(no subject)
Aug. 26th, 2013 10:09 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
seekingferretLast July we had Andrew Hacker arguing that algebra shouldn't be taught to everyone in the New York Times: http://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-necessary.html?_r=1&pagewanted=all This September we have Nicholson Baker arguing the same thing in Harper's- I haven't read the article, as it's behind a paywall, but he spoke on the Leonard Lopate show yesterday and I listened. http://www.wnyc.org/shows/lopate/2013/aug/22/do-we-really-need-need-algebra/#commentlist
Baker's most frustratingly patronizing argument in the radio interview was that it was unfair to high school mathematics teachers to be forced to teach students who were simply never going to be good at algebra. I wanted to ask him if the mathematics teachers he was bravely stepping up to defend were actually complaining. Of course they're not, at least not in number: I've not met a lot of mathematics teachers who believe that their students are simply not capable of learning math.
Both Hacker and Baker dismiss the claims that competence at algebra correlates to professional success by arguing that our system unfairly penalizes people who would otherwise be successful if only they weren't required to take algebra. Baker complains that because colleges require algebra for admission, students who would successfully complete college if not for this requirement are denied the opportunities college would afford them. "It isn’t more than a statistical correlation, but people pounced on this and said, my god! Algebra 2! It’s the mystic door! If we force every child go through this door successfully, if we make them do it and we make them succeed, then they’ll all be above average and the world will be a better place." For me, the funniest part of this quote is that it involves analyzing the meaning of a statistical correlation: something that's only do-able with a very solid grounding in algebra. Actually, this is the second funniest part of the quote. The funniest is the idea that if you eliminated one of the requirements to graduate college, more people would graduate college. Of course this is true. We could eliminate literature courses to the same effect.
Of course, Baker misses the point that there are numerous professions that legitimately require algebraic competence- accounting, engineering, market research, chemistry, to name but a few... and none that are unavailable to people who do possess such competence. Nobody will ever turn you away from a job because you have too much algebra- the presumption ought to be that someone arguing against algebra ought to have a higher standard of proof than an argument that a statistical correlation is skewed.
Both Baker and Hacker also claim that they don't seek to eliminate math training for these students who are to be exempted from algebra. Hacker's solution was "to create courses in the history and philosophy of their discipline, as well as its applications in early cultures. Why not mathematics in art and music — even poetry — along with its role in assorted sciences? The aim would be to treat mathematics as a liberal art, making it as accessible and welcoming as sculpture or ballet." Because sculpture and ballet are extremely accessible and easy and don't require any hard work to master. Baker believes that algebra should be taught at a simple level, "so you get a sense of what's out there and whether you have a head for it" The same way a person is taught history, you know, just to have an idea of what's out there in the world of historians.
The truth is, it's entirely possible that as an adult you'll never have to solve a system of linear equations. I don't think anyone really disputes that. I'm a mechanical engineer and I don't solve systems of linear equations very often myself. But the math I learned, I didn't learn so that I would know what's out there. I learned it so that I would be able to use it. I learned it so that when presented with problems that required that toolkit of skills, I would know how to approach them. Can you work around it, avoid any situation that requires you to do math? Sure. When you're an adult, you can work around virtually anything you don't want to have to do. But you're inevitably at a disadvantage against the people who are capable of doing the thing you're avoiding, and I don't understand why we would want to institutionalize putting people at a disadvantage as substantial as not being capable of approaching mathematical problems.
Baker's most frustratingly patronizing argument in the radio interview was that it was unfair to high school mathematics teachers to be forced to teach students who were simply never going to be good at algebra. I wanted to ask him if the mathematics teachers he was bravely stepping up to defend were actually complaining. Of course they're not, at least not in number: I've not met a lot of mathematics teachers who believe that their students are simply not capable of learning math.
