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Ed Hartouni
Trad climber
Livermore, CA
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Division with Roman numerals---fuhgettaboutit.
when I encountered them (and it is strange that they were taught in math) I did try to figure out how to divide with them, it wasn't a part of the course, but it was an interesting question in my whatever-the-grade-was mind...
I didn't come up with a solution (not surprisingly) but I had a lot of fun playing around with it... and multiplication too...
One reason to at least mention Roman numerals is to illustrate what a miracle place-value notation is.
the power of zero!
Chaz, given your story, why do you feel compelled to participate in this thread? Common Core cannot be even a slight concern of yours.
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jgill
Boulder climber
Colorado
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Boy, who would think long division would come under such fire. As Rich mentioned the algorithm is fundamental in mathematics.
How much of critical thinking ability is genetic? Is there a crucial window of opportunity? How much of mathematical ability is genetic? (the great breakthroughs are most frequently seen in practitioners under the age of thirty-five). Is it like musical ability - prodigies like Mozart writing serious music at age 11? Idiot savants can multiply enormously large numbers or do similar things without any real understanding of the theory. How does all of this fit together in a curriculum designed to bring all students up to an acceptable level of proficiency? Is this even possible in the age of Facebook, Twitter, Tweets, instant electronic connections. How many of the posters here have had children go through the educational system? Have watched as thinking skills materialize and mature? Questions, questions, questions.
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rgold
Trad climber
Poughkeepsie, NY
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How many of the posters here have had children go through the educational system? Have watched as thinking skills materialize and mature?
My daughter was educated in the Arlington (NY) public school system and as far as I'm concerned got a great education. Was every teacher fantastic? Of course not, but the overall effect was excellent, all without the Common Core by the way, but before the general rejoicing starts the New York State Regents did have standards that were tested by exams and those results were part of the student's final grade in the course, and the AP courses she took were also governed by standards-based exams.
With the very few crappy teachers she had, we were sympathetic, up to a point, but also took the point of view, "how will you make the best of this?" We didn't complain to the school, and we didn't bad-mouth the teacher in front of our daughter. Life isn't perfect and you have to learn how to make lemonade when what you've got is lemons.
She then went to Boston University and double-majored in Philosophy and Musicology, but her goal from a very young age was, I think, to become a professional musician and she never took her eye off that prize.
I never thought much about "thinking skills" at the time and looking back on it, I don't think I have any conveyable sense of "development." There are perhaps two things we did that might be considered unusual. The first is that we didn't turn on the TV until the end of middle school. She thought the TV was a device for playing videotapes until, finally, we turned it on so she could watch the olympics. Lots of luck trying to keep technology at bay nowadays, but we thought it was important at the time and I haven't learned anything since to change my mind. I am beyond grateful that cell phones were not part of her growing up, and that the internet became a presence only later in high school.
The second thing is that we enrolled her in a gymnastics class quite early. Not for the reasons you might think though. It had nothing to do with athletics; I have a pretty negative view of organized athletics programs for kids. We did it for reasons that are echoed in my comments about mathematics above. It seemed like the best experience a young child could have that would show them that they could, through hard work, lots and lots of practice, yes frustration and confusion too, manage, over time, to do amazing things they could not initially have conceived of as possible. And have fun along the way. I couldn't think of anything else that would give them the experience of looking back and saying, "a year ago this was unimaginable."
There was a third thing but I can't take credit for it. At around seven, maybe a little earlier, she begged for a piano, and that began what has become her career. That was all her. But the fact that she, of her own accord, got up at 6AM every morning before school to practice, right through high school---I'd like to think that came from what she had learned from gymnastics, the confidence that you could master things with work that didn't seem even remotely possible, the ability to persevere, and the fortitude to withstand the frustrations that are an inevitable component of learning anything hard.
