Hmm, that reads like one of my more raggedy posts. Pretend I was going somewhere with that, because it's been in various states of composition for about a day, and it's time to post it.
Shouldn't it be possible to find an empirical answer to this debate -- if the reformers are correct, it should be possible to demonstrate that various reforms improve students' ability to learn Math.
They do. That's why the traditionalist have been particularly vicious with Dr. Boaler, because she's done the really large n, conclusive studies.
it should be possible to demonstrate that various reforms improve students' ability to learn Math.
At what level, though?
3: Maybe she said it too fast and they heard she did "large, inconclusive" studies?
their approach often seems to boil down to the "either you get it or you don't" style of teaching math, which tends to exclude traditionally underrepresented groups
Like me. I am traditionally underrepresented in college-level STEM classes.
It's true. I've never had any of Halford in my math classes.
The 3rd-7th paragraphs might be a decent summary, but the overall messages is a great example about how frustrating attempts philosophers to engage in public policy issues can be. No, bringing up Wittgensteinian considerations does not in fact advance the debate. Ugh.
8: If only they would pass over in silence.
Like intestinal gas on a crowded bus.
They are right that in order to do college-level math, you need quick retrieval of some algorithms. Stopping to use a calculator for trivial calculations does prevent you from staying immersed in a harder problem. But you also need numerical reasoning, and that needs to be developed.
This, from the OP, seems really right. I mean, obviously any method of math education that left high school students unable to do arithmetic fluently would have gone off the rails somehow, but is there any evidence that reformist math education does that?
Unfortunately, students have never been able to master the algorithms, (esp fractions) as a population. I think they've shown that reform math doesn't make it any worse, though. And does help students learn to reason mathematically.
I never thought of fractions as an algorithm. I always figured it for half-assed division.
Heebie, thanks for posting this. I always got the algorithms right away in classes, although the logic to them sometimes took me much longer (like, years, embarrasingly). I was mystified by illustrations representing units (like, big blocks for tens, small blocks for ones) but had no problem computing answers. It's neat to see people gathering good data on how students will learn best if they're not the sort who would be successful with any method.
(However, I will say WTF to students who can't manage basic computation in college. I think it's amazing how poorly they do when the problem isn't presented in the context of a particular chapter in math class. My favorite example is a friend who was helping a student calculate what they needed to get on the final to pass a course, "Well, let's see, it seems that You got a 10%, a 30%, and a 20%. We drop the low score, and the final is 40% of your grade. This means you need . . . a 113% on the final to get a D." Student asks, "Then what would it take to get a C?")
13: I'm erasing the long answer I just started in favor of waiting until I'm on a real keyboard.
I read the article. Everything is an algorithm.
My kid's school will apparently use something called "Singapore Math" which I hope doesn't involve caning.
I'm still mystified that pedagogical video games haven't become more widely used. Half the Unfoggedariat spent the last week collecting teeth; surely someone can write something to addict kids on mastering simple algorithms.
Wait, is this really how reform math is taught?
In one widely used and very representative math program -- TERC Investigations -- second grade students are repeatedly given specific addition problems and asked to explore a variety of procedures for arriving at a solution. The standard algorithm is absent from the procedures they are offered. Students in this program don't encounter the standard algorithm until fourth grade,
Because that seems silly not to at least mention the standard algorithm, as one possible way of solving the problem.
FILL YOUR POCKETS UP WITH EARTH
GET YOURSELF A DOLLAR'S WORTH
IF 1.5 CUBIC FEET OF SOIL COSTS $16 AND $1 OF EARTH FILLS YOUR POCKETS, HOW LARGE ARE YOUR POCKETS?
19: It really is withheld. Consider a concept like "borrowing" in subtraction. Traditionally kids have absolutely no idea why they cross out the zero, replace it with a little 9, and add a 1 in front of the digit that's too small.
(In defense of teachers: generally the teacher does understand it and does give an explanation, but elementary school kids are really too young to understand it if they're just told the explanation. So the kids end up just memorizing the steps without knowing what they're doing.)
So with reform math, the kids might work it out themselves using blocks one day, representing different digits, and each team might come up with a different procedure, but none of them will come up with the "cross out the zero and write a 9" method, and it's withheld until they can see the point of it.
Reading 21 might give the impression that I myself do not understand how borrowing works. Isn't that droll.
At the heart of the discipline of mathematics is a set of the most efficient -- and most elegant and powerful -- algorithms for specific operations.
Isn't the study (and knowledge of) of algorithms basically a reasonably specific field predominantly of interest to applied areas? Like, there's no particularly reason for a working mathematician to have much knowledge of specific algorithms unless they're an algorithmist, and even then...
They're not talking about real algorithms. They're talking about algorithms like "find a common denominator for fractions in order to add them without having any clue why you need to" and "borrowing" and "multiply by the reciprocal when you need to divide", etc.
Arithmetic tricks, you mean? I'd always thought that one of the points of mathematics was that it wasn't arithmetic...
I always multiply everything by 5.8. I call it the Hick Constant.
25: right, which is why the detractors start to look like knee-jerk contrarians.
Also it really drives them crazy that math Ed people generally don't have graduate studies understanding of pure math, despite the fact that math Ed people are primarily focused on k-12.
But I guess if you thought that maths was basically a way of training up people to take STE papers at college, you'd be a bit pissed if the mathematicians started asserting the autonomy of the discipline and all.
But I guess if you thought that maths was basically a way of training up people to take STE papers at college, you'd be a bit pissed if the mathematicians started asserting the autonomy of the discipline and all.
Oh those last two are me. Whut up, iPad.