Both Hacker and Baker dismiss the claims that competence at algebra correlates to professional success by arguing that our system unfairly penalizes people who would otherwise be successful if only they weren't required to take algebra. Baker complains that because colleges require algebra for admission, students who would successfully complete college if not for this requirement are denied the opportunities college would afford them. "It isn’t more than a statistical correlation, but people pounced on this and said, my god! Algebra 2! It’s the mystic door! If we force every child go through this door successfully, if we make them do it and we make them succeed, then they’ll all be above average and the world will be a better place." For me, the funniest part of this quote is that it involves analyzing the meaning of a statistical correlation: something that's only do-able with a very solid grounding in algebra. Actually, this is the second funniest part of the quote. The funniest is the idea that if you eliminated one of the requirements to graduate college, more people would graduate college. Of course this is true. We could eliminate literature courses to the same effect.
Of course, Baker misses the point that there are numerous professions that legitimately require algebraic competence- accounting, engineering, market research, chemistry, to name but a few... and none that are unavailable to people who do possess such competence. Nobody will ever turn you away from a job because you have too much algebra- the presumption ought to be that someone arguing against algebra ought to have a higher standard of proof than an argument that a statistical correlation is skewed.
Both Baker and Hacker also claim that they don't seek to eliminate math training for these students who are to be exempted from algebra. Hacker's solution was "to create courses in the history and philosophy of their discipline, as well as its applications in early cultures. Why not mathematics in art and music — even poetry — along with its role in assorted sciences? The aim would be to treat mathematics as a liberal art, making it as accessible and welcoming as sculpture or ballet." Because sculpture and ballet are extremely accessible and easy and don't require any hard work to master. Baker believes that algebra should be taught at a simple level, "so you get a sense of what's out there and whether you have a head for it" The same way a person is taught history, you know, just to have an idea of what's out there in the world of historians.
The truth is, it's entirely possible that as an adult you'll never have to solve a system of linear equations. I don't think anyone really disputes that. I'm a mechanical engineer and I don't solve systems of linear equations very often myself. But the math I learned, I didn't learn so that I would know what's out there. I learned it so that I would be able to use it. I learned it so that when presented with problems that required that toolkit of skills, I would know how to approach them. Can you work around it, avoid any situation that requires you to do math? Sure. When you're an adult, you can work around virtually anything you don't want to have to do. But you're inevitably at a disadvantage against the people who are capable of doing the thing you're avoiding, and I don't understand why we would want to institutionalize putting people at a disadvantage as substantial as not being capable of approaching mathematical problems.
(no subject)
Date: 2013-08-26 03:36 pm (UTC)Because I also am not entirely sure that people ought to be taught as much math as they are being taught now. Or at least not the algebra-geometry(-trig-calculus) standard sequence for the college-aspiring student.
Though I also agree that the reasons they give are stupid, and are they serious about math as a liberal art, what, that is about the stupidest thing I've ever heard. And I certainly agree that anyone who is thinking of going into a field even remotely related to science (or who might later decide to -- like my friend the literature Ph.D. who did math competitions as a child, who started writing programming manuals and is now a programmer) ought to take that mathematics sequence.
But as it is right now, there are a lot of people who, as far as I can tell, aren't actually learning anything in these classes, suffer through them, forget them as soon as they're done, and as adults tell me things like "Oh, algebra! I never got that stuff." I think it's a waste of everyone's time, quite frankly, if that's going to be the outcome. And it's true that most people don't use algebra in their everyday lives.
But. Do you know what most people DO need to use in their everyday lives? Statistics, probability, and logic. And this never gets taught as part of the regular curriculum in the school system (unless, I guess, you go to some really cool school -- even my math-and-science magnet didn't require it).
If I ran the world, or at least the US educational system, I'd require only as much algebra as you needed to understand simple statistics, probability, and logic. (You probably need to be able to think in an algebraic fashion, although quite probably what kids learn in "pre-algebra" would be enough for what I'm envisioning.) I would make statistics, probability, and logic mandatory for high school graduation. I would make it the top priority, math-wise, that kids got out of school knowing two things:
a) the difference between correlation and causation
b) a->b does not imply b->a
(well, I can think of other things they should come out knowing, like what an exponential function is and how that relates to one's credit card bill, and maybe that requires a bit of algebra too. And things like how to calculate a 15% tip, or at least a 10% tip. And yes, I have had someone ask me to calculate a 10% tip because she didn't know how to do it.)
