Maybe you could send his sister to help. She's probably old enough to use an imaginary blaster.
I assume these are imperial stormtroopers ala Star Wars? Then isn't the appeal in being Luke Skywalker, or whoever was the hero/heroine of the movie in question?
Tell him if he misbehaves there are some men in Oregon who would be happy to look after him for a couple years.
Huh, I confess that didn't even strike me as an especially masculine fantasy, though I think that's my oddity rather than yours in categorizing it that way. Under attack plus fighting off = heroic, plus you can extend the scenario for as long as you like. Exciting! Plus there's the appeal of being holed up in your little base of security, which is much the same appeal as being in a cozy cabin in the midst of a howling storm, or being in the pub in Shaun of the Dead, or whatever.
"what the fuck is the appeal of this scenario?"
Does he even own a lightsaber?
My sense of how the "Wow, gender really is innate!" thought process works is that it's about selection of particular bits of the kid's behavior as what's genuinely significant. When Pokey wanted to wear a skirt to school, I don't recall you thinking of it as a significant data point in favor of "Wow, there really is no innate difference at all between boys and girls!" (Not that you should have, it would have been nonsense as meaningful evidence of anything of the sort.) But some violent fantasy play does make you wonder whether it really is all about innate gender.
Does he even own a lightsaber?
Hokey religions and ancient weapons are no match for a good blaster at your side Moby.
If you showed them some respect, then maybe you wouldn't have raised Space Hitler, Junior Grade.
My daughter tried watching Lego Friends, which is an action-free cartoon for girls, and found it too boring, so she switched to watching Lego Ninjago, which is a cartoon for boys about ninjas.
6: oh, that's true.
It really comes down to whether or not I personally can see the appeal. I see the appeal of skirts and sports, but I just do not enjoy being attacked by storm-troopers.
9: those two are so hideously gendered.
That sounds like a modernized version of Ralphie's fantasy in A Christmas Story.
Yeah, I think 6 gets it right. There's a famous mathematician who is very outspoken about gender differences in mathematics (well, and other things, he was the one who thought it was only natural that RWM was better at crosswords than me because she's female). I'm pretty convinced from personal interaction with him, that he has come to this point of view because it's the only explanation he can come up with for why his daughter doesn't like math as much as he does. If he'd had a son who didn't become a mathematician he'd have had to find some other explanation.
Well, for me as a Jewish boy raised with stories about the Holocaust there was no choice -- the storm-troopers were coming. My only choice was whether to imagine that I had superhuman powers and could defeat them all single-handedly. Even I could handle that decision.
15: That gets you "Magneto" not "Han Solo".
"I see the appeal of skirts and sports, but I just do not enjoy being attacked by storm-troopers."
But there are no actual stormtroopers here. (I assume.) People enjoy pretending to do all sorts of stuff that might be less fun in real life. I would not enjoy being a ballet dancer but I would not be completely baffled if Small God Daughter announced she was pretending to be a ballet dancer. (She's still keen on flying fast jets when she grows up, by the way.)
but I just do not enjoy being attacked by storm-troopers.
Have you ever tired it? If not, how can you be sure?
Wearing a skirt, fighting stormtroopers...
http://www.dailymail.co.uk/news/article-1324390/The-hero-kilt-tackled-Panzer-division--accepted-surrender-23-000-German-soldiers.html
18: that quote was not a real attempt to argue that pokey is being the most boyee-boy ever.
22: no, I didn't think it was - I thought it was more along the lines of "how can he be enjoying pretending to do something that I don't think would be fun, either in real life or even in pretence?"
Yeah, ok, so ajay 21 got me started and here I go.
Question, if this is about Star Wars TFA: Is the lead, Rey, portrayed as "feminine" or "androgynous?" I look at the stills, looks like shorts with extra material, head hair is short or tied back, etc. If androgynous, is this a good or feminist thing? Do we care that much about "science, realism, practicality" that our warriors must be portrayed in functional appearance?
Cause, anime, Sailor Moon. One anime style is to have their woman warriors embedded in a "feminine" private identity. Is this wrong for a role model of women warrior? Swords and tutus?
Actually, the series I am watching this week Twelve Kingdoms based on a series of novels.
Short:Ordinary Japanese schoolgirl gets transported to Magicland where she fights monsters with a sword, and humans off screen, and becomes a queen with hassles.
Thing is the visual tone here is like Tang China:
Everybody, M & F, wears skirts or tunics or very loose pants
Everybody, M & F, has shoulder length or longer hair.
And they fight this way.
Is why I put "androgynous" above in quotes, cause there may be at least two representations of androgyny, and short hair and tight pants maybe not the best.
Can parents still try to provide an environment that steers kids away from the dark side of the force?
The original question I was going to ask those who have seen SW:TFA after looking at the stills is if little kids watching the movie would be clear about Rey's gender.
Why do they have to do that? Another series I'm watching, just to show this is common, has the woman fighter pilot all "femmed up" makeup, colorful hair clips, brightly colored outfit, accessories. Nothing to get in the way of functionality, but enough to mark her gender. She's still tough as nails.
Is this wrong?
