And now for something completely different...
Well, not really, but kind of different.
I realize that my niche here has become discussing science-based medicine, evidence-based medicine, and the atrocities committed against both by proponents of so-called "complementary and alternative" medicine, but every so often I need a change of pace. Unfortunately, that change of pace was something I came across in the New York Times on Sunday in the form of a commentary so bad that I seriously wondered if it was a parody or a practical joke. Alas, it wasn't. I'm referring to an article by Andrew Hacker, and emeritus professor of political science at Queens College, City University of New York, entitled Is Algebra Necessary?
The short answer is yes (actually, hell, yes!). The longer answer follows. First, though, let's start out with the premise, which hits you in the face in the very first paragraph of this incredibly misguided and, quite frankly, mind-numbingly silly proposal:
A TYPICAL American school day finds some six million high school students and two million college freshmen struggling with algebra. In both high school and college, all too many students are expected to fail. Why do we subject American students to this ordeal? I’ve found myself moving toward the strong view that we shouldn’t.
Hmmm. I wonder what Hacker would say if I were to rewrite his paragraph thusly:
A typical American school day finds some six million high school students and two million college freshmen struggling with English and English composition. In both high school and colleged, all too many students are expected to fail. Why do we subject American students to this ordeal? I've found myself moving toward the strong view that we shouldn't.
Or substitute history or science for algebra in the same paragraph. Actually, come to think of it, if we deemphasize algebra, we might as well add science to the mix, because without algebra it is damned near impossible to become proficient at any science. It's the very minimal that is necessary to understand basic physics, for example, and perhaps not even enough for that given how much of physics is based on calculus. However, algebra is probably enough to undergird a basic understanding of classical physics that is adequate for an average educated citizen to need to know. Of course, without algebra, chemistry would be completely indecipherable, at least anything quantitative. Forget about reaction stoichiometries, kinetics, and the like. That will be out of reach, except for mushy generalities. Then forget about biology and biochemistry as well. No enzyme kinetics, membrane potentials, half-lives, or anything quantitative. And for you budding doctors out there, forget about medicine! A solid understanding of all these sciences, and more (pharmacology and human physiology in particular) is beyond your understanding if you don't understand the basics of algebra.
It's not just science, though. Without the basics of algebra, it's really difficult to understand the basics of statistics. We live in an increasingly data-driven world, and our citizenry is already pretty statistically illiterate anyway. But, heck, it's too hard; so let's drop it.
Hacker's "logic" (such as it is) for recommending that not everyone should be required to have a basic competence in algebra is strange, too. Get a load of this:
This debate matters. Making mathematics mandatory prevents us from discovering and developing young talent. In the interest of maintaining rigor, we’re actually depleting our pool of brainpower. I say this as a writer and social scientist whose work relies heavily on the use of numbers. My aim is not to spare students from a difficult subject, but to call attention to the real problems we are causing by misdirecting precious resources.
The toll mathematics takes begins early. To our nation’s shame, one in four ninth graders fail to finish high school. In South Carolina, 34 percent fell away in 2008-9, according to national data released last year; for Nevada, it was 45 percent. Most of the educators I’ve talked with cite algebra as the major academic reason.
For someone claiming to rely heavily on the use of numbers, one can't help but note that Hacker's arguments are not particularly powerful and play a little bit fast and loose with numbers himself. He cites a lot of statistics, but his interpretation of many of them leaves something to be desired. (Hey, that's something that a good grounding in algebra and other mathematics would help those of us reading Hacker's little proposal guard against, isn't it?) For instance, Hacker says that "most of the educators" that he's talked with cit algebra as the major reason why our high school dropout rate is so high, but he doesn't cite any actual...oh, you know...figures that support such a blanket statement. For example, he cites various failure rates at algebra proficiency tests but doesn't show evidence that these are the primary reason why these high school students dropped out of high school or, more importantly, compared these figures with the numbers of students who fail other core topics that all high school students are expected to demonstrate minimal proficiency at. That is the very minimum information necessary to put the figures describing students' difficulty with mathematics and algebra into proper context. It wouldn't surprise me at all if students who drop out don't just fail algebra. They probably fail a lot of other major core curriculum topics as well.
True, hacker does cite some numbers that suggest that seem to indicate that freshman mathematics is a barrier to retention in college, but a better question to ask is: Why are freshmen so woefully unprepared in something as basic as algebra, such that they have difficulty learning it as a college freshman. If a student arrives in college without a basic understanding of algebra, as far as I'm concerned that student is not ready for college, any more than a student who can't read and write at a sufficiently high level. I can understand, although not necessarily support, an argument that perhaps calculus is not necessary for all college students. Perhaps, it could be argued, students who are not majoring in a science don't need to take calculus or that perhaps a year of statistics could be substituted for a year of calculus. One could even make the argument that in the "real world" statistics is a much more useful topic to have been exposed to for most people. Those would not be unreasonable arguments.
Instead, Hacker claims that mathematics is "used as a hoop, a badge, a totem to impress outsiders and elevate a profession’s status," giving examples that veterinary technicians are required to be proficient at algebra for their certification but never use it in diagnosing or treating animals. (Oh, really? How do they scale up drug dosages?) He also cites Harvard and and Johns Hopkins medical schools as requiring calculus for entrance, "even if it doesn’t figure in the clinical curriculum, let alone in subsequent practice." Well, there are a lot of things required to get into medical school and taught in the first two years of medical school that do not figure in subsequent clinical practice or the curriculum. Much blood has been spilt on the floor, metaphorically speaking, arguing what sciences should be required in order to be a good physician. Hacker might have a point that physicians don't need to be proficient in calculus (although it helps if they wish to go into, for instance, radiation oncology), but that is a separate issue than whether students need to know algebra. Physicians, for instance, do need algebra for many things, including calculating blood gases, drug dosages, half-lives, cardiac outputs, and a number of other parameters. True, there are now many minicomputers and medical instruments that automatically calculate these numbers, but to understand the significance of the results, and, more importantly, changes in the results requires an understanding of the underlying equations, which in turn requires an understanding of algebra. Perhaps that's why Hacker mentioned calculus instead of algebra. In fact, one wonders if what we have here is a big case of math envy, given that he harps on the use of mathematics as a means of adding prestige to a field.
Be that as it may, what does Hacker propose instead? Well, this for one:
Quantitative literacy clearly is useful in weighing all manner of public policies, from the Affordable Care Act, to the costs and benefits of environmental regulation, to the impact of climate change. Being able to detect and identify ideology at work behind the numbers is of obvious use. Ours is fast becoming a statistical age, which raises the bar for informed citizenship. What is needed is not textbook formulas but greater understanding of where various numbers come from, and what they actually convey.
So, let's see. Quantitative literacy is critical to being an educated citizen who can weigh public policies, but algebra isn't necessary? Silly Hacker, what he is arguing here is not that a basic understanding of algebra isn't of critical importance to all citizens, but rather that it's taught badly. And I agree! Mathematics and algebra are all too often taught badly, with no good hook into the real world usefulness of the disciplines. No wonder students lose interest! They're never taught just how deeply mathematics of all types underlies, well, pretty much everything quantitative in society. Later, Hacker proposes:
Instead of investing so much of our academic energy in a subject that blocks further attainment for much of our population, I propose that we start thinking about alternatives. Thus mathematics teachers at every level could create exciting courses in what I call “citizen statistics.” This would not be a backdoor version of algebra, as in the Advanced Placement syllabus. Nor would it focus on equations used by scholars when they write for one another. Instead, it would familiarize students with the kinds of numbers that describe and delineate our personal and public lives.
It could, for example, teach students how the Consumer Price Index is computed, what is included and how each item in the index is weighted — and include discussion about which items should be included and what weights they should be given.
Except that it would be rather difficult to understand in the first place what a weighted average like the CPI is if the students don't understand the basics of algebra to begin with.
The bottom line is that we as a society have to decide what it means to have a well-rounded education. In general, we all tend to agree that reading at a certain level is essential. We can argue what, exactly, that level should be, but in today's society it's no longer possible to function well if you can't read and write, particularly in this increasingly Internet-driven world. Similarly, an understanding of mathematics is essential, and, from my perspective, algebra is actually a pretty low bar. True, many, if not most, people will never use much algebra, but the habits learned and the methods of using mathematics to solve problems will be useful almost no matter what a person does in life. Then, of course, there are the sciences and humanities, in particular history. If one-third of students are doing poorly at a subject that is so basic, such as algebra, then the answer is not to drop the requirement or to absolve those students who are having trouble passing it, but rather to find ways to teach it better. No one expects that everyone can excel at every topic, but there are certain topics that one should have a minimal proficiency at in order to be considered educated.
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Count me as a casualty of an awful algebra teacher. He graded our whole class on a curve otherwise many of us would have gotten a failing grade. He appeared to be quite a mathematician but not a teacher and lasted just that year. Next years geometry teacher was much better.
Another barf inducing NYT screed.
The problem with algebra is that students might actually have to do homework rather than bs their way through it. One can creatively grade a rambling, brain damaged attempt at an essay as good, but it takes some effort to convert wrong answers into full credit on an algebra test.
To make the parents and college admissions office happy, teachers must give little Timmy an A, and the less quantifiable the subject matter the less work it is to invent one.
I just forwarded a link to this blog post to a friend of mine who spent a few years teaching remedial algebra to freshmen at a good Midwestern university.
I love the idea that people that use the various machines in medicine, or really any walk of life, don't need to understand what's going on inside, the equations in use or what the machine is doing at all. Never mind that without doctors feeding back to technologists there would never be impovements in function here.
Don't worry! Those other, clever people sort out the machines, we just use them. Someone else will do the math for me!
So I suppose we end up where we are today, most people consider math to be hard and computers to be indistinguishable from magic.
I'm not sure if I had a point in the above rambling, so I'll make one now. if we don't even bother to tech kids basic algebra, many won't be introduced to it at all and intake for technical discplines (doctors, scentists, engineers etc) will drop off a percipice as we make these careers look even harder than they do now. This would not be a good thing for any country that wishes to lead the way in the modern world.
*facepalm* I have many ideas of what I think schools could do better and how, and also think that high school science courses should have more emphasis on the way science is done and how it applies to everyday objects and situations. I can't fathom perceiving a high school education as adequate without Algebra I and basic statistics. I could understand where they're coming from arguing that Algebra II shouldn't be required, but the first year of high school algebra includes a lot of basic, important, ubiquitous concepts.
I definitely think the way math is taught needs major overhauls. I have specific ideas on this, but it would need a lot of refining and then testing lest it be yet another ineffective education fad.
I have two children who struggle with math. But struggling with a subject is not a bad thing. At a time of universally lowered expectations and overinflated egos, struggle and challenge are not to be avoided. Else, be prepared to sit back and enjoy the view while China and India eat our lunch.
Okay...So he wants people to know nothing about things as basic as equations or averages ? So, his goal is that commerces and employers defraud poor Americans ? Because checking that the change is coherent with the price of your purchases and what you gave to the cashier is basic algebra...granted markets are perhaps less used in the USA than in France or Italia, but still...
The problem is most definitely that it's being taught badly, especially at the college level. I loved math as a high school student, got excellent grades, and took one course of AP calculus. My math teacher was a woman, btw.
I got to college, hoping to continue my studies, walked into the first day of freshman calculus, and got a math grad student who told the class his English was so bad he'd be explaining things in Korean, then started scrawling on the chalkboard. I was at a school that subsequently became infamous for having a high level admin say that girls were bad at math. There was a terrible culture in that department and I very quickly dropped the course and never went back to math in college, earning a BA rather than a BS in my science major because of it.
Perhaps, had I not been an 18 year old college freshman, I would have known how to fight for a decent instructor and more respect in the dept., but there it is. And that was a fancy private university. I can't imagine what less enfranchised students in overcrowded local college lecture halls have to deal with.
Aah algebra. I remember that from high school... interpolating logarithms (by hand, not with a calculator) and all that fun.
Do I remember how to do it? Hell no. I'd have to get out an old textbook and look it over again.
Is algebra necessary? SHIT YES!
I had a similar experience to AllieP - I went to take Calc for my B.Sc at a local college. I was in the first week of class and had a question. I waited until lecture was over (she didn't like interruptions during lecture) and posed my question.
Her response? "You look like an intelligent individual. I'm sure you can figure this out on your own."
I said, "I have one other question for you: can you sign my drop form?" I mean, I'm not going to stick around in a class (and waste my money on it!) with a teacher that's not going to be available for questions.
I waited for another semester and a different professor and had no issues.
Two thoughts: First, thank goodness Hacker is emeritus and not actually professing anymore. Second, he should stop picking on mathematics. At least his work is eligible for a Nobel Prize.
On the same day as the pathetic editorial about not needing algebra came out, the NYT ran another editorial, right next to it, titled "Medicaid After the Supreme Court's Decision." It contained this statistical gem: "Deaths among people ages 20 to 64 dropped in the three expansion states by about 1,500 a year, adjusted for population growth, whereas death rates in the comparison states went up" - note that the author compares a total against a rate. This is an excellent example of what John Allen Paulos calls "innumeracy" and is an excellent argument for more algebra training.
Coincidentally, this was my Joke of the Day yesterday:
Physics
A college physics professor was explaining a particularly complicated concept to his class when a pre-med student interrupted him.
"Why do we have to learn this stuff?" one young man blurted out.
"To save lives," the professor responded before continuing the lecture.
A few minutes later the student spoke up again. "So how does physics save lives?"
The professor stared at the student for a long time without saying a word. Finally the professor continued.
"Physics saves lives," he said, "because it keeps certain people out of medical school."
There may be parts of the school curriculum that are there for historical reasons, that contribute neither to someone's future plans nor to their existence as a well rounded individual (though I realize the latter is thought pointless in these utilitarian arguments). Algebra is not one of them. I majored in history. I actually use algebra and stats fairly regularly.
This is a new one. Usually, they argue about why kids shouldn't be forced to learn trig because "only engineers use that." My husband, father, and father in law all have math degrees. I once threw that one out just to see their reaction, and a look of incredible pain came over all their faces.
A political science professor suggests that algebra should be replaced with "political science math".
That's as reasonable as me thinking algebra should be replaced with microbiology.
Another round fired in the war on knowledge. The 1 % trying to keep the 99 % as ignorant as possible so they can manipulate them.
Do you know what else we learn in algebra, physics, geography, or history classes? We learn HOW to learn. We travel the road from confusion to competence. Then we start the next chapter and do it again. Over and over. A great teacher makes it exciting. A good teacher makes it possible. A bad teacher breaks the chain, and the students never do become competent.
I thought the point of giving kids calculators in grade school was to make more time for mathematics instead of arithmetic.
The skill and competence of your teacher makes a huge difference. I was lucky enough to be taught mathematics by a teacher who was infectiously enthusiastic about the subject. He studied at Oxford and Princeton and worked on cracking the Enigma code with Turing at Bletchley Park during WW2. I owe him a great deal.
I wrestled with algebra in high school. I took it again and wrestled with it again when I got my first B. Sci. I am now going for another bachelor's and have taken it again (and in middle age did better at it than I did in my teens and twenties). I am now looking forward to pre-calculus for the second time around in my current degree program - I dropped it the first time for medical problems. I will still have calculus after that.
As a physician assistant, I frequently needed algebra. You'd better have it if you do things based on such measurements as body surface area or glomerular flow rate (Google it.). I was hampered from assisting more effectively in the research I was employed in by my weak understanding of statistics and my lack of calculus.
I have always shied away from math because it's not easy for me, but there have been so many days that I regretted not having tried harder - "I'm never going to use this stuff" - because mathematics is the language that expresses how things happen in the real, physical, world we live in.
*facepalm*
I read the entire text on NYT, it's just mind-numbingly stupid.
One question comes to my mind: what level of Algebra is actually taught in US schools? (I am German). Does he refer to more abstract concepts such as Linear Algebra or just 'calculating simple stuff with x and y instead of numbers'? If that is really what he referes too, skipping Algebra in school is like sending kids out to go to college without knowing any math at all.
PS: One of my favourite idiotic statements in the text without a morsel of proof: "It’s true that students in Finland, South Korea and Canada score better on mathematics tests. But it’s their perseverance, not their classroom algebra, that fits them for demanding jobs."
... Slightly on/off topic:
These kind of arguments seems to be coming a lot from the arts lately, where they're trying to get more interest/funding by suggesting that creativity and innovation is somehow being overshadowed by you know, learning about mathematics. Apparently only ever learning the three Rs are making our students into feeble-minded sheeple.
As an artist, I wish I had a better grasp of mathematics. It took me a long time to get my head around tax forms and budgeting. I wish my fellow artists would stop harping on about making arts equal with science, as if the only way new innovations existed was with the creativity learned from band practice. Also, on a more personal note, if I had figured out that I liked science more than I thought (a recent thing) I would have taken more opportunities at school and university to learn them and be more employable in the long run.
What's worse is the seeming portrayal that arts is all about intuition and the underlying woo-mongering that the world would be better if we could just cut out the materialism and create a hippy-dippy all-loving educational system that treats every pupil as if they were special and *always* nurtures the specialness no matter which way the talent trends towards and no matter how much it costs the schools to implement. (According to one person I read, if it weren't for some smart attentiveness by one teacher, The Beatles wouldn't have existed, for all primary/secondary teachers ignored the *obvious* talent for one member of the band. It never occured to them I suppose that good art comes at the cost of time, experience, practice and luck and had nothing to do with attentive teaching or lack of)
It's an appeal to people who don't like the idea of "teaching to the test" but don't actually have a better way of quantifying learning; and the parent's wish to see their child nurtured in every way. This is education freedom - like health freedom, it's not so much about choice as it is about promoting their own special-snowflake style education, where truly, no one gets left behind and artists can feel safe in the knowledge that no one ever looks down on their careers again.
(... Sigh... I really wish artists would learn more about science so if nothing else, they wouldn't get upset about criticism of their ideas or work. Scientists don't seem to take it personally: why do they?)
I bring this up because it's a startling trend I'm noticing coming from my own field, and I'm willing to bet most skeptics haven't seen much of it yet.
I was very fortunate in that I had good teachers and heard no stereotypes at home about women being poor in this subject ( because they were amongst the business types in my family)- during my diverse and far-flung educational odyssey, I was placed in an achievers' group at age 10 or 11 and wound up tutoring other students for fun and profit. Later on, a high muckity-muck in stat gave me great encouragement, although I didn't follow down the pathway he had mapped out for me. I can't fathom how a person can truly understand research without confident knowledge in algebra.