If everyone came out knowing those things, I actually think it would be an improvement over the current system.
Of course, who would teach these things? That's another question.
(no subject)
Date: 2013-08-26 04:08 pm (UTC)Yes, I mean, certainly the algebra II course I was taught, specifically, was the bucket of algebraic concepts that they couldn't fit into Algebra I. It was an ugly, unpleasant class because unlike Algebra I or Geometry or Calculus, there wasn't any SYSTEM underpinning it, a sense that a concept learned would then be reapplied in the next part of the course. One simply had to soldier on, learn a concept, pass the test, and then move on to learning the next concept. I desperately wish that Algebra II could be better structured.
Can we be teaching math better? Yes. But on what evidence can these people say that these people can never learn math?
As far as statistics go, I mean, there's two layers of that, right? There's statistical analysis that sixth graders can be taught: what is a mean, what is a median, what is a maximum, what is a minimum? That doesn't require algebra, just arithmetic. But then there's the second level: what is a confidence interval, what is a margin of error, what is a normal distribution, what is a standard deviation? And those things really need calculus to learn properly, but you can fake the required calculus with algebra II and some lookup tables.
The first kind of statistics is what you need as a bare minimum for an individual to get through the world, but the second kind of statistics is to my mind the reason why people can't follow arguments about global warming or pharmaceutical treatments. I feel like the second kind of statistics is the bare minimum for humanity to survive. And confidence intervals are a complicated enough concept that even if you're never going to actually compute one in your adult life, you'd better have computed them as a student or you're never going to be able to interpret them when others present them to you.
And I certainly agree that anyone who is thinking of going into a field even remotely related to science (or who might later decide to -- like my friend the literature Ph.D. who did math competitions as a child, who started writing programming manuals and is now a programmer) ought to take that mathematics sequence.
My problem here is that algebra II is something you're taking at what age? Somewhere between fourteen and seventeen, depending. Who are these people who at the age of fifteen we're telling them that they're never going to be scientists? How certain are we of anything about the life trajectories of people at age fifteen? My uncle didn't figure out he wanted to be an engineer until he was twenty five.
(no subject)
Date: 2013-09-07 04:34 am (UTC)But your comment got me thinking: we always approach calculus from the algebraic side. What if, for this sort of class, we instead approached it from the probability side? Talk about discrete probability distributions. Do the Buffon needle problem (heh, okay, for that you kind of need geometry and trig, maybe a simpler geometric probability problem), talk about the law of large numbers... It seems to me that one could introduce the ideas of geometric probability and integration, even if it wasn't formalized, enough so that you could get the concept of, say, what a probability density function is and why you would care.
And we don't even need the more advanced concepts to talk about things like the correlation of Y and Z vs. Y causing Z, or to talk about why a study that shows that 5 out of 8 patients treated with Agent A had a (binary forced choice) good outcome might not be sufficient for you to invest all your pennies in Agent A. (True story, this last one: my uncle, a medical doctor, was trying to solicit investment in a startup he was affiliated with. Their research was... unconvincing.)
Oh! I had another idea: instead of algebra, teach programming. I suppose that the logical flow of programming isn't really that much different from the logical mindset needed to do math, but I could imagine it being a little more approachable and immediate-gratification (like, you get a program to run, and you Have Something). Maybe I'm wrong about this, though -- my parents forced my sister to take a C class in high school, leading to her abiding hatred of all programming whatsoever.