Rey's gender was very clear in the movie, even to kids.
It's fascinating (and really annoying) watching my mom try to map her "gender is innate" theories onto Zardoz's behavior. I'm sure she just feels like she's alert to signs that we're missing because we're fooling ourselves but it comes off for all the world like she's some kind of police detective trying to entrap Zardoz into admitting that she likes putting clothes on dollies.
As a compromise, maybe try to get her to put clothes on doilies?
I see the appeal of skirts and sports, but I just do not enjoy being attacked by storm-troopers.
Fantasy play doesn't have to be just about fantasy fulfillment, it can be about coping with things that frighten you. Even as a presumably sane adult, I have the occasional daydream about "What would I do" in some scary situation, whether realistic or less so.
TL:DR -- the appeal might be "this is how I'm coping with my fear of storm troopers."
27: Really? How was her gender represented, especially as different from masculinity?
Just "woman" without qualities?
Not trolling, really curious.
Twelve Kingdoms mentioned above, although ungendered in fighting and ruling, does seem to me to be gendered about nurturing.
As a practicing heterosexual, I found her more "gamine" than "androgynous" or "masculine".
Wow, a word I totally didn't know. Even after looking it up, I think I'd never run across it. On point though.
Have you been skipping your heterosexual practice?
It's not the scenario, it's now it makes one feel. Epinephrine is often the drug of choice.
31: Despite being rough and tumble Rey presents as female. She has long hair, she fairly obviously has make-up on (although not ostentatiously so, more like the Hollywood minimum for women), (these are more properties of Ridley than Rey) she has a higher voice, and she has a slender but curvy frame that I think even most children would code as feminine. She's referred to as "she" and "the girl" by other characters. Also note the constant outcry of "[young girl I know] wants to be just like Rey."
Rey's gender was very clear in the movie, even to kids.
As any young child can tell you: boys have light sabers, and girls have sarlaccs.
Not knowing big words, I'd say she presents as "women's soccer player hot." She's got the standard longish hair in a pony-tail of athletic women who are being athletic in a feminine way. Her costume is not something a man would wear (e.g. the arm skin and the way the lines direct your eyes to her boobs). There's very little androgynous or masculine about her, she's just sporty. Compare to say Furiosa.
I didn't realize my eyes were being abetted.
Also, "gamine" isn't a bigger word than either "soccer" or "player".
There's very little androgynous or masculine about her, she's just sporty. Compare to say Furiosa.
...who is literally wearing a corset on top of her clothes throughout the film! That's fairly feminine, no?
I didn't say there was nothing feminine about Furiosa (her neckline is also something that men wouldn't wear), only that there's some clear androgynous/masculine aspects in stark contrast to Rey.
She's got the standard longish hair in a pony-tail
Hey, that's my hair!
As far as the bare arms, x'd chest, and side material, I can show you that on macho guys.
Last one: In the SF anime with the fighter pilot mentioned above, the hardass woman captain of her ship wears the shortish ponytail, and tight functional two piece, more sports bra than cleavage
The woman fighter pilot apparently belongs to some sort of subculture like Romani, Gypsys, Sioux, Sikh, Maori. They are sparsely intermingled with the main society, but we get to meet another ship's captain, male and older, and a old scientist, male, in a wheelchair.
They are distinguishable by tasteful but obvious bright blue facial tattoos.
Last because American pop culture is so fucking boring
She didn't have bare arms. She had sleeves with bare shoulders.
Also, if a man *were* going to wear a corset, it would be that corset.
Or bare whatever part of your arm is right below the shoulder? I don't know how to describe it but it's nothing I've seen on a man.
Here are some fashion terms and styles for women's garments.
43: None of what we said was proof positive that a person is female, but no single aspect of gender presentation would be, anyway. You asked if a child will understand if a character is female, and in my judgement what we said was sufficient for most (but perhaps not all) children to realize that she's female. Many children have a long hair==girl mapping.
Men with pony tails usually either have what I call "MIT ponytail" (long not particularly well-maintained and usually paired with an old t-shirt and a generally relaxed fashion sense) or are man-bun types who would inevitably have a large beard that they pay attention to and probably use a straight razor and have opinions about shaving soap. Those are your coded masculine pony tail options.
There's also "record producer ponytail".
If only Oregon State would provide a detailed description and classification.
Is that still a thing? I'd assumed that only existed in the past.
Oregon State still exists. As per "Miracle on **th Street", you can mail stuff to it and therefore it exists.
I'm perplexed by the staying power of the ManBun. It seems to be thoroughly mocked on all corners of the internet, and it looks (IMHO) quite terrible on most guys*. And yet! it remains a common hairstyle.
*with apologies in advance to any ManBunned members of the commentariat; I'm sure your ManBun looks great.
large beard that they pay attention to and probably use a straight razor and have opinions about shaving soap.
Mixing types, I think.
Straight razor and shaving soap is for the clean-shaven dandy who has opinions about knotting ties. The bearded man (hypothetically speaking) has opinions about beard oil and (let me tell you, this one is the best) beard butter.
That is, the standard of proof was established in "Miracle on **th Street", not that anybody tries to mail something to Oregon State during that movie.
