A typical American school day finds some six million high school students and two million college freshmen struggling with reading and writing. We ought to face reality: most of these students might graduate, but they’ll never crack another book in their life, the bulk of their written communications skills require nothing more than their thumbs and a tiny screen and fleeting comments that require neither punctuation nor even lower case — Y U NO WRT ME? — let alone grammar. If they make it to their version of advanced studies — business school — the epitome of literacy will be the 5 line, six words per line bullet point slide in PowerPoint, and most of the lines will consist of stock phrases.
Meanwhile, the schools invest time, money, and teachers in futile efforts to make students with the attention spans of mosquitos try to read short stories, and even novels…and then, in the inevitable standardized test, they are challenged to extract meaning from at best three paragraph snippets. They then regurgitate trivialities in the stock 5-paragraph essay: I’m going to tell you 3 things, here’s thing 1, here’s thing 2, here’s thing 3, I just told you 3 things.
Why are we wasting time on these antique skills? You know they hate reading, they don’t want to read, and once we stop nagging them about reading, they’ll avoid it altogether for the rest of their lives. Why read a book when you can just wait for the Hollywood version, which will also include breasts and explosions? These are also skills most people won’t need in whatever jobs they end up doing.
So here’s my proposal: let’s stop.
We’ll save money. School can be abbreviated, getting the kids into the workforce faster. We won’t need to train teachers; any babysitter will do. And most importantly, graduation rates will soar right through the roof. And as we all know, graduation rates are the only numbers we need to determine whether our students is learning, and our schools is teaching.
I’m certain this idea will have enthusiastic Republican support, and that the Democrats will follow along.
I know, you don’t believe I’m serious. Then how can we believe Andrew Hacker? He seriously proposes in the NY Times (which will apparently publish anything nowadays) that we should stop teaching algebra. Algebra! The one basic, elementary mathematical principle we should expect our kids to learn, and he considers it superfluous.
His reasoning is bizarre.
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.
Shirley Bagwell, a longtime Tennessee teacher, warns that “to expect all students to master algebra will cause more students to drop out.” For those who stay in school, there are often “exit exams,” almost all of which contain an algebra component. In Oklahoma, 33 percent failed to pass last year, as did 35 percent in West Virginia.
Um, yeah? Math is non-trivial, and it’s conceptually difficult for some students to master. But that is true of every single thing worth learning. The purpose of an education is not to get a diploma, but to learn challenging and useful knowledge, and his approach is to redefine education to be something anyone can get with little effort — in essence, he’s making an education achievable by more people by stripping out the difficult learning part. But that’s not an education any more!
And to remove algebra from the curriculum…I can scarcely believe it. We live in a technological society. Not learning algebra in the public school system means those kids will not be prepared, will not be qualified, to do anything in science and engineering. I’m serious: if you don’t know algebra, you can’t do basic quantitative chemistry, and if you can’t do that, you can’t do biology. At all. Not the molecular/biochemical/bench side, not the ecological/evolutionary/field side. You can’t do physics, that’s for sure. Forget math and statistics. If you’re not capable of grasping statistics, forget psychology, too.
You can probably still be a competent English major, I admit. But wouldn’t we be better off if all the English majors had an inkling of the foundations of science, as well as all the science majors having a touch of the humanities and social sciences? Shouldn’t we expect that even those people who choose not to pursue a college degree ought to have a bare minimum of competence in math and history and language and science and art, if we’re actually going to deem them educated?
Setting algebra as a minimum is actually setting a low bar. If a third of the students are failing that minimal expectation, then the solution isn’t to simply disappear the requirement, but to teach it better. Or admit that students who can’t read, who can’t write, who can’t do a simple algebraic manipulation, are not educated. Period. No excuses.
And if you’re going to do that, you might as well write off any delusions about having a well-informed citizenry.
Someone, somewhere, once said that “the purpose of the American education system is not to educate, but to produce good workers”
Engineering, biology, physics, etc can all be outsourced, er, offshored. Americans don’t need algebra to flip hamburgers or sell cell phones.
The first thing a well-informed and educated citizenry will do is vote – and they’ll do so according to platforms and issues and well-explained policies, not soundbites and tribal affiliations and kneejerk reactions. As if either of the two sides of the MiliDustrial Party would want that!
…right up until they need to figure out how many tomatoes produce enough slices to go on the burgers, or how many family member discounts get taken off the total. *sigh* But that’ll just send them running to the managers, who’ll actually have come from private schools with adequate teaching and nutrition.
-.-
I hate our school systems so much. I was failed in regards to English and math. Science I excelled in but without a grounding in math or English I was unable to take that passion to college.
We need more teachers, better teachers, we need to attract these excellent teachers with passions for math and language. Teachers with passion will pass that passion on to children who have an aptitude and at the very least, impart the base skill set upon those with disinterest.
After I left school I found a passion for storytelling but had no tools by which to tell a story. I was labeled dyslexic, dysgraphic, and ADD; with those titles I was passed through English and math classes without learning anything.
… Still cannot do math, but I at least taught myself to write.
@Pteryxx
The other day I went to a popeyes chicken joint. The woman at the counter, barely out of highschool, sighed in relief when a credit card was whipped out. She said, “I love those, so much easier to deal with than counting out correct change.”
You can’t get a factory job either, since those factories that are left in America depend on their employees to handle the basics or… are you ready for this?… Statistical Process Control. You’d better be able to read a bunch of gauges and micrometers, understand graphs, and generally be comfortable around numbers.
*curls up in corner and weeps*
I managed a mid sized pharmacy towards the end of high school. One day the power went out but there was tons of light from the windows – but everyone (including some older folk) said – “Well can’t make change without the registers!” (mechanical, this was about 1978). So I spent 20 minutes teaching folks how to make change by hand. They were able to learn it. But the point is, we need to get these dummies to understand addition and subtraction first! That sounds insane, but I’m fairly sure things have gotten no better since ’78.
Frankly given how much I use Algebra in MMOs, I have to find this whole thing pretty funny.
Learn math kids, it’ll help you play videogames.
Heck, there’s algebra *and* geometry in tabletop RPGs.
The problem is that we’re teaching our kids to be anti-intellectuals. Creationists herding them right along that path too.
“Algebra” is, of course, an Arabic word. So it’s a filthy stinkin’ Mooslim idea and we need to get rid of it. Heck, Obama probably learned algebra at the madrassa.
Society’s major ill, illiteracy, does not need innumeracy to accompany it. Why does it seem that this country is the only one where expectations are to lower standards, rather than raise them?
@ georgemontgomery, Consumers, the goal of American education is to produce consumers. Of course, they’ll need to work in order to be able to buy. But I guess they can hitch us all to treadmills or something.
Wasn’t there a golden-age science fiction story about a future culture in which math was something that only the elites were ALLOWED to learn?
Unfortunately it’s not just the US of A. New Zealand’s education system isn’t that great either. See here for the Ministry of Social Development’s discussion of our adult literacy and numeracy rates. Short version: only about 50% of our school leavers have the level of numeracy necessary to actually pass their last year of high school.
I’m one of those squishy English types. I took just the math I absolutely needed to get into a good school (which was up to Calculus) and no more thereafter. I figured I’d never need any more, and I was right.
But even I realize this idea is dumb. I’ve never needed calculus, analytical geometry, or most of the really most of the math I learned after 9th grade. But Algebra? That’s simply the foundation of analytical thought, as far as I’m concerned. It teaches you how to rearrange a problem until you can get a handle on it.
If this lawmaker said we should quit making Calculus a college requirement and replace it with Statistics, which is probably more widely useful, I’d be listening. (I actually enjoyed calculus, but really, it’s useless outside the hard sciences.) But ALGEBRA???? Sheesh.
It is evident that math competency is lacking by the fact that I see so many answer then following problem 5+5-5+5×0= with 0.
I’ve lived in China for more than a decade. Since I’m a teacher, and have raised two kids here, I have been in and around many schools, from pre-schools to universities. The drive to learn, or the stereotypical crazy parental push to study, is real, yet exaggerated. There are higher learning expectations here, and some of it, such as the insanely competetive and overly stressful “high school exam”, is more because of a lack of schools, than being pushed to learn. Most of what I see is just about believing that children can and should learn more, earlier. Chinese kids start learning basic geometry even in pre-school, no exageration. Almost any Chinese teenager is competant in Algebra by the time they finish middle school, even the ones that’ll drop out. Not to mention they are at least competent in reading English at a level comparable to native speakers. And there are many other places in the world, even some in the US, with high expectations as well. From my experience though, most American parents have very low expectations. They think learning is scary, and not fun, and pass that neurosis on to their children. They don’t push their kids to learn, study, do their homework, or be accountable for their education. I saw it for several years, couldn’t stand it, and left for greener pastures.