To take this back to the original topic, I dunno, I can totally see why people think algebra is this weird woo-woo thing unrelated to anything else. Literature, or history, you can kind of see how it relates: it's about actual people, after all, and it's pretty clear that writing well is a plus pretty much no matter what job you're in. And I think people understand that science is sort of related to real life (and yes, if you have a good physics teacher you start to see what all that math is for, but as far as I can tell a lot of kids have checked out by then). And, you know, I totally get what you're saying, and agree, that the sorts of logical thinking skills you pick up from upper-level math classes are applicable no matter what you do in life -- but I feel a little bit like the math classes themselves have sort of lost track of that, and so there's this disconnect where people don't realize that the point of these classes is to learn these skills (and a lot of people aren't learning them). And there is so much math and logical-thinking-skills-related sorts of things that are both really interesting and actually applicable to life! Why not teach that?
As for who gets to decide: well, I think by high school, kids have already sorted themselves into the pots of "is willing to take an advanced math track" and "is never going to use math at all as far as it can be avoided." (Whether this should be the case is another question entirely, but I think that it is how it is.) I am willing to bet that your uncle was in the "willing to take an advanced math track" category, although I am also willing to be told I'm wrong. Myself, I can't think of anyone who hated math in high school who went on to hold a technical position.
(Note: I'm moving around the goalposts a lot by claiming we have to take into account the part where math instruction is often terrible, and then advocating for solutions that would require a lot of really good math instruction. I know :) )
(no subject)
Date: 2013-09-08 04:08 pm (UTC)No, it's
No, in my opinion the reason to teach mathematical tools is because they are useful, and this is a true fact whether or not people can avoid using them. Here's an example of what I mean, an actualfax math problem I saw someone post on FFA a few weeks ago:
The poster had significant student loans that if they continued to pay off at the expected rate would take about five more years. They had just gotten a raise at work, and were uncertain if they should put that money into paying off the principal faster, put it into a retirement account and continue paying off the loans at the expected rate, put the money in the bank to build up a short-term emergency cushion, or do something else.
And the mathematical answer to this problem is that it depends on a whole bunch of interest rates: The interest rate on the student loans, the interest rates you get in your retirement account, the inflation rate. These are all somewhat variable and predictive, but we can make some approximations, set it up as a set of equations, and solve.
Or alternatively, you can go online and find an online investment calculator, plug in those numbers, and get an answer. Or you can find a friend or an investment counselor and have them do A or B for you.
As an adult who doesn't have to solve this for a test, there's always a way to solve a math problem without actually sitting down and doing the algebra. So adults can go around saying "I'm a successful grownup and I never use algebra." But what I'm saying is, that doesn't mean they couldn't have used algebra. Algebra isn't an all-or-nothing proposition for grownups, it's just a tool that makes life easier. This is what the people who say they never use algebra are missing, that if they did know algebra, they would be able to use it instead of a workaround.
What's so bad about the workarounds? Maybe nothing. But maybe there's a cost: You owe your friend a favor, you owe your investment adviser a percentage. Maybe your result isn't as accurate- the online investment calculator misses a factor and you don't know how to modify its result to account for the missing factor. If you're not afraid of setting up the math, you can solve your problems on your own terms without that cost. And when you make that decision about handling your money because you set up the math yourself and solved it, you know all the assumptions you made. If one of those assumptions is proven wrong or changes, you are aware and can modify your math. If you are uncertain about some of your assumptions, you can hedge appropriately.
It seems to me that one could introduce the ideas of geometric probability and integration, even if it wasn't formalized, enough so that you could get the concept of, say, what a probability density function is and why you would care.
And we don't even need the more advanced concepts to talk about things like the correlation of Y and Z vs. Y causing Z, or to talk about why a study that shows that 5 out of 8 patients treated with Agent A had a (binary forced choice) good outcome might not be sufficient for you to invest all your pennies in Agent A. (True story, this last one: my uncle, a medical doctor, was trying to solicit investment in a startup he was affiliated with. Their research was... unconvincing.)
So the problem with this is that without the math, this stuff has the potential to be worse than useless, it has the potential to trick people into thinking they know more than they do. I know a lot of people who aren't mathematically oriented who have been taught qualitatively that there is a difference between correlation and causation and that small sample sizes can lead to significant sampling error, because it's pretty easy to teach qualitatively.