I have to say that I also worried about gymnastics. The awful body-image pressures, the injury potential. And so I was more than relieved when, after maybe six years of it, she said she was done. (She then moved on to basketball, to the horror of her piano teacher, who rightfully worried about finger injuries.)
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Majid_S
Mountain climber
Karkoekstan
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IMO, Majority of Americans are programmed not to remember anything in general and not just math. There may be political reasons behind this however, not knowing math makes it easier to f*#k up in savings and to do daily calculations on where you are financially.In short sentence, you are always broke therefore you must always work till the day you die.
Go to any street in Asia, ME , Africa or even Europe and ask couple of kids that you want to add this plus that and they know the answers but here in America, even behind the cash register, you buy a burger for $5.01 and you pass a $10 bill ,you got to wait a minute for machine to figure out the $4.99 change before cashier boy can give your change back.
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Chaz
Trad climber
greater Boss Angeles area
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Majid,
If an employer in the U.S. doesn't foot the bill for a cash register that figures the change automatically, that employer will go broke.
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yanqui
climber
Balcarce, Argentina
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True story from SLC, Utah that took place (I think) back in the late eighties: on the way home we went through a drive-in because a friend, who was with us in the car, wanted to grab something to eat. As I recall, he ordered a hamburger (around $2) some french fries (about $1) and a coke (also about $1). When we got to the window the kid working there said: "That'll be $8" (I don't remember the exact amount here, but it was something like double what the order should cost). So my friend says: "No way, can't cost that much". Then the kid looks back down at the cash register and, shaking his head, says: "Sorry sir, but the order costs $8". So then my friend says: "Look, a hamburger costs about $2" and the kid nods in agreement, "a french fries costs about $1" which elicits another nod of agreement "and a coke is about $1. So the order should be about $4". Now the kid was getting kind of nervous and he starts looking back and forth from the cash register to my friend and then he says: "I'll have to go get the manager". After a few moments the kid comes back with the manager and the manager asks: "What's the problem sir?" And my friend explains how 2+1+1 should equal 4, not 8. So the manager looks back down at the cash register, then starts talking quietly with the kid and after a few moments answers back: "but there's also tax on the order". This response evokes audible guffaws from the driver (me) and causes my friend to totally lose it. Keep in mind, sales tax in Utah at this time was about 10%. "There's NOT $4 of tax on a $4 order" screams my friend, his arms waving wildly in the air.
Anyways, I can't recall exactly how much more discussion it took to finally get things straightened out, but somehow the anecdote seemed to be relevant to this thread.
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Ed Hartouni
Trad climber
Livermore, CA
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My daughter grew up going to public schools, New York (Westchester Co.), Massachusetts (Amherst) and eventually college at UCDavis...
yes, it was an amazing thing to know someone from their very beginning to becoming an adult, a real privilege, and to have helped out along the way an honor.
While she is troubled, as the rest of us are, with coming to grips with what we aspire to be and what we are, she's a great person.
What does this have to do with "Why Americans Stink at Math"?
To infer that mastery at math is something only people with access to elite institutions of learning could achieve seems a very tired theme. While not everyone will become a mathematician, everyone benefits from learning mathematics. And it is learning that is becoming more and more important.
Why not convey to our children the benefit?
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rgold
Trad climber
Poughkeepsie, NY
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To which I would add, we don't know who among our young children might or will become a mathematician, scientist, etc. Assuming (correctly) that only a minority will do this but that we don't know who that minority is, should we create an educational system that prepares no one for advanced careers? The genius of America's attempt at a non-elitist education system is that we assume, at least in principle, that everyone might become a rocket scientist (etc etc). We don't say, look, here are the little rocket scientists, we'll give you an enriched education, and here are the little burger flippers, you'll never have any use for the rocket-scientist stuff so we won't tax you with any of it---we don't do this because we know that neither group is going to end up where we predicted.
The price we pay for giving everyone a chance is that some people will look back and say they've gone through life and never needed any of it. With apologies to those who were afflicted, I think this is preferable to any of the alternatives.