You can’t even increase or decrease a recipe without algebra! And forget trying to build anything without it. Or figure how many miles you probably have left on the amount of gas you just put in the car.
Another problem is that too many (not all) parents don’t value education. Many may SAY they value “education”, but what they actually mean is “passing grades no matter what.” Then the administrators pressure the teachers to pass the students no matter what, which is added to the pressure from the parents, which is added to the pressure of the government…
..and as soon as the students recognize that this overwhelming outside pressure is allowing them to get by without learning all that much, they end up in the world selling cell phones, having kids, and imparting the value of “education” (ie, just pass the classes no matter what) on to their children.
All the incentives are in the wrong places–or at least many of them. The district in which I worked didn’t require middle school students to pass any classes (a widespread phenomenon, from what I’ve gathered), and would not hold any student back unless the parents signed off on it. The parents would virtually never sign off on it, so there were NO consequences to the students for not passing. By the time they got to high school, they simply *did not believe* they had to pass their classes (in high school, required classes were required; you passed or you took them over). They could be sitting in a class with juniors and seniors who had to repeat the class, and still didn’t believe they had to pass the class. I had one freshmen repeat my class the very next year, and around November he exclaimed, “Hey! Isn’t this what we did last year?” Getting him engaged at all was a huge challenge because he had already been taught in middle school that passing wasn’t necessary, so paying attention wasn’t necessary. His freshmen year was filled with constant messages from adults–teachers and counselors mostly–that he had to pass. After middle school, he just didn’t take the messages seriously.
Too many students are getting the idea of “passing no matter what” confused with actual education, and seeing that those who “passed no matter what” don’t seem to know all that much. Education, they then think, must be largely a useless game those in authority force you to play for some reason (possibly just to make “school boys” and “school girls” look good and everyone else look bad). Once they’ve learned that lesson from the reality of the pressures around them, it is extremely difficult for the best of teachers to remove.
I have my suspicions that this plan is being floated by ALEC as yet another piece in the ReThug war against Americans. They really don’t want anyone in the 99% to have numbers-literacy. I had to look up the word for that: numeracy. (The fact that I didn’t remember the word for the concept scares me a little). The reason the 1% don’t want a population with numeracy skills is because that population is easier to bamboozle on everything.
Global warming ? What do those numbers on the graphs mean ? Can’t tell, if you have no idea about magnitudes and percent changes. Credit card debt ? Can’t calculate the number of weeks you need to work to pay off your card if you have no sense of which number is the denominator of the fraction. Just pay the minimum, like everyone else who has been kept deliberately ignorant. And stay in debt forever serving the owners of CitiBank and BofA.
It’s not so much that any person will need an specific algebra lesson, it’s that every person as an adult needs to have enough basic numeracy that they don’t just go blank when they encounter “math” in the real world. A year of algebra is about the amount of formal education in math which is needed to get past that shut down.
Less math at school ? Probably not enough to get most students to a reasonable comfort level with the type of numbers they will need to handle for making sensible decisions in life. And as PZ already noted, no algebra is an insurmountable barrier for working in science, so a college student would have to take remedial algebra if they skipped it in high school.
I would hardly believe the NY article were serious about cutting algebra, except for my paranoia that somewhere they’re making legislative plans to do exactly that.
Brilliant. What an awesome plan. Let’s extend this logic to post-operative infections. If a surgeon would just avoid performing surgery on people the post-operative infection rate would drop to zero!
Of course, it might cause problems down the road, but why would we worry about that?
You know, if we paid teachers for shit, or did something about the tenure system, then maybe the American education system wouldn’t be in such dire straits.
*disgruntled, unemployed college English teacher*
Oh, also–as an English major, we DO have to have a minimum competency of 2 basic science course with a lab, a senior level science course for a non-major, and one other science course, plus math through college algebra and major-specific maths (I did basic stats.)*
*In the US
Also, algebra classes teach about interest rates. Thanks to math skills, I can make calculations that tell me which rates are rip off.
I’ll be honest, I’m not that good at math, but algebra was one subject I did like. I’m appalled that someone would suggest we stop teaching it.
Yep, we were teaching that much “algebra” to our kids when they were still in elementary school. Rearrange the problem until you can solve it with the tools you know, then plug your solution back into the original problem to see if your answer makes sense.
I feel sorry for other people who never get that in their educations.
Anyone who isn’t able to do high-school algebra is not competent to be an adult in a first-world country.
The year was ’62, ’63 or ’64. I was in the Navy and I was on a Greyhound bus going from NYC to Boston. I was reading an Esquire magazine and I remember an article in that issue that discussed the intentional dumbing down of Americans in order to develop a more malleable, less contentious citizenry. As I have seen the changes that have taken place (dropping the classics, de-emphasizing languages, math and history, the aggregation of news sources) in the subsequent years, I have often thought of this article. I have tried to find it in Esquire’s archives – with no success. Of course, that was a long time ago and I could be “mis-remembering”, but it does seem that access to high quality education, like wealth, seems to want to belong to “them’s that got” or to a select few of highly motivated or well-parented individuals. Meanwhile, more Americans believe in angels than in evolution; most can’t find Vietnam on a map; most can’t name the Vice President.
The Redhead’s mother doesn’t do “algebra”. She doesn’t solve for X, but does up ratios and proportions, and eventually comes up with the same answer as her daughter who writes and solves a simple equation in a fraction of time.
@4 nesetalis
I had much the same experience in school. I’m not sure why (my memory of my younger years is -very- hazy) but I didn’t get the foundations of maths from grade 1 through to about grade 5 or so. This led to a deep aversion to maths throughout the rest of primary and high school as I considered myself far too inferior in the subject to be able to grasp mathematical concepts. Solving chemical equations in high school did help somewhat, as I loved the puzzle solving aspect of it but tbh, we only did a little of that (and while I passed grade 11 chem with flying colours, I miserably failed grade 12 chem because of a massive conflict with the teacher which resulted in me basically being kicked out of the class).
Since then I’ve become very autodidactic and have a deep and abiding passion for all things science and I would dearly love to work in a science position (particularly astrophysics or something like that). However, I find it very hard to learn in a structured environment (one of my many failings, hahaha). So I pursue my other love, music.
Still, I resent the fact that I was denied opportunities to pursue a science career right out of the gates of high school because of what I consider a failure of the schooling system (though the blame now probably rests as much with me as it does with the schooling system simply because as I get older I realise more and more that if I get off my arse and pursue learning opportunities I could overcome this deficit).
I really wish China would put a man on the moon. Perhaps that would spur another “Sputnik moment”.
Just for reference, I come from Australia.
Why not just eat them?
PZ Meyers said: Not learning algebra in the public school system means those kids will not be prepared, will not be qualified, to do anything in science and engineering.
I’ll take this a step further. If you don’t know Algebra than you don’t know how to think.
Math classes, especially in junior and senior high school at least up to the Algebra level are not about learning math; they are about learning how to think in a logical step-by-step fashion. They are simply using math to do so, because the structure and logic of math make it excellent for such practice. Learning math teaches basic problem solving skills in a highly organized way which may be difficult to learn in other ways.
brucegee1962 has it right: That’s simply the foundation of analytical thought, as far as I’m concerned. It teaches you how to rearrange a problem until you can get a handle on it.
Not enough teachers focus on this aspect of it when faced with the inevitable “but why do we have to learn this stuff if we’ll never use it?” whining.
“Statistics”!? That’s that lying commie liberal moving-numbers-around trickery. Who needs it? I mean really , what good is math…
http://youtu.be/Qhm7-LEBznk
Fortunately, this is just one NY Time’s columnist’s opinion and not the consensus in this country.
That said, I’m glad you brought it to my attention, PZ, because of the startling statistics illustrating just how uneducated some of our citizens truly are.
It’s no wonder that they’re unable to break loose of the chains of indoctrination they’ve inherited.
Like I’m doing in that there pitcher. ——>
I work for a battery company, and in a discussion about warranty rates, one of the sales people mentioned that many companies were doing away with a pro rata on your warranty. The math just confused people. It’s F’in division and multiplication…..