But if you were to ask them what a sufficiently large sample size to be convincing was, they couldn't tell you, because the answer is variable, depends on the size of the population and your definition of 'convincing'. It requires actual mathematical analysis.
Similarly, a person who knows that correlation is not a proof of causation is well-equipped to be skeptical of statistical claims, but they're not well equipped to accept statistical claims. If they can't carry out a t-test, can't look at the r^2 value of a regression, how do you persuade them that a statistical analysis does establish evidence of causation?
[A Rabbi I know, who is not very educated when it comes to math and science, gave me another anti-evolution book last week and I was reading it. It began with a lot of nonquantitative discussion of the difference between correlation and causation, under the heading "Creating an Educated Consumer of Scientific Information". If by educated consumer of scientific information you mean a skeptical consumer, sure. And skepticism is obviously an important part of the scientific process. But it needs to be counterbalanced with actual, viable (quantitative) tools for identifying times when skepticism is not proven out.
The book, for example, talks about Barry Marshall and h. pylori. It's a case I argue about a lot with people. The book cites it as an example of a time when the scientific establishment was taking inaccurate information about the behavior of the stomach on faith, and needed a rebel from outside the establishment to use skepticism to prove them wrong. But Marshall's self-inflicted ulcer did not itself vindicate him, and people telling the story often miss that point. One data point does not a scientific revolution make. At best, Marshall's demonstration provided evidence that a legitimate trial might be worthwhile.]
So what I'm saying is that it's problematic to teach math half-way, because it tricks you into thinking that you can make a qualitative evaluation of a statistical result. And we're talking about the math that is used every day to talk about how the world works- political polls, environmental studies of global warming, medical trials- things that the average person really ought to be able to think about correctly.
Oh! I had another idea: instead of algebra, teach programming. I suppose that the logical flow of programming isn't really that much different from the logical mindset needed to do math, but I could imagine it being a little more approachable and immediate-gratification (like, you get a program to run, and you Have Something). Maybe I'm wrong about this, though -- my parents forced my sister to take a C class in high school, leading to her abiding hatred of all programming whatsoever.
I mean, I think computer programming is an immensely valuable skill to learn also in the modern world, and there are many times that I wish I were more skilled at programming because there are many tasks that I would automate if I could. But again, I don't value computer programming as a means to another end (learning logical thinking), I value it because programming is really useful.
And in many of the examples I've cited, some forms of computer programming could substitute for mathematical prowess. So I'm not altogether opposed to this, as long as by computer programming we mean actual study of algorithms instead of monkeying around with Visual Basic.
As for who gets to decide: well, I think by high school, kids have already sorted themselves into the pots of "is willing to take an advanced math track" and "is never going to use math at all as far as it can be avoided."
Yeah, but that wasn't really what I was arguing. Of course kids have decided by that age whether or not they're willing to take advanced math classes, but that doesn't mean that the ones who have decided they aren't willing aren't capable of taking advanced math classes. Kids decide lots of things about their lives in high school. My point is that by not requiring them to take the math classes, you're ratifying that decision. You're telling these stupid 16 year old kids who don't have a real clue what they're going to do with their lives that it's okay to shut out a world of potential careers.
(no subject)
Date: 2013-09-12 08:32 pm (UTC)I see what you're saying about logical thinking skills being necessary for other things (like writing a logical paper, although I will also append here that I got okay but not top grades in non-philosophy liberal arts classes in college until I learned to make my papers a little less logically-flowing and a little more free-flowing connections), and I do agree that math is useful as a Thing.
But at the same time, I do think that there are some non-mathematical skills learned in math/science/programming that are useful in life but which aren't the actual skill. The idea that quantifying things is useful, for one thing; the idea of typical behavior, the idea of testing hypotheses. (See also: Yuletide wank. *rolls eyes* There are a couple of people in the discussion who clearly from their comments have mathematical training, and some who clearly do not.) You could try teaching these things directly, but I think it's much more likely to come as a result of being immersed in a mathematical/scientific mindset.