Men with pony tails usually either have what I call "MIT ponytail" (long not particularly well-maintained and usually paired with an old t-shirt and a generally relaxed fashion sense)
You'll be saddened to learn that it doesn't disappear at less intensely educated levels.
56: I think $20 beard oil and $10 combs belong in the other thread.
Also it's cute when Hokey Pokey dons a man bun. He has been dressing like Inigo Montoya for the last few days, wearing all his fanciest clothes. He looks like an adorable dandy.
Back in the late 80s, Spy magazine had a taxonomy of male ponytails by length and fashion-presentation generally that was really funny. The only line that's stuck with me was for the longest category of ponytail, held back by a macrame band and attached to someone working on the technical side of a record studio, and the column in the chart labeled "Reason for ponytail" was "Why must something be cut, simply because it grows?"
And here it is. I misremembered -- the long ponytail was on a potter.
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I have a threadjack which is somewhat related to both gender and money. I am happily married but realize that I feel like I'm permanently crashing in someone else's house. I have been decluttering/reorganizing and it's been good for other reasons, but it hasn't made much of a dent in this estrangement. I've never really been a nester -- my childhood bedroom was the one place I controlled aesthetically, and part of that was painting whatever I wanted all over the walls with acrylics -- and have lived either in fairly extreme student poverty or with partners who did nest and have a household's worth of stuff. Conventional wisdom has the nesting thing as a feminine trait and the "I just need a TV, a guitar, and a box full of clothes" as a masculine trait, but I bet it's more randomly distributed. So I have two questions:
- how have people negotiated combining households aesthetically and... pragmatically? Any instructive stories?
- how have people who could happily live in a truck in the Google parking lot adapted to a more settled existence with a more settled/nest-y partner?
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I've never heard of "beard butter". I wonder if that might make my wife not hate my beard, which she says is too prickly?
Is that still a thing? I'd assumed that only existed in the past.
I saw it (on a fretless bass player, no less) a couple of years ago. But not very common, certainly.
63: Largely, by letting Buck do whatever he wants with our space furniture-wise and esthetically.
Yes. One of you has to give up. It's what I did. The plus side it is really does take less effort to be the one who doesn't give a shit.
64: partly, yes. Will depend on how long your beard is. A prickly beard is partly a dry beard with a lot of loose hairs, and the beard butter helps with that by moisturizing the hair and letting you groom it more easily.
63: We settled all the decorating issues by me issuing an early and firm "No beige" directive and then not interfering in any other of her aesthetic decisions for the next 15 years. That worked very nicely.
Beard butter sounds like the sort of thing that must have made an appearance here at some point.
But maybe I would have liked it back when I sported a manly man beard. On my face.
A revolution without beard butter is not a revolution worth having
"Beard butter" sounds like something that happens if you don't wash your face for weeks.
Our compromise is that I got to pick the location and cost of the house, and RWM gets a budget of 5-10K a year to do mostly whatever she wants to the house for the next few years. I give input when asked, but it's basically her vision.
74 Your dog fetches beard butter or do you feed your dog beard butter or does your dog really understand beard butter?
Help me out here.
Or, he puts beard butter on his dog's fur.
63: When we moved from apartments into a house together, my stuff wound up dominating the house because we moved it first and more of her stuff wound up in the garage.
Part of solving it was buying some furniture together (we bought two 4'x7' high book shelves that we affectionately named "the monoliths"). Another was rotating the plates and silverware, so hers became the everyday set.
Over time, we've replaced furniture--she's usually the one who takes the lead on declaring furniture done. We shop for the replacements together, but she has style and opinions; I mostly make sure it's comfortable and sign off after adding my 2 cents along the way.
76: We sometimes give her butter, and she winds up with butter on her beard (she's a miniature schnauzer).
It puts the butter on the fur or it gets the hose again.
64 - 68 is right. It's likely to have a decent effect.
You probably don't need to invest in anything fancy though, or at least not until you find out whether it works or not. A little grapeseed/jojoba/whatever oil will work reasonably well if you rub it into your beard (in small amounts) after you get out of the shower.
As an unfashionably aggressive girl, what I remember about adult reactions is that even committed egalitarians were dismayed or disgusted by it, even (once) when they agreed that I was acting like the kids around me. Disgust looks like a common reaction to effeminate boys, too. Haidters gonna hate.
63: post-worthy IMO. We operate with mutual veto in any shared space. That combined with not getting rid of anything u til its worn out means verrry sloow aesthetic adaptation. Like, decades. Thrifty!
Our real problem is a clutterer and a not-clutterer.
I desperately need a post on handling 82.3.
83: Moving to separate households has been fantastic, but that's probably not good advice generally.
When the storm troopers attack, we can make barricades out of the clutter, and after the battle it will be all tangled up and full of corpses and then surely we can agree to throw it away!
When the storm troopers attack, we can make barricades out of the clutter, and after the battle it will be all tangled up and full of corpses and then surely we can agree to throw it away!
86 is trying to convince 85, but 85 knows better.
"How can you think of throwing it away after it saved us? We've been through so much together!"