Then again, our VP’s have trouble understanding basic stats, just explaining that we don’t have statistical confidence to tell two different conditions apart was painful. We’re F’d, because these are they guys making multi-million dollar decisions that affect thousands of employees.
Imma play the opposing side here. It’s not that I have any issue with math, or even basic algebra…
But.
At least for my education, I spent a good majority of junior high math messing around with factoring rules and orders of operation that quite frankly I’ve never seen used. That stuff is necessary for higher math, but for a basic education, we might be doing a real disservice to the most in need students by focusing on those things, when we could instead be spending time on more fundamental and practical concepts such as numerical literacy. (Graphs, statistics, finances, etc.) Just my two cents.
Also, I don’t think PZ’s modest proposal is that far off. Current English HS teaching methods are poison. We’re better off without them. Teach kids to hate reading. Yeah, that’s smart.
On a more serious note, I’m a highschool drop-out and do not recall a job I’ve worked where knowing Algebra was not either necessary or incredibly difficult to do without. I worked at a yarn mill once. It was the kind of job where you fed something into a machine, pressed a button, and watched it for 8 hours; the kind of job pretty much everyone could do with some training, or so I thought at the time. I had to train several people on the machines and consistently the biggest issue were basic math skills. Nothing even remotely complicated; I’d even done the difficult part by writing the equations they needed to use already in the process of learning the machines myself, but getting management to give me people who could at least just plug in the relevant numbers seemed an impossibility.
But the whole argument over what you “need” to know has always struck me as rather missing the point. The more math you know, the more you’ll notice where you can use it because it changes how you perceive the world. My math skills are pretty limited, but in using what I do know I’m constantly running into situations where I would like to know how to do something but don’t. At the yarn mill, one of the things I used Algebra for daily was to minimize the loss of wool when running them through the machines. I could also just have eyeballed it, and every other employee did, but eyeballing it never would have gotten me the same material efficiency. Most people “eyeball it” because it works well enough, and when you learn ways to get around not knowing more math then yeah, you’re not going to notice where knowing more math would be helpful or when you’re suffering for not knowing more.
Addressing the earlier issue PZ raised on reading and writing skills, I have a book that teaches me all I need to know about the English language. It contains under 11,000 unique words, making it simple to master. Using it as a text book will also help teach history, law and philosophy. I am of course talking about The Book, the King James Bible.
It has maths, for example. 40 is a really important number that isn’t taught enough these days.
Better, it has biology. I am proud that I learnt from Leviticus than an insect has as many as four legs.
You’re ignoring the subtext. He’s proposing stopping teaching algebra *in public schools*. Because only poor kids go to public schools, and they don’t need anything but basic skills.
No matter what the public schools do, good private schools will keep high standards in math and science so that they can brag about acceptance rates.
I’m glad other people feel the same way. At the very least, teach basic algebra!
By the way, as an American high school student, I have to say, writing and foreign language need more work. At my school, nobody ever takes the foreign language teachers seriously, and very few people actually learn much besides what’s required to graduate; writing, so far, seems to consist mainly of the same five-paragraph formula previously mentioned.
But what do I know. I’m an American high school student.
Speaking as a Canadian with an MBA…
IME, business schools up here at both undergrad and graduate levels require a solid grounding in algebra at the very least. A typical business degree curriculum is packed with economics and statistics. So lots and lots of graphs, regression analysis etc. If you’re taking stats or economics beyond the introductory level, calculus is a requirement, as curves from real-life data don’t tend to be straight.
Oddly, I found that the courses that are the most dreaded in the MBAs up here are the accounting courses. Not because arithmetic is hard (because it isn’t, or at least shouldn’t be) but because the vast number of accounting rules you have to master is frankly intimidating.
I recall doing okay in cost accounting but I stomped on my dick during the HR courses. Not good at HR, where “not good” could also be written as “abysmal.”
For me, algebra – particularly unit analysis – come up everywhere.
Not all the time, but eventually a problem comes along where there’s no other solution. Then another. Then another.
I don’t understand how people get by without it.
Several points:
– I strongly recommend reading dy/dan, Dan Meyer’s blog (sorry for name spelling). He taught algebra to remedial students and his blog includes lesson plans that caught his students’ imagination. Most recommended is his series entitled ‘what can you do with this?’ (follow tags). It is possible to teach algebraic thinking to the non-mathematically inclined if one uses good tools (without getting lost in what Meyer calls pseudocontext).
Also, Meyer thinks that things would improve significantly if geometry was taught before algebra, because more students have an intuitive grasp of geometry than of algebra.
– My daughter completed Algebra I this year. In late spring they learned about solving quadratic equations. I asked my daughter how the formula can be derived from first principles. She didn’t know, the teacher neither showed them nor had them derive it themselves. She just gave them the formula, and they spent time learning a rap routine to help memorize it. ARGHHH!!!
Obviously in 20 minutes or so I had my daughter derive the formula, with me just asking questions, going from the simplest quadratic equations to more complex and general ones. Why not do things right? Why waste the students’ time? This is so disrespectful of the students’ intelligence.
Seems The Enlightenment has ended. Authority is now the leader. Looks like The King does know better.
If I remember right Math and English are the only 2 endeavors of importance that make up the first 3 years of college. It can be a struggle but the reward is beyond comparison. “Things are going to slide, slide in all directions
Won’t be nothing
Nothing you can measure anymore”
The Enlightenment is dark now. There was not much of a fight–was there! More like the primal shrug.
Leonard Cohen–The Future
“The Future”
Give me back my broken night
my mirrored room, my secret life
it’s lonely here,
there’s no one left to torture
Give me absolute control
over every living soul
And lie beside me, baby,
that’s an order!
Give me crack and anal sex
Take the only tree that’s left
and stuff it up the hole
in your culture
Give me back the Berlin wall
give me Stalin and St Paul
I’ve seen the future, brother:
it is murder.
Things are going to slide, slide in all directions
Won’t be nothing
Nothing you can measure anymore
The blizzard, the blizzard of the world
has crossed the threshold
and it has overturned
the order of the soul
When they said REPENT REPENT
I wonder what they meant
When they said REPENT REPENT
I wonder what they meant
When they said REPENT REPENT
I wonder what they meant
You don’t know me from the wind
you never will, you never did
I’m the little jew
who wrote the Bible
I’ve seen the nations rise and fall
I’ve heard their stories, heard them all
but love’s the only engine of survival
Your servant here, he has been told
to say it clear, to say it cold:
It’s over, it ain’t going
any further
And now the wheels of heaven stop
you feel the devil’s riding crop
Get ready for the future:
it is murder
Things are going to slide …
There’ll be the breaking of the ancient
western code
Your private life will suddenly explode
There’ll be phantoms
There’ll be fires on the road
and the white man dancing
You’ll see a woman
hanging upside down
her features covered by her fallen gown
and all the lousy little poets
coming round
tryin’ to sound like Charlie Manson
and the white man dancin’
Give me back the Berlin wall
Give me Stalin and St Paul
Give me Christ
or give me Hiroshima
Destroy another fetus now
We don’t like children anyhow
I’ve seen the future, baby:
it is murder
Things are going to slide …
When they said REPENT REPENT …
@42 chakolate
you are right on the target. This is the elite class taking over. Seems to be a done deal. In U S the assault on Public ed has been on-going for more than 30 years.
There is no reason to think it will let up.
Hello Choir.
I was just driving home with a brand-new flash drive in my pocket, trying to figure out how much I had paid per gigabyte (while driving a stick-shift, mind you). I calculated $.75, checked my answer two ways, and was proud of my shopping and my skills.
They could teach maths better, this English major says, but they need to teach it.
@almulhida
I laughed out loud when I read this. Some of those elitistjerks threads approach peer-reviewed journal status.
Now that I’ve outed myself as a WoW player, I should just slink to the corner and lurk again. :)
If North Carolina and Virginia can redefine climate science and oceanography, and Louisiana, Kansas and Texas (among others) can redefine biology and history, algebra is just the next step down that path. We are becoming the Idiocracy, hoist by our own retard(!)
As an outsider to the school system, I was homeschooled, the thing that strikes me as the biggest stumbling block for many students is the expectation that by age x they should achieve y.
I didn’t learn to read until I was about 10. My parents didn’t push it, well not much, but they read to me and my brothers daily and I went from not reading at all to reading adult fiction over the space of about two years.