21: Ok, I guess I can see that getting second-graders to understand why borrowing works is probably impossible. On the other hand, is there any sensible way to do subtraction WITHOUT borrowing? I mean, I guess you can count in unary, or do guess-and-check, but that just looks bad. Like, "this school is making my child stupid," bad.
I'm still not sure I understand why you do borrowing in subtraction. I mean I get that it works, so maybe the answer is "because it works."
I'm still not sure I understand why you do borrowing in subtraction.
It's very simple.
Oh wait maybe I see. So if you have 23-5, it's like you're breaking it down into 13-5 (comprehensible!) and then 20-10, since you've already added 10 to 3. Look out second grade because HERE COMES A GENIUS.
Oh wait I forgot to make the next step explicit -- you have to add (13-5) and (20-10) together to get the answer. Hot damn third graders here we go I am all over your ass with math!
I think it's probably clearer if you say that you are borrowing ten from the twenty.
But, see, Robert has now constructed some knowledge, and so he's got a better grasp on it than if he'd just memorised the rule.
The pros and cons of reform math: greater risk of death in grades 2-4 due to inefficient arithmetic, but better chance of success in college-level science/engineering due to actually understanding what an eigenvector is.
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So, mineshaft, if one was hypothetically hoping to talk one's mom out of marrying a forty-ish years younger safari guide as a means of getting him into the country so he could be sugar mama'd to (after he had been turned down for a student visa), how would one approach that?
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21: you would actually be getting them to figure out borrowing. Ie "one blue block is worth ten yellow blocks. Here's a way to represent 35 in blocks. Now remove 18 of them" and get the kids to figure out that they need to convert a blue block into yellow blocks.
So if you have 23-5, it's like you're breaking it down into 13-5 (comprehensible!) and then 20-10, since you've already added 10 to 3. Look out second grade because HERE COMES A GENIUS.
Why is 13-5 better? I'd rather say it's like this:
23 - 5 = 20 + 3 - 5 = 20 + (-5) + 3 = 20 + (-2) = 20 - 2 = 18.
But you'll get kids who come up with a method like "remove as many yellow blocks as you can. Then convert a blue block in order to get the rest" and that solution is distinctly different than the order forced by the standard procedure.
Love the scrupulous adherence to the 40-comment-on-topic rule.
Also, uh, man. Have never had to deal with that problem.
41: It must be weird to have one's hunch that one is a secondary character in a romantic comedy confirmed.
Bridget Jones was the main character, and IIRC that's what happened to her mom.
Did I already post about this under my pseud? Oh well? Shit fan-hitting incurs presidentiality, I guess.
41: If she marries him, the odds of her being murdered are 2/5 and the odds of his being murdered by her are 1/6. What are the odds of any murder in the marriage?
So anyhow let's workshop this. Any approaches come to mind?
"Here's the deal: You split up, he gets half. Still worth the risk?"
No, he won't. She already has what she claims is a pretty iron-clad prenup drafted (and has suggested -- strongly suggested -- that I look it over).
Goddamn free-associating brain. I was momentarily puzzled to find myself sitting here singing to myself "if this a role call, kill the director".
Oh wait, maybe the lyric is actually "rom-com". Anyway.
"Here's the deal: There are no iron-clad pre-nups, especially for young safari guides from Africa."
"I've touched the rain down in Africa. There's nothing that a hundred lawyers or more could ever do."
49: I don't actually remember you doing so, no.
Back on the topic, my son's school tried to teach him math with all the Montessori blocks and beads and stuff. It really didn't take. It mostly seemed to work for kids who didn't have an innate desire to argue with everybody.
So, outline your fears for the situation for us. Because it needs to be outside of the purview of "two consenting adults are living a wacky life!" to justify interfering, and then your specific concerns should drive the conversation.
58: hopefully you and google are on the same page.
41: He's not going to stick around to be sugar mama'd; he's going to last as long as it takes to get the green card.
41:
(A) Speak to her pastor. Surely if he can provide a scriptural argument against the marriage, she will not go through with it.
(B) Call ICE and denounce them.
(C) Find a more appropriate fiance, then push her into the lake, so that he can rescue her.
(D) Cameo by Paul Hogan "That's not a knife. THIS is a knife."
(E) She probably has an age-appropriate platonic friend who is secretly in love with her -- contrive to put them together in some kind of stressful, absurd situation, possibly involving a wager, and watch the romance unfold.
(F) You have a brother who was kidnapped by pirates as a child, right? No doubt he and this fellow are one and the same. Prove it, and everybody comes out happy.
(G) Pay your personal physician to convince her she has a brain cloud, and should sacrifice herself to a volcano god. Everything should work out satisfactorily.
61: I don't remember seeing it here either.
60: yeah, fair enough. So, assuming the prenup holds up, and he is not actually trying to gets his hands on her newly mildly substantial fortune (a completely fair assumption; I don't think he's trying to do this), my issues are: 1. The asymmetry (in terms of money and life station) between them is so massive that there is very little chance it will actually work out. 2. The whole process of securing immigration status for a spouse is a giant, painful ball of suck, and I don't think she's prepared for that -- and I think the suckiness will roll downhill onto her friends and relations. 3. She is a very forceful person, and I don't think there's any way that she could actually know that he is entered into this freely and without constraint, and I don't think she really understands that (for instance, he has a daughter in his home country, but the opportunity to go to the US and get an education could be so great that he feels obligated to leave her behind). 4. The asymmetry between them is so great that if it DOESN'T work out, it has the chance to be absolutely disastrous for his life and family back home, 5. the whole thing is making her act selfish and oblivious to the needs of not only her family but also her friends and her life in general here in the US, and finally 6. it makes me incredibly uncomfortable that she is essentially buying herself an almost entirely dependent lover who is roughly the same age as her child(ren).