There can be a post. I'm not committed to the threadjack strategy.
I am realizing too that part of the problem is that, when lower-income, we moved to this nice-for-what-it-is apartment in an optimal location, after which rents exploded, and now moving at all (without both changing jobs & leaving the state, etc.) is looking like a once-in-a-lifetime moon shot. Even moving into a similar apartment now would be at least $600 more a month. I think everyone gets the Bay Area "oh, we'll never be able to buy," but not so much the problem of not being able to rent a slightly larger space three blocks away without doubling your rent.
This would all be okay if I didn't quietly, at a low background level, loathe the apartment. There's some Stockholm Syndrome creeping in, where it feels like home. But.
The obvious solution is not to have FEELINGS for THINGS, positive or negative.
(tripping over someone else's stuff) Thus I refute you. Ouch.
Is it Something Happened whose protagonist is constantly injuring his knees on the low tables in his home?
I'd bet a lot the IDP has read Something Happened.
Joseph Heller? Sure. I'd been a fan of Catch 22 since HS. Don't remember anything about We Bombed in New Haven, and may not have finished it.
91 reminded me of Dedalus section 3 of Ulysses
nacheinander ... nebeneinander
Should be Dedalus in section three, but it took me a while to remember "Proteus"
Okay, Sam Johnson contra Berkeley.
Dedalus shutting his eyes and tripping on a stone is a comic allusion to above, and a shift to creation by the artist. Maybe
Can't find the Moment
I'm with urple on 82.3; the Cold War between those who don't even notice clutter and those in whom clutter leads to murderous feelings could use some input from the mineshaft ("Toss the clutter into the mine").
Is this a good place to talk about the research showing 90% of elementary school teachers have math anxiety and it seems to affect young girls disproportionately? I had a weird situation that I don't think I can anonymize sufficiently. How young do girls start showing that annoying math-is-crazy-I-couldn't possibly understand it even though I knew this in-August thing?
The only references to that study I found* described it as being done on a pretty small group of teachers (17), and specifically female ones (not overall). Modeling attitudes towards the material is a really huge part of teaching older students, and I don't know how much that changes over time (I doubt it's as much of it with younger children, given the importance of other stuff that matters less when students get older). But I doubt it goes away entirely when the students get younger.
*when typing a description of it into google and reading like the first three links so grain of salt etc.
99: Talk away -- I find this stuff fascinating, and my experience of my kids' elementary school math teachers is that they definitely modeled math anxiety/incapability, and presumptions about girls and lack of interest in math. My kids didn't take any damage, I think, but I was aware and horrified.
I swear to God Newt came home from school one day, and his teacher had told the class that the formula for the sum of the interior angles of a polygon was 180(n-2) where n was the number of sides, but it wasn't perfectly accurate because she'd checked a pentagon with a protractor and it was a couple of degrees off. She was generally a good teacher and a lovely person, and I suppose she gets points for empiricism, but wow. I told him to raise anything mathematical she said that puzzled him at all with me immediately.
It's only exact if use the International Prototype Protractor that they keep in Paris at Bureau international des poids et mesures.
How did she get a regular pentagon to measure? That's not exactly an easy thing to draw. I guess she found one in the book or something?
Finding non-mathphobic elementary school teachers is really important but also seems really really difficult to me. Generally people go into elementary education because they want to work with kids, not because they're interested in knowledge. Furthermore, math skills are so highly compensated it's going to be really hard to hire people who have them to elementary teaching jobs. You can get lucky once in a while with someone who likes and is good at math but likes kids even more, but not at scale.
Why would she need a regular one?
106: You don't need much in the way of math skills to not be math-phobic, though. In elementary school, a teacher needs fluent arithmetic, minimal algebra, and being comfortable with the small amount of math they do need. The issue isn't any level of unusual skills or mathematical interest, more comfort with the topic at all.
Oops, I'm a dumbass. Someone take away my phd.
107: So she'd only have to measure one angle, rather than measuring five and adding them. Which is what she did -- as I recall Newt's report, she said the angle was a little over 110° rather than the 108° the formula predicted.
108: I dunno, fractions already come up in elementary school, and in my experience anyone fluent with fractions already has top 5-10% math skills. You don't run into anything harder than fractions until proofs.
Yeah, when you put it like that, I see your point. But you don't need unusual math education: someone who'd done well in math through eighth grade and never took another math class could function fine as an elementary school math teacher.
I can prove fractions if you have me a pineapple and a big knife.
112: I don't think a graduate degree in math is necessary for doing a good job teaching elementary school math or anything, but I'm not sure what you're saying is true to that extent. My reasoning is that with things like math there are a lot of ways to explain/teach/etc. basic mathematical concepts, but a smaller group of ways that do that in ways that make later steps in math make sense. How you teach something like fractions, or even just multiplication, can make a big difference to the difficulty of the conceptual leap from elementary math to algebra, and it's that kind of thing that makes knowing stuff about math important to teaching math at lower levels.
I mean, it also depends on who is setting a lot of the curriculum and what textbooks/standard exercises are involved and so on. But to teach something reasonably effectively it is important to know what people are going to have to learn afterwards, especially when what you're teaching is really foundational stuff.