As far as maths goes I had trouble with learning from my parents because, as I am now finding out, I have to learn the why of things: I cannot stand learning a formula without understanding why it should work. I was even uncomfortable with basic addition, I could do it but for some reason it irritated me, until earlier this year I got a book from the library that started with sets and built on that until it gave me an understanding of why 2 + 2 equals 4.
I guess my point is that people learn at different rates and education should be about having the answers on hand when a person, be they 5, 15 or 50, asks ‘Why?’ not, as seems to be the case in New Zealand, trying to force people to learn something they have no interest in.
I do however agree that everyone should be able to do basic, hell why not aim for advanced, algebra but I think the current system fails far too many people and should be rethought and rebuilt.
I can only suppose that this Andrew Hacker fellow would not make a very worthwhile teacher. It seems to be the case, time and again, that the most popular teachers are those that both respect and challenge their students. Simply throwing one’s arms up and assuming that young people are incapable of reading, counting (or whatever the skill may be) generates a self-fulfilling prophecy. I’ve not seen any evidence supporting the claim that the youth of today are less capable than the youth of generations passed, so any explanation of lower performance must invoke conditions external to the individual. Given that, and the popular culture within which teachers must educate, the challenge is great indeed, but it’s certainly a challenge worth taking!
There is a bad kink in our education system, which is why I teach so much algebra to students in college. They didn’t learn it in high school, so they’re having to take it in college. In my humble opinion, a lot of the problem is based on the innumeracy of elementary school teachers. You can get a teaching credential even if you have a shaky grasp of math — which you will then be teaching (badly)! In general, the students in our credentialing programs are the most math-phobic on our campus. It’s a self-perpetuating system. Unfortunately, if we get serious about making sure that grammar school teachers are competent in math as well as in other subjects, we will run head-long into the concrete wall of teacher shortages.
Getting “rid” of Algebra in high school is one of the effects of Common core. Your fellow blogger Blag Hag really liked the idea of Common Core, and posted a piece on it. You can find it here: https://proxy.freethought.online/blaghag/2012/06/fixing-math-education-or-how-i-learned-to-stop-lecturing-and-love-the-common-core-standards/
I’m not finding it now, but recently I linked to an article showing that US students in the richer districts are performing on par with those from other countries… according to this article, IIRC, poverty in the US accounts for ALL the decrease in US student performance. If I can dig the bloody thing up I’ll re-link it here.
But until then…I have seen so many incoming students who were screwed over by their high school lack of education in math. Algebra is our minimum requirement for any program in science and math — and we’re getting all these students who don’t meet it.
If I had my druthers I’d keep algebra, but make the next course statistics. After that, it would be geometry for the college bound and practical math for everyone else. It is appalling how many people cannot balance a checkbook or understand interest rates.
Additionally I’d bring back shop classes, because it really isn’t necessary to attend college to be a plumber, mason or electrician.
That nearly forces me to tears. Admittedly, I am not particularly proficient at math, but I can do Algebra.
I did manage to find this:
http://www.nytimes.com/2011/12/12/opinion/the-unaddressed-link-between-poverty-and-education.html?pagewanted=all
@ almulhida
As a professional video game designer, I use math extensively in designing them too! :)
—
It’s really sad what low expectations do to kids. If you set them up to think that math is super-hard and they can’t be expected to be smart enough to grasp it, they’ll believe it, and lose all confidence in their mental abilities.
It’s frustrating this happens so much with math, because when taught right it can be a powerful tool for building confidence.
On this subject I’d highly recommend John Mighton’s book “the Myth of Ability.” In it, he lays out strategies for teaching math in simple steps, so that kids are amazed with their own progress and ease with the material.
That feeling of exceeding expectations is infectious, and boosts their commitment to their studies across the board.
He also raises a great point about how limiting it is to think about “usefulness in the workplace” as the reason for teaching something. That’s not education, it’s vocational training.
We don’t teach music out of the belief that most kids will find jobs in orchestras, or Shakespeare because we think Victorian English looks great on a resume.
We teach these things because they are beautiful, and familiarity with this cultural richness is part of being a well-rounded, conscious human being.
If we were graduating students who had no idea music could be moving, or who felt no sense of awe looking up at the stars, we’d be rightfully enraged that our schools were emotionally stunting our youths.
But the vast majority of students now leave school thinking math is something you use to do your taxes – without the slightest inkling of the beauty and majesty of the great theorems, the surprisingly intricate complexity arising from simple logic, as unveiled by millenia of humanity’s greatest minds.
And we don’t even know what we’re missing.
The one thing electricians and other trades need above all else is to manipulate equations. I’ve spent far too many heart-breaking hours coaching not-very-good-at-maths students trying to get into (or through) vocational courses. These are students who never intended to do any other kind of further study but they’ve always been keen on mechanics or other practical activities. Watching a teenager who only ever wanted to work with cars watch his dream job slide away drowned under incomprehensible symbols is deeply saddening.
I’m afraid that I agree with whoever mentioned ‘elementary’ school teachers. Anyone who ever tried to teach algebra, percentages or ratios to students who don’t understand fractions knows what I’m talking about.
Different (US) colleges have different approaches to academic requirements. Mine (small liberal arts college) had no core curriculum and virtually no requirements beyond completing a major.
stoopid question from a foreigner:
what exactly is encompassed in “algebra”? sorry, when I was in High-School in Germany, there was only “math” and “geometry”, so I don’t actually really know what all these different words for specific kinds of math encompass. I only have vague ideas. :-p
dmgregory.
Yes! The Myth of Ability is an absolutely wonderful resource. I’d heartily recommend it to anyone dealing with primary and high school students.
It doesn’t matter that you won’t run Mighton’s version of volunteer tutors. The clarity and simplicity of his ideas as he sets them out in the introductory chapters is worth every hour you might spend in reading and absorbing his message.
It also cuts down any frustration you might feel when dealing with students who don’t ‘get it’. All you have to do is to reflect on what you’re teaching. You can bet London to a brick that somewhere in there is a smallish conceptual step you never noticed before that needs explicit teaching. If it comes up often, it’ll take you about 30 minutes to knock up your own targeted work program to provide the necessary instruction and reinforcement.
dmgregory @ 62 – Well said.
PZ, Mr. Hacker did not propose, as you allege, that high schools stop teaching algebra. He suggested they stop making algebra a required course for graduation. Not at all the same thing.
@Jadehawk
Algebra is a system of math where there is a function with an unknown, and the point is to find what the unknown is, or the relationship between unknowns, and what kind of curves they form.
You don’t know much about how our underfunded public schools operate, do you?
Removing a subject from the requirements for graduation puts it on the chopping block at the first sign of budget troubles. It also means that a lot of naive students will assume they don’t need the subject…until reality smacks them upside the head.
flatlander100 @ 68
Not requiring algebra sends a message: you don’t need algebra. There are a lot of students who will refuse to take it if they don’t have to.
Well-to-do parents will insist that their kids take whatever courses they need to get into a good college, and will hire math tutors like me to make sure the kids do well.
Parents who never went to college won’t know that they need to do that, too.
And the classism just gets worse.
@PZ
How can students reach college without even basic algebra?! It is suicide, especially in the sciences! Worst of all, failing classes also mean wasting money down the hole. I guess high schools these days are failing hard.
In re: your modest proposal…… many years ago now, the hustorian Carl Becker, who’d begun his college teaching career, suggested a new plan for granting college degrees. Upon enrollment and the immediate payment of four years tuition, each student would be issued a degree dated four years hence. For those four years, the student would have the right to attend any classes he might wish to and, of course, to attend all university football games. Professors then would have only students in class who wanted to be there, those who only wanted to party, go to football games and get a degtee would get what they wanted. Have to confess that once I’d been teaching at an Enormous State University for a decade or so, I was no longer certain Becker had been kidding.
On needing math to play games
You should see the pokemon people. Playing that game expertly means you have to know something about statistics. Also, I saw the bulbapedia article on catch rates, and I was amused they had equations and everything.
so all “solve for X” sort of math? does that include math with multiple unknowns, or is that something else? does the Pythagorean theorem count as algebra, or something else (it fell into “geometry” when I was in school)
PZ @79 If your post was meant for me, I know a great deal about school underfunding. You’re making unfounded assumptions, which you are quick enough to call out in others…. usually with very good reason. Second, I did not argue tg,hat Mr Hackers,’s suggestion was a good one, merely that, in your high dudgeon, you ‘d badly mis-stated his suggestion. Want to take his argument apart, have at him… but you owe him stating it accurately. Again, you’ve called out a lot of people for mistating your arguments. Sauce for the goose…..