To summarize, I think that the downside of running off and marrying this guy is huge, but I don't yet have a good way of explaining how huge or why I think that.
Some of my concerns expressed above definitely might be nonsense.
So, assuming the prenup holds up, and he is not actually trying to gets his hands on her newly mildly substantial fortune
Assume we live in bizarro-universe. Or, more charitably, assume that he's not trying to do this but that this will be a likely consequence of her actions.
I guess also it just seems like it's really hasty; she hasn't spent more than a month or so in the same place with him all told, and a good chunk of that she was paying him to guide her safari. He does seem like a totally nice guy, albeit incredibly bored when he's hanging out with this elderly woman who goes to bed at 9:30 or so. And I just really worry that he has no socioeconomic choice but to go along with what she says.
for instance, he has a daughter in his home country, but the opportunity to go to the US and get an education could be so great that he feels obligated to leave her behind
Oof, this part sounds pretty awful.
The urge to troll this thread is very great. VERY GREAT, I say.
66: sure, that's a worry, too. Especially since I have begun to be mildly worried about her ability to manage her shit without real impulse control problems, and especially especially since she recently took specific steps to take financial care of her siblings but has not done the same for her children or grandchildren. All that sounds (and feels) pretty craven, but there it is.
6. it makes me incredibly uncomfortable that she is essentially buying herself an almost entirely dependent lover who is roughly the same age as her child(ren).
That was my first thought. My uncle was widowered and then married a woman from the Philippines that he first met through some internet site created specifically for that purpose. He doesn't have any kids, so they can't be made uncomfortable, but other people were.
61: Sadly, you've definitely mentioned this here before. Someone brought up Bridget Jones that time as well.
On the general problem I've got nothing, other than being supportive if she needs anything. How's the guy as a person? Do you spend much time around him?
I have begun to be mildly worried about her ability to manage her shit without real impulse control problems,
Oh, why would you say that?
Ok, 1. isn't fair - most relationships fail, in general, or they succeed until they fail, etc. and the asymmetry is super common with reversed genders. So I think that one is not okay to raise.
3 and 5 are fair. For 4, he must be aware of the calculation, no?
73: Eh, well, she's extremely forgetful, and then there's stuff that could either be the obliviousness of the rich or something different. Buying (expensive) things and then forgetting about them, that sort of thing.
I guess also it just seems like it's really hasty; she hasn't spent more than a month or so in the same place with him all told, and a good chunk of that she was paying him to guide her safari.
Could you suggest that they arrange to spend more time together, before taking any major action?
How's the guy as a person? Do you spend much time around him?
He and I have not quite bonded, for what I think are somewhat obvious reasons, but he seems like a pretty good guy all things considered. My dad likes him loads, which doesn't seem like it would be a given. He has mostly seemed bored when he's in this country, as I said earlier, but he is apparently a fantastic safari guide, and is generally very intelligent and charming.
They've met once, and he's already tried to come to the U.S. and he's been denied? Odds are pretty good that they'll be denied at the consulate with only one meeting if there's a forty-year age gap.
I did all of shiv's paperwork for his visa/greencard, and I spent a lot of time on immigration forums, and there's a lot of unhappy stories that start with a middle-aged divorcee meeting a twenty-something guy. In some cases they went through two or three years of denials and appeals, and then the guy got here, and left as soon as he could.
76: I have suggested just that, but he can't get into the country right now, which makes things more difficult, and also that suggestion seemed to really just bounce off my mom -- her theory is that she hasn't had a serious relationship in a very long time and there's no time to waste, especially with the time it takes to complete the immigration process.
Sometimes Big Brother can be your big brother.
I semi-seriously think that you might want to consider hiring a sexy gigolo/the Apostropher to seduce your mom.
78: Yup, that's exactly the kind of thing I'm worried about. They have met more than once -- they met once on safari, she arranged for him to come her on semi-false pretenses, she went on another safari, he came back on a tourist visa -- but there have been notable reversals: she tried to get him a student visa and he was rejected, and then he (recently) tried to come back for the balance of his tourist visa (after having been rejected for the student visa) and got sent back at the airport.
81: I am semi-seriously convinced that his helplessness in this country allows her to behave as simultaneously a lover and a mother figure, and that's a big part of the appeal. Which I do not like one bit, no, but which I imagine isn't actually a good reason to try to talk her out of it. But which would make Operation Apostrophogigolo more difficult.
Aside from jeopardizing the inheritance, most outcomes seem to fall into "sometimes you gotta let people make terrible mistakes" territory.
What if your mom hired a younger woman to marry him? Would that get him past immigration officials?
OK, not the Apostropher, then. What about one of the younger, more helpless commenters? Trapnel is pretty good looking based on photo evidence and needs some cash.
Ulysses, I'd be consumingly focused on the squickiness of the power differential but that's just because that's a hot button for me.
I think the answer is buried in your own comment:
2. The whole process of securing immigration status for a spouse is a giant, painful ball of suck, and I don't think she's prepared for that -- and I think the suckiness will roll downhill onto her friends and relations.
If the real question is "How do I stop this?" then I would attempt to do so with practicality on exactly this issue.
Can you get her to consult with a really good, brutally honest immigration lawyer? Who is going to tell her how miserable and lengthy the whole process will be? Who is going to open her eyes to all of the nine million things that have to happen between Point A and Point B?