Hilariously, woo-meisters I survey carp about the low level of education youngsters suffer, proposing drastic reforms- Why? They're biting the hand that feeds them! In reality, the reason they have so many customers and acolytes is BECAUSE of poor educational systems that allow kids to go on without acquiring basic skills in literacy and numeracy which makes them prime targets for pseudo-scientific hacks selling their wares, be they bad products or worse theories.
In an era of frightening economic trends, political manoeuverors make bank on the general public's inability to comprehend economics which also requires grounding in algebra. How can anyone believe that the price of gold will just keep on accelerating as if there were no tomorrow- as if it had no basis in buying patterns! Similarly, bad products ( investments, newsletters- and believe me, that is an entire other area of woo) and ideas abound in this realm as well. So when there are a few quarters of negative growth, why not cut back on governmental spending? That'll fix things up really good!**
@ Krebiozen:
As I watch my US and UK prices come in on television, the crappy washing-machine-part Olympic tower looms in the background! It is so bad that if they eventually chop it up into tiny parts to be purchased for a worthy charity, I will get one! And proudly display it on my wall.
** Sarcasm.
,
OT- but is vaccine-autism lunacy ever truly OT @ RI?
( I should think not).
@ Thinking Moms' Revolution today, "Snap" appears to diagnose a relative's child as well as recommend a diet and woo-friendly doctors and then claims victory. Yes, she did.
@ flip:
Hello. Educational freedom. I know. Awfulness.
I,for one,am going to come to this guy's defense.In addition to autism,I have a whole slew of learning disabilities.One of these,is a particularly nasty form of dyscalculia.The stereotype of the number crunching aspie/autistic,who can calculate pi to a million decimal places,is just that,a stereotype.
American schools are still stuck in the outdated 19th century,post-Sputnik,whatever model,that one of their main jobs is to prepare students for,and track them for,college.The simple fact is,not everybody is college material.What we need is a system,where,somewhere in middle school,students,and parents,are given an option to opt out of the traditional school model,and replace it with a mixed program of academics,and on the job apprenticeships,so a young person might be able to jump right into a job,by the time they are eighteen or twenty.
I know that in a number of European countries,especially Germany,and Scandinavia,such practices have been in place forever.It's about time the US joined the more rational countries of the world.
Please someone send this to the New York Times. It is embarrassing that they published that. Thanks for the post Orac.
Roger:
I don't think dyscalculia is a reason not to teach algebra. It's a reason to find ways to accommodate people with dyscalculia and help them to learn math.
Again, science fiction was there first, with Isaac Asimov's "The Feeling of Power." The 1957 short story describes a future where mathematics has been completely forgotten because of calculators (a good 15 years before they become common) and one man rediscovers the rules of multiplication. My favorite bit is where a general suggests putting human pilots in guided nuclear missiles (figuring trajectories with pencil and paper) because that will be cheaper and easier to replace than guidance computers.
It isn't the algebra they're expected to learn that's causing students to give up and drop out--it's failing to achieve a passing grade in whatever subjects they're having trouble with.
So instead of dropping algebra, let's just eliminate testing and pass everyone. That'll fix things.
(/sarcasm off)
Yet another uncaring idiot doing his bit to dumb down the population so they won't be inclined to do troubling things like using their own minds and questioning their "betters."
Making mathematics mandatory prevents us from discovering and developing young talent. In the interest of maintaining rigor, we’re actually depleting our pool of brainpower.
How can you develop ANY kind of talent without teaching kids basic skills? And no, requiring kids to learn basic skills does not deplete brainpower, it enhances it.
I say this as a writer and social scientist whose work relies heavily on the use of numbers.
In other words, he says this as a knowing hypocrite who seeks to deny other kids the opportunities he enjoys.
My aim is not to spare students from a difficult subject, but to call attention to the real problems we are causing by misdirecting precious resources.
When you have a cushy job with a newspaper that doesn't require (or even want) you to question the established mindset, it's easy to think of effort directed toward other kids' betterment as "misdirected." Are there no jails, no workhouses?
American schools are still stuck in the outdated 19th century,post-Sputnik,whatever model...
"Whatever?" Is it "19th century" or "post-Sputnik?" If you can't even get that straight, then you're too dumb to be telling others how to educate their kids.
What we need is a system,where,somewhere in middle school,students,and parents,are given an option to opt out of the traditional school model,and replace it with a mixed program of academics,and on the job apprenticeships...
In other words, let's have kids spend less time learning things that will help them live up to their full potental, and more time doing unpaid work. Let me guess...you think Newt Gingrich is a bold innovator, right?
Also, I notice PZ and Democratic Underground are taking this hack named Hacker down. Glad to see this backward idiocy is at least being noticed.
Replace "algebra" with "biology" in Hacker's article, and you'd have the creationist agenda.
@Denice
I wouldn't mind so much if it were based on you know, evidence. There's actually some good studies out there on music helping with maths. Usually if they cite stuff it's from "arts experts", not scientific studies that actually show that arts does what they say it does.
But then they go off the deep end by talking about the arts as if music lessons will save your kid from ending up an office drone unable to breathe. It smacks of projection to me.
I work in a particular area that requires some understanding of the laws of physics in order to make the art. Knowing about chemical compounds and the way materials interact is helpful too. The truth is a little from each goes a long way. Yes, we should push for more funding in the arts: but not at the expense of understanding how to read and write and count. Artists will need those far more than the "educational freedom" people try to present.
In their defense, a lot of this is coming from artists themselves, so I guess you can't blame them for using non-scientific arguments. (Which kind of makes my point above about needing both)
@Roger
Having experienced some of what you mean (not being college material or having an aptitude for sitting still in class and preferred making things)...
I think it depends on where you live. I am always confused by the American system where it seems you don't study a single focused course (correct me if I'm wrong), but instead choose from a range of subjects. Here in Australia we choose a specific course which will follow to a specific career. This means that you or I can attend a university/college that is more practical and less academic. Most of my time spent at uni was not on writing essays or doing research, but actually learning and practicing in a real-world environment. (Most of our "exams" were based more on participation in class activities) There are also government programs here which are designed to get people connected with local businesses and offer on-the-job training, and are generally aimed at school-leavers or uni graduates.
But also, I think that there will be problems no matter how the education system is structured. How do you get around the issue that not everyone is suited to sitting in a classroom? How do you measure improvement without some sort of exam or assignment? Not every teaching method suits every student; the good teachers mix up the activities so there are fewer bored students.
From a purely anecdotal experience, when I did my final years of high school there was "easy maths" (algebra) and "hard maths" (parabolas and other things); two different subjects entirely. I flunked the latter and passed the former. For some reason I have a better head for algebra than I do for other types of calculations.
harey,
The term "algebra" as it is generally used in US secondary education typically is used only to refer to the algebra of the real numbers (with a small amount of complex algebra sprinkled in). The more general definition of "algebra" typically used by mathematicians is not the algebra taught in US secondary schools. You won't see Lie algebras, linear algebra (at least not rigorously taught; some algebra courses do deal with a small amount of matrix arithmetic), Boolean algebra, or any other more general algebraic system. Typically, most of the algebra involved is solving first and second degree polynomial equations.
@Raging Bee
In my experience, the people who had internships with local companies before graduating had a greater chance of actually landing a job when they do leave. (Internships are paid work here) As with all things: it's not what you know...
Roger Kulp,
I agree with you, not every kid is college material. However, that's the whole point of a high school education. High school is the last chance for those kids who aren't college material to get the academic background they need to be successful in life.
Removing mathematics requirements from HS curricula is a dumb idea, even for those kids who aren't going on to college. In past times, there were plentiful blue-collar jobs that didn't really require much in the way of academic ability. Pretty much anyone willing to actually do the work would be qualified for such tasks. The modern economy is different. Even in the manufacturing sector, jobs require skills and training. A basic level of academic knowledge certainly is helpful in preparing one for a job in the modern economy. Further, and even more importantly, learning how to learn and how to solve problems is a crucial skill today. That's why math is necessary.
This entire hatred for Algebra stems from the fact that it requires some significant effort to understand. Also, as has been pointed out above, it requires good teachers to allow us to understand the subject, rather than approach it via rote and memorization.
When I had just entered high school, I'd just barely get a passing grade in math. I thank my tutor who had a very clear idea about the subject and a great knack for teaching. He made me slog like a slave driver. The end result - I absolutely love math (especially vector calculus) and I ended up scoring 99% in math.
Sadly though, everyone is not fortunate enough to have such inspiring and interested teachers
@ flip:
One of my cousins never got a degree but creates 'movie magic': at age 20 or so, he started working for a firm that sent him- over time- for training in the US, UK, Germany et al where he learned various skills utilised in recording, robotic cameras and editing and his formal title is some sort of engineer. He was always a decent student but never really cared about it and never made elaborate plans for his education: fortunately, the elderly gentleman who owned the company saw promise in him and sent him to the right schools. I venture that most readers of RI have seen his work in the many movies he's worked on.
And he is extremely hipsterish-looking lately so I assume he fits in everywhere he works.
AllieP:
At my large state university there were three days of lecture, with two days of quiz sessions. The latter were smaller, with a teaching assistant (usually a graduate student) who gave more personal attention, explained concepts and did actually qive quick quizzes. I had some very good enthusiastic teaching assistants, who also had office hours to further explain the concepts.
My problem was that as an over enthusiastic science nerd I wanted to take calculus, chemistry and physics my first quarter. The advisor had me substitute an English class for one, and I dropped the chemistry.
The mistake was that I should have had the calculus before physics. I actually learned the calculus concepts in the physics class before we go to them in the actual math class.
My younger son was one the huge percentage (up to 50%) who did not get into the engineering program at that same large state university (there is a shortage of lab space, and almost every class requires some kind of lab time, and in one that includes a metal foundry). He was getting a bit put off by some of the classes (material science, statics, etc), but he likes the math. So he switched to the math department on the teaching track, to hopefully become a high school math teacher.
He has been a swim teacher since tenth grade, and it really a very patient and understanding teacher. So I hope he will be part of the math education solution. Only time will tell.
Wildly OT...
Denice,
Ah yes, The Monstrosity as I have christened it. I hope the engineer/architect who designed it had a good grounding in math! I keep expecting to see it has toppled over. They are currently charging £15 per person, plus £10 to enter the Olympic Park, making £25, over $50, to ascend the tower to enjoy the stunning views - kerrching, as they say - so I doubt they will be dismembering it any time soon.
A couple of days ago I finally went and had a look around the Westfield shopping mall, which you have to walk through to get to the Olympic Park, and don't think I have ever seen a greater temple to Mammon, with more people than on Christmas Eve in Oxford Street. Picked up some good bargains though.
It helps a lot to do it in this order. My high school didn't actually offer calculus, so to stay active I did it by correspondence course from the University of Wisconsin system. It was at a pretty simple level (Thomas & Finney), but it got me into honors freshman physics and honors calc, where we did the whole thing over again rigorously using Spivak.
@ Krebiozen:
Also wildly OT:
Oh boy! It's going to become some sort of icon, isn't it? Like a lesser, crappier Tour d'Eiffel or that miserable World's Fair globe at the US Open! Eternally obnoxious and nearly indestructible..
Hope you get to see something better than it @ the venue.
I'll watch Wimbledon redux...
And I suppose Temples of Mammon can be useful for the economy. I seem to recall having traipsed ( with money in pocket) around a few *older* establishments there as well as those in Paris and NY. .
Well, since anecdotes are evidence to the author of this op-ed piece: I dropped out of high school in the ninth grade. I took high school level algebra in middle school and aced the courses. So, obviously, going through the "ordeal" of failing classes didn't contribute to my dropping out.
And, seriously, we're calling struggling and potentially failing a course in school an "ordeal"? What a wonderful life this guy must lead if that's the worst of what he's gone through in his life.
@Roger
I can't speak for the rest of Scandinavia, but the portion in which I live, if you're not going to college, you can go to a trade school - but you still have all the core classes, algebra (and higher math) included.
You just have your carpentry, etc classes on top of those.
For what it's worth; the US does have 'technical' high schools - there were two in the area where I grew up. Regular courses that satisfied the state requirements, and trade courses alongside them.
I'm not a math whiz, and struggled through the minimum requirements at high school. I enrolled in the local junior college and was told I'd have to go through it all again in order to take the ONE math class I needed for my major because, of course, I'd managed to forget all my algebra during my gap year and bombed spectacularly on the intake test.
Fine and so be it. I slogged through two semesters of algebra and I'm still not sure how I passed. Then I enrolled in the one math class required for my major: Math for Liberal Arts.
It's the only math class I've ever aced. In fact, it was fun!
Why? Because all that dry math I'd choked down was finally applied to real-world situation. From comparing credit cards offers, to calculating mortgages, to (the basics of) statistics. It was so much easier when I could use the math practically.
So, based on my experience, I think the presentation of the material is critical. Show students how this math is going to impact their daily lives and the dropout rates will sink like a stone.
This blog is too hard on Hacker's article. Many of the comments sound as if they haven't read the article either.
I'm one who understands the importance of science. But, all the time I spent struggling with quadratic equations and polynomials actually turned me off science and math at a young age, so much so that there was no chance of me being a scientist. Everybody is not going to be a practicing, working scientist, so why must we waste so much time learning skills we'll never use? The time would be better spent teaching us critical thinking skills so that we could be better voters and citizens in general.
You could argue about which kind of med students need algebra, and which don't, but that's not the centre of the article.
Algebraic literacy is a specialised skill that not everyone needs. Being able to perform algebra is not a requirement for most people's careers, and for many people, it is little more than a hoop.
The blog writer's suggestion that we switch the word 'algebra' to 'english' and see how Hacker likes it is just plain dumb. Hacker is not saying anything about too much language skill instruction. His criticism is aimed at algebra and algebra alone. It's a discussion worth having.
We can't teach everything, so instead of leaping to the defense of algebra, let's prioritize high-school math topics by how useful they are in daily life.
I'd put a basic understanding of probability as #1. Algebra is a ways down, and pre-calculus is close to the bottom.
I hated mathematics though could always see the point in arithmetic.
(Wavey lines as I wander back to the past and my early days in the RN)
I could never see the point in calculus or algebra until one day, while training on a ward, a patient was prescribed a highly toxic drug but, rather than be given I/M, S/C or even I/D (is anything given intradermally these days?) it was decided he needed it I/V.
So it had to be given very slowly in an infusion of Normal Saline over a fairly long period.
I'll never forget my astonishment at watching a very junior houseman (I think you call them Interns) casually sit down, work out how many drops from the IV line it would take to deliver the drug over a 12 hour period.
From that he worked out the volume of each drip so worked out how much of the drug would be administered in each individual drop.
I have no idea if he was just doing it to impress but if he did, It worked.
(Having thought about it he could have made the whole thing up. But I don't think so)
I love this site, most use science, I just fall back on anecdotes.
Narad:
The high school I was at was going to start offering calculus the year after I took trig/intro to analysis (now called pre-calculus). Our class got to review the proposed text books.
The trouble was that my dad retired, and was moving to another state to a tiny town, which was then not offering calculus.
Fortunately, I had already obtained enough credits to graduate after my junior year. So I only went to two high schools instead of three.
I’m with Orac: Hell, yes!
This guy (Hacker) has it backwards. It’s not that the standards for high school and college are too high – it’s that the standards for elementary and middle school are too low. You don’t fix the system by getting rid of standards. You fix the system by prioritizing quality education for younger students, so they can achieve the already minimal standards we have.
If Mr Hacker is describing himself, he sure got that part right! My opinion of his analysis is that he’s promoting a bunch of excuses for poor performance.
I disagree, Mr Hacker: it is easy to see why potential poets and philosophers need math. It’s not because they need to apply to their profession – they need math because they vote!
That reminds me of the hospital in Idiocracy. No one knows how the machines work. Patients are diagnosed by inserting some probes and the computer reads the input. The place seems to run on machinery made by the last competent people, who tried to idiot-proof it all.
---
As for my math history, definitely using algebra in my life. I'm doing some GIS programming that requires some geometry knowledge. And, of course, I need knowledge of algebra, statistics, and probability to understand what's going on in the world around me. !!SCIENCE!! is happening all around the world, and since the media's so often incompetent, I have to watch out for how they're potentially distorting the story, and that quite often requires an understanding of math.
Hacker's writing for folks like me: The people who did well at everything in school BUT math. These are the people who become woo addicts and Journalism majors, among other things.
Well, I'm going to wildly guessimate- before I depart- that woo-meisters, like those I survey, are not breathtakingly skilled in mathematics- except of course, lower level skills like adding up receipts at their virtual stores, figuring profits, dreaming about future growth. They don't really need much algebra for that. Their knowledge of statistics used in research is beyond comprehension- especially their own.
I'm sure Frege, Gödel, and Russell would be fascinated with this one.
@ Peebs: I can recall having to show my nursing skills during rotations through pediatric units. You didn't get a "pass" until you correctly figured the drop rate per minute...especially difficult when you were using the mini-drop IV set-up, on a very young infant:
http://www.pharmacy-tech-study.com/ivinfusion.html
It's so much easier now with IV infusion pumps.
(I should perhaps further note that formal logic is a prerequisite in any undergraduate philosophy program that I've ever heard of. The intro sequence at my alma mater was taught from The Logic Book, which I seem to have gotten rid of but recall as being propositional logic. They must have had to do predicate logic as well, certainly if progressing to a postcollegiate degree program. Might as well get the hang of axiomatizations down sooner rather than later. Maybe Hacker fancies himself a "philosopher" by default or something.)
I will give this guy one thing - statistics is an under-taught subject, one that is absolutely necessary for a well-informed populace. Generally speaking, we suck at statistics, and I believe this is a big contributor to bad decision-making and the appeal of pseudoscience.
For algebra (indeed all of math), I agree that it's an instructor issue. My own anecdote - I struggled with math until high school, where I had an excellent AP calculus instructor. I ended up testing out of the intro classes at college - the big-class rote ones that turn people off of math - and ended up getting a math minor. So good instructors do make a difference - but they require investment, and an investment of time and brainpower as well as money.
Rosie Redfield: " We can’t teach everything, so instead of leaping to the defense of algebra, let’s prioritize high-school math topics by how useful they are in daily life. . . .I’d put a basic understanding of probability as #1. Algebra is a ways down, and pre-calculus is close to the bottom."
How, exactly do you teach a basic understanding of probability without algebra? That's like teaching a basic understanding of composition without teaching grammar.
But why only prioritize math? History, literature, geography, science, and most foreign language classes are also fairly useless for most Americans in day to day life.
If we really prioritize, we can cut education down to 6 years, no problem. If all we need is basic reading, basic writing, and basic math, why require anyone to go beyond 6th grade?