Finally, to suggest that deleting algebra as a required course will put it on the same budget chopping block as, say, art or music (usually the first to go) is highly unlikely I think so long as schools have parents who hope their children will go to good colleges and becone doctors or engineers and the like.
Aaaargh, the school system. So much I hate about it.
This. Ugh.
I enjoy writing. Mostly, anyways. But I like the kind of writing that I can do on my blog, or in comments, where arbitrary structure and grammar goes out the window to make way for artistic license. But when I’m writing an essay for a class?
I always, always refer to that as bullshitting an essay. I’m not writing. I’m taking ideas and fancy words and the fact that I know what makes for a complete sentence, and chopping them up and putting them into the right boxes. I always get fantastic scores, because again, the fact that I know where commas and periods and capital letters go means that I am a fucking virtuoso writer. But the shit I churn out is so devoid of any feeling or thought, because that would make it not fit the pretty format. Bullshit.
As far as teachers needing to be more well-paid and passionate, God Yes.
I felt like I was good in math up until 7th grade, when I started pre-algebra. My teacher was, in my opinion, awful. I couldn’t grasp a thing she taught, and it was discouraging as hell. And at the end of the year, she actually told the class that if they had trouble in the class, they should drop out of pre-AP math and go to regular. She actually discouraged children that had qualified for the pre-AP track from continuing on with classes that actually had some semblance of rigor to them.
I didn’t listen to her, and in 8th grade Algebra I had the best damn teacher in the world. I have always described her as “Math teacher because all of the rocket science positions were taken”. She loved math to the gloriously nerdy extent, she taught it well, and she got me back into feeling like I could do it, and I ended up back at being best in the class again. All of it was because she actually had a passion for what she taught and truly wanted children to learn, not just ‘earn’ a diploma. I recall her talking about teaching her 6 year old Algebra- I was simultaneously heartened to hear that, and insanely jealous of that kid’s upbringing.
This teacher also mentioned once how teachers are actually disincentivized from achieving more. They start out at one pay ( I think $9k a year?) and because it’s so low, they get benefits that bring them over some level of income. But should they get a promotion or a raise or what have you, they will end up over the level that makes them eligible for aid, but under the level of income that they had with their previous salary plus benefits. So damn fucked up.
Hell, this teacher had a lot to say about how fucked up the education system was. Lots of complaining about how their funding is based on pass rates, and how this lead to easier curriculums and fucked up tests, not to mention explicitly teaching the tests instead of valuable information. I am so grateful for witnessing that complaining. Honestly, it inspired me to want to teach someday. Not as my actually career, just at some point. Just because she made me realize how damn valuable a good teacher is.
Anyways, on math in general, I find it so sad what a bad rep math gets. I love math. It’s difficult sometimes, yeah, but the thing about math is that if you learn it correctly, you learn methods to solve problems, not just formulas. You can (in my opinion) solve ANYTHING with basic principles. Even if you go into a test and forget all of the formulas, you can still usually figure out a good answer based on pure logic. It’s not easy, but I respect math so much for that. I wish there wasn’t such a prevailing idea of “iiick, but that’s haaaard!” about it.
And of course, these basic skills that let you do anything will be taught in an algebra class, provided you have a good teacher. To think of removing fucking algebra… argh.
@jadehawk
is the equation for the circle. Algebra is not just, while very important, finding the unknown, it is also about determining the properties of function. Is the function even or odd, what happens when you approach certain limits, does it go up or down to the left and right side, is it periodic? Those are some of the examples.
Well, pythagorean theorem is more along the lines of geometry, but it is extremely useful in algebra. You can use it to find the distance between two points in a linear equation, for instance. Also, yes, it includes equations with multiple unknowns. For example:
I teach in a small school district in Missouri. Our curriculum is based on techniques used in schools in Singapore, and we have kids doing algebraic stuff in elementary school. Why? Because our kids are exposed to math as a language that can be used to learn about and understand things in the world around us, not merely as a series of pointless algorithms to be memorized and banged away with at the appropriate moment.
I’m all for tossing that sort of algebra and math ed. out the damn window, along with all the lousy textbooks Texas shits all over the rest of the US. But to say we should ditch algebra? When our average in every way kids in our district can do algebra without realizing it in 2nd/3rd/4th grade? Lolz. Our education system is built to get kids ready for the work force of 1888. Go to school, learn rudimentary shit, get a job, work it for dozens of years, and then retire and go home with a nice watch and a set of wooden bowls. We don’t live in that world anymore, and because we don’t live in that world we instead need to expose our kids to a lot of different stuff and prepare them to answer tough questions and solve big problems. Some knowledge of math would be helpful in that endeavor!!!
Superb piece, PZ.
This is one of my “hot button” topics as well…and the problem isn’t new. Indeed, the English majors are part of the problem–and were 40+ years ago.
When I was at UC Berkeley, the humanities departments pretty much insisted that there be “science” courses for non-majors. Courses thoroughly watered down from what anyone in any sort of science or engineering major was expected take. On the flip side, there were no non-major English courses. Bit of a disconnect there, guys.
I have long felt–having seen the results of what comes out of high schools–that calculators should be banned in high school. The kids can’t tell if the answer they got on a calculator is even of the same order of magnitude as the correct one, let alone if it’s close enough that it *could* be right. At the high school level let them use slide rules and log tables if they need aids.
Now if the kids are scared by Algebra, it occurs to me to give them a choice. They can take (and pass, damnit!) Algebra, or they can take (and pass) a course in networking. One where they will have to calculate IP block sizes and determine which address is the broadcast and which is the gateway. Make them configure actual routers. They should know what address blocks are available for any private use. Once they get all that down. Start them in on IPv6…because they’re going to need it.
Given that choice…I wonder which course they would actually take?
ok, thanks for the explanation, ibyea.
that’s some incredibly basic and necessary stuff that would be cut out of graduation requirements, then.
Yes it does. Which gets me right back to my obsession with learning maths for trades. When you look at the equation wheel in the centre of this page – http://www.sengpielaudio.com/calculator-ohm.htm – you realise that people *could* memorise all those formulae separately. But the much better option is to understand the relationships and be able to manipulate them to solve particular problems.
You want to work out resistance when certain other variables are set? Or do you want to work out the effects on your setup if you substitute a material with a higher or lower resistance into part of the circuit? What happens if you change other elements? Unless you can reframe equations to expose the unknown variable that you’re looking to solve for, you can’t do this.
Without algebra, you might be able to apply a rigid formula inflexibly (and a lot of safety and building regulations require such uniformity). But we’re all better off if mechanics, plumbers and electricians actually understand what they’re doing. And algebra is a minimum requirement for that.
Btw, I struggled through algebra in high school and struggled through chemistry, which I loved, because of the algebra. But I understood why they were making me take it–to teach me to think.
That’s the reason I give when suggesting to young folks that they take Latin if offered. Had four years of it in high school. Heck of a lot of hard work, but by God you learned to systematize and analyze, and since then English, French, Italian, and Spanish have been leaps and bounds easier to handle, too. Plus we had a Latin club with a funny mascot, we had spaghetti dinners, our club had “proconsuls” not presidents, we puzzled the other kids with SPQR, and we secretly called an unpopular teacher “magna vaca.” We knew what the symbols on the dime meant. Making models of the Roman Forum was as fun as making models of molecules with sticks and balls. We felt special and knew we were learning something truly greeat in history, despite the amount of work. Good times!
I tell young ‘uns that I’ve used it every day of my life since then and that I’ve never regretted it. That’s *learning.*
@jadehawk
Not only that, you would be learning some useful applicable stuff in algebra, like calculating how many gallons of gasoline you used up, figuring out how much of a rip off the interest rate is, why growth is unsustainable and therefore a danger to civilization, how to do percentages/fractions/ratios, and stuff.
flatlander100 @ 68
It was more than not requiring algebra to graduate. Hacker also took issue with mathematics in college entrance requirements:
I used to teach at a school where lessons were not compulsory (Summerhill, for those who are interested) and I think that compulsory lessons and the authority relationship between adults and children in school are the principal reasons why children fail.
I think that if you do have a compulsory system (and yes, I can’t see that changing soon) then it ought to be properly funded and teachers given more security and respect, but as long as we force children to attend lessons we will force them to fail. Young kids are desperate to learn; sitting them in a classroom for N hours a day is possibly the best way to put a lot of them off. Of course algebra (along with a whole lot of other things) should be easily available to those who want it.