If the answer is no, maybe you should just Xerox selected excerpts from Elizabeth Gilbert's most recent book (the one after Eat Pray Love). The ones about the misery of being separated from her Big New Love by immigration meanies.
85: Sure, that seems likely. But my mom is a very smart woman from whom I have learned much. It is strange and implausible to see her doing things that I know are not smart because she taught me they are not smart. And more than that, I feel like she is implicitly violating the moral standards she raised me with. And more than that, those moral standards emerged at least in part because her father married a much younger woman who eventually stiffed the kids on the inheritance. To see her replicating the same patterns (but with even more uncomfortable colonialist overtones) is painful and confusing, and I want it to stop, dammit.
Can you get her to consult with a really good, brutally honest immigration lawyer?
She claims that she has done this. Unfortunately, I feel like "this is extremely difficult and most people are unable to accomplish it without a great deal of heartache, if they find it at all possible" has mostly served to this point in her life as a cue that she should be trying to close that deal.
85 was maybe not the most serious suggestion.
Well, in that case, I think Cala is likely right. Especially since he has already tried to come on tourist and student visas, and if he is coming from a developing country. It's very hard to imagine the consulate granting him a visa even with an American wife.
Are you sure he's actually single, btw?
Are you sure he's actually single, btw?
Not particularly. High-status males in his tribe (of which he is one) generally take more than one wife, and he does already have a daughter, so who really knows. My mom certainly thinks he is single.
Ten bucks says he has a wife. Your mom may have met his nice sister, about his age, who seems really sweet to her brother...
Hah, geez. My mom built him a house back home; right now his sister is living in it with his daughter.
93/94 is pretty amazing to read.
Mmm-hmm. He gets his greencard; leaves your mom; maybe goes for citizenship; petitions for his wife and daughter.
I think the sister actually may have a husband and kid who are living there as well? But yeah honestly who knows. What I think my mom doesn't understand is the depth of the gulf between them and how difficult that makes communication or understanding.
I would be perfectly comfortable with 98, I must admit.
What your mom doesn't understand is that there are websites and internet cafes that coach people on how to use American divorcees as "paper wives." It's also completely possible that he's a nice guy, perhaps reasoning to himself that he's not doing your mom any real lasting harm. But this smells to high heaven, and with luck, the consulate will catch it if it's a problem.
93/98 via the message-boards may be the way to go. "I have a friend whose husband is Canadian, and she was telling me about landmines in the immigration process, and she said your situation sets off all sorts of red flags. So I went hunting, and found the following twenty horror stories that fit your pattern. Here mom, let's game out these twenty horror stories that look really similar to your situation."
100: It'd probably be pretty rough on your mom.
What I think my mom doesn't understand is the depth of the gulf between them and how difficult that makes communication or understanding.
Or -- and I don't mean to be too harsh here -- that may be part of the appeal: Someone who can be slotted effortlessly into a role, and who won't muck things up by becoming an actual human being with independent desires and preferences.*
It doesn't even have to be in a creepy colonialistic sense. It can just be in a lonely, wishful, I-just-want-someone-I-can-project-things-onto unconscious sense.
*Except of course he *does* have them -- not expressing those preferences right now is a merely a function of the power dynamic...and just like all those mail-order brides, once he gets here that will change.
At least she didn't meet him through an unsolicited e-mail. Which is a lame way to pretend the following is on-topic for this thread rather than a recent dead one.
Received in my work e-mail today:
Hi JP,
We are running a promotion called Helicopter for a Conversation.
If you (and up to 2 additional co-workers) will join us for a 15-minute conversation, by telephone, we will send each of you a remote control helicopter.
We will ask a few questions to determine if Never heard-of-em can benefit your network at some point in the future, and answer any questions you may have.
Are you interested?
Bidding for JP's co-worker for a day starts at $50.
103: Yes. Maybe less rough than some other outcomes, though.
101 is pretty brutally plausible, of course.
104 is entirely correct, of course, yes.
Serious question (for anyone) - what does "High-status males in his tribe (of which he is one)" mean in terms of poverty? If his poverty is not acute*, does that change how much Ulysses should be concerned for him and whether he's being coerced by the assymetry?
*and I don't really know what this means. I'm just trying to say "is there a point where he's motivated by greed, not need? And if it's so, don't worry about protecting him."
A typical kind of scenario. Morocco, but the flags are similar.
what does "High-status males in his tribe (of which he is one)" mean in terms of poverty?
Well, nothing, really. His tribe is not urbanized or anything, so wealth is generally measured in cows. He does have a lot of cows (like 400, I think, per my mom?).
My guess would not be coercion. (And this is totally ex recto.) It's more like -- the guy is young, America is supposed to be a place that is good for a young guy, unemployment in his country is high so he can't move out, get married, and so forth, and student and visitors visas are often extremely hard to get for someone who isn't wealthy or well-connected.
So... not exactly greed, or need.
The thing is, you can have enormous status and resources in your home country, and yet still not have any realistic hope of getting to the United States permanently.*
If that's what you want -- and for some people it is their dearest dream -- than almost any path that might get you there could be given serious consideration.
I also would not underestimate the desire of a parent to help his child. Opportunities for women (in education, work, etc.) are overall still better in the US than in many other parts of the world.
*Not counting the diversity visa lottery that 13 million people a year enter and 55,000 win, and which will be canceled this year if Congress passes immigration reform.
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Kanye and Kim named their baby North. As in North West.
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109: Actual cows or just 400 cattle of various ages and genders?