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yanqui
climber
Balcarce, Argentina
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How many of the posters here have had children go through the educational system? Have watched as thinking skills materialize and mature? Questions, questions, questions.
My daughter (who is a dual citizen) is going through the Argentine public school system, which is at least as bad as the American version. I don't believe this is necessarily a bad experience for her. This year (in March) she started 7th grade and has her first real math teacher, a trained accountant, who is not half bad (math, in the grade school she went to, was basically non-existent). There are about 40 kids in her grade and the level of math among this group sets the bar pretty low. She is certainly one of the best (if not the best) in her grade in math and seems to like the subject, which already makes her a bit of an outsider, culturally speaking. I believe it can be a good experience for her to develop some emotional strength in establishing her independence from the group like this.
When I read the article from the NY Times in the OP I tried asking her that simple question that so many Americans apparently got wrong: which is bigger 1/4 or 1/3? I was a bit suprised she didn't immediately know the answer (she hasn't worked much with fractions in school). After she hesitated for a few moments, I said: "Try thinking about it this way: imagine the table there divided into four equal pieces and then into three equal pieces". She immediately answered that 1/3 was bigger than 1/4.
Yesterday she was doing some kind of interesting exercises for class with prime numbers. One of the questions asked if the sum of two prime numbers was ever prime. She was patient with Dad when he said we should really think about that one for awhile. We figured out together that if neither of the primes was 2 then the sum was necessarily even, so it couldn't be prime. Then we looked at some examples of "twin" primes. We saw that 3, 3+2=5 and 3+4=7 were all prime and I asked her if she thought this sort of thing could happen again, for bigger primes than 3. We checked it with some examples: 11 and 13 are prime, but 15 is divisble by 3. 17 and 19 are prime but 21 is divisible by three. Then we figured out together the reason that if p is a prime bigger than 3 and p+2 is prime than p+4 is divisible by 3. We did all this without writing anything down. Finally I asked her if she thought the amount of "twin" primes was infinite. She said she didn't know. I told her that this was a famous and extremely difficult problem that best mathematicians hadn't been able to solve for hundreds of years, but in the last few years mathematicians were getting very close. I told her the story about Terence Tao and we looked at some pictures of the boy genius on internet and I also told her about some of the very recent and extraordinary work that "almost" solves the twin prime conjecture. She seemed pretty interested and in terms of the "critical" thinking aspect was able to construct the arguments we developed with very little help from me.
I think it woukld be great if her school and culture at large offered much more opportunity where she could engage in activities like the one I just described, but I'm afraid that just aínt gonna happen.
PS rgold: We have "Netflix" in the house and I occasionally buy movies from itunes (Amazon is unavailable in Argentina) but other than that, we don't have TV in the house and Ceci doesn't seem to miss it. I also feel she has a pretty good "nuclear" peer group with her closest friends being more studious (i.e. valuing "education" more) than the norm, and therefore also finding themselves a bit outside the mainstream.
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kev
climber
A pile of dirt.
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I believe that at some point earlier in the thread it was questioned if undergraduate mathematics education majors to need to math beyond what they're going to be teaching. I think that this type of thinking is an example of why we suck at math. The fundmental lack of people getting why this is important (especially for teachers) and troubling.
Ed, you left out another long division twist : long dividing two infinite series to get another
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wbw
Trad climber
'cross the great divide
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Topic Author's Reply - Aug 5, 2014 - 09:29am PT
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To infer that mastery at math is something only people with access to elite institutions of learning could achieve seems a very tired theme. While not everyone will become a mathematician, everyone benefits from learning mathematics. And it is learning that is becoming more and more important.
Why not convey to our children the benefit?
When will we ever use this? Ah, the question that often comes from the student hoping against hope, that this question that distracts the teacher may just get them out of the homework assignment the teacher planned.