I was lucky at school. I was good at and interested in academic subjects. But school retarded my emotional development really very badly and I can’t say I’ve recovered the lost ground very well even at the age of nearly 40.
Anti-racism – people of all races are people. Feminism – women are people. When do we get “children are people” to even that partial and problematic level of acceptance?
A diploma on your wall that did not have any algebra requirements is worth less than the wall paper it covers.
You might as well stop teaching critical thinking skills.
I’ve taught algebra at the high school level, in a low-rent neighborhood of a major city, in a “repeater” class populated mostly by Hispanics and African Americans.
In my experience, what prevented most of these students from grasping algebra was their own irrational fear of looking “stupid” in front of their peers. Instead of focusing and applying themselves, they simply “tuned out” or “acted out” to avoid the anticipated pain and embarrassment. This problem was exacerbated by the fact that several of the students were one or two years older than the majority, and although one or two years may not sound like a big deal if you’re in your twenties or thirties, to a teenager it can be the pinnacle of humiliation.
Too bad we can’t have much smaller class sizes, because the I believe the idea of putting 30 kids of differing maturity levels and learning abilities together in one room is a deeply flawed concept, particularly when it involves the subject of math, where real, demonstrable skills are required. One cannot fake these skills, or talk one’s way out of solving simple equations. The resulting embarrassment felt by young people in math classes who aren’t picking up on the concepts quickly enough can stigmatize them for life.
I can teach anybody algebra. I can’t do it when students are virtually paralyzed with the fear of “sounding dumb” in front of their classmates. One-on-one tutoring should be required in math, not just a “nice to have”, because most parents won’t seek out tutors until the grades have dropped to emergency levels. And by then it might be too late.
Ah yes. Bullshitting out essays. I remember it well.
I was particularly bad. I’d create my entire essay in bullet points first. Lots of copy/paste to make sure the structure fit. Three ‘supporting facts’ for each paragraph’s contributing idea, each with a reference from a different source than the other two. Copy/paste the contributing idea to as a bullet point in the intro and conclusion.
Then go back and turn each bullet point into a sentence.
Then go back and apply proper paragraph formatting.
Final sweep to check punctuation, etc.
Done! A+
My ‘research’ would usually take place in class, so that was already accounted for. Busting out the essay itself was over and done with in 30 minutes.
I didn’t understand why it was so hard – they explicitly taught us to do it that way. It was practically cheating.
This is brilliant.
@nohellbelowus
A related (though less severe) issue is also being afraid of looking too smart.
Not sure if that’s also a US thing, or if that kind of bullshit tall-poppy syndrome crap is more of an Australia/NZ thing.
Otherwise though, I completely agree with you Re: fear of looking dumb being one of the biggest stumbling blocks.
Today I was writing an assessment test that we plan to use for software developers.
Suddenly I’m wondering if I should throw in a couple of algebra questions just to see what happens.
One on one is OK, but for some students it can be stressful because they see too much focus on their perceived inadequacies. My husband and I used to tutor such students with much of the session being on computer (with strict rules about sticking to the task and the difficulty level set). I didn’t teach much – I “prowled” listening for the self-talk. My job was nagging, literally. No, you are *not* too dumb to do this. You just haven’t done enough practice yet. Try it this way. Write it down. Have another try.
That paralysis often comes from the fear of any mistake at all being yet more evidence of abject failure. These discouraged students are much more likely than the A students to make the perfect the enemy of the “good enough” or the “better than last time”.
And discouraged is exactly the right word. They’ve lost whatever courage it takes to risk making any error of any kind. No matter how small, no matter how easily rectified.
I half BSd my AP European History and Biology exam in the essay section, and I got a 5. :)
Although it was only on one essay in both exams that I BSd in.
While I understand your frustration, this sort of reaction is also part of the problem. You often DO need to learn the rules – and, yes, be asked to demonstrate that you know them, tedious as it may seem – before you can bend/break them to achieve something greater.
Sure, there are ‘outsider artists’, especially in the visual arts, who produce amazing works with no “formal” training and no set rules of which they’re aware. But even there, often the most effective pieces do manage to follow ‘rules’ concerning colour schemes, layout, etc., even though the artist isn’t consciously aware of them. Hell, there are even some specific instances where learning “the rules” can inhibit your ability to break from them.
But effective communication with language depends on using a shared set of rules. You simply cannot get your point across while completely ignoring those rules. Lewis Carroll was great at playing with words and grammar, but also clearly understood the fundamentals: what would have been produced instead of “Jaberwocky” or Humpty Dumpty’s ‘mastery’ of words, without that understanding? Now you might insist that formally testing Lewis Carroll would be unnecessary, and I’d be inclined to agree. But how would YOU manage to pick out a budding “Lewis Carroll” from a class of 30 students, especially early on?
IME, students (and parents (!!)) who whine about (their children) being “forced to conform” to “arbitrary rules” because they’re soooo brilliant that they’re beyond them… often aren’t. Now YMMV, of course: maybe you’ve only ever met students who really are brilliant with wordplay, writing fantastical prose that is a joy to read, or perhaps you yourself are a literary genius. Perhaps you would benefit from having a teacher who spots your brilliance and actively encourages you to let it shine. No, I’m not being sarcastic here: I have also had the privilege of working with some truly exceptional students and peers.
BUT: given that in the current system teachers have to deal with dozens of students, mostly sorted by chronological age, and must somehow rank them in relation to each other… what exactly would you change? What’s your ideal system, and how can we get to *there* from *here*?
Please-
For the love of fuck tell me it hasn’t gotten that bad?
Please tell me that the up and coming generation isn’t batshit stupid?
Please tell me that they can ACTUALLY be taught to read?
Please tell me that “fuckwit*” isn’t going to be enshrined as a replacement for proper English?
Please tell me I don’t need to move to Mars-or suffer the downfall of Humankind?
Or should I just cap myself now?
*R U Getng Ths?
@poose
Don’t worry.
Predictive texting might save us yet!
[/sarcasm]
boring “kids these days” comment is boring.
Essentially you Americans are set up to fail if you can’t even work out that ‘mathematics’ is a plural word, and thus needs to be shortened (if you must) to ‘maths’, not ‘math’.
HTH :0)
Ibbica:
That “given” makes the ideal totally impossible. It’s like saying “given that women’s place is in the kitchen, how do we achieve women’s equality in the workplace?” Most of the “dozens” of students will be there under duress. The amount of time taken up by compulsory schooling means that a great deal of what anyone does will be meaningless busywork. Ranking and testing end up being a way of punishing uninterested kids for being uninterested.
Sure, there are ways to improve education within the constraints of the present system. But complaining about kids being disengaged without acknowledging these incredibly demotivating circumstances strikes me as being pretty unperceptive.
Indeed, and well said. I observed this phenomenon many times.
As humans we naturally seek to minimize pain, and maximize pleasure. Math is pretty painful, by definition. I always tried to convince my students that if they were in pain while doing their math homework, that was good evidence that they were trying hard and learning at their maximum rate. No pain, no gain, in other words.
Not sure if it worked!
Just remembered. For those who are educators or just interested in maths education, there’s another writer worth reading.
Daniel Willingham
http://www.aft.org/pdfs/americaneducator/spring2010/RotherhamWillingham.pdf There are other terrific items of his you can search for in the American Educator archive if you’re interested.
Add this to John Mighton’s ‘The Myth of Ability’ and you have a head start on good education practice and good guidance on remedial teaching.
I remember my 4th grade teacher assigning a problem in the book for homework, and then cancelling it without explanation the next day. The problem was to show some simple addition or subtraction on a number line, but she apparently did not know what a number line is. And of course all the grade school teachers (1-8 grade) skip most or all of the “word problems” since they don’t know how to do them. High School algebra didn’t really teach much except a few formulas — nothing about how to derive the formulas or how they might apply to real problems, or even much about what they had to do with graphs.
Some people here complained about doing only short, formulaic essays, but I was never taught even that much in school.
US schools stink.
@ibbica 97
I think you’re misinterpreting what I’m saying in that blockquote. I am certainly all in favor of learning and respecting the rules, and using those rules in order to break them in the best possible way (After all, what makes the rule-breakings so special is being sure they stick out as a subversion).