It's possible the teacher discovered non-Euclidean geometry.
If there was an inscribed pentagram and she said the right incantations that might've done it.
114: You know, in the abstract that sounds persuasive. In actuality, though, I don't think I do agree -- like, what would be a bad way of teaching fractions or multiplication that successfully gets correct answers to problems, that would mess up a kid in later math? I can't think of one. And of course, I'm not talking about the ideal math teacher, just ones who are better than the average now.
I think it's less important that the teacher be a consummate mathlete mathonaut than that they aren't mathphobic and are just generally comfortable with working with numbers and logic. If a kid asks "why doesn't this work," they need to be able to say why, not "because I said so." We expect that of children now via the Common Core; I hope we'd expect teachers to be at least one step ahead of them.
102 makes me think I'm not cut out for parenthood; that would be aneurysm-producing in person. Need to remind myself that we are surrounded by teachable moments.
like, what would be a bad way of teaching fractions or multiplication that successfully gets correct answers to problems, that would mess up a kid in later math?
"Just google it, kids."
119: Mara, in second grade, is on at least her third and maybe fourth technique so far this year for multidigit addition and subtraction, though she also considers it "cheating" that she mentally uses her favorite method first so she can double check the answer she gets with the new method when she gets there. I think a lot of the training for teachers now is focused on making sure they do understand what's going on and why.
AIMHSHB, my son did much of his fifth grade math homework by reading the questions to Siri and writing down her answers. She is good at math.
like, what would be a bad way of teaching fractions or multiplication that successfully gets correct answers to problems, that would mess up a kid in later math?
rote memorization without understanding any of the underlying concepts?
124 is right. Basically all math teaching that relies on "rules" for solving problems (without providing any accompanying understanding of the concepts behind those rules) is terrible. And there's a lot of math teaching like that.
It's hard for me to picture how that would actually work, though. Almost any method that reliably gets you a right answer, is going to be about equivalently conceptually transparent to the user, don't you think?
I mean, it'd probably be somewhat damaging to insist that one method was right and others were wrong; convincing a kid that the difference between two functional algorithms was important would be a bad thing to do to them. But that's not an error you'd need particular advanced mathematical knowledge to avoid.
126: no, it's more just like "we call two numbers written over top of one another like this "fractions". Here are the rules for adding fractions. Here are the rules for multiplying fractions. Now, go do these 100 problems to practice using these rules."
I can prove fractions if you have me a pineapple and a big knife.
This was a Bloom County cartoon (though using a grape and a watermelon).
You can't cut a grape with a watermelon.
Or to put it another way, I can certainly see ways to do a bad job teaching math to elementary school students, and focusing on rules at the expense of concepts is definitely one of them. (Having no clue at all, like Newt's teacher, is another.) But knowing mathematical content past an eighth grade level isn't, I think necessary or helpful to avoid that sort of thing.
Mostly people who are comfortable with and really understand elementary math do end up taking more math, so my imaginary perfectly competent but no math past the eighth grade teacher doesn't exist. But the more advanced math isn't itself helpful, I don't think, it just goes along with people who don't hate and fear fractions.
I think 127 is probably more correct than 126. It might be conceptually transparent to you, but for much of the class, that transparency is going to depend on how it is explained.
Oh god, so many opinions, but I'm out and about running errands. Elementary level math teaching has come a long way in the past 20 years and the new methods are much, much better.
122: Everything I've seen of math in the common core (usually in the context of some mathphobic parent complaining about it) is really quite good. So it's certainly possible that it's going to make a big difference. But in our culture it's also really hard to convince someone that they can understand math once the phobia appears, so I'm a bit skeptical about how much curricular reform can do.
130: the problem is that the teacher who is himself bad at or fearful about math frequently knows the rules for getting the correct answers, and so can parrot those to the children, but doesn't himself actually understand the concepts very well, and so can't actually do a good job of explaining what's going on. Or sometimes they try to explain, but get it wrong. People more fluent with math don't have those problems, at least not to the same extent.
LB may be on to something in 112. Like maybe what we should do is just make sure that future elementary school teachers never get frustrated at anything after algebra. Put an emphasis on not challenging them, but instead making them really really comfortable with math through Algebra 1 (including some elmentary but not exactly in the standard curriculum topics).
I'm willing to believe elementary math teaching has gotten much better in recent decades. I hope it has. But I nevertheless have a hard time believing that being reasonably comfortable oneself with mathematical concepts isn't still a valuable asset for a math teacher.
That's clearly happened to some extent. My son's math problems are very obviously being taught with an eye toward algebra and have been since second grade at least.
I mean, maybe the pedagogical techniques have improved sufficiently that now that teachers themselves are absorbing understanding simply by virtue of teaching the material. That would be nice.
By contrast LB is really uncharacteristically completely wrong in 117.