I have mixed feelings about your statement that it has the potential to be worse than useless. Because on one hand, I think it's better to err on the side of skepticism than on the side of blind acceptance, and I feel that it's better to give people tools to be skeptical than to give them no tools at all. The only thing is -- and I do see where you're coming from on this -- that I think it is not really in human nature to be skeptical, so being skeptical about some things can often lead to being blindly accepting of other things. E.g., we should always follow the rebel who's questioning the scientific establishment because of this one data point where they were wrong! Or, we should always unquestioningly not believe scientific studies! Which... is really just a different type of logical/statistical fallacy.
I mean, it turns out Barry Marshall was right about h. pylori, and I must say I find the story personally compelling (like, it would be convincing enough to get me to try antibiotics for my ulcer) if not reaching a scientific level of proof. But for every Barry Marshall, there's a Pons and Fleischmann. And if one were to catalogue all the times someone went against the confirmed scientific establishment, I would bet a large amount of money that a statistically signficant number of them were in fact incorrect... That's another one I'll add to my curriculum: confirmation bias!
I think... in my dream curriculum, I would approach this question in a data-driven kind of way. Let's flip coins one time, ten times, a hundred times, a thousand times. How many times do we do this before you start being suspicious that the coin is heavily biased? Now maybe you're really suspicious that I tend to bias my coins. How many times do we flip a (different) coin before you're reasonably convinced that I didn't bias that coin? What does it mean to be "reasonably convinced," anyway? How does this depend on how biased we suspect the coin is? Then we can start talking about how statisticians formalize these kinds of questions, even if we don't actually get far into what the actual math means.
This whole conversation is making me simultaneously interested and depressed. Interested, because it's giving me ideas as to what I might want such a curriculum to look like (and I have at least one small
test subjectperson I might potentially practice on :) ). Depressed, because it's really bringing home to me how hopeless I feel like it is to teach anything like this -- either your curriculum or mine -- in the wider world, which demonstrably needs it *sigh*(no subject)
Date: 2013-09-12 09:36 pm (UTC)Yeah, the Barry Marshall story is dramatic, and maybe one year we should request Barry Marshall RPF for Yuletide, but it's terrible science.
ut at the same time, I do think that there are some non-mathematical skills learned in math/science/programming that are useful in life but which aren't the actual skill. The idea that quantifying things is useful, for one thing; the idea of typical behavior, the idea of testing hypotheses.
No, you're right about this, there are some useful skills you'll get in a math class that aren't purely quantitative. I just think the math you learn is the more important thing you get out of the class than those skills.
I have mixed feelings about your statement that it has the potential to be worse than useless. Because on one hand, I think it's better to err on the side of skepticism than on the side of blind acceptance, and I feel that it's better to give people tools to be skeptical than to give them no tools at all.
Yeah, but I'm not convinced that teaching them statistics with limited quantitative justification is actually a legitimate tool to be skeptical.
I think... in my dream curriculum, I would approach this question in a data-driven kind of way. Let's flip coins one time, ten times, a hundred times, a thousand times. How many times do we do this before you start being suspicious that the coin is heavily biased? Now maybe you're really suspicious that I tend to bias my coins. How many times do we flip a (different) coin before you're reasonably convinced that I didn't bias that coin? What does it mean to be "reasonably convinced," anyway? How does this depend on how biased we suspect the coin is? Then we can start talking about how statisticians formalize these kinds of questions, even if we don't actually get far into what the actual math means.
This is great pedagogy, I think, but if it doesn't lead to actually defining confidence intervals in some fashion I'm not sure how much it gets you.