Years ago, when I took chemistry, microbiology and physiology it was a great feat to even enroll in these classes as they were impacted. On the first day of class there were always masses of students standing around and forming a line outside the door waiving add cards at the instructors. Back then the science classes had no prereqs. The instructors were frustrated over this because “half of their classes were failing due to a lack of understanding algebra”. These classes were prerequisites for those wanting to get into programs in the allied health fields.
On the first day of chem. the instructor wrote a simple algebraic equation on the board and told the class if they could not solve this they needed to get up and give their seat to someone on the wait list. He suggested they come back after successfully completing an algebra course.
The physiology and microbiology instructors wrote the same equation on the board the first day of class but took it one step further and included a paragraph from the text. The argument was that students taking the classes did not only lack the math skills but also the reading comprehension to successfully complete the class.
Nowadays, there is a algebra prereq. requirement to take chemistry, and a chemistry and English comp. requirement to enroll in microbiology and human physiology as there should be.
Apparently the "Why Algebra?" has been going on for some time as this article which is a booster for algebra education shows).
Another resource for real-life maths (including algebra) uses is here (it's a link-out to a NASA site).
There was a show my wife watched, called Numb3rs if memory serves, in which a maths professor used his skills to assisst his FBI agent brother in solving crimes.
I couldn't tell you how accurate the show was, but if it is then conceptually it's another point in favour of algebra and other maths.
Narad,
Blockquote fail. Optician appointment eagerly awaited.
Then again, if you're good in math class you will not be Governor of Texas.
Hm. How 'bout a pop quiz required before one could become a state governor, with questions randomly chosen from linear algebra, statistics, differential equations
and what was the 3rd one?
I just remembered an incident at a hospital I worked at when a doctor got a decimal point in the wrong place, when calculating the dose of digoxin for a baby. The baby survived, somehow. I suspect that's the kind of error you only make once.
@ Krebiozen...Digoxin and Lanoxin (oral elixir), are scary medications. I know, I titrated my infant's Lanoxin, each day while he was on tube feedings.
How about this major mistake with heparin IV flushes?
http://www.cbsnews.com/2100-18560_162-3936412.html
@ Krebiozen...Digoxin and Lanoxin (oral elixir), are scary medications. I know, I titrated my infant's Lanoxin, each day while he was on tube feedings.
How about this major mistake with heparin IV flushes?
http://www.cbsnews.com/2100-18560_162-3936412.html
Yikes. A thousand-fold overdose of heparin? I remember talking to some friends of mine who were paid more than twice my salary, yet if they made a mistake the worst that could happen was their company lost some money. In the medical field, the consequences of a lapse of concentration can be a lot more serious.
Yikes. A thousand-fold overdose of heparin? I remember talking to some friends of mine who were paid more than twice my salary, yet if they made a mistake the worst that could happen was their company lost some money. In the medical field, the consequences of a lapse of concentration can be a lot more serious. I can't imagine how I would feel if I found out I had made a mistake like that.
Apples and oranges. Artistic and literary creations are just that: creations; artists actually put something of themselves into their work, so it's very hard not to take it personally. Scientists, OTOH, deal with phenomena that exist independently of them as persons (if Darwin and Pasteur had actually made the deathbed statements cranks attribute to them, it would have zero bearing on the correctness of germ theory and natural selection). They deal with discoveries, not personal creations; the scientist who treats his ideas as personal at best is impeded in his efforts and at worst becomes a crank.
An artist can't help developing a degree of attachment to his creations. A scientist has to avoid getting attached to his theories because they could turn out to be wrong at any time; they're awfully fickle companions.
I had a great geometry teacher in high school, but the algebra and trigonometry teachers were awful. Vectors saved me. There was no AP anything where I went, but I loved chemistry and physics (and still do). I ended up in network security/computer forensics... Go figure. Thankfully, I'm not a doctor.
Please don't use this silly NYT piece to make inferences about political scientists as a group. Many of us are quite sensible about the importance of math (and, heaven forfend, statistics and even calculus) as a vital tool in understanding the world.
Story problems, not so much, but that's a different issue.
The dumbing down of education is tragic. It's one reason why the magical thinking behind quackery has gained a foothold.
Ken Mayer
Professor of Political Science
University of Wisconsin-Madison
I suspect the author doesn't know what algebra actually is or how it is used. Or he has in mind one small portion of algebra not realizing how much stems from this one small portion. I understand what he is trying to say, but he's trying to say it from a woefully ignorant (as in "lack of knowledge") background.
Ken:
Life is a story problem. You encounter them all the time.
You have room to paint, how much paint do you buy? If it comes to two gallons plus a bit under half a gallon, is it more economical to buy two quarts or another full gallon?
You need to get from Point A to Point B, and a certain amount is at freeway speeds with some surface streets, how should you allow for travel time? How much fuel will you need to budget for?
Which is cheaper per can: a 20-pack of soda for $5.99 or buy four 12-packs at 3.39 per pack (price only for four or more)?
Would it better to get the thirty year mortgage or the fifteen year mortgage at a slightly lower rate? How much compound interest do you get with a CD that compounds monthly versus daily?
On the latter, it is perhaps sufficient to know about those financial equations. Personally I think its relationship with a very important transcendental number is just cool.
Hello everyone,
perhaps you can help, this old dog here always had problem with math (which come down to my speed of writing, I suffer badly from dysgraphia). Usually, I can understand the concept well enough but the thing is the speed at which the instructor give his courses.
For a calculus course, it's given in 36 hours to cover half a textbook but I'd need something north of 80 hours for the same content; basically, I'm the poster boy for distance education with courses on a dvd, I can click pause or rewind if needed.
What I'm looking for is for excellent self-learning textbook, the kind of textbook for which I could learn on my own without any outside intervention. I'll be taking a sabbatical from school for at least a year and I intend to work regular shift in a factory (which I applied last week). I need a textbook for pre-cal with trig, calculus, matrix & linear algebra and finally, statistics.
Can you help me?
Thanks
A.L.
I'm actually not very good at maths in general - I find it dificult, and there are some concepts I've just never been able to grasp entirely (non-real numbers, for example).
But I am an engineer. It's critical to at least understand basic physics and maths. Not just for people in my profession though.
As people have said above, anyone with a medical background. Accountants. People deciding how large to dig a swimming pool. People working out which route is faster.
Possibly the only people with no use for algebra are political "science" majors...
I'm actually not very good at maths in general - I find it dificult, and there are some concepts I've just never been able to grasp entirely (non-real numbers, for example).
But I am an engineer. It's critical to at least understand basic physics and maths. Not just for people in my profession though.
As people have said above, anyone with a medical background. Accountants. People deciding how large to dig a swimming pool. People working out which route is faster.
Possibly the only people with no use for algebra are political "science" majors...
Kat:
I love them, I am a big fan of Euler and Fourier. Though I mostly did structural dynamics and vibration.
You must be like my husband. We were in the same differential equations class. He hated it, I liked it (I hated the instructor, I like differential equations). He majored in electrical engineering, going into computer stuff. I tease him that he only has to count with "0"s and "1"s.
But you are right, that most people do not need to go past calculus, or even algebra. But you really cannot skip it entirely.
You certainly are at a disadvantage- if you have poor skills- trying to comprehend various measures when making investments or attempting to follow news about them There are many who use this fact to sell people advice, methods et al most of which are bogus.
Please don't draw any inferences about political scientists from this piece. Most of us are quite sensible about the importance of math (even statistics and calculus!) as a too for understanding the world.
Story problems not so much, but that's a separate issue.
The dumbing down of education is a tragedy, and one reason why medical quackery has a foothold.
Chris: I've always liked engineering (civil/construction) for the physics side of it, plus I get to play outside in the mud. Maths was just a means to an end. I think it's that way for a lot of people, but I admire those who genuinely enjoy it!
That said, I don't currently use my skills in English Literature, or Music. But I don't regret having studied them - it's part of being a well-rounded individual.
My favorite part of the article is where he says
I just...what? How does he get to just decide that this is true?
The late and much missed Jacob Bronowski was a mathematician and philosopher of science who liked to point out that creativity in art and science are much alike. They both call for making connections that have never been made, or made in the same way, before. He also pointed out that mathematicians are often talented musicians as well, and the reverse seems to be true - in World War II, the British turned military bandsmen into codebreakers with great success. It may be that his most important point is that eras of great scientific advances are usually ones of great artistic ferment as well, the two seeming in some ways to drive each other.
It might also be pointed out that unless kids are exposed to hard subjects against their will, many will never find out what they are capable of, and many who might have gone on to excel in fields like science and engineering will instead take the easy way out, as kids so often do.
AdamG
And Hacker totally misses the fact that struggling through and mastering classroom algebra is one of the things that teaches perseverance.
Hacker (in article): " Making mathematics mandatory prevents us from discovering and developing young talent. In the interest of maintaining rigor, we’re actually depleting our pool of brainpower. I say this as a writer and social scientist whose work relies heavily on the use of numbers."
Firstly, seeing how Orac's blog on this issue panned out, I'm thinking that Hacker's main reason for holding the beliefs he professes there is that he is shite with numbers! Also, the making mandatory of mathematical studies is not 'for rigour' ... it is about attempting to foster some sort of competence with quantities, space, data and various structures that exist in the more abstract levels of conceptualisation... like group theory, which helps us to count stuff we couldn't count 'by hand' (as it were). The guy's a bloody idiot!
Redloh: "Count me as a casualty of an awful algebra teacher. He graded our whole class on a curve otherwise many of us would have gotten a failing grade. He appeared to be quite a mathematician but not a teacher and lasted just that year."
Our maths teacher at school was exactly the same: great at maths but not so good at teaching it. The whole maths thing started making sense to me when I began studies in engineering in 1991... 13 yrs after leaving school.
Spectator: "The problem with algebra is that students might actually have to do homework rather than bs their way through it. One can creatively grade a rambling, brain damaged attempt at an essay as good, but it takes some effort to convert wrong answers into full credit on an algebra test."
Bingo! When I taught maths and had to grade student assignments, the basic thing was that you can start off with 100% of the available marks - and it would be errors that reduced your overall score on the test.
JohnV: "A political science professor suggests that algebra should be replaced with 'political science math'."
And PSM is .... maths for the bloody incompetent, right?
harey: "PS: One of my favourite idiotic statements in the text without a morsel of proof: 'It’s true that students in Finland, South Korea and Canada score better on mathematics tests. But it’s their perseverance, not their classroom algebra, that fits them for demanding jobs.'"
I live and try to work in Finland. These people are fiercely proud of their PISA test results but what I've found as a result of doing freelance lectures in what we might call 'quantitative techniques in applied social studies' is that - after they leave school - they tend to be frigging useless at the stuff. The issue with PISA is that the results are not reliable since many subjects have national moderation but no continental/federal moderation. Now where's that elastic tape measure gone ..... ?
RK: "I,for one,am going to come to this guy’s defense.In addition to autism,I have a whole slew of learning disabilities.One of these,is a particularly nasty form of dyscalculia."
SpLDs such as dyslexia and dyscalculia, etc, are NOT reasons to weaken the mathematical curriculum ... ever! They are reasons to support the development of methods by which those experiencing SpLDs - and I'm speaking as one such person and one trained in understaning and remediating for these things - to get a better grip on these issues than we otherwise would in a mainstream setting. See what I wrote about my late grasp of maths above, and also bear in mind that my specialty in teaching maths was in fact remedial teaching for adults taking examinations in grade school and higher mathematical topics.
Raging Bee: ".... he says this as a knowing hypocrite who seeks to deny other kids the opportunities he enjoys."
Are you saying the guy is a total arsehole???? ;)
Evan Gough: " His criticism is aimed at algebra and algebra alone."
Yes. And algebra is the basis for which just about everything else in mathematics rests. You can't do statistics and probability without good basic skills in algebra; you can't get to grips with understanding the nature of numbers without having a bloody good grip on algebra; you can't get into solving equations simultaneously - either as equations or as elements in matrices without a bloody good grip on algebra; we even deal with a lot of trigomometric stuff algebraically... and the same goes for geometry. So ... sure ... let's get rid of algebra. And while we're at it, let's take anatomy and physiology out of the medical and nursing curricula - you know, because they're such intensely hard subjects, and replace them with stuff that people can easiliy ace. Would you want a doctor and a nurse with THAT sort of training looking after your health? If so, you're pretty much on your own!
Rosie Redfield: "I’d put a basic understanding of probability as #1. Algebra is a ways down, and pre-calculus is close to the bottom."
If it's 'a ways down' then your understanding of probability is going to suck.
Prof. K. Mayer:
"Please don’t use this silly NYT piece to make inferences about political scientists as a group. Many of us are quite sensible about the importance of math (and, heaven forfend, statistics and even calculus) as a vital tool in understanding the world.
Story problems, not so much, but that’s a different issue.
The dumbing down of education is tragic. It’s one reason why the magical thinking behind quackery has gained a foothold.
Ken Mayer
Professor of Political Science
University of Wisconsin-Madison"
Thank you, Professor.
Just about everything in mathematics involves the manipulation of quantities - concrete or abstract - whilst keeping an equation balanced; and this manipulation of quantities is the essence of what is done in algebra (certainly at the levels taught before anyone even thinks about going to university). Skimping on the teaching of algebra will inevitably lead to the worsening of mathematical competence further down the road, because if you cannot properly manipulate quantities and retain the balance of an equation.... you may as well forget trig, geometry, calculus, linear algebra, set theory, group theory, ring theory, in fact ... everything (including proofs, in which proofs are inevitably essayed algebraically).
lengthy comment in moderation... dealing with a few comments in one hit before i head off to do stuff....
autistic lurker
It may take a few hours and a bit of frustration but there are **excellent** self-paced maths courses of all kinds online - free. Start with some of the high school oriented courses and look around. What you need is one of the nifty tuition style courses that does a pretest to clearly identify your start point.
After that, the progressive learning and retesting ensures that anything you have problems with is automatically revised until you're ready for the next step. And if you ever get fed up with it? It cost you nothing in the first place. You've learned something. You can give it up with no cost or guilt. You can find another course that best suits your new needs.
I guess I am going to be the respectful opposition here, but it's not because math should not be offered. Allow me to start with the obligatory disclosure that I have a bachelor's degree in theoretical math from MIT and a doctorate in biochemistry from CIT (funny that Hacker should mention these two institutions in his otherwise poorly written article). One thing I learned during my formal studies was that some of my fellow students had an awful lot of talent in math, and it went way beyond mere perseverance. There seems to be a wide range in the ability to make the mental connections that go into the various levels of math, and this distinction seems to be deeper and more distinct than for other academic abilities (see below regarding a different article on the subject).
I think that some mathematical abilities have to be there from the start, and there are students who just don't have the right wiring, so to speak. Or to put it another way, somebody once pointed out that when it comes to word problems, there are two kinds of students -- those who have always been able to do them, and those who never have and never will. I don't know if it's quite that stark, but it's obviously pretty close to the truth.
And that leads to a much better researched and well written study that came out in the Los Angeles Times a few years ago:
http://www.latimes.com/news/local/la-me-dropout30jan30,0,1678653.story
Basically, it argues pretty persuasively that there are students who would otherwise get through high school, but just lack that mental something that is required to understand and perform algebra at the high school level. I strongly suspect that this is the case, because I have tutored students (generally the children of friends) who lack ability and are trying to survive in math courses. There is always that moment when I am trying to get across something that is terribly obvious to me, but is not obvious at all to the student. Sometimes I can help them to grind through the material. The problem is that when it comes to advanced algebra, there is a lot of material that requires the right kind of mental wiring.
The question that Duke Helfand raises in the LA Times article is whether a student who would otherwise be able to graduate, and who has given it a try again and again, should end up a failure or a drop out for this and only this reason.
I think it's a fair question. I have reluctantly come to the conclusion that maybe we should allow a little flexibility into the system. That does not mean that we omit math from the curriculum for the majority of students who can handle it, but we might temper our righteousness with a little mercy for those who can do everything but algebra.
And one other point. I have been a volunteer judge in the state finals of the high school science fair for more than 20 years, and I have seen lots of really superior students. I don't think that these students are the products of failing schools.
In my own work (molecular and cellular biology), I find that I use algebra at some level pretty nearly every day of the week. My colleagues, believe it or not, come to me to check their own calculations. I'm all for strong math training, both in theory and in practical calculation skills, but it's not for every single student.
@Denice
I've had a less-glamourous but still similar experience. Some people I knew took pity on me when I was struggling to find my first job out of uni, and taught me their trade. It helps having the right kind of aptitude for this role, but really I was entirely learning on the job. They were willing to train me up; this is a rare quality in employers/colleagues I've found.
However now, I find that knowing how to do accounting would actually get me more work. Arts admin is practically the only full-time well paid job and without accounting skills, you can't get the job.
It would have been nice if my uni had also taught - along with proper resume writing and budgets, which they taught in brief - how to actually keep the books.
This is probably what I was trying to get at before: the artists who are going on about this educational freedom seem to either forget or ignore that any successful artist also needs to be a successful business person. Which means understanding how to add, subtract, etc. Instead they harp on about nebulous and unquantifiable ideas such as creativity and innovation and nurturing.
I'd be more on their side if they said "If your son/daughter has an aptitude for the arts, then we should ensure it is funded well: but still have a basis in science and maths so they can be more assured of building a profitable business". Instead of what they actually seem to be saying which is "Every child has an aptitude for the arts, and we need to make science and maths secondary because they stifle creativity and they'll grow up to be some middle management flunky".
... /end soapbox. Really, stop me before I continue on. ;)
@Johanna
Couldn't agree more.
@Evan
Did it occur to you that having an understanding of maths and statistics might help those of us who aren't scientists to better read and criticise studies that are produced by scientists?
For me, I have to rely on Orac and others to interpret studies because when I read about probabilities, etc my eyes glaze over. If I had more of a mathematical mind, I'd be able to better judge for myself what science says and what policies I want to support and what politicians I want to vote for. And I say this as someone who struggles with equations.
I actually wish I remembered more of my chem, psych and maths classes. I find the more I read about science and skepticism the more it would help me evaluate claims.
Example: how much anti-vaccinationism would there be if more people could understand the probability of getting hurt by the vaccines vs the probability of getting hurt by the disease?
Please forgive the long, somewhat off-topic, rant...
@ebohlman
I disagree. I am quite capable of separating criticism of my work vs criticism of me. It's hard to learn, but most people I know understand that you can't please everyone and make no attempt to do so. The best you can do is please yourself, and the rest you either take on board for improvement, or throw out if you disagree.