The fundamental issue with elementary math is that the symbols mean something. They're not just strings of symbols and rules for manipulating them. Because the rules for manipulating fractions are so different from what comes before them, fractions really bring out this issue, but it's not essentially an issue about fractions. a(b+c) = ab + ac, not because that's a formal rule that also applies to a/(b+c) = a/b + a/c, but because a rectangle with side lengths a and b+c can be divided in two by a vertical line to give two rectangles with side lengths a,b and a,c respectively. Fractions are important because it's the first place where the rules are sufficiently complicated that it's really hard to get them right if you don't understand what they mean.
135 is exactly right, or at least matches the experience I had when I was given a very unfortunate teaching assistant assignment back in, I think, 2010 and was supposed to help students use a bunch of statistical rules of thumb for a low level philosophy of science class taught by someone pretty inexperienced who had been given the class at the last minute and was mostly reading the lecture notes of the person who had created the course. Not actually having taken any statistics courses myself made the whole thing into a kind of futile nightmare, because while I was totally capable of grasping and applying the rules to get the right answers without any trouble I had a very, very limited ability to say why you put one number in one place and a different number somewhere else.
Also 124 -> 117 is a nice summary of my experiences in elementary through middle school math. I'm not even sure if I was taught poorly in elementary school (though there was a lot more drilling) but the jump from mostly arithmetical stuff straight into algebraic concepts in a class taught by someone who expected everyone to have learned arithmetic as if it were pseudo-algebra was not remotely beneficial to me in the long run.
Also 138 pretty much describes what all my peers at the time had gotten and I hadn't. It wasn't pretty.
Typically good students learn the rules for fractions well enough that they can do a straightforward fraction problem, but the moment you embed it in a more complicated problem they'll be distracted enough that they start using the incorrect rules that come naturally to them.
126.1: I can't find it now, but I read a blog post by a physicist a few years ago complaining about how his first year students had been taught algebra. He was puzzled by the fact that they seemed to approach each manipulation as though it were one discrete "trick" that applied in a particular situation. They could generally come up with the right answer, but they couldn't see how things related to each other.
142: Were your parents insufficiently insecure?
140 makes good sense, not that I'd ever heard that explanation with rectangles in it before.
My kid's 3d grade math homework is mostly conceptual-ish stuff that seems good, a lot of it obviously geared towards algebra (they use x and y symbols already a bunch). Then they also do something called "rocket math" which are nightly timed drills to see how fast you can do arithmetic problems, guess to have that come quick and easy. She always seems like 20 problems below her rocket math "goal."
140: I may be being unrealistic about to what extent conceptually understanding fractions or multiplication necessarily depends on knowing later math. It seems to me that someone might have a sufficiently rich understanding of what fractions mean, graphically and conceptually, to teach them in a way that wasn't blind rote, without knowing much more advanced material. But I could be wrong about that.
And saying 'eighth grade" was silly of me. What I was really thinking was that someone who was fluently comfortable in any high-school math: algebra, geometry and so on, would be fine teaching elementary school math. Being too bad at math to teach it well at the elementary school level would be about discomfort with those sorts of topics, rather than, e.g., if they've ever been exposed to calculus.
Rocket math is normed to a kid with very insecure parents.
We'd moved from Africa to suburban PA when I was in fifth grade, and sixth grade was where pre-algebra stuff kicked in so it was kind of unavoidable. I was a badass in American fifth grade though because lots and lots of drilling makes you blindingly fast at doing math problems in a way that actually being dragged through the concepts in an algebraic way does not (like, not even memorization but practically reflex).
I'm not sure they cared much one way or the other, though. They weren't exactly suburban strivers which I guess was good in some sense but it kind of screws with you as a kid if like 90+ percent of your peers have parents who are.
I've heard stories about suburban PA, but I'm never sure what you can believe.
According to Khan Academy I have a fifth grade math level, so I'm kind of a native informant in these conversations.
also applies to a/(b+c) = a/b + a/c
I'm missing something.
4/(1+1) = 2
(4/1) + (4/1) = 8
Have you heard good stories or bad ones? I have some priors about which of the two categories is more believable...
(There may be a marked difference between which general parts of PA the suburbs are in, though.)
Did you mean (b + c) / a = (b/a) + (c/a)?
because lots and lots of drilling makes you blindingly fast at doing math problems in a way that actually being dragged through the concepts in an algebraic way does not
Boy, looking at this makes me think that maybe I am just completely wrong in my thinking. That is, my unexamined assumption was that dumb rote learning really doesn't work in math -- if you're successfully fluent in getting right answers, you've gotten to a sufficient understanding of the concepts somehow -- and that the problem with bad teaching will show up immediately, with kids who find getting right answers difficult and painful. But that doesn't sound like your experience at all.
I suppose I could go see for myself, but that would involve either a tunnel or a bridge or a town with no bars.
154: I think he meant to multiply rather than divide?
That's what the serial killer's defense lawyer said.
The whole point was that it was wrong, but students do it all the time because it looks like a rule that's right. I could have said that more clearly though.
It's hard to know how to frame a concept if you're not super clear on how it gets used later on.
152, 154: No, I get it now. He was saying that blind application of rules without understanding would get you to make mistakes like a/(b+c)=a/b+a/c , and that you need the conceptual understanding to avoid it.