I have no objection whatsoever to helping to build mathematical intuition with experimentation. I think it is great! But okay, they have this mathematical intuition about sample size based on coin flips. Then years later they are reading an article about a field test of a drug on a hundred people with a medical condition. Each of those people has a different probability of dying from the disease because of other confounding factors (diet, environmental exposure, age, genetic conditions, stress, phase of the moon), and each of those people has a different change in probability of dying as a result of taking or not taking the medicine. How are they supposed to know whether a hundred people is a big enough sample? Most of the time when I read about medical studies in the popular press, I have no idea myself because it's so complicated and confounded. The coin flip analysis is not really generalizable without doing a bit more mathematical work.
So I guess the answer is to just be generally skeptical? Or maybe the answer is to just be generally trusting of science and trust that the peer reviewers/ government regulators/ scientific competitors/ various other ipsos custodiet will catch them when they make a mistake? In other words, maybe the answer is what I was saying above, that as adults it's not that we don't need to know math, it's that whenever we need to know math we can usually safely farm it out to someone else.
(no subject)
Date: 2013-09-17 04:13 pm (UTC)So I was thinking this would be more to introduce the idea that sample size is important, and that it can depend on several factors, and that one should maybe at least have some sort of justification for one's sample size. I suppose I'm lazy, too -- I must admit that when I read about studies, I almost never work through the math and figure out whether the sample size is big enough for the number of factors and the number of things they're testing, etc. But I will feel a whole lot more confident about the study if they actually say to me, hey, actually, we're trying to test too many things here, so the fact that we saw "something" here at this confidence level is not really that relevant, but look, this result we are much more confident about.
I absolutely feel that one must trust the process of science to a certain extent. Even if I did work through the math, there's a very good possibility that since I'm not in the medical field, I'd miss something subtle about some sort of confounding factor or assumption that it wouldn't even occur to me to take into account. Even in the hard sciences, there's a lot of trust involved -- no one has time to work through Professor Y's work to find the subtle incorrect physical assumption he made that throws off all the careful math he built on top of it, we just trust that when Prof. L says it's not right, and Prof. G checks both their work and agrees with L., we believe them because we know L. and G. do careful work and aren't likely to be wrong about something like this when they've worked through everything, whereas Y. has a history of being sloppy like this.
(no subject)
Date: 2013-09-17 04:59 pm (UTC)(no subject)
Date: 2013-08-26 09:41 pm (UTC)*blinks* Have you ever taken sculpture or ballet? Sure the basics are accessible, but mastery does require hard work. Same with math, though the basics aren't quite as accessible, but I think that's an issue in the wider cultural world, not an issue with math itself.
IMO learning algebra teaches logical thinking skills, and that's why it should be taught.
(no subject)
Date: 2013-08-26 10:13 pm (UTC)-Noah
(no subject)
Date: 2013-08-27 01:18 pm (UTC)IMO learning algebra teaches logical thinking skills, and that's why it should be taught.
I think this is actually a poor reason to teach math in particular over something else. Literary criticism teaches logical thinking skills just as well: when I write an essay I'm using the same logical pathways as when I construct a formal proof. When I build a literary argument I'm using the techniques I learned to conduct scientific experiments.
I think the only legitimate reason to teach math is because math, in and of itself, is useful. It is not a means to an end. It is a valuable skill.
(no subject)
Date: 2013-08-27 03:21 am (UTC)I see all of this as an argument against Bob Moses, who is my hero. He wants to make it possible for everyone to take and master algebra in eighth grade. He believes that depriving children of good math instruction is a way of keeping them from interesting and remunerative professional lives.
To argue that we teach math badly because math is itself unnecessary or too difficult is just ridiculous. It's also difficult to teach people to read, and many people don't read for pleasure in adulthood. Should we limit our literacy instruction, only requiring people to know enough to ride the subway without getting lost? How about foreign languages, no one really needs those. Science? Science is for brainiacs, it shouldn't ever be required instruction in a school.
Why not just teach children to line up and write their names, and send them home?
(no subject)
Date: 2013-08-27 01:41 pm (UTC)Problem is, I think it actually is an education problem, not a graduation problem, no matter what Hacker and Baker claim.