I hated this baby. Hated hated hated hated hated this baby. Hated every simpering stupid vacant audience-insulting moment of it. Hated the sensibility that thought anyone would like it. Hated the implied insult to the audience by its belief that anyone would be entertained by it.
110: Oh, yeah. I mean I'm not even sure I'd say that's subtext. It certainly seems completely obvious to me that's what's going on. I feel like on some level it's also obvious to my mom that's what's going on, but then she keeps talking about him not deserting her when she's old(er), which, of course he will, right?
I mean as far as this being a way of achieving opportunity for his family, he definitely talks about that very openly; he wants to run for office in his home country, and made my mom redraft the prenup so that it specified that he could go visit home five times a year (which is a heck of a lot of transatlantic travel, but anyhow). Actually, my previous sense of things had been that he was pretty explicit with my mom that he would want to come to this country for the opportunity and she was sort of like "oh, he loves me and wants to be with me".
113: I am afraid I don't know.
109: Did he have deeds to the cows? I mean, not to impugn his character any more than necessary, but it seems like it would be pretty easy to point out a bunch of cows to some clueless Westerner and be like "See all those cows? Those are mine. I'm kind of a big deal, actually."
Midwesterners: The ones who want details on the cows.
To continue 115, one of the things I've been worried about is that she hasn't been clear with him about how she sees the relationship, that she has been to willing to cast it as "oh yes I will sponsor you to come to the US and get an education for your family" as opposed to "come and be my much younger live-in lover". The marriage aspect confuses that picture, of course.
But...really? MY cows?
I have no idea if cows have deeds in that part of the world. Or if they have deeds in any part of the world. Are there deeds to cows?
He gave my mom four cows, in theory, although they did not make the journey to this country.
I'm now convinced that Cala's right about this being a scam.
I think you have one serious conversation with your mom, armed with as much supporting evidence of this type of scam as possible - anecdotes, websites, whatever you can drum up. Then you leave her with print outs of everything, and let her do what she will. Potentially she makes a five year mistake (as opposed to a lifetime mistake, which does not seem to be on the table).
119: If she's doing it to be nice to a young guy who wants an education, she's committing immigration fraud.
125: and conversely, if she was trying to get a student visa for a guy she was actually, dating, she was committing immigration fraud then, probably, right?
No, because she doesn't sponsor a student visa.
126: If she didn't know what type of cows he owned, the financial aid form must have been wrong.
What about one of the younger, more helpless commenters? Trapnel is pretty good looking based on photo evidence and needs some cash.
You're a funny man, Halford.
What happens if Mrs. Grant incorporates a nominal stateside safari-park business; the young fellow gets a nominal bachelor's degree in zoology and wildlife management; and the safari-park business requests to hire the animal-scientist on an H-1B visa, all of which is entirely above board except for the diploma-mill degree and the nonexistent safari park?
400, I think, per my mom?
This is the math thread, so let's see;
400 = number of cows
Assuming mom is being defined biologically, 1 = number of moms of Ulysses S. Grant
Calculating, that means 400 cows per mom = 400 cows total. Oh, and wait, I think I just learned the property of identity.
On the bright side, Mrs. Grant could write one hell of a 'Modern Love' column.
In this country, there are more school children carrying on studying maths up to age 18 than ever before. Which largely seems to mean that there are more of them doing maths that they don't actually understand. There's been a huge kerfuffle recently over an exam paper that was too difficult - http://www.bbc.co.uk/news/education-22887009 - basically some actual thinking was involved rather than just going through the same style problems again. I read (on The Student Room) one person complaining, "how was I supposed to know that sin 50 = cos 40 ?" ffs.
Anyway, as I started reading this comment thread, kid C and I had a nice chat over breakfast about how he was looking for a function that would produce a graph with wavy steps. He came up with x + sin x which was exactly what he wanted (and not something whose shape I had in my head).
Kanye and Kim named their baby North. As in North West.
Named in homage to the 18th century British Prime Minister, their historical hero.
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Not sure if this is worth a front page post, as I don't know how much interest people have in photography, but the NYT ran a very interesting interview with Henri Cartier-Bresson yesterday and today.
http://lens.blogs.nytimes.com/2013/06/20/henri-cartier-bresson-living-and-looking/
http://lens.blogs.nytimes.com/2013/06/21/cartier-bresson-there-are-no-maybes/
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Kanye and Kim named their baby North. As in North West.
So he is in fact North West by West? (out of Kardashian)
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For anyone still bothering to read Krugman, like todays column
Chapter 3 of Michal Kalecki
"According to [my] first theory the absolute level of profits is determined by capitalist consumption and investment. According to [my] second theory the relative share of profits in national income is determined by the degree of monopoly" (Kalecki 1991, p. 121, emphasis in original).
1991 is publishing date of complete works; original papers are 30s and 40s
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Given asilon's comment I'll contribute a thought about math: I was raised on the earlier versions of the reform, and when it comes to stuff like subtraction and crossing out the number/borrowing a one, I learnt it algorithmically first with some "understanding" thrown in. I really appreciate that i understand it that way, and it was much easier to learn othe number bases (for example). But objec manipulation alone - or cool tricks for understanding - aren't enough for retention. I did a new-fanged calculus course in high school (because I thought that was fun) and while it was fun to try to reason stuff out I'm not sure what if anything I retained. Learning algorithms for calculus, and understanding later, is more useful. Maybe.
This sounds a bit like the debates about language immersion - at first, parents worry because their kids can't read in either language and they panic, but it generally evens out by grade 5 or so.