I'm not fast like that anymore, in that if someone asked me what 11 times 12 was or what you got if you divided 52 by 3 was I'd have to pause to think about it, but I still find doing basic arithmetic stuff in my head easier than a lot of the people I know who have a lot more math under their belts than I do. So it's not necessarily even that I learned it badly or anything. As long as the plan was mostly functional day-to-day "what is this per ounce price compared to this other per pound price at the supermarket" stuff it worked pretty well. But the mismatch between something that prepares you for that and something that prepares you for trigonometry (for example, because that was the last math class I had to take and as a result the last one I did take) is pretty huge.
not because that's a formal rule that also applies to a/(b+c) = a/b + a/c,
The whole point is that this *isn't* true - that this is an incorrect symbolic generalization from the other, correct expression, and so some understanding of the meaning is important to not make that mistake.
Fwiw, the study in question seems to be here: http://www.pnas.org/content/107/5/1860.full
It's confusingly written and all circumstantial, which is not to say invalid, but the identified problem is "female teachers have math anxiety" and the only solution implied is "reduce female teachers' math anxiety." They don't even speculate about how it might be manifested in the classroom, at least not that I could see. (The teacher saying "aargh, I'm clueless, ha ha ha!" in a girly way after making an error? The teacher making lots of errors and seeming generally not confident?) It's hard to know what to do with the results as such.
Like in students heads a(b+c) = ab + ac is just a thing you're allowed to do to strings of symbols and isn't something that's special about multiplication because of what multiplication means. And then they apply that in all sorts of places where it's not true like thinking (a+b)^2 = a^2 + b^2 or a/(b+c) = a/b +a/c.
Yes, I see my misunderstanding, thanks.
Going beyond elementary school math, that reminds me of learning logarithms and exponents in High School, and that they have their own set of transformations for manipulating equations which occupy similar functions as multiplication and addition in algebra but are just different enough that it's easy to get confused.
I've retold this story a fair number of times, but this is a thread for it: parent teacher conference in fifth grade, Sally's teacher said that she's doing very well on all the math work, but seems bored, probably because she's hitting that middle-school age where girls lose interest in math. I suggested that maybe she wasn't feeling challenged enough, and asked if there was maybe some enrichment work she could be doing, and the teacher dug up some algebra module she had lying around and threw Sally in the back of the room with her best friend to work on it. So it all worked out okay, but again, wow.
Of course the fact that (a+b)/c does actually equal a/c + b/c only makes it harder for students. (But dividing by c is just multiplying by 1/c, so that one really is just the old rule in disguise.)
167: Yeah, that's another brutal one. Especially because so much less time is spent on it than was spent on fractions.
The thing that in my experience is even worse than fractions or rules of exponents is anything that involves taking cases or statements that are conditional. The first big spot this comes up is inequalities in algebra. I find that's the single toughest thing for calculus students. (It's really really really hard for people to understand that x is sometimes positive and sometimes negative, rather than thinking x is positive and -x is negative. It just totally breaks the symbol manipulation paradigm.)
165 -- your native informant can confirm that 165 is correct as a description of how dumb people think about math. And, I absolutely remember math being taught as just a series of rules and tricks like that to memorize. And this was at officially very good schools. It does seem like the curriculum has gotten a lot more conceptually-oriented everywhere since I was a kid, though.
169: That is the sort of thing that led me to the thinking in 155 -- that someone with a poor conceptual understanding is going to run off a cliff really fast when they try to rely on blind application of rules learned by rote, so looking at whether a kid can reliably get right answers on elementary school arithmetic is going to be a good guide to whether they understand it well enough to move forward.
OTOH, after listening to MHPH, maybe I'm just wrong about that.
172: I don't run into many problems in daily life that require more than something in the elementary school arithmetic (with maybe a little moving numbers back and forth over an equal sign), though. So it really might. I mean, I did manage to get through all of highschool math without failing at stuff and all, and I even remember some small fraction of it. I'm not an engineer or anything, and if you don't use math at work it's mostly going to be adding stuff up, dividing things, and so on. I just suspect mostly that I'm more comfortable doing that stuff in my head about which most people (sensibly) think "why would I need to be able to do that in my head when the phone I carry everywhere with me is capable of doing way more advanced math problems all on its own?"
I manage to do statistical programming while having to say "the alligator bites the bigger portion" every time I do a comparison.
149/155: Tatsu and Hitsuji both learned their times tables in Japanese, which are amazingly fast to say and are drummed rigorously into every kid by the end of second grade, and both boys are constantly amazed that their British peers have to stop and think of the answer to, eg, 7 x 9. They also had to do large volumes of maths drills most nights in Japan. It does seem to have paid off in terms of rapid recognition of the right sort of patterns to use for calculations in more complex problems, as well as reflex memory of the results. Both are treated as outstanding in maths here - Tatsu's maths teacher in Year 7 described him to me as a "mathematical genius," though in Japan he was in the bottom half of his class.
173: Say what you want, but I learned a very nice alternate algorithm from my A Beka elementary school math book. I used it for years! (It's listed as Method 5 at https://threesixty360.wordpress.com/2009/06/10/the-first-bunch-of-ways-to-multiply/.)