Secondly, if approached as a business, then one has to recognise when changes need to be made in order to make more of a profit. You don't need to cut off an artistic vision in order to do so. (And actually, I have found artists who were willing to shortchange *saftey* for the sake of artistic vision. So some artists need to get their heads out of their asses and recognise that safety is more important and that when you're criticised as being unsafe, you don't get all huffy and respond as if the other person has just called you nasty names)
An artist actually *needs* to learn detachment: if you are being commissioned, yes you fight your point of view if there is a legitimate method that is better, but at the end of the day the other person is paying you to make something to their specifications. If there is something that is physically impossible to do (and I've found most non-artists request things that are physically impossible) then fight for that: everything else is up for grabs.
You need to learn to let go on subjective issues. If a gallery lies open with no visitors, they don't shrug their shoulders and say "the public just doesn't get our style". No, they go out, collect marketing info, and changes what needs to be changed. Otherwise they go out of business.
See Chris' point about buying paint too: you have to be able to take criticism when say, you've made a mistake or you're doing something wrong. Knowing how to, for instance, properly calculate electrical input/output is an important part of some artistic endeavours. Not everything in art is subjective and there's a lot that requires a modicum of technical/mathematical training where you actually can be right/wrong in a binary way. If you plug in an electrical device and I say that will overload a circuit, will you as an artist get huffy about "subjective criticism" - I think not. And yet, some artists actually do that and genuinely believe it hampers their artistic vision if you criticise them in *any* way.
An artist needs to be flexible otherwise they get nowhere with their work. Hobbyists have a far greater chance at producing art that doesn't require any improvement or feedback from their audiences. But there you hit on another issue: if art is about capturing your attention, and you don't capture it, what's the point of making the art? You may as well just hang up the painting in your own house because no one else will care about it.
Thirdly, there is a great unwillingness on the part of the artists I know to not openly criticise someone else's work. This is partly due to the fact that we get enough criticism from "outsiders" that supporting one another is helpful; at the same time it allows and fosters a growing number of crappy artworks that hinder any ability to get traction amongst the general public as an artform worth paying attention to. I know a number of people who will refuse to recommend certain companies to the general public because they produce crap: but won't call these same companies out amongst their peers. Does it help improve the artform if we hide our mistakes? Or does admitting those companies produce crap force them to try harder and create greater innovation in the long run?
Also just as with science, there is a way to offer criticism and a way to deal with it. I've written many arts reviews, and I always criticise the manner in which the art is presented (ie. the techniques used) and offer suggestions for improvement: insulting an artist simply because I don't happen to like that particular style is not something I do. I point out the good and the bad, and discuss *why* they were good/bad. And when I subjectively don't like the ideas or the presentation, I say so and admit that other people may like what I don't. Some people will agree with me, some won't. But I only ever pick on the technique and not the ideas.
For every review I've ever written, artists have thanked me for my honesty, my willingness to point out the faults, and appreciate that I'm not panning *them* but rather their methodology. If I can't hear an actor speak, that's not insulting *them* but suggesting they need to improve their diction or that they needed microphones. Is it subjective? Perhaps. But if I hear other audience members mention the same issue, then I'm betting that no one's going to consider it an aesthetic comment but rather a methodological one. (And again, you'd be surprised at how tetchy people can be about commenting on technical issues)
A scientist can likewise be personally attached to an idea, but if their methods can be improved, they get called on it. Nobody bats an eyelid. It's expected. If I however, commented that an artwork in a gallery has been badly painted, I'm seen as unsupportive or worse "unappreciative" or it's "not my thing". (It's the arts world version of the different ways of knowing fallacy) Why can't we admit that some art is just badly done?
I agree that there's not *much* crossover, but I personally am sick of walking out of a gallery or theatre or whatever and holding my tongue because god forbid I offend someone that I didn't like what I saw. Scientists fully understand that as soon as they publish their work it will be ripped to shreds. I find that incredibly brave and takes far more guts than I have ever seen from most artists when it comes to pushing out their stuff, and certainly far more than I have ever put into my own work. Artists take the risk of putting their ideas out there... but won't follow through when it comes to braving critique.
As a last point: most artists I know are heavily into astrology, alt med and other woo-based ideas. If they were more accepting of criticism in their work, then convincing them to be more critical of other things that affect their health might be easier.
Personally I'm at a crossroads where the wankery of the art world has me fed up. As you can tell ;)
A different take on the article:
http://dailyhowler.blogspot.com/2012/07/elite-delusions-times-sets-its-…
Math requires clear thinking and concentration - why would we want to train people to have such skills? I'm saying that even if you never use it, that part of your mind needs exercise when you are young. I will help you to not become a fool.
As for math teaching, in high school I find it sucks, and I think one of the problems (unlike other commenters) is that teacher actually doesn't get it. The other is that it is faith-based math teaching (do you believe pi is irrational? Why?) and that is anti-math!
I think there are allot of math/science folks out there who might want to switch and teach math, but the cost of switching to the teaching field is too high at the start. They essentially have closed the shop. You need teaching credentials (teaching statistics to graduate students doesn't count). How good you are at math is less important. This is also true of science classes, where what teacher actually says about subjects like natural selection would sometimes put biologists in great pain. Why not get some people in there who actually were excited about science and math. I'll point out that if Ed Witten offered to teach math or science at high schools near me, he would be rejected as unqualified.
Now reading Shakespeare and Goethe and Mark Twain - who ever uses that? (I'm joking - it is also essential.)
Ken:
So you have never painted a room in your house, estimated the length of time and how much it will cost to drive to another town, borrowed money to buy a house or car, or even put money into an account with periodic compounding of interest? Wow, how did you miss all of that.
flip, I know a young lady who is going to be graduating later this year with a BFA (Bachelor of Fine Arts) in Art (ceramic sculpture), and a BS (Bachelor of Science) in Math.
I wish I knew of her exhibition earlier. I think I am going to keep a look out for her work in the future.
Wow, did someone say "soft bigotry of low expectations?" Looks like that bigotry is not so soft anymore...
I’m one who understands the importance of science.
But you don't seem to understand the importance of math within science? That alone proves you're not qualified to speak about this issue.
But, all the time I spent struggling with quadratic equations and polynomials actually turned me off science and math at a young age, so much so that there was no chance of me being a scientist.
Just because you got turned off a subject doesnh't mean that subject is useless. I got turned off police work, but that doesn't mean we don't need trained cops. Your personal peeves and past grudges have no more place in this debate than mine.
Everybody is not going to be a practicing, working scientist, so why must we waste so much time learning skills we’ll never use? The time would be better spent teaching us critical thinking skills so that we could be better voters and citizens in general.
This isn't just uncaring bigotry, it's SELF-FULFILLING bigotry. IF you don't learn algebra, you won't get a job in any field that requires it, so you'll never use it, so why should you learn it?
Even, I strongly suggest you and your friend Hacker go dumb down someone else's kids. The Iranian mullahs might like your educational philosophy, butr we decent Americans have no use for it.
I'd say the most important thing secondary (high) school mathematics teaches is the careful application of thorough, step-by-step, "show your working" reasoning, as I believe someone upthread suggested (if not as explicitly).
That is, in my opinion, a crucial part of good critical thinking, and as a matter of course a very useful skill in "real-life everyday" work.
Boy, am I ever glad I didn't go to school in the system Orac proposes, because I never would have gotten out of high school. I flunked out of grade 10 advanced math with 28% (bad teaching, general inaptitude), and moved back to the general, took it as long as I had to (completed grade 11) and then quit. Went on to get a bachelor's degree in English with a minor in modern languages, and then a Master's in Language and Professional Writing at Canada's answer to MIT. I would have been completely shut out of higher education if algebra and calculus were mandatory, and personally, I think I get along pretty well. I am a technical writer working for a very big IT firm.
Somewhere along the line, I also wound up writing a peer-reviewed course on basic inferential statistics as it applies to occupational safety, and I still couldn't pass a high school algebra course. Figure that one out.
Yes, I'm dyscalculic too. The way it manifests with me is that you can teach me any damn math thing you want, and I'll understand it and be able to use it...as long as I keep doing it. As soon as I stop for more than half an hour (or, squid forbid, sleep)...poof, gone! I literally have proofs I can't interpret (now) written in my own handwriting to demonstrate it, too. It's like it loads into RAM but then never writes to the hard drive.
Frankly, if I were going to teach survival-skills math, I'd teach probability, estimation, and basic money management, in roughly that order. Being able to run a mushy Fermi-numbers calculation can get you pretty far, even if your brain interprets math generally as radio static.
I don't know if I had a good algebra teacher in high school. I coasted through Alg 1 and similarly half-assesed the start of Alg 2. It was after getting a mediocre score on m first Alg 2 exam that I realized that, you know, if I actually paid half-attention and gave any effort at all, this stuff was trivially easy, so that's what I did. Ended up with an A+ thee rest of theway.
Probably says more about me than the teacher.
As for story problems, not only are these not irrelevent, there are pretty much what math is all about! I liken it to sports events. The rote problems you see in books are like the drills you do in basketball practice. It teaches you things like proper technique and form. But story problems are like the game. You have to be able to apply the skills you practice, but it isn't just doing the problems.
People who only can solve the equations but not set up and solve story problems are like basketball players who can only do practice drills and are unable to perform in game situations.
Lastly, I still contend that the problem with algebra is not high school or college, but starts with poor math prep in elementary years
I struggled quite a bit with algebra and ended up not being truly happy with math again until Calculus I (which I absolutely adored).
Not letting me post my comment on here - says I am duplicating what I already said, and I don't see any comments for me on this post???
Hacker is correct. Let the kids who have a predisposition for math and science take algebra and spare the millions of children who will never use it. If at some time they change their minds they can catch up. It is far easier for a motivated student to learn something than one who has no interest in the subject. When the student is ready the master shall appear.
Offal, I've seen you argue here many times for the right of parents to evaluate the evidence regarding vaccines and make decisions for themselves.
How would parents be able to understand and evaluate statistical evidence at all if they didn't understand algebra?
MMMindy
Exactly!
We cannot wait until high school and then expect to be able to fix the problem.
Back when the Canadian dollar was worth $0.75 American someone wrote an angry letter complaining about how the bank was gouging him by charging a $1.34 Cdn for a US $. He thought they were making 9 cents per dollar on the transaction instead of 0.7 cents. Merchants were able to get away with taking US dollars at $1.25 Cdn instead of a reasonable exchange rate of $1.33 less a little bit.
"When the student is ready the master shall [sic] appear," see?
Here is someone whose promising career as a science was cruelly cut short by attempts to teach him sciency stuff.
In an alternative universe, he was not exposed to equations and stuff at a vulnerable age... so again, there was no chance of him being a scientist.
To everyone:
Woa, apologies for my little rant. Chalk it down to it being late and needing a little timeout - really should put a keyboard lock on my computer to prevent things like that :)
Also, thanks for teaching me about a new word: dyscalculia. Looking it up on Wikipedia makes me think I might have some issues with it myself.
@Chris
I wish I had graduated with both sciences and arts. I'd be much happier for it.
@Adam
How would parents be able to understand and evaluate statistical evidence at all if they didn’t understand algebra?
Give me an example of statistical evidence related to the vaccination decision that requires an understanding of algebra.
@ flip:
Oh, I was just about to implore you to rant on..
I am one of those rarities who studied both arts and sciences...I arrived at a large university at a young age and didn't know what I wanted to do; I was able to study in various locales and acquire a few degrees. I was considered to have talent as an artist at a young age ( producing work for money) and also did very well in mathematics and writing. So I acquired a liberal arts baccalaureate with many courses in life and social science. The grad stuff is in economics with degrees in psychology.
I think that you can learn accounting and budgets through the net although I don't know the best resources. When I say I studied economics, it was all theoretical and the nuts and bolts business-y stuff I figured out on my own for investing etc.
Unfortunately, many people in the arts look askance at practicalities as though it tarnishes their vision.. it just makes life easier. My cousin with the 'glamourous life' thinks that I- and adman cousin B- have the glamourous lives. Nothing could be further from the truth- altho' we look the part.
Anyway,hang in there.. anything worth doing takes time, effort and dedication. And the art world is filled with wankers as is the business world, the scientific world et al.
Knowing what a variable is seems like it might help.
Mr. Schecter:
Here you go. Knock yourself out, there are over nine thousand papers that are free to download and read.
As I recall there are several comments on this blog where you exhibit your lack of math skills. They are very amusing.
Your inability to answer my exceedingly simple question directly proves my point.
@ Sid:
I do believe that what Chris and Narad mean is that statistical analyses of data- like that in research on vaccines- is based in algebra. If you don't get algebra, how can you understand these analyses?
Oh, I was hoping you would go down this route.
http://en.wikipedia.org/wiki/Incidence_(epidemiology)
How is it possible to understand incidence rates without understanding basic algebra?
Sid, are you really going to argue that either
(a) understanding incidence rates is not important to the vaccine decision or
(b) you do not need to understand basic algebra to understand how incidence rates are calculated?
What, precisely, do you think "algebra" comprises, Bob?
Adam, more generalities? Narad, I took algebra in high school and help my daughter through it, so yes I know what algebra is. Again, any specific algebraic equation pertaining to vaccination. And even if you can provide one it does not prove one needs study the subject for a year or two when in their teens. People can learn at any age and as I said, should a topic become relevant one's ability to understand it will increase along with the motivation to understand
And incidence and prevalence is a rather simple concept
Perhaps it wouldn't be so simple if you hadn't taken algebra in high school and help your daughter through it.
From the wiki linked above:
That is a specific algebraic equation pertaining to vaccination.
Jesus Christ. Look at the basic discrete SIR equations. What do you think R⁰ is?
^ Should have been a sub zero.
Maths is hard.
http://en.wikipedia.org/wiki/Mathematical_modelling_of_infectious_disea…
Here Offal...Knock your self out:
Try looking up mean, median, mode and range. Then try looking up the p value for some of those *great* studies you are fond of linking to:
http://www.scribd.com/doc/7885761/Basic-Statistics-and-Epidemiology-a-P…
@Denice
:) Thanks - glad someone didn't mind!
Accounting and budgets I'm getting better at. A recent debacle using an accountant left me doing my own taxes for the first time, and fortunately it forced me to be far more detailed about how I keep my books than I normally would. (Because of course they did all the work for me previously) It made me immensely happy to figure out what is usually a very daunting task.
I can understand the issue with artists not dealing with practicalities. In my particular case, uni prepared us for everything *but* business techniques. We spent a modicum of time (no more than 10 hours all up probably) on budgets, but it mostly focused on how to write one up and not on keeping the books once the money is spent. Likewise with marketing, it focused on press releases and getting attention: but not with taking the temperature of your target audience and making improvements where necessary. I find that we're usually taught how to create the art, but not what to do once it's out there.
The biggest and best thing that happened to me was in learning website marketing practices. This forced me to see how people approach your marketing and how by changing what you do slightly, you can still get your audience interested: without ever actually changing the nature of the business. This in turn made me see how art needs to be approached as just another business, and that artistic vision can be the same but the methods by which you present it can be improved. In fact, treating it in this "cold, hard" manner has made me make many many improvements that I wouldn't have otherwise; both in an artistic sense and in a viable-business sense.
I think it's not an outright unwillingness or ignorance (I was never naive enough to think it would be easy or that I had some rare talent). The people who were pros, and acted like it, usually understood criticism and were willing to compromise. The people who were pros or amateurs, and acted like the latter, were always the ones to take offense. However, there is always the pervavise unwillingness to take the criticism into a public sphere. That I take issue with.
Too right. I've just finished reading Brian Deer's addendum to his anti-SLAPP case and remembered just how bad some "scientists" can be.
I was taught that each of the levels of Math built upon knowledge gained in the previous class - Algebra to Geometry, to Algebra 2, to Trig, to Calculus to Calculus 2....if you didn't get the basic concepts, you'd be lost down the line - which is why so much emphasis was placed on the beginning.
Seems that our foreign economic competitors realized a long time ago the importance of a science & math-based education....and we used to...a shame really.
Some idiot called Sid Offit: "Your inability to answer my exceedingly simple question directly proves my point."
He answered very directly. If you don't know what a variable is, you've sod all chance of understanding anything in statistics.
Were you born this stupid, or have you been practising intensively?
@David
Offal is that stupid. He keeps it his stupidity in tip-top shape by making asinine statements like the ones he's posted here.
Sid,
Here's where algebra comes in. Given the known number of cases of vaccine preventable infectious diseases in the years immediately before the introduction of their vaccines, the rates of moderate to severe complications experienced with those diseases, and the cost and side effects of medical treatment for the diseases, calculate the odds that in the absence of vaccines one or more of your children would:
- catch one or more of these diseases at some point in his/her lifetime
- suffer a serious complication from either the disease or treatment
For extra credit, calculate the expected additional cost of medical care for your family. Extrapolate this to the population of your home country.
Bonus question: Assume vaccination rates of 50%, 70%, and 80% of the general population. How does this affect your answers above.
People can learn at any age...
If they don't learn certain basic things at a young age, they'll have much less opportunity to learn more complex stuff at ANY age. And yes, algebra is BASIC; and there's huge amounts of other concepts and skills that are based on algebra, and that can't be learned until one learns algebra.
Offal's comments here show once again both how willfully stupid he is, and how totally uncaring he is when it comes to the most basic legitimate interests of other people. Why is this little guttersnipe still tolerated here, when all he does is piss on the carpet? Seriously, Orac, you can find smarter dissenters than this, even within the antivax crowd. There's no need to let the homeless loonies wander in just to privide extra "entertainment" for us.
I do have to agree with Sid that indeed many children will never use algebra. I would not consider this is a justification for letting kids skip the subject, though, but rather a tragic symptom of the low standards we have in our culture.
A girl growing up in a conservative part of Afghanistan will likely never learn to read. Some would argue this means she doesn't need to go to school. Would you argue this, Sid? Of course not. Illiteracy is a huge barrier to her self-determination, and part of how she will be bound to her male guardians throughout her life.
Knowledge is not a burden. It is an asset. Children who understand algebra will be much better equipped with far more options ahead of them; they will be able to work out when someone is defrauding them, for instance. They'll be able to work out gas mileage, and they will be much better equipped to run the family budget in adulthood. They will have the tools to begin understanding statistics, which will certainly serve them well should their friends suggest going to the casino together, and to help understand scientific research that can help them guide their own medical decisions. (You are an advocate for people doing their own research and not just listening to the doctor, aren't you? That's a good thing; we've got the Internet and PubMed; people should use it. But they'll need basic algebra.)
If millions of adults grow up to forget algebra, that is a sign that something is wrong with how we teach the subject and how we as a society value knowledge. Not a sign that algebra is useless to them. The only way it can be useless is if it isn't understood.