I will say that I think, from watching Newt and Sally, that the reform math can be annoying and unpleasant for the faster kids -- someone who can follow the reasoning for why borrowing works from the teacher's explanation of the standard algorithm is going to be bored and frustrated going through the motions of pretending to develop that understanding by inventing alternative methods of subtraction. (That is, I listened to a fair amount of grousing about "And now we have to explain why 14-6 is 8 by drawing shapes. And now another way. And now another way.")
I don't think this is terribly important -- the faster kids are going to be a bit bored no matter how you teach things -- if it's working for the kids who weren't getting it of their own accord. But it might explain some of the anti-reform animus, if it consistently makes the quickest students annoyed and cranky.
115: You know, I really don't think there's anything useful you can do. If he's a decent guy, which it sounds as if you think he is, he's in it for the immigration potential and the situation may not be too ugly to unwind when that goes south, assuming it does. Luckily, as well as there not being anything useful you can do to snap your mother out of it, I don't think there's anything useful you can do to make the situation work, so you're free to be as friendly and supportive about the whole thing as you can without changing the odds that it will go on any longer than it has to at all. Being the bad guy wouldn't do any good at all, so there's no need to take a stand.
But it might explain some of the anti-reform animus, if it consistently makes the quickest students annoyed and cranky.
I'm pretty sure that absolutely anything without a healthy dose of go-at-your-own-pace will consistently make the quickest students annoyed and cranky.
This is an excellent response to the OP link. K/eith D/evlin is trustworthy and smart.
Well, right -- like I said, this doesn't make it a bad idea. But the particularly reform aspects of the math my kids got seemed to be perceived by them as particularly irritatingly timewasting. I don't think this did them any more harm than any other aspect of their schooling that wasn't perfectly tailored to their special snowflakedom, and if it helped out other kids in the class it's worth it. But I can see that reaction driving hostility from adults as well.
143: Nia has had a hard time with math and was in a specialized go-at-your-own-pace computer program plus seeing a math specialist to try to get her basic understanding of how numbers work to where it needed to be, but as far as I could tell her homework at night would be whatever everyone else in the class was doing. It was incredibly frustrating as a parent to look at the paper, try to figure out what the questions meant and how she was supposed to be figuring out the problems if she even had the capability to do so and then help her get through it.
This reminds me that I'm not pushing her as hard as I need to on rote memorization of math facts this summer. Ugh. But I do give myself credit (and probably have here before) for eventually realizing that since she was unable to count on number lines reliably but fine at playing board games, I needed to make her a board game for doing math. It worked beautifully, but by then there was only a month of school left anyhow.
I could tell her homework at night would be whatever everyone else in the class was doing. It was incredibly frustrating as a parent to look at the paper, try to figure out what the questions meant and how she was supposed to be figuring out the problems if she even had the capability to do so and then help her get through it.
Reason #329809 elementary-age homework is for the birds.
145: I know, I know. But as a foster parent, I really can't just slack on that and call it a principled stance. And she really did and does need extra practice. It's been nice to have her summer bridge homework book so she can dip into something that interests her and stop when she's no longer motivated. I wish it worked that way during the year.
142: One thing I didn't like about it was the claim that ability to do fluent computation isn't important anymore now that we have calculators. I don't think this is an argument against reform math -- I think it's probably as good or better a way of getting kids to the point where they can do numerical computation fluently, and if it improves their reasoning skills it's a serious improvement. But I don't believe that a high-school/college kid who's heavily reliant on a calculator for arithmetic is going to have an easy time moving through algebra and calculus.
There's a crossover point, of course; before calculators it was much more important to be fast and accurate with really laborious arithmetic than it is now, so it makes sense for the emphasis in early math education to have shifted somewhat away from computational speed and accuracy. Not all that far away, though.
145: I know, I know. But as a foster parent, I really can't just slack on that and call it a principled stance
Not criticizing you! Just cursing the darkness.
On the "why not video games to teach math" question, this game is kind of fun. I don't know whether it teaches "algorithms" or "reasoning" -- it's mostly just about adding or subrtracting quickly -- but if you set it to the harder levels it sure gets hard.
And I just re-read it, and he really doesn't say that as much as I thought he did. Just this bit:
But in today's world, we have cheap and readily accessible machines to do arithmetical calculations, so we can turn the educational focus on understanding the place-value system that lies beneath those algorithms, and develop the deep understanding of number and computation required in the modern world, and prepare the ground for learning algebra.
set me off.
147: I agree with that. You've got to internalize some calculations so that you don't get bogged down in a problem.
President Grant, to your 75, if forgetfulness and questionable judgment is a newish thing, and your mother is over 60, I have the unfortunate suggestion that you might want to look for other signs of mild cognitive impairment. Executive function (judgment) can be affected pretty early, before the more obvious stuff like getting lost or forgetting names or appointments. The "good" news is that if this is the case, it will become more obvious with time and complicated paperwork might become the stumbling block that would slow or halt the green card process. I really hope that's not the case, but I figured I'd throw it out there since you mention that this seems dramatically out of character. (I might be totally off base here, FWIW. My mother has Alzheimer's; she was diagnosed at 59 but something was clearly wrong for a few years prior. I hope this is totally inapplicable for you, but it sounded like maybe something you hadn't considered.)
I just had an odd conversation with Newt, where I realized that no one had ever formally taught him Roman numerals, and (a) he didn't really know how they worked, although he sort of knew the smaller numbers, and (b) he didn't know how useless they were for doing computations.
Obviously, there's no direct pedagogical purpose to learning Roman numerals other than history and so you know the copyright dates of old movies, but it left me wondering if there might be some educational value in teaching them as a comparative; teach the kids how Romans did arithmetic (which, honestly, I have no idea for anything too hard to do mentally offhand), and compare to the ease of Arabic numerals, and see if that sparks any better conceptual grasp of place value and so forth.