But for the record, I have never met students who are brilliant with wordplay, who are so brilliant that they’re beyond the rules. That’s what I’m saying. Knowing how to use the rules has actually made me one of the best students, because our teaching is so piss poor. Many students cannot use the rules properly. Basic rules.
Now, my issue with arbitrary rules? That issue is more with arbitrary formats. Not because of how it holds back brilliant students or whatever, but because it holds back damn near everyone.
Anyone can fill out a form. I hope. And that’s all you do in the stock 5-paragraph essay. You fill out the form. This involves no thought, no teaching how to convey your thoughts- just ‘fill out this form.’ Every essay I can ever remember writing has been that exact form, because teachers teach that ‘this is the exact and only format an essay can take.’ That is not teaching how to effectively form an essay.
What would I change? I would change the idea that making everyone pass so we get is more important than requiring students to actually think (because then some might fail and we’ll lose funding!)
Wow. I thought English schools were bad, but that sounds crazy.
Does the US have anything like Teach First?
Its a scheme to get high scoring (1st/2:1) oxbridge graduates into teaching (especially in maths/sciences given the perpetual shortage of these teachers)
After you complete your BA (3years) there is a short, high intensity summer, and then you go straight into 2 years in the country’s worst ranked schools. Completing this gets you a PGCE (teaching qualification) and (they claim) a shoe in for higher level teaching posts (ie heads of subject).
I know I keep getting emails about it, and although I personally won’t be doing it, and I’ve heard complaints about the summer prep not being enough, I know a lot of people who are planning to do it, or are currently doing it any really liking it, most of whom would never have considered high school level teaching before.
It does – it’s what Teach First was adapted from.
American education is why physicist Lawrence Krauss in his lecture “A Universe from Nothing” told his audience, “Ask any European high school student what is the sum of the angles in a triangle.”
An Australian television program asked questions for “man in the street” of different ages on simple geography, history, and math. One of the questions was, “How many sides are there to a triangle?” Need hardly to say that several people could not answer correctly. The other questions were equally simple and gave people trouble.
The Krauss lecture is on Youtube and a must see.
Give up algebra because it is too hard for the kiddies? Made me think of the following quote for some reason:
As someone who loves, and is quite proficient in, almost all areas of biology, I have a two year technical degree in forestry and am presently finishing my master’s in nursing, I can state, categorically, I have no use for algebra except in the most elementary form. I do nursing calculations, build barns, decks, and sidewalks on my little farm, figure out mileage etc. all without the benefit of algebra.
The area of my brain, I swear, that can process higher mathematics is…………..dead. I’m no good at music either. Please, don’t think I’m exaggerating here. I’m 59 years old, and have (tried) taken elementary and college algebra four times, wasting thousands of dollars, and probably lopping a decade off of my life because of stress. I…don’t…..get……..it. After the most elementary algebra, when I get to factoring polynomials, I’m entirely fucked.
Truly part of this is I have yet to meet a competent mathematics instructor. They are incapable of understanding how someone doesn’t get it, and generally have the teaching ability and social skills of a hyena, (do I sound bitter here?). In addition, every college I’ve ever attended, (I have a total of four, soon to be five, post-secondary degrees), has an absolute insufficiency, if not total lack, of skilled tutors to help struggling students like myself out. I’ve waited in line for hours to see a tutor at a state university, and was given three minutes the one time I was actually able to see the sole tutor the school supplied for that class.
My point is this; I’m an extremely competent, skilled, well-compensated registered nurse. I do intravenous calculations, weight-based drug protocols, including pediatric protocols, interpret lab results, myriad other mathematics related tasks, and have never used algebra. Not once. Just a little food for thought.
As an undergrad I always complained that we chemists had far too little maths. 2 semesters of Calculus, no Probability (not even Intro to Probability) and no Group Theory or Manifolds – how can anyone be expected to understand Quantum Mechanics when half the tools are missing? When I visited years later I learned that even the miniscule calculus had been dropped. Man, what incompetent chemists they must be churning out these days. Fortunately the prospective chemists (if we can even call them that) are still required to learn Algebra in high school.
How can one survive being poor and not understand algebra? There are so many ways the economy is geared to screw you on that level, that basic numeracy is kind of important to being able to eat.
Anyway, the whole topic brought this to mind:
[youtube http://www.youtube.com/watch?v=VxkHM4DUDKM&w=400&h=225%5D
#17: It is evident that math competency is lacking by the fact that I see so many answer then following problem 5+5-5+5×0= with 0.
True, but to give them a sporting chance wouldn’t you at least give it to them as (5+5)-(5+(5×0))= ? I remembered that multiplication takes precedence over addition and subtraction but had to look up whether addition or subtraction had the next highest precedence. If you use brackets even a chimp can figure it out.
@AlanMac
How did you get that embed to work? Mine seems to have come out wrong.
@Grimalkin: *nods* Gotcha. I suspect I was projecting a bit of my own experience on your comments!
@roland72:
Hm, I guess I wasn’t clear; I was describing characteristics of the current system, not requirements of the ideal. So it was meant to be more like “Given that most women are currently* not employed outside the home, how do we achieve women’s equality in the workplace?”
I specifically meant to leave open the possibility of an answer leading to the equivalent of “Provide to more women opportunities for employment outside the home”.
But my question remains: How do we get *there* from *here*? All the complaints in the world won’t change much if no practical solution is offered, and a practical solution must consider the current situation. If the answer is a complete and immediate overhaul of the entire system: what do you plan to do with the students who are currently in the system as it is now? Is there a way to make the change gradual, or is there too much baggage and we should just write off a half-generation of people as ‘lost’? Like I asked in the last ‘in vivo experiments’ thread: What specifically would you have us do instead, right now and in the future?
*Er… place this specific claim into its appropriate historical and social period, please.
dmgregory #62
*tilts head sideways, seeking joke*
Nope, still don’t get it.
Yay, for once my college degrees will actually afford me some credibility! I have two degrees, one in chemistry, the other in math. I decided to include the latter partially to better prepare me for my current work (MSc theoretical chem – hopefully followed by a PhD), and it did just that. Math is ubiquitous. There is no job or profession that doesn’t utilize it is some way. I can certainly understand that some teachers are just awful, but that is no excuse to just chop algebra altogether. Algebra, as in the limited version taught in schools, is foundational. It is both a means of solving a given set of problems, and a tool in science. Without algebra, you cannot fully understand trigonometry, calculus, the complex number system, or any computer aided approaches to science. Without those, you cannot be a chemist, physicist, engineer, astronomer, or even a biologist. You cannot be a pilot, a manager (or at least one of the rare competent ones), a teacher, a programmer, an architect, etc. If you do not understand basic math, your career options are limited to the most basic forms of manual labor (not that there’s anything wrong with that, I would just hate to see an entire generation forced into it).
Some students are just stupid. However, those are in the smallest of minorities, and I refuse to accept that 30% cannot pass some imbecilic exit exam (let’s get rid of those instead, plz) solely because of any decent math teachers. Hell, let’s increase the math requirements instead! Make calculus a required course. Make more than one year of any given science course required. Make basic logic a requirement. Make programming required.
@ ibbica
This is a difficult question, you are right. The biggest problem is the incredible political resistance to fundamental change in the way we approach education. Speaking from the UK point of view(strictly England & Wales as Scotland and NI are educationally separate) there have been some attempts to introduce some level of real self-government into state schools (=public schools in USAian). The best known ones at the time were Risinghill comprehensive school in Islington, London, Countesthorpe comprehensive in Leicestershire, England, and William Tyndale primary school, also in Islington. These were all 30 years ago or more.
All these experiments at treating children as if they were people were thoroughly strangled by local authorities; as soon as the Daily Mail readership hears about this the old tropes of “loony lefties” and so forth come out. This sort of scandalising is what stops any kind of progress in publicly-funded education. I’d be surprised if it was any different in the US or indeed anywhere.
All of the schools which allow genuine choice about lesson attendance in the UK are private, which brings its own problems. However, some progress has been made. It is now unthinkable for staff to beat kids at school, only a generation or less after it was commonplace and accepted. I think we have Summerhill and other progressive places to thank for that, at least in part.
What to do now? I would like brave headteachers to run schools – particularly primary schools – with much more emphasis on giving kids time to play. I would like to see the notion of compulsory lessons questioned and questioned again until those who actually make decisions are forced to justify them and find that they can’t. I would like to see some element of genuine democracy in schools – real powers of discipline given to the body of kids as a whole – which is the only sure-fire way to deal with bullying I have ever seen. There are a million things; but of course even these small things will be resisted tooth and nail by ignorant parents and teachers. It’s a long, long fight, but eventually I firmly believe we will look back on compulsory schooling and authoritarian education with as much horror as we look back at Victorian 8-year-olds working down mines. From a mental and emotional point of view I don’t think there’s much difference in the damage they do.