To touch on Calli's comment, algebra helps adults function in a modern, technologically developed society with complex problems. Without it (and without the maths that follow from it), they are increasingly at the mercy of unscrupulous hucksters (like, say, Mercola) or political demagogues (such as, say, the forces behind the US Tea Party).
Knowing algebra (along with other basic maths & science concepts) helps individuals and communities retain liberty. Neglecting it is a path to intellectual and economic impoverishment and political disenfranchisement.
@Composer99: Bravo.
" If a student arrives in college without a basic understanding of algebra, as far as I’m concerned that student is not ready for" high school...
FTFY
At the risk of being a little redundant, I would point out that the core issue is not whether math is valuable or not. It is whether there are some students who just cannot do it no matter how hard they try. The argument that children should not have to give it a try is silly. Math should be a part of every kid's early training. But for those who do give it a try and cannot succeed, we ought to think about letting them get some kind of diploma based on some serious work.
By the way, I tend to disagree that teaching statistics in lieu of algebra and/or precalculus is a good thing. I do understand that statistics is a part of epidemiology, and in the case of complicated diseases that exist in highly variable genetic backgrounds (like cancer for existence), statistics become a central element in any kind of hypothesis testing.
But when it comes to understanding cell biology and biochemistry, I think it is safe to argue that chemical kinetics, equilibrium theory, and just plain organic chemistry are the more critical paths to knowledge. The analysis of pathways (defined by a series of gene products and reaction products that lead from one to the other) is a core part of cancer research at the moment. And disciplines like chemical kinetics are a subset of calculus -- differential equations for rates and integrals for accumulations of substances, either toxic or protective. And of course thermodynamics uses a lot of algebra and some calculus. Organic chemistry is full of trigonometry and takes in a whole world of math involving handedness of three dimensional structures.
Perhaps I've gone on a bit here, but there is another point to be made regarding what this blog refers to as woo, and the people who promote it. I would argue that having even a basic handle on modern biology involves taking all those math classes along with basic and organic chemistry, thermodynamics, biochemistry, and cell biology. It's not a knowledge base you pick up by googling for nutritional supplement remedies, nor is it something you will pick up by reading anti-vaccination propaganda. And of course actually knowing something about the theory and practice of medicine is another world entirely.
I think we should be able to distinguish between legitimate arguments based on real quandaries (like what to do about the kids who drop out of high school due to lack of math talent, but are doing reasonably well in everything else) vs the arguments that are tossed up here by intellectually dishonest people who just want to keep flogging long-discredited arguments. One group is suffering and is worthy of our consideration; the other is just a group of trolls.
@Calli Arcale
This - The difference between the curios and the incurious. The incurious inevitably become the ignorant. In the case of Sid, they become the proudly ignorant.
I gave the example of the American tourists who thought the that a merchant valuing their US$ at $1.25 Cdn when the Canadian $ was only worth $0.75 US was giving them a good deal when they could have received $1.32 - $1.33 Cdn by exchanging their money at the bank.
@Composer99
But, but ,but this liberty could come at the expense of the liberty of corporations and wealthy people to trash the environment and screw everyone over. Some rich wanker might not be able to afford the ceramic brake option for his Porsche and that would be a very bad thing indeed.
Bob G:
I dunno; in my opinion, if a child is intellectually incapable of learning algebra (and I don't mean linear algebra here, I mean the really basic stuff that our high schools call algebra), that's a sign of a major learning disability. Perhaps those with such severe disability should be able to earn a diploma, but I have mixed feelings about that. And I say that as a parent of a learning-disabled child. What, exactly, is the diploma supposed to mean? If you graduate high school without algebra, you are innumerate; it would be like graduating high school with a third-grade reading level. Now, it's nice for everybody to graduate, but how low can our standards go before they become meaningless?
A person who cannot grasp algebra or who is functionally illiterate can certainly become gainfully employed later in life (though I would hope they have someone looking after them), and they are valuable and important people. But can they be described as completing the standards of our education if they haven't? Perhaps you could have a secondary diploma program for these people, but their disabilities tend to be so particular and personal that I'm not sure that would make sense either, and it might feel like sort of a consolation prize for not achieving the "real" diploma.
I have a relative who is mentally disabled; he managed to get a diploma despite it. Math was a very big struggle for him; he barely eeked by. But eek by he did, and he is justifiably proud of having done so. I think if someone is showing a lack of aptitude for algebra, they shouldn't be given a free pass; they should be given additional instruction and support, since this would be a sign of academic need. Don't give up on them and don't let them give up on themselves either. ;-) In the long run, it will be worth it.
I agree with Calli. If someone is incapable of learning algebra (not simply unwilling to put in the effort) then we shouldn't pretend that they have actually completed a basic education anyway.
Incidentally, right now I believe you actually *can* graduate without a meaningful understanding of algebra. I believe you can get Fs in math and still graduate, as long as you do well enough in other courses to compensate in your overall GPA*. So the right question maybe isn't "should we devise a way for these people to graduate" since the answer is "no, we've already got one."
*I had a good enough GPA to graduate college despite flunking a class. Of course, it also helped that I went fuming up to the dean to demand to know why I was even registered with that class, as I had dropped it before the semester even started because of a time conflict with another class. Stupid bureaucracy....
I really did like to hear that our Canadian students had such perseverence--I'll pass it on to the teachers of my aquaintance. But, I'm sure they already know this.
I am impressed with Dr. Hacker. He really has "gone emeritus" as the saying goes.
I have the feeling that much of the problem is not at the level of teaching algebra but long before it, in elementary schools. My impression here in Ontario is that a lot of elementary school teachers are really not that confident in how they handle math themselves and thus may a) convey a sense of their own dislike or discomfort with math and b) have a problem teaching what they may not really understand themselve. I remember, as a Gr 11 student, doing my mother's math homework before she went off to teach it the next day :) Well it was "New Math".
Thus by the time a student is in Gr. 7 or 8 (roughly 12-14 years of age for non-North Americans) they may already have some math anxiety and, quite possibly, a poor grounding in the very basics of math and arithemetic.
Also as someone said a long time ago (Snow?) there is no shame in being innumerate. Lots of people will admit to being innumerate who would be mortified to have to admit to being illiterate so there is little or no social downside for not being good at math.
Somewhat in disagreement with Bob G. I am not so sure that there is as much innate "math" ability as people may think: It easily could be bad teaching and little encouragement,--See remarks on social costs above.
There is an interesting program out of Toronto called JUMP
from http://ckc.tcf.ca/org/jump-math
It was started by an actor/writer/mathamatician, John Mighton more or less by accident as a tutoring approach to complement standard school teaching--Mighton's story of how that happened is in his first book and it is funny. It seems to be moving into Canadian and US schools now though from what I read on the JUMP site this is more that teachers are finding it works better than the tools they have. . It seems to teach in all the wrong ways such as encouraging Gr. 3 students to count on their fingers! I don't know if any North American school boards have officially adopted it.
Mighton,BTW, is not exactly a light weight or likely to be a quack.
I think the academic research evidence that I have seen for the program is still a bit weak, possibly due to a lack of funding to research outcomes but the one or two evaluations that I have read look favourable.
@ Autistic Lurker
Have a look at the Khan Academy -- it may have some of the things you want. www.khanacademy.org/
@ Brian
If your children are fairly young you might want to have a look at JUMP as a parental resource. No reason you or someone else could not use it to help increase knowledge and liking for math. I think there are still free sample materials available on the JUMP site and a single package of materials looks pretty inexpensive for a quick try-out.
Oh and if the USA wants to give up teaching algebra, feel free, we need the boost to our exports. And I'm sure Japan,Finland etc agree. Sheeh
Calli Arcale @10:08 am 2 August 2012
Very well said!
Anecdote coming up, but pertains to the thought: I attended a university with a national reputation in the area of education, and, particularly, elementary ed. Consequently, a large number of the students, particularly females, are el ed majors.
So if I, as a male science major, was chatting with random female students at parties or in the dorm, with stimulating small talk like, "What's your major?", I would meet a lot of el ed majors (either that, or what I called "I Don't Know Business" majors - "What's your major?" "I don't know...business" Guys were just as likely to be I Don't Know Business majors, though; el ed majors were predominantly (>90%) female)
So I learn they are el ed, and I tell them that I am a chemistry major. The most common response was, "Ew. Math and me never got along." Grammar either, apparently, but oh well.
But even then, all I could think was, wait a minute! You are supposed to be teaching our kids. How do you expect to be able to teach math effectively if you have such disdain for it, so much that you boast of it? The standard response from the education people is, "I am teaching children, not math" but that is meaningless platitude. You are supposed to be teaching children lots of stuff, including mathematics, and prepare them for things they will need to learn as they grow, so don't give me this "It's not my job" crap.
I said the same thing early on in this thread, that the problem is not algebra, it is math teaching in elementary, and this is why I came to that conclusion in the first place. I have met too many el ed majors in my life who are math phobes. How in the blazes can we expect our young people to get a good preparation in a subject when the teachers openly admit they hate it? It's like expecting me to teach electrochemistry. I guarantee you, I'm not going to do a good job at it. Not just because I don't know it sufficiently to teach it, but because I detest it so much that I have no interest in talking about it for whatever amount of time I need to.
I'm a classics major myself, studying ancient Rome and Greece. I think at least some algebra is very important. It teaches symbolic thought and how to find things which, though different, are functionally equivalent.
Mind, I think learning Latin and Greek would be highly beneficial as well, but I don't hold out much hope of that happening. I have found the experience incredibly enriching, and it has done a great deal to improve my grammar.
I think that people need both art and science. They fill different niches, if one is left out, you get a lopsided human.
David Ed., C. P. S. E, you moron. Should you ever post an intellegent comment on this blog I shall be quite astonished.
And David, if I had a bullshit degree such as a masters in
education, I certainly would not go around advertising it
Some idiot didn't just write he/ she uses algebra to figure out gas money right?
@sid
Yawn, still hitting way below the Mendoza line in terms of intelligence and witty repartee, eh?
@sid - wow, don't like to be pointed out how wrong you are? No even one iota of information or retort other than pedantic insults? I'm so disappointed.
I have to wonder if that was the real Sid.
I note that the name doesn't have initial caps, and don't recall seeing that in the past. I'd also expect Sid to come up with something like "C P S E F G H I J K" iif he was going to make some of someone's degree (like he has room to talk), because such things are his style.
But the biggest thing that makes me wonder is that, while I have seen Sid hang around after he has been made to look like the idiot he is, I have never seen anybody so completely and totally spanked has Sid has been in this thread even come back to the same forum, much less the same page of that forum.
Of course, I could be wrong. He could just be that stupid *and* drunk.
@ Johnny: I noticed the same differences with what are purported to be Offal's posts. The content, as well, just seems "off' to me. I suspect someone is posting under his 'nym.
Such things have happened before. I remember when someone was impersonating Little Augie; the impostor's posts were easy to identify with a little experience, as they were significantly less vile than the genuine article.
I would urge anyone, however, who thinks that impersonating even vile and stupid commenters is a positive or justified action, to PLEASE STOP. We have facts and logic on our side; we don't need to stoop to depriving even idiots of their voices.
Johnny, you should seek help for your delusions. And "Wishing you were on Mars" isn't a location.
@ Offal: Are you confirming that you are the real sid offit...?
Either something has happened to Mr. Schecter, or this is an imposter.
I dunno, "Should you ever post an intellegent comment on this blog I shall be quite astonished" sounds like precisely the sort of mishmash he'd produce if he were trying to simultaneously try to get the use of 'shall' and the subjunctive correct.
Chris, it's really me. Capitalization failure was due to my using an iPad.
(I'll also note Eric Partridge on the general subject: "Conditional clauses have always caused trouble to the semi-educated and the demi-reflective; to the illiterate they give no trouble at all.")
That's disappointing Sid, I had hoped you would add something at least somewhat constructive, but instead we get nothing but childish insults. You certainly are slipping.
Hey, look, Sid's back!
Care to respond to my earlier comments?
Specifically, how do you expect parents to properly evaluate scientific evidence to make an informed vaccine decision if they do not understand algebra?
Adam, give me an example of how I would use algebra when deciding to get a flu shot this month. I'm sure you'll be getting one. Which equation did you apply to which question to make that decision?
Sid, I've already done that in my comments above.
When getting a flu shot, one might want to consider the local flu incidence. an understanding of basic high-school algebra is necessary to understand how incidence is calculated.
Again, I ask if you are really arguing either that:
(a) understanding incidence rates is not important to the vaccine decision or
(b) you do not need to understand basic algebra to understand how incidence rates are calculated?
As a reminder, you asked very clearly for
To which I responded with wiki's definition of incidence:
Do you agree or disagree that this is a specific algebraic equation pertaining to vaccination?
Mr. Schecter:
Here you go. Knock yourself out.
You're not answering my question. Let's assume incidence is important. So, what is the incidence of flu where you live now? What is it expected to be this flu season. How does that factor into your decision? How reliable are the predictions.? Would you get the vaccine even if you could not answer any of these questions?
C'mon, Sid, do it in your attempted British accent.
Sid, you're being obtuse. I doubt you are arguing in good faith.
I'll give you a personal example though, because why not. I live in Seattle. Recently it came to my attention that I am up for a Tdap booster. I don't love getting shots, especially ones that make your arm sore like I know the Tdap can. However, I did some research and found the following report on WA's Department of Health site (pdf link):
http://www.doh.wa.gov/Portals/1/Documents/Pubs/348-254-PertussisUpdate…
I looked over the data extensively. There are at minimum 5 pieces of data in that document that require a basic understanding of algebra to understand properly. This includes the graph of pertussis incidence on the last page. After reading this document, I went and got my Tdap the next day.
So that brings us back to you, Sid. I have 2 questions. Is the information in this document valuable to parents making a decision regarding pertussis vaccination, whatever that decision may be? Is an understanding of basic algebra necessary to understand the facts presented in this document?
LOL - Sid, you asked a question, got the answer, didn't like it, so now you're going into spin mode....again, very disappointing.
Again, sid batting way below the Mendoza line in terms of intelligent thought, which is utterly not surprising.
I shall read it and respond, Adam.
I think Sid is stymied by the fact that Algebra is a lot more prevalent than he realized, hence the back-sliding and "read between the lines - WHY DO I NEED MATH, BIG GUVMENT BAD!!!!"
I've got 50 quatloos sayin' this fresh error wasn't intended as irony.
I'm in California and we had a similar outbreak here in 2010. All the incidence data tells us is if we're at an elevated risk at a certain point in time. If I were worried about pertussis I'd get the shot regardless of what the data said because the shot would last over a time frame featuring varying incidence rates. But since pertussis is generally mild in adults, I'll take my chance with the illness while at the same time building a more long lasting immunity. As to algebra, I don't know how deeply one must delve into it to understand that an outbreak is on going and that rates per 100,000 are elevated.
If I'm missing something walk me through your process and tell me which equation and which figures you used that provided more insight.
@sid - actually, you asked for what algebraic equation would relate to vaccines. You got your answer, several in fact, showing where a knowledge of algebra is necessary to understand the information - so your comment above is off-track and not related to your original question.
Mr. Schecter:
So you are cool with both coughing your lungs out for three months, and the possibility of passing it on to an infant. And you actually think you'll get long lasting immunity? Good luck with that, because as a bacterial infection the immunity can disappear in just four years:
Duration of immunity against pertussis after natural infection or vaccination.
Pediatr Infect Dis J. 2005 May;24(5 Suppl):S58-61.
Also, remember, if you survive tetanus or diphtheria, there is absolutely no immunity. Just like if you get a strep infection. Bacteria just happen to have a nasty habit of being able to not give long immunity. It seems to have something to do with being much more complicated that viruses.
And yes, tetanus is fairly rare, but it does exist in the environment. And it may not be long before your anti-vax friends brings back diphtheria.
What denotation wouldst thou give to this "time" that you speak of, Sid, that another might be measureth against it?
("Ye"?)
Sid, how can you draw this conclusion without an understanding of algebra? I think your disagreement stems from a misunderstanding of what algebra is. How would you define a 'basic understanding of algebra'?
Here's another example, this time from VaxTruth (yes, I know, but it's illustrative here). This is from the VaxTruth page titled "The Flu Vaccine–What Your Doctor Won’t Tell You (Or Probably Doesn’t Even Know)"
Is VaxTruth assuming a basic understanding of algebra in its reader, Sid? Would VaxTruth's authors agree that algebraic calculation of metal concentrations is useful for parents to understand?
Is it maybe possible that you took a position in this thread to be contrary, but refuse to admit when you're shown to be incorrect?
Admitting your own error is not a weakness, Sid.
@Narad
...should get kicked in the teeth, I shall not lift a finger.
Correction
@Narad
…should you get kicked in the teeth, I shall not lift a finger.
Again, so disappointing Sid.....
It's just the original error over again, Sid. Not only are you popping from the subjunctive to the indicative, you're getting the subjunctive wrong in the first place.
@Adam
Sid, how can you draw this conclusion without an understanding of algebra?
So simply knowing that an epidemic is ongoing doesn't tell me I'm at an elevated risk? And knowing cases per 100K this year as opposed to a normal year has no meaning? Besides incidence is irrelevant if the illness causes no worry to the person considering a shot.
As to the mercury example, algebra can be useful to some but I've not found it to be relevant. I'm quite comfortable in my rejection of the .
Finally, you still haven't shared your specific though process with us. Did you even have one. Not being able to support your assertions IS a weakness.
@Chris
coughing up my lungs for three months? When does that happen? Give me a link saying that's likely to happen. And the latest pertussis immunity study show 30 year to lifetime protection. Funny how you guys always miss that one
Sid, I'm disappointed that once again you've decided to run away rather than owning up to what you've written here.
How, in the future, can you expect other commenters here to respond to your comments and questions given that you are prone to behaving in such a manner?
Narad, is English your second language?
This says a lot more about you than it does about algebra. Again, what is your definition of algebra?
Adam, why so difficult to tell us your thought process in detail? It's like pulling teeth with you. How did you specifically use algebra before you got your booster.
@Chris, you are quite wrong about the immunity from diphtheria. See Microbiology for Physiotherapy Students
By B S Nagoba, Basv Raj Nagoba P86 - Available doing a Google book search
@Silly Sid: I had pertussis as an adult. Obviously it didn't kill me, but I certainly could have well done without coughing until I was breathless after speaking 2 words, coughing until I vomited, inability to sleep for months without drinking cough syrup with codeine like it was water, and the mild case of reactive airway disease I've had ever since.
And, since the disease antibodies don't last much longer, if at all longer, than the disease, I'll happily get vaccinated for it as often as possible. You can enjoy pertussis. I would rather not ever have it again.