One thing I didn't like about it was the claim that ability to do fluent computation isn't important anymore now that we have calculators. I don't think this is an argument against reform math -- I think it's probably as good or better a way of getting kids to the point where they can do numerical computation fluently, and if it improves their reasoning skills it's a serious improvement. But I don't believe that a high-school/college kid who's heavily reliant on a calculator for arithmetic is going to have an easy time moving through algebra and calculus.
In my work - tremendous amount of Excel - obviously almost all the computation is automatic, but it would be very bad if we didn't have a deep fundamental grasp of basic math, letting us intuit what the results should be, notice the impact of formula errors, and explain the formulas' numinous workings in layman's terms with simple examples.
154: Do they still teach a unit in Base 4?
how Romans did arithmetic (which, honestly, I have no idea for anything too hard to do mentally offhand)
They just hired Greeks to do it for them.
And I really don't know how the Greek number system worked. I have a vague belief that small numerals were letters in alphabetical order (α=1, β=2, and so on), but I don't know what happened for larger numbers.
And now I know. Looks easier than Roman numerals, but still annoying.
I guess it really isnt' decimal. It's just listed that way to show how to convert to decimal. Stupid ancient people.
Well, it's base ten, as opposed to hybrid five/ten weirdness like Romans.
You mean the words? It works like you'd expect -- a word meaning 'forty' then a word meaning 'three'. I don't actually remember forty -- something like quadraginti? and then three is tres.
But the words didn't work like the numerals, it wasn't something like "Ten less than fifty plus one one one". Words were like you'd expect in base ten.
163: Not sure I understand the question. Do you mean what was the Latin word for 43? Quadraginta tria. But maybe you're asking something else?
159, 160: still does work that way, in a handful of contexts, roughly parallel to where we'd use Roman numerals. So, e.g., World War II is Ο Β' Παγκόσμιος Πόλεμος.
Huh. And I just googled to remind myself of 'forty', and I'm wrong about the subtraction. It doesn't match up to the numerals structure, but numbers are structured like you'd expect up to numbers ending in seven, and then eight and nine you subtract. So it'd be forty one, forty two..., forty seven, two less than fifty, one less than fifty, fifty.
Obviously, there's no direct pedagogical purpose to learning Roman numerals other than history
Reading clocks?
I'm old enough to have got the tail end of New Math in elementary school.
I remember learning about the commutative and associative properties while learning multiplication tables.
I believe Tom Lehrer has a song about New Math.
"Now that's really four tens, so you make it three tens regroup and you change the ten to ten ones..."
*except for Swiss French, which has a word for seventy.
Which is also the Swiss French word for mouthwash.
Reading clocks?
Do you actually read clocks by looking at the numbers, rather than the angle of the hands?
The problem with Greek numerals was that they were sort of decimal, but not fully positional, which meant that you still needed an abacus for simple arithmetic. Which was odd, beause the Greeks learned most of what they knew originally from the Phoenicians who learned it from the Babylonians, who understood positional notation even though they didn't have a computational zero (they left a space). They also used base 60, which was fun, and explains minutes and seconds.
I wonder, though, whether the Reform approach is more susceptible than straightforward drilling of optimal algorithms to degradation in the hands of an incompetent teacher.
Honestly, I think once the teacher's incompetent, the method won't necessarily help, and the particular style of incompetence matters a lot. I think reform math might be more robust to an enthusiastic, hardworking teacher who themselves had trouble doing arithmetic, because it'd give the kids more hope of being able to reason their way out of a hole. Straightforward drilling might work better for a teacher with different problems.
One thing I remember from the parents' night presentation on the math program is the teacher asking "What's 200 minus 180?", and then asking if anyone thought that borrowing successively from the tens and hundreds column was the best way to solve that problem.
Sure, because those are round numbers.
You can use intuition to say "What's 241 minus 76?", and instantly say "roughly 160".
I believe Tom Lehrer has a song about New Math.
Linked above, thank you very much.
Do you actually read clocks by looking at the numbers, rather than the angle of the hands?
For non-cardinal hours/minutes, sure. I can't tell at a glance between, say, seven and eight on a clock-face. Or rather, it's quicker to just read the numeral than to think through "well, it's far enough closer to nine than to six that it's probably x past eight rather than s past seven".
Or rather, it's quicker to just read the numeral than to think through "well, it's far enough closer to nine than to six that it's probably x past eight rather than s past seven".
This is one of those "wow, people are different" moments.
This thread is still about math!?
This thread is still about math!?
Not entirely, no, just at the moment.
Math education is one of those sticky topics like sex; people usually have things to say about it.
(Though if you're doing both correctly, math should be considerably less sticky.)
In my limited experience sex gets you a lot stickier than maths education.
and then asking if anyone thought that borrowing successively from the tens and hundreds column was the best way to solve that problem.
This sort of thing makes me skeptical about various education reforms in general. Sure, that case isn't best handled the traditional way, but that's not a normal case. And guess what? The presenter is getting the desired answer to that rhetorical question from a bunch of folks taught the old way.
That said, I was a New Math child, and my kids' education seems to be Reform Math. From what I've seen, in my childhood I essentially taught myself Reform Math. They're learning the way that I actually did things, as opposed to the way I was taught them.
Wait, 200-180 doesn't require borrowing from the 10's place. Was the example 200-195 or something similar?
Thank goodness for the digression into safari-guide immigration. Grant--that'll be tough to watch. Sorry.