OK, to be more specific. I am really in favor of understanding concepts and doing what used to be New Math kinds of stuff. I remember my own elementary school math classes having lots in them that, as Moby says, were clearly geared toward algebra-style thinking. But I also went to a school where, starting in kindergarten, everyone sat at their own desk and did written work. (I was given sheets of arithmetic drills to do when I finished early.) I thought the Common Core stuff looked good on paper three years ago when I looked at it before K.
In 1st grade and toward the end of K, they've been doing "strategies" for addition. They have to decide whether to draw and count, use a number line, etc., to get the answer. They weren't at memorizing plus tables yet, that I know of. (She knows most of hers.). So one day Bianquette says she can't do some problem, which two weeks earlier she said was easy, and she has that attitude (it seems to me). So I start asking her over the next few days what strategy she's using for something. Sometimes it's a strategy that would work for a much simpler problem, like drawing and counting, but not for what she has in front of her (which she could do a month earlier using appropriate methods). Sometimes it's totally inappropriate, and when I ask why, she says its just the one she chose.
I get the sense that there's an expectation that at this stage they're just going to be guessing, and that this stage their is little expectation for them to get the right answer. It's easy to imagine this kind of guessing and attitude of math being hard is being modeled by other kids, especially but not only girls, in math circle type discussions, and at this stage not being considered much of a problem.
It has, unfortunately, been expressed to me, by someone who should know better, that the new Common Core standard not only emphasizes strategies but also de-emphasizes getting the right answer.
I'm becoming slightly unconvinced that a first grader can cognitively consider and select strategies, but I hope I'm wrong about that.
I manage to do statistical programming while having to say "the alligator bites the bigger portion" every time I do a comparison.
That stupid saying fucked me and caused me to get problems wrong for years. Here is how alligators work. An alligator is usually bigger than what it is eating. It is a bad ass, large beast. It has a big wide mouth that opens to eat smaller prey. So, logically, the little end of the turned-over v should be pointing to the thing that's greater (i.e., the alligator). The wide open mouth part of the alligator should be pointing to the thing that is smaller, i.e. the alligator's prey that the alligator is about to eat.
I do simple algebra all the time. Like, Deon Lewis was rushing for 4.8 yards per attempt when he got injured, and Blount was sucking, so I tried to figure out how well Blount would have to do each remaining game to match. Or, if I'm living in Celsius land, for some reason it is easier for me to convert 1.8x+32 every damn day than to bodily understand what 28 degrees C is.
Would it help if you used a python instead of the alligator?
On the article, according to a piece at kqrd.org in October, 2013, by Annie Murphy Paul: A meta-analysis (right word?) by Ray Hembree in 1990 in the J. for Research in Math Ed. shows elementary education majors have the highest percentage of math anxiety. A study by Sian Bellock, et al., in 2009, describes an experiment that showed girls were affected by female teachers' math anxiety. It says 90% of early elementary school teachers are women; that may be why that number stuck in my brain.
This was at the bottom of a lot of the articles from last summer about how kids get math anxiety when their parents try to help them (if their parents also have math anxiety).
122: What Mara is doing sounds great. The best method to solve a math problem is the best method that works for you, so she should cheat away, so long as she can at least sorta remember the other methods in case they end up being better on different kinds of problems.
That's actually kind of impressive that they're teaching that as early as second grade. I have epsilon more hope for the future.
140 takes a surprisingly strong position on the Platonist/formalist distinction. Real mathematicians are formalists in the streets/Platonists in the sheets, and I recall UPEGTI being mathy, so I conclude that Unfogged is sheets.
Nothing in 140 requires Platonism (except perhaps reference to "rectangles" if you want to be a lb). You could mount basically the same argument as a nominalist: a(b +c) = ab + ac because if I have a piles of b + c things, then, if I also have a piles of b things and a piles of c things, then, in the two cases, the things are equinumerous with each other. Saying that doesn't require Platonism.
Neb would be a great elementary school math teacher.
Equinumerosity is a concept that comes easily to third graders.
Fair enough; s/Platonism/anti-formalism/g.
I suspect that once you get into the generalized abstract nonsense fields of math formalism starts looking a lot more attractive. Like, maybe the reason we use "+" for this relation is related to its origins in describing quantities of things, but by the time you're characterizing it as a binary relation with such and such properties over a set with such and such further properties and the following distinguished elements blah blah, I mean, it's starting to look a lot like it's all formal. (Until someone uses it to steal your bank account info, probably.)
That's where the streets/sheets comparison I made comes into it the most. With formalism, if you do it right you're never wrong, only useless.
Right, but there's a reason you don't teach ring theory to people who don't already understand fractions really well.
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VSOOBC. RIP Tripp. (From the other place.)
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VSOOBC. RIP Tripp.
Thank you for sharing; I'm saddened to hear that.
Oh no. I'm sorry to hear that.
Oh man. I am sorry to hear it. Thank you for letting us know.
What a bummer. I was wondering a few months ago why we never saw him around anymore. He wasn't even 60, from what I gather.
RIP. How sad. He was a really decent, interesting guy.
Thanks for telling us about Tripp. I'm very sorry to hear.