I'm amazed that anyone could try to pick up this affectation and be so incredibly dumb about it. Would you like a version of that sentence that is correct, Sid? Here: "Were you to be kicked in the teeth, I would not lift a finger." Simple. "Should you to be" is wrong in terms of person, Bullethead. Switching to the indicative halfway through is even more wrong. Expressions of resolve and intention are also not simple futurity, so the second invocation of 'shall' is about as bad as the first.
As soon as you provide me with your definition of 'a basic understanding of algebra,' i'd be happy to outline my thought process for you. Otherwise, how would I be able to explain how my thought process fit your definition?
I think we have reached an impasse, Adam. Should you decide to move forward, I shall be quite happy to continue the debate.
It's not an 'impasse'. You asked me
How am I supposed to answer this if i don't know what your definition of algebra is?
I've been very charitable with you. I've answered your questions respectfully and provided links that demonstrate my points. You've done neither of these things. You refuse to even define a term upon which your argument is based. How do you expect to convince anybody of anything if you continue to behave this way?
Sh*tty F*ckwit said:
David Ed., C. P. S. E, you moron. Should you ever post an intellegent comment on this blog I shall be quite astonished.
sid offit
12:05 am
and
And David, if I had a bullshit degree such as a masters in
education, I certainly would not go around advertising it
OMFG! :P
Total ad hominem.... why? Because he's too stupid to come up with anything sensible.
Pity that he doesn't get that my M. Ed. is in the psychology of teaching, learning and development, isn't it? And that my undergraduate studies included a substantial mathematical content, which enabled me to do the remedial tutoring I used to do. But then... Sh*tty Offal doesn't get much, does he? I'm glad I'm not him .....
comment in moderation about the anus californicum specimen that keeps farting on here ...
Mr. Schecter:
Give me a citation like I gave you. That page did not even mention pertussis, and was not a citation. I will admit to being wrong about diphtheria, but not on strep and tetanus.
And because you are too lazy to look up the citation I gave you, it says: "infection-acquired immunity against pertussis disease wanes after 4-20 years."
Here is another citation, and it says "A major challenge for pertussis control is that neither natural infection nor immunization induce life-long immunity against subsequent infection."
Narad, let me help you.
Should you ever post an intellegent comment on this blog I shall be quite astonished.
Should = if [condition]
(then)
Shall = will [consequence]
If you ever post an intellegent comment on this blog I will be quite astonished.
"@Chris, you are quite wrong about the immunity from diphtheria. See Microbiology for Physiotherapy Students
By B S Nagoba, Basv Raj Nagoba P86 – Available doing a Google book search"
C I think we would rather stick with the CDC Case Surveillance Manual for diphtheria, Offal:
http://www.cdc.gov/Vaccines/pubs/surv-manual/chpt01-dip.html
"Diphtheria remains endemic in many parts of the developing world, including some countries of the Caribbean and Latin America, Eastern Europe, Southeast Asia, and Africa. In the 1990s, a large epidemic of diphtheria occurred in the former Soviet Union where diphtheria had previously been well controlled and this renewed interest in the factors associated with persistent circulation of toxigenic C. diphtheriae.[10,11] During the past decade, many developing countries have achieved high childhood immunization coverage with DTP/DTaP vaccine resulting in significant reduction in diphtheria incidence.[12] However, sporadic cases and outbreaks still occur among population subgroups.[10,12] A feature of these outbreaks is that the majority of cases have occurred among adolescents and adults instead of children. Many of these adolescents and adults had not received routine childhood vaccination or booster doses of diphtheria toxoid. Rarely, outbreaks occur in well-vaccinated populations with intense exposure to toxigenic C. diphtheriae, but disease is usually mild and with fewer complications and no fatalities.[13]"
I don't know. Offal's posts smell suspiciously like those posted by The *SFB* Thingy Troll.
http://www.ncbi.nlm.nih.gov/pubmed/19876392
Our results support a period of natural immunity that is, on average, long-lasting (at least 30 years) but inherently variable.
Can't wait to hear what M. Ed., C. P. S. E. has to say.
Offal's post still smells like the *SFB* Troll's posts.
No, Sid. If you want to play at this pretension (which I highly recommend, as it makes you look like an utter buffoon), "should" does not accept the second person.
Mr. Schecter the abstract said " Our results support a period of natural immunity that is, on average, long-lasting (at least 30 years) but inherently variable."
Do you notice the words "variable" and "average." Those are words used in algebra, and I see you do not quite understand what they mean. There was lots of math in that paper, and I sincerely doubt you understood any of it. Not everyone gets the long term natural immunity, it seems that some folks the immunity can disappear quite quickly. Which is noted on that paper in Figure 6, notice where the line on x-axis starts.
As the one paper I cited (and it includes several studies, not just one) says about a particular set of cases: " A prospective cohort study in the Netherlands documented B. pertussis infection clinically and by laboratory techniques in both the first and reinfection episode in 4 children.7 The second episodes of pertussis were milder than first infections and may not have been diagnosed outside of a research setting. This study provided well-documented evidence that the duration of infection-acquired immunity in children may be as short as 3.5 years."
So, yes, that was a small study. So there was another mentioned in the same paragraph: "A study in Senegal of 8419 children documented 2 episodes of confirmed symptomatic pertussis in 137 unvaccinated children (0.02% of 6131 children) and 73 previously vaccinated children (0.03% of 2288 children).16 The mean time between the first and second infections was 7.1 years [95% confidence interval (95% CI), 6.6-7.6)] in the unvaccinated children and 5.1 years (95% CI 4.5-5.7) in the previously vaccinated children."
“should” does not accept the second person
Really
http://www.macmillandictionary.com/dictionary/british/should
used after 'if' or instead of 'if' for describing a situation that may possibly happen
Should you need help, do not hesitate to call me.
AdamG,
I wonder if it was poor algebra skills that led to VaxTruth writing:
Of course I feel compelled to give the true figures. According to the FDA the mean amount of methylmercury found in light canned tuna between 1990 and 2010 was 12.8 micrograms per 100 grams (approximately 4 ounces) and the maximum recorded was 88.9 micrograms per 100 grams.
For the mathematically minded, the table in the link I provide gives parts per million, which is the same as milligrams per kilogram, or micrograms per gram, 0.128 ppm is the same as 12.8 µg/100g, 0.889 ppm is the same as 88.9 µg/100g, and an ounce is 28 grams.
So according to my calculations (assuming I haven't made an error) the average amount of methylmercury in light tuna was 43 micrograms per 12 ounces, with a maximum of 299 micrograms per 12 ounces. VaxTruth are, not surprisingly, way off.
Yet again, Sid runs away from owning up to his actions. I'll continue to play, though, Sid, because I enjoy batting you around and because this thread is an excellent example of your debate non-tactics.
Since you can't provide a single definition of algebra, I'll help you out. Each state has its own requirements for Algebra I competency, but let's just consider my home state of Washington's (pdf link):
http://www.bsd405.org/portals/0/curriculum/MSPMath/one%20page%20quick%2…
When making my decision regarding the Tdap booster, I used the following concepts:
And finally,
A8E Read & interpret graphs
So, Sid, ball's in your court. I've played your game. There it is, right in the state standard for Algebra I. Part of learning Algebra is learning to read and interpret graphs.
Now, I'll ask again. Clearly the ability to read and interpret graphs is necessary for understanding the evidence regarding the vaccine decision. Is it maybe possible that you took a position in this thread to be contrary, but refuse to admit when you’re shown to be incorrect?
Sid, as you are the one trying to hypercorrect, descriptivism gets you nowhere. "Should" in this example is nothing more nor less than a solecism for "if." Moreover, the (here, hortatory) subjunctive isn't broken, as in your own monstrosities.
Adam, I trying my best here. Anyway, you almost answered my question. But you don't say how you used exponential functions for example. I hate to keep asking but what did your analysis of the data tell you? How did that affect your decision? So you feel you need algebra to decide. I don't. Are you saying the only way to make a decision is your way. Then I must be making a mistake no vaccinating. Tell me what my mistake is. What are the pieces of information I need to make the right choice.
@Chris
Yes, 4 people is quite a small "study." I noticed several studies (20%) found near life long immunity. And one 20 years. I'll have to check why they rejected the studies of near lifelong immunity capping protection at 20 years
It basically shows that immunity can wane in a very short time. And I notice you are ignoring the larger study from Senegal.
This part of the data points near the origin of Figure 6 in the paper you posted. Notice that line did not start after "10."
Sid, you're completely dodging the question, and everyone here can see it. I am not going to explain to you in great detail how exponential curves relate to that document when you can't even be bothered to define what algebra is. I am not entering into a debate with you about whether or not to vaccinate. That wasn't my point. My point is that if you truly want people to make that decision for themselves, they need at minimum an understanding of how to read and interpret graphs. Being able to read and interpret graphs is a core component of high school algebra curricula.
How did you personally come to this decision, Sid? How can I be sure that it did not involve an understanding of basic algebra, given that you said earlier you have taken algebra and even help your daughter with it?
Sid is using some form of this equation. "Risk to myself from vaccination" is X. If X > 0, then the answer is "no."
Mind you, I'm an English major who got a C in algebra and a D- in geometry. It drives my sister crazy when I do simple math by counting on my fingers.
http://calculuscourse.maa.org/sample/Chapter5/Projects/SIR%20Model/SIR7…
Cripes Sid, this is why your blog is so vapid.
Three hints, Sid:
1) You asked for any algebraic equation relevant to vaccines. Receiving one, and then asking for one specific equation and for all the variables to be plugged in for you, is moving the goalposts, a sign of failure.
2) What you are doing now is essentially the famous creationist "god of the gaps" fallacy, applied to mathematics. It does not fool anyone, except those who are so desperate that, like you, they will sprinkle sugar on the **** of failure and chomp down on it pretending it's the brownie of success.
3) Merely being stubborn in abject failure does not constitute an "impasse." There is no "impasse" between those who recognize The Protocols of the Elders of Zion as the plagiarized racist fiction that it is and those who stubbornly cling to the belief that it is authentic evidence for their anti-Semitic paranoia (or am I overestimating you, Sid, by guessing that you are reality-based enough to be in the first camp?)
Allow me to speculate a little about how I think anti-vaxxers might be cogitating:
I will use hugely rounded numbers ( you may substitute "small, medium, large", if you like). SBM/ vaccine advocates postulate that a small risk is associated with vaccines ( 1 in a million) but that the illness itself would have serious consequences about 1 in a thousand times ( medium risk). So, easily we accept the smaller risk ( i.e. vaccines)
Here is where anti-vaxxers depart from commonality of thought with the SBMers: they have been led to believe that autism is caused by vaccines AND that autism occurs about 1 in 100 children ( large risk).Thus they believe that vaccines 'damage' is 1 in 100 ( plus the 1 in 1 million we accept). This is obviously a much greater risk than the medium risk of the illness itself: they cannot accept the large risk of vaccines as they see it.
Why we cannot get through to them is because that 1 in 100 risk is inscribed deeply in their souls as an article of faith. Reasoning and mathematics will not put a dent in that because it has nothing to do with reasoning: it is an emotional reaction to figures ( large risk) not based in reality but on spurious research and propaganda.
AdamG:
"When making my decision regarding the Tdap booster, I used the following concepts:
A1E Exponential functions
A3:Function Characteristics
A3A Relations, functions, domain, range, roots, inde/dependent variables.
A3B Representations: symbolic, graph, table, words, connections between
A6: Data and Distributions
A6A Use summary statistics, compare data sets
A6B Make valid inferences based on data
And finally,
A8E Read & interpret graphs"
This, for which I thank you, underpins what I said earlier in the thread about algebra being the basis for understanding statistical concepts - which are all written in algebraic form. The impression I get is that your state is using the algebra stuff to provide the basis for a good understanding of symbolic manipulation in things like statistics and demonstrate statistics as a very socially important application of algebra skills. A bloody good aim, as far as I am concerned. And - absolutely - those are the key algebra skills I would expect people to need in order to understand the data in order to make a sensible decision based on that data.
Which is why I feel sorry for any offspring that Sid Offitshead might have, given that he has an obvious lack of these very important skills.
algebra can be useful to some but I’ve not found it to be relevant.
Ah, so what Sid is seeking is an application of algebra that is relevant to him. Alles klar.
Novalox, thanks so much for introducing me to the Mendoza Line -- a wonderfully handy image.
Anecdote:
While I had a very talented teacher for Algebra I and II in high school, I made it through only by rote memory and brute force. I hated it.
Six years later, I took an algebra review course before attempting the GREs (Graduate Record Exam) and the GMAT (Graduate Management Admissions Test). To my great surprise, I thoroughly enjoyed the course and did very well, and went on to take undergraduate classes in Algebra I and II while waiting to start my graduate program.
Surmise: for some reason, my brain hadn't matured enough at 15 and 16 to think algebraically easily, and by 22 it had.
Out here in California, the University of California has a series of coursework requirements, commonly known as the a-g requirements. Here's what UC says about the math requirement (3 years minimum; 4 years encouraged):
How can one become "fluent" without algebra? I submit it cannot be done.
It seems pretty obvious that thinking algebraically is necessary to correctly understand the world, which explains why Sid, who wishes to misunderstand it instead, wants to keep algebra at arms' length.
Perhaps Sid would like to tell me how I figured these stats out without algebra: http://justthevax.blogspot.com/2012/08/washington-state-pertussis-outbr…
I guess if anti-vaxxers could actually think, they wouldn't be anti-vaxxers.
I imagine group theory represents frank restraint of trade in Sid's mind. Think of the Rubik's Freedom Cubes!
Science Mom, do you use algebra when cleaning out the rat cages?
Mr. Schecter, have you figured out when the line starts on the x-axis on Figure 6 of the paper you referenced?
Yes Liz , that's why kids are deeply in debt after graduating college: they spend precious years studying irrelevant concepts they shall never use. Time to cut off taxpayer money from the university system and let these self indulgent concepts die a natural and well deserved death.
So neither you nor your daughter know how to read a graph. A failure we have witnessed here from you repeatedly. We can all now assume she does not have the qualifications to apply to the University of California, or any other real college. Because most serious centers of higher education actually value math skills.
My daughter's acceptance in the university she starts at soon would have been rescinded if she did not take a math heavy course her senior year of high school, even though she had algebra in the eighth grade. Her last high school math course was pre-calculus, but that was her junior year. Her last year of high school was at a community college (there is a similar program in California), where she completed the math heavy course for the university by taking statistics.
Really, I am surprised that someone who does real estate speculation like yourself does not understand the concepts used in compound interest. That is just bad business, and your lack of basic math background should be enough to keep anyone from ever engaging you in any business deal.
Here it is: Robert Schecter does not know how to do basic algebra, so anyone who wants to deal with his commercial real estate business should know this.
I have no commercial real estate business. I invest in the commodity and equity markets. I have nothing against math or algebra. It is simply not essential for most people and should not be forced on kids and students. I don't think formal coursework in algebra is necessary to read a graph. My daughter and I have both taken and passed algebra, so if we can't read graphs it simply means even if you force a child to take a subject you can't force them to retain the information contained in that class. I wish your daughter much success in college and afterward and hope she gets some use out of the math courses she attends.
@Liz Ditz
You are welcome.
Guess from his comments, he's trying to surpass the titanium sombrero.
@sid
And we see why you had to go to fire school. Thank you for that piece of unabashed stupidity.
But yeah, someone dealing with commercial real estate who doesn't value the use of basic algebra isn't anyone I, nor anyone with some common sense, would want to deal with.
Okay, my error. You just can't read a basic graphs.
My daughter will be majoring in linguistics by taking Swedish. This is her third non-native language after Japanese and French. Since she will be going for a degree in the psychology of language, she will be using statistics, and that includes the ability of reading a graph. Because one of the pre=requisites to take a basic statistics class is to understand the basic equation of a line: y = mx + b (m = slope, and b = y-intercept).
Which seems to be a skill that handicaps your family. You should work on that. Because it is making you look like a fool on this blog.
Oh this is just precious. Of course it has to be someone else's fault you and your special snowflake can't navigate basic graphs. And your insults well, aren't. Try a bit of honesty Sid, for starters concede that you made a gross misstatement about the utility of algebra and how it can relate to vaccines. Or not and no one will be shocked.
pre=requisites should be prerequisites
Good luck to those who apply to university who actually forget the basics!
Forgetting useless information isn't a bug, it's a feature.
@sid
Yawn, another ill-inspired attempt at insult.
Do try again, you amuse me.
Sid, do I really need to re-paste the state algebra 1 standard that includes 'reading and interpreting graphs?' You may not think that formal coursework is necessary, but every state standard I've looked up disagrees with you.
Where did you learn to read a graph?
As compared with not studying irrelevant concepts so that they can later be comically misapplied?
Sid Offit 1:04 am: Science Mom, do you use algebra when cleaning out the rat cages?
LoL .. Arsehole!
Sid Offit 1:45am: My daughter and I have both taken and passed algebra, so if we can’t
read graphs it simply means even if you force a child to take a subject you can’t force them
to retain the information contained in that class.
No, it means either that you are both too lazy to remember important stuff, or that you bribed
the living crap out of the external assessor(s) involved (and given the amount of money that
would be involved in the second of these options, I'm going to bet on the first one!).
Chris 1:56am: Since she will be going for a degree in the psychology of language, she
will be using statistics, and that includes the ability of reading a graph. Because one of the
prerequisites to take a basic statistics class is to understand the basic equation of a line:
y = mx + b (m = slope, and b = y-intercept).
Absolutely, Chris! The first thing one learns how to solve in basic algebra is the linear equation,
which is the basis of linear regression work in statistical analysis. I work with my ex-missus on
training days to teach people about testing methods and data analysis for checking who it is
really that's writing in FC stuff. And the most recent of these was given to a group of
mostly speech therapists, whose training in Finland involves studying for a master's degree.
During this degree course they study many things, including a lot of psychology (it actually
forms a very substantial minor subject in their transcripts), and an entire subsidiary in statistics
for the behavioural sciences. And yet they cannot get their heads around the science that
demonstrates beyond all doubt that FC just doesn't work at all. So much for the usefulness of
Offishead's tactic/strategy/anti--intellectualism of forgetting what he deems to be useless stuff.
As has been repeatedly stated here, were he to actually be bothered to retain that stuff and
use it to inform his decision-making, he'd not find much of any appeal in the anti-vax stupidity
that's going on just now. His attempts at rebuttal of this point are less than jokes, and show
more about his own personality failings than any constitutional inability to comprehend
mathematical concepts (such as we find in both dyslexia and dyscalculia). Offishead simply
does not want to learn anything that goes against his preconceived and ill-conceived
idea of how the universe works, and resists any information that would demonstrate that he is
just plain wrong about something. It's definitely a personality flaw.