KR, you're talking about zequals: http://www.guardian.co.uk/science/alexs-adventures-in-numberland/2013/apr/04/zequals-symbol-sums-mathematics
Also, did I ever tell anything about the toyboy tour guide one of our teachers repeatedly brought back from a country y'all can't legally visit, who my dad the immigration officer removed from the UK on two separate occasions for different visa violations, who she eventually married and who therefore became a British citizen, and who eventually stabbed a guy I went to school with (and hated) dead outside our local pub?
Also, did I ever tell anything about the toyboy tour guide one of our teachers repeatedly brought back from a country y'all can't legally visit, who my dad the immigration officer removed from the UK on two separate occasions for different visa violations, who she eventually married
Hoping she married your teacher rather than your dad. Or the visa violations.
Oh wait, the teacher is the she. Oops.
As long as it all worked out for everybody in the end.
Maybe the stabbed-guy isn't happy.
The teacher, the toyboy, the schoolmate, the wife, and your father.
It just encourages the use of a variety of techniques ("strategies") to get there, in contrast to the traditional "one best algorithm" approach.
That sounds great (in theory, at least) because it acknowledges that there can be multiple valid approaches to solving a problem, and that the true first step in solving a problem is deciding how to approach it.
I have to hide my own annoyance at my son's homework, which sometimes asks that he estimate results that he is fully capable of doing correctly in his head. (But I am compelled to admit, he sometimes fails to recognize when he's come up with an absurd answer, and would probably benefit from doing a rough estimate first, or last. So...)
Poor kid. His mother is super-anal about him doing all of his homework and getting straight A's, or something close. So I am also super-anal about this. But God knows that when I was his age, I wouldn't tolerate (and wasn't made to tolerate) bullshit homework assignments.
That sounds great (in theory, at least) because it acknowledges that there can be multiple valid approaches to solving a problem, and that the true first step in solving a problem is deciding how to approach it.
Reform Math kids go on to become Perl programmers. Whether this is great or awful is left as an exercise for the reader.
KR, you're talking about zequals
Why isn't the usual "approximately equal to" symbol good enough for that writer?
President Grant, like Cala I am guessing that the State department will not let your mother's marriage/sponsorship of a green card get past the ground level.
I mean, according to lawyers there is a chance that my husband (who I am legally married to, have been co-habitating with for the last two years, is my age/equal, not from a developing country and is gainfully employed and owns a house in the UK (ie, has a reason to return to his home country)) will be denied a *tourist* visa to the US if we're not extremely careful, because he already has had one tourist visa denied. (Our fault, we were trying to bend the rules a little, if not actually break any.) I know that you fear the trouble that will come from trying to fight endlessly against these kind of decisions, but I do think that in this case the horrible immigration policies of the US will work in your favour.
201 - I used to hate estimating, and then when I was about 30 I realised it wasn't just annoying and now I do make people do it.
My kids can all do maths, and I'm just really glad none of them went to primary school because I think they would have found the maths there really annoying.
Halford, I used Singapore Maths books with my lot, and I really liked them.
From what I can gather, there was some kind of anti-whatever-the-former-math-curriculum was revolt at this school, so they've recently instituted "Singapore Math" (still have no real idea what this is) instead. I think the complaint was that the former curriculum wasn't hardcore enough but really who the hell knows.
I used My Pals Are Here (and then Maths Matters with kid C), but there are also US reprints with imperial measures. They are very thorough on showing how stuff works, and drawing models to work through problems, and then show you how to write it out nicely. So I guess they appeal to both sides to some extent.
I have sat through God knows how many interviews with young people who had good college grades in STEM disciplines (and therefore presumably had facility with lots of algorithms) but nevertheless had piss-poor quantitative intuition.
THIS. So many times this.
I drill my interns in commonsensical doublechecking constantly, but I wouldn't need to do it if they had those skills already. And they are smart kids.
Oopsie. 212 was me, lousy formatting and all.
We only hire people with some statistics, at least the ones I work with, so they're pretty good about noticing stuff.
Oh wow, the links in 135 are very definitely worth a front page post. Everyone go read them!
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Thanks to Unfogged, after a few days of a really runny nose and headaches, instead of thinking "eh, allergies, they'll go away soon" I keep thinking "... but what if it's a spontaneous CSF leak and meningitis?" So I guess I mean: I hope wrenae's doing okay now.
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My daughter's too young for this, but I overheard some moms in my town a couple of years ago complaining about the math curriculum and homework assignments (between 2nd and 45th grade, I think). The kids had to explain their reasoning in words. I can see how this would be difficult for an eight year old. I can see how it would help them learn. I can see how it might help a more verbal child. I can see how it would be frustrating for a less verbal kid who was good at math. But then the mom said something like, "my kid isn't an abstract thinker," so he shouldn't be asked to do this kind of thing, and I lost some of my sympathy. Can you be "good at math" and "not an abstract thinker" at the same time?
(I myself got a lot of extra drill because I finished the work too early and they had nothing else for me to do. We had kind of a reform-y curriculum that optionally extended to 11th grade, and seemed to me not to teach pre-college math very well.)
I can endorse 185.3, but it seems to me that I could do the reform/constructivist/understanding thing because I had a lot of facts to think easily about. (Times tables on the porch while shelling peas, etc etc; later, exercises in How fast will this pond empty if we use both hoses? and Let's just keep putting bricks on this until it breaks and But can you do that with six objects?)
writing two different ways to determine if 2 is even or odd, and explaining the answer
That seems like a very good exercise.
We didn't use the peas as counters, though, we just wanted to eat them. Straight up rote memorization for the times tables.