Even though I am portraying this from a jaded point of view (it's meant to be humor, in case that's not obvious), and the question can throw some math teachers back on their heels, here is my response. Note: I rarely tie my response to how a specific math concept will lead to wealth and happiness.
Studying math is taking a journey. What you learn today may very possibly never be used in your daily life, but if one engages in the journey, I guarantee it will be beneficial. Engaging in mathematical thinking teaches one to organize one's thoughts, think critically, systematically and to reject unreasonable solutions to problems. Engaging in math is a workout for the brain. One's ability to grasp complex ideas is greatly increased as one gets further into the journey. It's not about what we're learning today in math class. It's about what one gains from a journey that takes many years, and at times may be quite frustrating.
I also tell my students that if they have never experienced the joy of solving a difficult problem in math class, which I believe is accessible to all students, I hope they have that experience in my class.
I took those hard math classes in college that Professor Gill refers to. Did I understand everything in my real analysis class? Definitely not. But having that experience of thinking, beating my head against the wall in frustration, and persevering so that at least I had some level of understanding absolutely helps me to be a better math teacher for high school students. (And I also found the process to be very rewarding.)
Getting back to the Common Core, if it is true that many (if not most) math concepts are simply part of an important journey, and not in-and-of themselves critical to one's education, why can professional "educators" not resist the urge to pack so much into a curriculum, that a classroom teacher has to rely on more superficial methods to teach math??
In Colorado, there was a law passed in 2010 that basically takes away the "tenure" for public school teachers who cannot demonstrate measurable growth for their students. Thus far, the only practical way to measure that growth is through standardized tests.Everyone is so freaked out that their students won't show that growth if they don't tick all of the huge number of items on the curriculum, that many just don't find the time to go deeper into concepts where real thinking takes place. Again, the promise of the Common Core has completely been thrown out by the folks that wrote it, and in my mind that is a huge missed opportunity.
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rgold
Trad climber
Poughkeepsie, NY
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wbw, on the (unlikely) off-chance that you don't know about it, the MAA has many resources on "when you'll use this," see http://www.maa.org/careers
Some interesting tidbits: CareerCast ranked "mathematician" the best job in the country in 2014. PayScale found the top 15 highest-earning college degrees have mathematics as a common element.
There's also We Use Math, http://weusemath.org/ , out of Brigham Young University.
As someone who embraced mathematics for its own sake and not for what it might or might not do for my earning potential (just like climbing!), I am always a little hesitant to fall back on vocational justifications. After all, we study art, music, poetry, history, and a host of other subjects without inquiring about their immediate application to future earnings, so why does mathematics get singled out for this type of question?
But there is an answer. Mathematics is a gateway subject. A gateway to a host of professions will beyond the top 15 highest-earning college degree careers. Professions most of the kids and some of their teachers may not even have heard about. Close that gate and you've shut off a vast array of future opportunities. And that array is growing, as more an more fields become "mathematicized." A somewhat recent example is biology.
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Chaz
Trad climber
greater Boss Angeles area
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What would it take to prevent parents from taking their kids to Mexico for a month or more at Christmas?
I've heard reports sometimes 1/3 or more of the class is absent for the first few weeks of the calendar year, because they're visiting Los Abuelos down in Mexico.
Parents used to schedule vacations around the school calendar. Most parents still do, but a growing percentage just don't care.
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Chaz
Trad climber
greater Boss Angeles area
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Do you think I made that up?
Talk to teachers in Fontana. Then tell me where their students are when school starts after Christmas. They're not in school.
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wbw
Trad climber
'cross the great divide
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Topic Author's Reply - Aug 5, 2014 - 11:32am PT
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Chaz, I have more attendance issues with the kid that is in Europe or Costa Rica for an extended vacation when school is in session, than the kids that are (as you say) visiting Los Abuelos.
I posit that the fact that we do not strive for a non-elitist education system in any real or meaningful way is the very reason we "struggle" compared to other countries academically.
