,400 seconds or 5 years? [/POUND-TEACHERS'-HEAD-AGAINST-WALL] [/REPEAT]
I'm a grown man and I can't be asked to point where this went wrong without it taking out of my whiskey time so sort of speak it affects me as well. Across continents!...
After thinking about this question for a while (yes, it is bugging me), I think the point was this: there are three numbers in the sentence: 86,400, 1999, and 78,570. I think she is supposed to pick the largest (absolute) number. If so, this is a double crime. It is asking her to ignore the context in which the numbers are used and then compare them as equals. Noooooo! This is a habit I would never try to reinforce.
Me, too. I've been interacting with my 3rd grade daughter a lot over the last few months and one of the things that I naturally do is that I (almost) always use units when talking to her about physical quantities and I give her a hard time when she doesn't. It's having an effect. When I used to ask her how tall she was she would just give me a number (in centimeters) and so I would deliberately misinterpret it as being in feet or miles or something equally silly. As a result, now she includes the units. And this is becoming the case with nearly all physical quantities even if we haven't every talked about them before (meaning that I've never had the opportunity to ride her on it). And I can see a real improvement in her ability to work with different units for the same thing, particularly time. Just a couple months ago she would add a length in months to a length in days because they were both just numbers to her. Now she almost always expresses them with the units and so she immediately knows that they can't be added or compared and is getting pretty good at working through the computations in her head to translate them to the same units. It takes her a while and she doesn't always get it right the first time, but she's only in third grade! Because of all the games we've been playing (and having her keep score), she's also gotten quite proficient at adding three digit numbers in her head. The first worksheet that they gave her in school was adding and subtracting single digit numbers. It was timed and they needed to get 60% of the way done in one minute to be "okay" and 80% of the way done to be "great". They didn't even have a ranking for getting 100% of the way done so that implies that they didn't expect anyone to actually finish it. She did the entire thing in 43 seconds. And I can't claim that she is any kind of a math prodigy. In first grade she disliked math (didn't claim to hate it), but now she likes it -- she came back from Taiwan with that attitude shift, but I have no idea if it is as a result of her experiences over there, or just a natural shift, but I'm trying to capitalize on it. I'm making sure she gets lots of opportunities to practice math and to see how it is used in the real world, even at her level (like keeping score in a game), and I'm trying to keep it as fun as I can. She is latching onto it more and more. Just yesterday I wanted to see if she could grasp the basic notions of algebra and so I wrote a number on a card that she couldn't see, but I tell her that that number multiplied by seven gives forty-two, could she tell me what number was on the card. She paused for just a moment and said, "Six!" I then asked her what if the number written on that card was such that, when multiplied by itself, gives forty-nine, and she came right back and said, "Seven!" I think this is because I am always asking her questions like, "How many points do I have to outscore you on the next turn to catch up to you?" or, "So if I pay you $0.50 for washing the dishes each evening and, as always, half has to go into long-term savings, how many nights do you have to wash the dishes to earn enough spending money to buy that $4 toy you wanted?" That one really tripped her up the first time I asked it, so I walked her through it step by step and she seemed to really struggle and I didn't think she followed it very well, which was fine. But I asked her an almost identical problem a couple days ago and she went and grabbed a pencil and paper and figured it out -- it was a pretty laborious route she took, but it was valid.
My daughter brought this question to my attention. She told me their was no way compare the numbers. I smiled and told her she was absolutely correct. She'll get the "correct" answer tomorrow. If it's what I suspect, her teacher and principle will be getting a long email from me.
YEAH!!!!! Big points for the little lady! Yep -- the same would be true here. I plan to ask my daughter this question and see what her response is. Whatever she answers will provide a good opportunity to either congratulate her or to educate her. I THINK there was a time when a teacher in public school was expected to know the math they were trying to teach. I know that that went out the airlock at least a few decades ago, but it seems to have gotten just progressively worse. Several of the math profs here have told me that the worst students among the math majors are almost universally those that are planning to go into math education and that it is extremely rare for a good math student to be planning to go that route. I doubt that this place is very out-of-line with most colleges in that regard.
But how can a number be greater than any other? Isn't every number just as capable and deserving as the next? Don't give me any back talk you bunch of mathists!