Chris 1:56am: Which seems to be a skill that handicaps your family. You should work on that.
Because it is making you look like a fool on this blog.
Well, the lack of which skill is the handicapping issue in his family, really. But your point
remains valid and accurate.
Sh*t Offishead 2:08am: Forgetting useless information isn’t a bug, it’s a feature.
Except that information that you claim is useless is more useful that you'd wish it to be. See
above note about your personality flaw. See, in my master's degree in education, we learned
about learning difficulties and how to differentiate between those issues and people simply
being too stupid to bother learning. We all know which one of these issues handicaps you.
Same imbecile 1:45am: I don’t think formal coursework in algebra is necessary to read a
graph
Thankfully, you don't get to decide this stuff. People who understand this education stuff better
than you do get to decide. I feel sad for your family. They must miss out on so much.
Wow, Sid has degenerated into simple insults now - and drive-by ones at that. He must be getting frustrated that the country hasn't bowed down to the glory of his libertarian politics....
I'm curious to know if there are any subjects that Sid feels should be compulsory: if so, why and if not, why not?
Are there any subjects at all that every kid must learn?
Forgetting useless information isn’t a bug, it’s a feature.
I never understood why people go to the trouble of forgetting things. It seems such a waste of time. You only have to re-learn them later.
Why don't you try spelling out your syllogism, Sid? I think we'd all find that real interesting. Here, I'll do most of it for you:
1. Algebra is not necessary to clean out rat cages.
2. ?
3. Therefore, algebra is unnecessary in almost every adult profession.
Please fill in 2. for us, Sid, please do. I'm sure we'll all just be fascinated by what you come up with. "There are few adult professions that require any other skill but the cleaning of rat cages"? Sheds new light on the value of a fire science degree.
I have something in common with Sid: investing. Not that it was my idea: it was foisted upon me and I got stuck ( but NO commodities, ever)- now I love it. However, I was- like quite a few other folks in my family- recognised to have abilities in mathematics. I never had any problems, took advanced courses including applications to economics/ psychology graduate work. All of this has come in handy.
What I can't wrap my head around is how he can comprehend the arcane and mysterious indices and valuations proclaimed by the financial oracles ( praise them!) about the economy, prices, trends and other facets of reality that often land upon our ( metaphorical) doorsteps saying, " Guess what's bad news today?" Nearly 4 years ago, I recall waking up nervously every day to see what the libor was doing. Or vix. It was a frightening time.
How anyone can comprehend and deal with this stuff without a decent mathematical background is beyond me. How can you understand someone else's analyses and apply them to your own interests? And graphs? Turn on any financial television channel, what do you see? Go to any website that provides information, what's there? Endless.
And let's be entirely frank: people who are skilled in this area earn more than those who aren't . Engineering, computer science, medicine, industry, research, banking, trade,...
Mr. Schecter's inability to read a graph does explain his total confusion over Figure 6 in a paper he posted. So, yes, it is a "bug" to forget simple useful things like how to read a graph.
@ Denice:
I suspect he's one of the "investors" whose strategy is just "pile into whatever did well last week." Doesn't bother to actually understand anything.
Chris
On the contrary, it is a feature for a contrarian or a libertarian as is any other form of ignorance.
@ Beamup:
Oh, I see, he attended the Last Week's School of Economics ( LWSE). Not that other place.
Writes Sid Potatohead, exhibiting reading comprehension fail
What I copypasta'd was the requirements for applying to the UC system.
Oops, Siddo, Grammar fail. (I don't have Narad's facility with describing the error, though, which is reminding me to brush up.)
The usual libertarian nonsense. The US's lack of investment in education will be hampering our economic growth for decades.
I wonder if Sid Potatohead can tell us what percent of the UC's budget is comes directly from state revenues (that is, taxes). I doubt it. I was surprised by the figure myself.
sid offit @2:08 am Aug 8
Declaring information you’ve forgotten is useless is an excuse.
@ Liz :
* they will never use* ( "shall" with "they" is only for sarcasm)
One of the most hilarious memes I have encountered in Woo-topia-
" the educational systemn is so poor/ it produces people who can't think" ( therefore customers)
This is Dunning-Kruger- tainted meta-cognition on a societal level: an under/ barely-educated woo-meister believes his level of education is superior to the average person's as well as that of doctors, biologists, educators et al based on his usual critiques of science.
Executive dys-function, they has it.
*shivers*
bloody hell - it's cold and empty in here..... and the lights don't bloody work!!!!!
M. Ed., C. P. S. E.
If that were my picture, I would have gone with the generic avatar.
@The Ditz:
The US’s lack of investment in education will be hampering our economic growth for decades.
Silly, unsubstantiated nonsense>
M. Ed., C. P. S. E.
too lazy to remember important stuff
Too smart to retain irrelevant stuff
FC
I’m curious to know if there are any subjects that Sid feels should be compulsory: if so, why and if not, why not?
Are there any subjects at all that every kid must learn?
It is a parents decision
Denice Walter
As I said before, a year or two of algebra is not required to read a graph or understand a balance sheet
Remember, this is the same Sid who, despite having an education in "fire science", forgot how fire worked for the sake of an argument in favor of privatized fire departments.
More on topic:
What if a parent decides not to educate their daughter because they consider females incapable of learning such things?
@Sid - given that most countries are pouring money into their educational systems, been using a year-round model highlighting the math and sciences, and perform both academically and economically better than our country, I'd say your opinion is about as relevant as the the crap on my shoe.
Parents are free to home-school, if they wish. I, for one, prefer a world in which we challenge our children with advanced subjects at the earliest possible age - because other countries are most certainly doing it, and if you want to maintain a technology-based economy, I'd prefer that we continue to develop it on our own & not become as reliant on China for IP as we have for manufacturing.
If you had had a relevant argument to make, you would not have bothered with an irrelevant attack on someone's appearance.
So what about that syllogism, Sid? Please provide the missing premise which makes your argument non-irrelevant, if you can.
Now THIS is "silly, unsubstantiated nonsense." Reading and interpreting graphs is part of the state standard of algebra 1. I've already demonstrated that to you.
Where did you learn to read and interpret graphs, Sid?
So what about that syllogism, Sid? Please provide the missing premise which makes your argument non-irrelevant, if you can.
I wouldn't be holding my breath for him to even know what a syllogism let alone fill in the blank. This is a fellow who has to resort to silly insults and name-calling in lieu of any evidence. But while we are on the subject and I'm feeling cheeky, Sid I've seen a picture of you; you are not someone who should be making recommendations for personal photo avatars.
Offal...did you really say this?
"Yes Liz , that’s why kids are deeply in debt after graduating college: they spend precious years studying irrelevant concepts they shall never use. Time to cut off taxpayer money from the university system and let these self indulgent concepts die a natural and well deserved death."
Excuse me Offal...aren't you a graduate of John Jay College...which is part of the CUNY system?
http://en.wikipedia.org/wiki/City_University_of_New_York
"CUNY is the third-largest university system in the United States, in terms of enrollment, behind the State University of New York (SUNY), and the California State University system. CUNY and SUNY are separate and independent university systems, although both are public institutions that receive funding from New York State. CUNY, however, is additionally funded by the City of New York."
So you got your *fire science degree* paid for by New York State and New York City taxpayers...then hightailed it out to California. So now you are bitching that some of your precious money is supporting the California State University system. What an ingrate you are.
About parents deciding what students need- rather than school systems, advisors, students themselves...
How does a parent know in advance in what areas a student might have interest or perhaps, hidden talents?
If kids are exposed to a liberal selection of subjects, there's more of a chance that they might find inspiration and even, their niche. What if your child wants to be a surgeon, software designer, translator or an architect, do you really think that their studies start suddenly when the enter higher education? Or is it more likely than their experiences in grammar school set the pathway for later work.
I am personally a mentor ( of sorts) to a young architect: she had to study science, mathematics ( lots), art history, design, beside liberal arts: she has had internships, practicums et al, worked in an art gallery and an architectural firm: she creates plans and 3d models.
And sometimes kids don't know what they want and need counselling. In a high tech world that will not magically revert back into an idyllic small town fantasy at the turn of the previous century, no one will be hurt by learning MORE rather than less mathematics/science. And as the world gets smaller, how wrong can it be to learn a foreign language: at the very least, it might help clean up grammar in your native one?
Sid,
You never bothered to answer my little word problem, suggest how to solve it without algebra, nor say it was irrelevant to the decision to immunize.
How about this one: someone with a contagious disease enters an area. People who catch this disease are asymptomatic but contagious for some number of days. In any given day, a person may com into contact with, say, 30-40 people. Assuming those people are not immune to the contagious disease, what is the expected progression of that disease throughout the population?
You know, seeing Sid here is making me realize that my D- in geometry isn't really all that bad.
@Denice Walter
How does a parent know in advance in what areas a student might have interest or perhaps, hidden talents?
Yes, in your utopia children are put into universal preschool at 2 months of age. So how could parents know anything about those children and their interests.
Expose children; don't force children.
@Mephistopheles O'Brien
I don't generally respond to gibberish.
Mephistopheles O'Brien is incapable of intelligent though
Mephistopheles O'Brien has a thought
That thought is unintelligent.
@dedicated lurker
How's that F in life making you feel?
@sid
Yawn, another half witted insult from the racist and idiot sid, how utterly predictable
Batting way below the Mendoza line again in terms of intelligence and logic as well as in insults, but then, what would I expect from a guy who had to go for a "fire science" degree.
If you keep striking out in terms of intelligent thought here, I guess you'll be aiming for that platinum sombrero in terms of intelligence, eh?
@ SidOffit:
Every firefighter needs to know basic algebra. Any less would make him a danger to himself and others. Fire science is a job where if you are not up to par with your math, you can get others killed, not to mention yourself.
http://firefightermath.org/
I don't see any reference in your comments that you are a firefighter, which is great. I doubt that you are from what I have read. But if you slipped through the cracks,, I suggest you get the hell out before you kill yourself or other people.
Sid Offit @August 8, 4:28 pm (my emphasis)
No, Sid, it’s not.
Ultimately, it’s the decision of the individual – in this case the child.
If you’re advocating restricting a child’s access to education you’re a bigger fool than I thought.
My beef with the notion of “do we need algebra?” is that I believe that when you set out to achieve a low standard is that’s what you get: achieving a low standard.
We can do better.
@novalox
Normally, I would not deign to address you, but the thread appears to be winding down and I require some entertainment.. What is your obsession with the Mendoza line. You repeat it incessantly.
Thanks for your input, Black-cat.
Most of those entering the fire academy have no recollection of algebra. One can take the test 10 or more years after graduation. As such relevant concepts would have to be taught or re-taught in the academy. Allow kids who dream of being firefighters take it in school and leave everyone else alone.
I took fire service hydraulics in college and unless you use it on a regular basis you forget it. When you get a high school grad who got a C in algebra you're basically starting from scratch. You think a lot of kids who took French in school remember any of it after the final exam?
@Chemmomo
Ultimately, it’s the decision of the individual – in this case the child.
Individual decision? Interesting concept coming from this blog. Yet you advocate forcing both school and algebra on a child. Seems contradictory. Since parents would likely be paying for the education (in a free society) after a certain age (and your correct here) a collaboration would have to occur. For example a parent may have the leverage to implement piano lessons but after a certain age parental desire may have to give way to a child's/young adult's resistance. It would be great if we could circumvent human nature / genetics and inculcate into our children an interest in that which we see value but that's not how the world works. There are a lot of interesting methods of education that could emerge if education were not such a top-down endeavor. Kids don't dislike learning. They like to read - if it appeals to them. Sadly due to the material presented kids learn to hate, rather than appreciate, both learning and reading.
Sid,
I understand you are on the Libertarian side of the political spectrum. I can understand advocating the Libertarian viewpoint for an educated and well informed population: that kind of population could probably succeed under self determination with fewer government regulations.
However, here you are now proudly proclaiming your own ignorance.
Could you explain to me how being ignorant goes along with advocating self determination?
Sid,
This is not about taking a language and forgetting it.
http://www.firehouse.com/news/10462630/san-francisco-firefighter-killed…
Here is an example of two firefighters that made a mistake. They should have known better but sometimes in EMS there is no second chance and you die.
They did not apply math to the situation and they are dead as a result.
Chemmomo, since there are an unlimited number of topics that may, at some point be useful, the entire population can be said to be ignorant of some discipline. I'd like to be able to survive a plane crash in the Amazon like the survivalists do on TV. But since such a scenario is unlikely to emerge , learning to deal with it would be a poor use of time and resources.
Sid, are you working in fire science?
I was a fire inspector with the FDNY for about 2 1/2 years. I moved to California ~22 years ago and now invest in the financial markets and write about the vaccination issue.
Sid, do you believe in educational standards at all?
Here’s the deal Sid: As a parent, it’s my obligation to give my child as much educational opportunity as my child desires by whatever means are appropriate. It’s not up to me to decide exactly what my child decides to study. My obligation as a parent is to provide the opportunity.
That, however, does not negate the need for educational standards for society – particularly for a society where we’re expected to maintain a certain level of self-determination. If we wish to continue living in a democracy, we need to provide our children with the tools to understand information. That does in fact include algebra.
My argument is (and always has been: you can go upthread and check) is that we need to challenge children to achieve more earlier, rather than making excuses for poor performance later.
As you said – children don’t dislike learning. What’s wrong with giving them the tools to do it, and incentive to try? Your dismissal of algebra is a dismissal of education in general. I said it before, and I’ll say it again: we can do better.
Your attempt to sidetrack into Amazon plane crashes (1:17 am) is a really lame diversionary tactic.
Seriously, Sid, what do you have against an educated population?
Sid,
So as a fire inspector, can you tell us whty these two men lost their lives. They should not have.
Chemmomo:
I am amazed, but not surprised, that Mr. Schecter is actually proud of his own ignorance.
@sid
Oh sid, your blatant insults and half-witted attempts at mockery are truly funny. I do like to poke at trolls, and you seem like good entertainment right now.
Please, do try a little harder before attempting such childish insults, and do try to attempt to actually engage in some actual intelligent conversation here without resorting to insults. It just makes you such an easy and target for me to laugh at and mock.
Sid, you may have worked as a fire inspector for FDNY 22 years ago but you are not one now. You may live in California but you are not working in the EMS as a fireman, paramedic or EMT.
Please do not ever pretend to be one of us. We work very hard and put our lives on the line and don't expectthanks. It really sucks to have idiots out there pretending to be us.
@Sid Offit:
So you say that you were a fire inspector. Explain to me the mistake that was made here, where the two firemen were killed.
Sid,
I'm still here. Why were these two men burned to death? What was the mistake?
Did it have to do with math? Can you answer this, Sid?
Sid, I'll give you a hint. It did have to do with fire science math and if they were thinking they would still be alive.
Sid Offal
In other words, you produce nothing, design nothing, create nothing, provide no useful services and write about a subject in which you are profoundly unqualified, possessing only the arrogance of ignorance. You are a useless f*cking parasite and a complete waste of air.
More of a pole in the plane, I'd say.
Sid, you are not one of us and how dare you pretend to be; you know nothing about us:
http://www.youtube.com/watch?v=jStc1jUIZt4
You are a horse's ass. You really are.
Sid Offit 4:18 pm: M. Ed., C. P. S. E., If that were my picture, I would have gone with the generic avatar.
If I were as ugly as you, I'd go with the generic avatar....
Fuckwit 4:28: Too smart to retain irrelevant stuff
No. Too stupid to retain useful stuff. Deal with it, fuckwit.
response to S(tup)id in moderation....
I really *doubt* the Offal worked as a NYFD "fire inspector" for 2.5 years.
As I recall I had to remind him about the Federal Life Safety Codes when he was complaining that his mother had to leave her bedroom during a fire drill...and the bedroom door was automatically locked behind her....when she was residing in a licensed elderly care facility. (And I did not have a *degree in fire safety* as Offal claims to have).
Several of my brother's colleagues (he retired from the NYCFD) were NYCFD Marshalls, who inspected the premises of the scenes of "suspicious" fires or where there were serious injuries of deaths attributed to these fires. They too, had also attained the rank of Lieutenant within the NYCFD after years as firefighters on the front lines.
@liady: I can research the records in the SFD but I need some names.... Not sure how to do it but I can find out.
never mind: this is just stupid. why would somebody claim to be something that they are not?
@ sid offit: You are indebted to the two firemen that died in San Francisco to give you life..... you need to get on your knees and bow....you fat asshole....how dare you claim to be a fireman.,,,you are not worthy,,,,,,
More of a pole in the plane, I’d say.
Narad's attempt to apply complex analysis to the political plane is all very well, but it implies that most of the occupants of that plane are at least partially imaginary.
I am informed that many of the daytime inhabitants of DC actually commute from outside the Beltway, which rules out the theory that they are quaternions.
@Sid Offit
August 8, 4:28 pm
"It is a parents decision"
Well, that's nice and definitive.
No seriously Sid: let's say you're homeschooling your children. What subjects would you consider absolutely necessary for their education?
I'm not asking whether or not all parents should follow this, I'm asking *you* what *you* think is absolutely necessary to *your own kids'* education.
Well, you've ever heard the saying "better to stay silent and be thought a fool than to open it and remove all doubt?"
Sid has a psychological defect of some kind that makes him believe entirely the opposite. He would rather say something that makes him look moronic, bigoted, or just outright vile than acknowledge that anyone he's arguing against has a point about anything. If he sees a photo of a young girl who has been scarred for life by a vaccine-preventable disease, he will say "Isn't she pretty" rather than acknowledge, like a compassionate human being, that the disease was obviously not "mild" for her and she has suffered harm from it. Moronic, bigoted, outright vile - somehow Sid thinks it's better to be all these things than to ever concede even the most blatantly obvious truth.
Blackcat, I can understand your ire...I work with first responders all the time and they are a great bunch of people.
Who in the great, spinning world would advocate for universal preschool at age 2 months? Isn't that an unfortunate economic necessity for some parents? Or a way to hold on to their current job? Do you really think that people do this because they *like* it? I think it's horrible.
Oh Sid, you miss my entire point! An ideal education would expose kids to a variety of subjects while they acquire the basics of language/ mathematics/ general information skills and then allow *their* choices to influence their later studies. In industrialised so-called western cultures, this is quite common for affluent students, even in governmentally sponsored schools.
And what does *force* mean? Did you *force* your daughter to speak English, use a fork or wear clothes? Or did you conform to societal standards in those areas? What is the difference? Because NOT having basic skills makes a person just as disadvantaged socially as one who doesn't use conventional eating utensils, wear clothes or speak the common language: an outsider without many prospects.