I think if you look at those international math tests that we allegedly don't do well on as a country, you'd find that the countries that do the best have a much more exclusive sample size that they draw on to take the tests.
In other countries, students get weeded out from an academic track in their education and get re-directed to trade schools. (Personally, I don't think this is necessarily a bad thing, but it certainly creates a more exclusive education system.)
In Colorado, poor (generally rural) school districts get a bigger share of the state funding pie (relatively speaking) than wealthier districts.
As a public school teacher, I truly believe that all students can learn, and it is my goal that *every* student in my class do so. Even though this is a goal to aspire to, I spend a lot of time in pursuit of this goal. Most of my colleagues that I have known over the years feel the same way.
Short of a socialist system (some might argue that the public education system in the US is the closest thing we have to socialism in our country), I don't know too much more we can do as a society to make education a less elitist system than what we have. Of course, it is the most motivated students (and those that come from families that support their education in some meaningful way) that rise to the top and become the elites.
Jammer, I would like to know more about why you say we don't strive for a non-elitist education system. What more might we do??
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wbw
Trad climber
'cross the great divide
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Topic Author's Reply - Aug 5, 2014 - 11:57am PT
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Jammer, as I understand it this is the result of a law that was passed in CO in recent history. I don't think rural districts have an advantage over poor, inner-city districts, but I can't honestly say I know the formula that determines how that state money is distributed.
In Boulder, we tend to get a lot of ballot measures for increased funding from Boulder taxpayers because with this law, we have budget shortfalls most years. These ballot measures are on top of high property taxes that I pay in Boulder.
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BLUEBLOCR
Social climber
joshua tree
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Jammer, I would like to know more about why you say we don't strive for a non-elitist education system. What more might we do??
Jammer's Jamm'in, but I'll add some too.
"What more might we do?" How about putting the monies in a general fund, like they do with the Parks?
Los Angeles Co. is buying iPads for every student at the tune of 6 mil bucks. Meanwhile in San Bernadino Co. here at Joshua tree elem. my daughters class has 9 old computers which they have to share with other classes.
And in Placer Co., Rocklin High got a new football stadium at around 3mil, while Placer High has dead grass and beat up old wood bleachers for the home team and the visitors gotta stand.
You may call it fairness through taxation. I call it Elite ism.
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jgill
Boulder climber
Colorado
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What does this have to do with "Why Americans Stink at Math"? (Ed)
What Largo calls "keeping an open focus."
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rgold
Trad climber
Poughkeepsie, NY
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rgold, I really would be interested in your answer to this question: Besides rhetoric and idealism, what leads you to believe we actually strive for a non-elitist education system?
Rhetoric and idealism, but in the opposite order. That and the fact that we do not in general determine career trajectories from exams given early in the educational process.
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rgold
Trad climber
Poughkeepsie, NY
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Your example of an objective test to determine career paths as opposed to the current system of having ones parents "legacy" largely determine which doors are open is then by my definition less "elitist". '
There seems to be little question that parents' education and social status confers a significant educational advantage on their kids. Some but not all of this might be cured by more equitable funding, but there is always going to be an advantage there that will never be completely leveled.
The existence of a career path test won't help at all because the less privileged kids will not do as well for many of the reasons they aren't currently doing as well and so be disproportionately shuttled out of the academic track for good.
We are far better off hoping that some of them will beat the odds, and in fact this happens with regularity, although maybe not on a scale to make much of a dent in national statistics. My institution, for example, is justifiably proud of its record with first-generation college students. Every year we graduate people who weren't supposed to make it this far, and in Mathematics I know several who now have PhD's. In the alternate exam-based career tracking, it is unlikely that any of them would have been able to do this, because their academic "coming of age" would have been too late for those filters.
As for "why Americans stink at math," I think the issues go far beyond equitable funding, and it is not hard to imagine equitable funding making little difference in the absence of other changes.
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