It takes a while for kids to learn that sometimes you have to do things that you don't like because they're necessary and have important consequences that occur over time.. Parents and teachers can guide them : it's called 'delay of gratification' and 'long term goals'- and yes, it becomes hip once you get the hang of it.
I often read health freedom advocates ( e.g. @ Natural News, PRN, AoA) who also skewer our elitist education, so I ask: read what some of my sister and fellow representatives of the orthodoxy write @ RI ( especially our most esteemed host) and then read the web woo-meisters' articles-
who would you rather your children sound like when they're adults?
-btw- learning foreign languages comes in very handy when you're a teenager abroad and want to meet the locals, eat and buy stuff... as I can personally vouch. Business travelers make use of it as well.
I have found through reading Alain's blog that LEARNING a foreign language, as opposed to sitting through classes in a foreign language with glazed over eyes, means the language stays with you even after decades of not using it. I can still read French. Algebra is the same way. Learn it, it stays with you. Everything you do in life that is based on algebra does not come with a sticky note that says "Algebra needed here." Reading graph is such a basic example
i learned algebra and use it often even with a job that is not science-based. I am one of those people who struggled for Bs and Cs in algebra and trig and calculus but easily got an A in geometry. I did take algebra I in eighth grade, not college. I had a hard time accepting that algebra is taught as a college course.
So as far as I see, the argument is that we should stop teaching kids difficult subjects like algebra in order to keep them from dropping out of school.
Of course if we're not going to actually be teaching them anything difficult--something they need time, instruction and effort to master--why is it that we're concerned they're dropping out?
Oooooh, Sid invested in the financial markets! That puts him at the innelekshal level of Donald Trump and the people who gave us deregulation and subprime loans! I just can't begin to tell you all how impressed I'm not.
I have no interest in living in a "democracy." I want to live in a free country. A country where on group cannot vote themselves the wealth of others.
Give me a break with the "society" nonsense. Society is people and children are in trust of their parents unless the negate that trust by egregious violations of that trust.
challenge children to achieve more earlier
There is a difference between challenge and force and the parents not the government are those who challenge
what do you have against an educated population?
What do you have against the renunciation of force against innocent people?
Militant Agnostic
you are a child. The allocation of resources is vitally important to an economy. Something the top-down planners in government are incapable of.
@creepy baglady
you do love your little licenses and certifications don't you
@black-cat
run, don't walk, to the nearest mental health institution
Denice Walter
I'll have to get back to you tomorrow.
Nonetheless, you seem to fail utterly when confronted with the free exchange of ideas. And it would really help if you could blockquote or something. I realize that inventing preposterous grammar stylings requires effort of some sort, especially when intended seriously, but still.
I agree. I've been slacking on the blockquoting on the new site.
No, Sid, you do not want to live in a free country; I think you've made it plain to everyone here that you want to live in a place where you are free to do as you please, and screw everybody else.
Try Somalia.
While I do not want to step on anybody's turf, I'll advance that it's more than that: I think Sid codes "free country" not just as absence of crude external hindrances (negative liberty), but as some sort of added lifting of internal ones. In short, the psychological diversion that negative liberty will somehow plop out positive liberty while it's at it.
Well, Sid's ignoring me. It's just as well I pre-drafted a reply because I suspected that he'd duck my point:
Sid, if you answer in some vague manner I'll simply consider a) you haven't thought about it and don't care to think about it, b) you're ducking the question because you don't want to admit that you might actually yes, teach them some sort of maths. Or reading. Or whatever.
My bet is that what you really mean is "I'll help my kid if they have a question, but I won't make them learn anything because that would take away their choices". It's a fair thing to want to give your kid options and allow them to pick their own path - but surely we can all agree that teaching a kid to read, write and calculate is necessary for *any* path they take?
Also, I say more to myself, why do I get the feeling that Sid is so totally of the "pull yourself up by your socks" deparment of thinking that he really just thinks education is a waste of time and that people would be better off learning whatever whenever they need it and with whatever resources they can find that doesn't cost them anything. (Ie. not a library I guess... that would use taxes. One wonders how anyone will get books... Oh yes, in Sid's world, no one is poor because free markets took care of that)
Sid's vision of the world is no more realistic than the old communist view of the world - both may look good on paper, but in practice, they ignore fundamental aspects of human nature & ultimately fail.
I mean, Somalia is a libertarian paradise - no government, no one telling you want to do & you can do whatever you like - oh, but that's always the caveat with Sid, it is okay until someone violates his rights, then it is perfectly fine for the government to get involved - but let's throw all of the "preventative & regulatory" crap out the window, right?
I mean, we wouldn't want to take steps to protect ourselves, we'll just wait until bad things start to happen, then we'll deal with it (but not until people have been injured or died, because we wouldn't want to interfere with the markets now, would we?).
As for education - we can easily see that a more educated population is a more successful population - advanced degrees lead to higher salaries, more job opportunities, and overall, a society that focuses on education is more successful overall & able to compete in the global marketplace.
Of course, Sid ignores the fact that the most dynamic economies in the world today, like China & the other South Asian nations, have highly effective and government run/supported educational systems with extremely rigorous standards.....Sid's goal would be to take us in the opposite direction & basically write off huge swaths of the US population (probably minorities - given his past posts) - which would lead to exactly the situation he doesn't want - larger numbers of people reliant on the government for support....anyone see the disconnect here?
Denice Walter:
Sid:
Typical Sid behavior. Whenever somebody makes a perfectly reasonable statement, replace it with an entirely ludicrous one.
" I want to live in a free country."
You're going to have to define exactly what you mean by "free country" here, I'm afraid. You can't possibly be speaking of a nation where no citizen is subject to any restrictions on their behavior whatsoever, nor has any obligations to their fellow citizens whatsoever, beyond what they themselves choose to embrace--can you?
Sid's desires are inchorent. He appears to be labouring under the illusion (delusion?) that freedom is, well, free. It most certainly isn't.
You can't guarantee the foundations of freedom, respect for rights to person, property, and transaction, without the ability to enforce them (that is, use coercion). Just examine what happens whenever there are breakdowns in social order and of enforcement of basic rights.
In addition, specifically with regards to the topic of this post, you can't maintain a free society in a socially and technologically sophisticated world unless a critical mass of the citizenry have a decent ability to communicate effectively, to think critically, and to understand the circumstances they find themselves in. As a foundation of other mathematics, algebra is essential to an informed citizenry. An ill-informed or un-informed (or, like Sid, deliberately ignorant) citizenry is liable to manipulation by demagogues, charlatans, scamsters, and would-be tyrants.
But because humans tend to be lazy, we can't assume that people will go out and become well-informed or develop the skills they need to succeed and to become citizens capable of advocating for their rights over and against the ambitions of others (whether as individuals, business or other private organizations, or government agencies).
Sid thinks he is a libertarian, but IMO the inevitable consequence of adopting his race-to-the-bottom preferences are either anarchy or authoritarianism.
Sid @ August 9, 11:27 pm
You’re still missing the point (your response is bolded)
Nobody’s talking about forcing children to do anything here. We’re talk about setting educational standards. No one is forced to graduate – if you don’t want to pass algebra, go ahead and drop out. Just don’t expect any school board to grant you a diploma if you haven’t learned the minimum knowledge that diploma represents. And lowering the standards for acquiring that diploma accomplished nothing.
Then there’s this response of yours (bolded again).
What on earth does that have to do with my question?
Chemmomo:
Aw, but Chemmomo, Mr, Schecter is a special little snowflake and doesn't wanna complete the minimum! He wants to take advantage of the herd immunity, clean water, roads, general police protection and all the other perks of living in a modern society without contributing.
I would love to see him try living in some of the places I have seen, and especially some that my brother has seen as an employee of the US State Department (where one house overseas came with a distillation apparatus because the tap water was literally full of crap).
@ Composer99:
I'd assert that Sid is in fact a totalitarian already. He thinks he should get to do anything he wants, but nobody else should be allowed to do anything he doesn't want them to do.
@JCG
That's almost exactly what Sid is advocating. It comes from a place of "you're not the boss of meeeeeeeee!" and is made holy by the chant "There are no rights but property rights and Ayn Rand is their prophet." Yes, it's naive to the point of childish. I know 5yos who have a better grasp of how the world works.
@Composer99
Beamup: I’d assert that Sid is in fact a totalitarian already. He thinks he should get to do anything he wants, but nobody else should be allowed to do anything he doesn’t want them to do.
No-no-no-no-noooooo! That's not a totalitarian.... that is a pillock!
If kids are exposed to a liberal selection of subjects
DW used the L word!!!
@ herr doktor bimler:
I actually said it twice! Why not? Say it loud, I'm L and proud! ( not *that* L- although where would ladies tennis and feminism be without them? and I am eternally grateful to them) I think Sid is reaching out to us because he realises that we're fun. I am expecting a response, which I was promised.
-btw-
While a person's appearance is totally irrelevant to the quality of their argument- someone has to say it, so I will.
David is good-looking ( and believe me , I know men). More importantly, he's smart and can swear better than anyone @ RI ( and that's quite an accomplishment!)
Not exactly the right person with whom to pick a fight, if you ask me.
Gosh, Sid, I certainly don't know what I did to inspire that little tirade. Your syllogism would be enlightening if the premises weren't patently false.
@Lawrence
The Somalia thing is nothing more than a silly leftist talking point. Who would be so foolish to believe the destruction of a government would somehow lead spontaneously to a libertarian society - especially when those in that society likely have no concept of the word. Besides, rightly or wrongly, the majority of libertarians see police, courts and the military a legitimate government functions.
China is prospering because it is moving away from statism. It risks its gains by an infatuation with central planning
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@Flip
I'm all for education. Sometimes people don't want to be educated. Sometimes the subject is of little use. And sometimes a person is not cut out for a certain path. And learning can occur should one become interested later in life. So do I feel kids MUST learn algebra at a certain time in a certain way? No
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@Shay
How do I screw everyone else by asking to be left alone???
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@Chemmomo
Are you familiar with compulsory education laws?
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@Flip
Reading and basic math would be the two I'd be most concerned about and they can be taught quite easily and while parental leverage makes their teaching rather easy. I spent many years teaching my daughter Spanish and German as well. She understands both but would never speak them. By middle school it became obvious she had no interest of her own. Additionally teens cannot be influenced as can toddlers. Besides what was I going to do , move in with her when she got married to speak Spanish to her? We also did piano for a number of years but the same problem presented itself. You can take a horse to water but you can't make them drink
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@JGC
No positive obligations
Jefferson sums up my views on what freedom is:
Rightful liberty is unobstructed action according to our will within limits drawn around us by the equal rights of others...
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@composer
You use coercion against those who violate the rights of others, not the innocent
People are not inherently lazy
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@Denice Walter
Mephistopheles O'Brien
Sorry. These threads get overly vitriolic at times.
In other news, something something nice kwashiorkor, Jello something something Phil Ochs.
Oh, and I hope Sid hasn't actually managed to italicize the thread.
Why should water, roads, and fire departments exist without the government, but police and military should not?
Given this, you strangely enough seem to have crafted a self that includes strong elements of both.
Why, no, it's not. And attempting to argue by aphorism is just plain sad.
especially when those in that society likely have no concept of the word.
Are we to understand that a functioning Libertarian society relies on its members being sufficiently educated to have a concept of the word "Libertarian"?
A less charitable interpretation would be that the Somalians have failed to seize the opportunities offered by having a minimalist government because they have the wrong skin colour.
Sid manages to catch precisely half of my drift: parents guide children towards language and social customs ( forks and clothes) rather than by using force so that they will be able to navigate and fit into their own milieu...... but he leaves out what I hinted: that it is rather negligent to not manoeuvre them towards BASIC skills that they will need in order to function in the same social milieu- if you can't read well and haven't reasonable numerical skills, you won't get too far and have few choices. I don't know about his experiences but no one ever forced me to learn anything.
@ Narad:
About that definition of "insane" ( -btw- isn't that legalese?)
Ugh!
How do I screw everyone else by asking to be left alone???
Unless you live on an island by yourself, grow all your own food, provide your own electrical power, and never leave, you aren't asking to be left alone. You're not alone now, and won't ever be.
Sid @ August 10, 9:54 pm
Sid, you’re still avoiding the question (and I’m going to paraphrase because I’m combining both issues):
what is your problem with an educated population, or having educational standards that may challenge some students?
I honestly just don’t understand your objections.
Another reason why algebra is useful - the coming zombie apocalypse! http://cdn.iwastesomuchtime.com/892012145214892012031479.jpeg
As an archaism. Would that some of the reformist mental-health codes of the late 1970s still meant something.
Mr. Schecter:
And you are very very wrong. But from you, that is to be expected. It is also a country where about 40% of the population is illiterate. You'd like it.
BASIC skills that they will need in order to function in the same social milieu
DW is way behind the times. At the very least you should be teaching children Pascal, or Python, or some other decent structured language.
@Sid
"Reading and basic math would be the two I’d be most concerned about and they can be taught quite easily and while parental leverage makes their teaching rather easy."
Wow, you actually answered my question. Thank you.
Ok, so what do you consider basic math?
And why would you "force" your kids to read and learn math but have issues with a public/private school system that does the same? What reading and writing is only necessary for your special snowflake?
Why do I get the feeling it's all about not liking the government telling you what to do, and has nothing at all to do with actual educational standards and improved mobility for people?
(Anecdotally, I hated my parents for trying to introduce me to ballet. I loved doing certain subjects and they removed me - against my protestations - from those classes in order to try new things. I understand why now, but I still wish they'd left me be. However, I am always grateful to them for pushing me to do better in the classes that mattered more, such as maths. I fully understand and agree with the idea that preferences should be taken into account for *some things*)
"When a child eats and is exposed to a fork it learns to use the fork – no force needed"
How does one learn maths? It's certainly not something you can easily learn from exposure. By the way, many people have difficulty using chopsticks, even after being 'exposed' to them.
"Those functions could be cut back dramatically and could be paid for either voluntarily or through some type of fee for use. what about the poor you say. "
I love how you seem to believe that all people everywhere can afford to, or would, pay for these things. That selfishness or simple inability to raise more money than just buying food and having housing seems to suddenly disappear under your worldview. If only we could put you in the business of writing laws, Sid, for I suspect your magical wand that makes all problems go away would quite possibly save the world. I can see the headlines now...
"What you’re describing sound like a society with heavy government control"
Bwahahahaha.... way to prove my point.
Learning history is evidently not a requirement in Sid's world either.
See he starts out perfectly reasonable, and then goes off the boil somewhere between an idea and the application of it.
DW: "While a person’s appearance is totally irrelevant to the quality of their argument- someone has to say it, so I will.
David is good-looking ( and believe me , I know men). More importantly, he’s smart and can swear better than anyone @ RI ( and that’s quite an accomplishment!)
Not exactly the right person with whom to pick a fight, if you ask me."
Wow ... *blushes* thank you, thank you and thank you .... and ... thank you xx
Flip says: "... it's all about not liking the government telling you what to do..."
I think you got it!
I notice something interesting in libertarian speech that resembles research in attributions of causation:
people might attribute success ( and failure) to a variety of causes- internal/ external, controllable/ or not- when you attribute a person's ( or a social groups') economic and/ or
occupational success ( or lack of it) PURELY to that person's ( group's) *actions* or some ingrained 'goodness' or 'talent' - you'll have a very skewed vision of the world. *Tres* Rand. Very young children often say ( social cognition research) that people are poor because they're "bad" and rich because they're "good". As kids get older, they begin to take account of other factors like effort, difficulty of the task and blind luck- even prejudice and stigma ( of course, I'm really getting this down to basics- tons of research there) and consider results to be based on multiple factors: in other words, which I nicked off my prof- they get "more liberal". Not everyone, apparently.
Despite my liberalism and artsy, atheistic internationalist attitude, I am desended from / related to *business people*- loads of them, I know details of businesses ( in 2 countries ) from about 1880- 1890 and tales about earlier ancestors- some of them hilarious- I could write a book.
-btw- I am watching Olympic men's hockey: AUS/ GBR- 2/1..
Libertarians despise considering external factors - especially 'governments' that assist a person- because you can't say you're a success solely based on your own effort, will and amazing talent ( which is ego-enhancing) if your government/ other people provided great schools, outreach to bright kids, encouragement/ goading et al,
@ herr doktor bimler:
I am timeless.
Languages/ technology like those you mention are why schools are necessary: most parents would be lost.
@ David N. Andrews, M.Ed., C.S.P.E.:
Well,it's true.
And I have been recently watching various sports where nice-looking, toned young men run around in short pants.
LIke hockey- current score Tanned/ Not So Tan: 3-1.
Seriously, I could have children that age, Scarey thought.
Sid - thanks for the apology.
@Denice
I agree - and also think a lot of it is down to pride. Of course, Sid makes the mistake in assuming that people actually *want* to be on unemployment, or be reliant on the government to pay for health services. However, we've discovered as a society that pride doesn't pay the bills and it's comforting/relieving when your neighbours pitch in.
"Rightful liberty is unobstructed action according to our will within limits drawn around us by the equal rights of others"
In other words the system currently in place, n'cest pas?
Or do you have some strange idea that without an enforcement mechanism--i.e., without the reasonable expectation that restrictions upon one's actions which preventing the infringing of the equal rights of others will be enforced-- people will uniformly elect to voluntarily limit acting on their own interests and act instead in the interest of the greater community?
flip: Sid makes the mistake in assuming that people actually *want* to be on unemployment, or be reliant on the government to pay for health services.
I have no problem with governments footing the bill for social and health services, because these can be paid for out of revenue raised in taxation. I'm going to offer Finland as an example of how it shouldn't be done:
1- you pay for health and social services via local and national taxation;
2- you then pay for health care via a yearly charge on top of the part of your tax that goes towards this facility.
Finland likes to make itself out to be a model state. It is anything and everything but that.
The assumption that Offalgit makes in assuming that everyone on unemployment wants to be on unemployment is... well, bloody offensive.
@David
I also am in agreement for having social security/universal health care. In my case - Australia - the model is good. Taxation pays for these services. If you want private coverage for health care, you can, but it's not done through taxes but a yearly charge. You also get a payment back via taxes or subsidisation of any private health care you purchase.
I have no problems with that. Having experienced both public and private hospitals, I'm glad I have both choices. Service had been good at both, but as we know... it's not the customer service that counts but the medical skill and expertise.
As for Sid... well, who know what his problem is.
Topically, this post over at Sharon Astyk's blog documents her ancestors' (and their communities') making sacrifices to be educated (including learning - gasp! - algebra) in mid- to late-19th-century New England.
flip: As for Sid… well, who know what his problem is.
I do. He's a prick.