Years ago on a forum I post on there was a discussion on pointless things learned in school and someone posed the question, “Has anyone here ever actually used a quadratic equation?” The poster clearly expected a resounding “no”. However, several people with jobs in science and engineering replied that they use quadratic equations on a regular basis.
I’m a Philosophy major, and I can say with a straight face that I use algebra every day of my life.
Not in anything directly relating to my major, I’ll admit. I use it in my hobbies. Algebra is fundamental math; it is arithmetic with variables. If someone can’t understand algebra, they fail to understand one of these concepts, and that is not acceptable.
Everyone needs arithmetic. You need it to use currency in an effective way. If you can’t add, subtract, multiply and divide, you cannot survive in the real world.
Variables are, if anything, even easier. They’re a space in which something can be inserted. If you can look at a machine, take out a part of the machine, and look where the part used to be, you can understand variables. Someone who doesn’t understand variables doesn’t understand that concept, or at least doesn’t understand how to apply that concept to mathematics.
Here’s the thing, though: look at a 1040 EZ tax form some time.
You need arithmetic and variables to fill it out. You need algebra to do you taxes. Simple algebra, sure, but algebra nonetheless.
Cutting algebra out of the curriculum is the stupidest thing we could ever do. Life is full of math problems. They are all word problems. They can all be expressed algebraically.
Even students with significant intellectual disabilities can learn useful maths skills. (Check John Mighton’s book referred to earlier.)
But I’ve coached such students through to good standards of shop assistant counting-out-change skills as well as ordinary money management / budgeting skill.
The ones we now think of as ‘stupid’ are just the same as the kids who left school at end of year 9 50 years ago able to manipulate fractions in eighths and sixteenths as well as imperial money and weights and measures calculations. The kids aren’t much different but the schools and ‘supporting’ culture are very different.
If kids could get out of school with an actual appreciation for learning they wouldn’t hate things like algebra so hard. Unfortunately it seems that literally everything about schooling is designed to kill off the natural curiosity of people within it. An emphasis on grading and “tougher standards” and such is the antithesis to the idea that learning has intrinsic value; kids learn because they don’t want to get an F, should we really be surprised that they pick the easiest material possible in light of that? Its a perfectly rational strategy for dealing with being graded like meat on a regular basis. There is also such a weird focus on kids x years of age learning subject matter y, and if they don’t they get branded as behind for the rest of their schooling years. Real people don’t fit into these standards very well at all, they learn things in a non-prescribed order all the time.
Without focus on age-based standards, algebra would be just another thing to learn, which could be learned when it is needed. Making people do things (that aren’t at all relevant to them) on a nonsensical schedule is a recipe for citizens who are totally apathetic about learning. I relearned algebra concepts over and over because I didn’t give a shit about them at all until college. Thats when I learned it (again!) and it stuck, because I was actually interested in understanding it. I passed standards tests in high school (until the meaninglessness of it all made me give up completely) but the lack of relevancy made the information vanish after I was done extracting good grades from it. Am I really more successful than people who learn it (because it is actually needed) the first time? I would hardly say so. I was just a lot better at memorizing and discarding information in order to pass a test as a result of doing it for years. Thanks school! What a wonderful skill set to pass on.
I really resent PZ’s cynical view of kids and reading too- as if every kid would hate reading as much as they do now without having been forced to over the years. Want to suck the fun out of a book? Make someone prove that they read it by writing a paper about it (with a specific number of pages, with certain spacing, and subject parameters). or you could make them answer inane “study questions” about it, practically shouting a conclusion at people instead of letting them interpret the book their fucking selves (like a good reader does). THAT is why we have Y U NO WRT? and apathy, not because kids are inherently anti-intellectual or anti reading. They never had a fucking chance to enjoy it in the first place. Kids accomplish a lot with support because its natural to want to learn about the world around us.
Godotiswaiting:
Yes, absolutely true. However the hidden assumption is that putting kids in a classroom and telling them about it means that they will automatically learn it. I think this assumption is false. It takes no account of the wishes of the kids.
Skeptifem:
This, a thousand times this. Add to that the lifelong hatred and suspicion of learning caused by telling kids who don’t/can’t play this game that they are failures, and you turn schools into perfect nurseries for anti-intellectualism.
Skeptifem again:
And compulsory schooling must be about the worst support system imaginable. It’s actually active anti-support.
Btw, I’m not entirely sure that PZ’s real views on reading were represented in this post :-)
and without someone forcing people to learn it in school, they won’t? Money (even more complicated things like systems of calculating monetary exchange) is much much older than compulsory schooling. Society didn’t collapse because people can actually learn without someone forcing them to, especially when an obvious benefit exists to learning the material in question.
Also, I know more than one person who is extremely talented in higher math who have poor arithmetic skills. They have difficulty with multiplication tables specifically. This apparently happened to einstein too. People like them get put in the slow class in math because they don’t pass inane timed tests, yet go on to do engineering level math classes because their actual understanding of math is way better than the average person. It blew me away to find this out because it had seemed (to me) that there must be some natural progression to the material taught in math classes, that you MUST master all the skills from early classes to be good at math later, but it doesn’t seem to hold true at all. I suspect that the same thing is true of many other subjects.
roland
perhaps not, I woke up several hours earlier than usual and could have interpreted things incorrectly.
Ironic,isn’t it. High School Algebra is the only class that has had real use in my adult life. The other classes may have been enjoyable or memorably boring but Algebra was useful.
I’m old enough to remember a time when every graduate of an accredited High School in Nebraska could enroll at the University of Nebraska. Freshman English was there to weed out those who weren’t College material. They’d give you some horrible book of length such as The Scarlett Letter each week to read, analyze and write about by hand or with a manual typewriter. Spelling, punctuation and grammar were important. If you didn’t have the mental discipline to do the grunt work to pass this course, the thought was that you didn’t have the discipline to do anything that required sustained effort at the College level.
As a side note, I’ll be the first to admit that my punctuation, grammar and spelling skills have deteriorated over the years.
I’ll also admit that Freshman English probably washed out what might have been some otherwise brilliant students.
ericpaulsen@114:
The whole point of having a standard order of operations is so that mess of parentheses isn’t necessary. The reason you couldn’t remember which came first, addition or subtraction, is that they are, in a sense, the same operation (just with different directions, if you like).
For example, 5 + (5-5) + (5×0) =? gives the same result as your formulation, and 5 + 5 – 5 + (5×0) =? will also tip the student off, no matter how they parse it. Then, all you really need to know for this equation is that multiplication/division binds tighter (or whatever terminology you use) than addition/subtraction, and that final set of parentheses disappears.
But according to Cognitive Load theory, this is the sort of thing that ought to be second nature. If this isn’t readily available from long term memory, then you are chewing up precious working memory on remembering order of operations. It’s like needing to think about where which musical notes correspond to the piano keys, instead of being able to go straight to them without consciously thinking about it. Since working memory is a terribly scarce resource, it means that there is so much less “thinking room” available for anything else, and maths (like playing a piece on the piano) will be very, very hard.
(See Pinker, How the mind works, and Sweller regarding cognitive load theory).
I keep hearing this bullshit around FTB and places like it. The argument basically says students should know X, because I think everyone should know it, and we should force them, because harder material is better. It is exactly what has landed us in this heap of shit already. There are several practical problems that you have failed to consider. Using force doesn’t make people learn, it makes them learn how to pretend that they know things so that they do not get in trouble (or so they can obtain a reward). What of people who will want to learn it when they are intellectually ready to, instead of on the schedule you propose? What do you think they will conclude when you force it on them early? They will conclude that they are just “stupid” about it and probably not try again later. This is doubly true for people who are discriminated against, assumed to be stupid by default (girls, non white kids, the poor, etc).
Also, I know *you* use programming and calculus, but the majority of adults do not. Why would you force people to learn things that they have almost no chance of using in their lives? Is the ultimate goal of schooling that everyone is ready on paper for a STEM degree in college? I must have missed the memo where we all found out that STEM degrees are the way to measure the intellectual worthiness of people. Is that the schooling you want? Or do you want schooling that is about helping people do the best they possibly can, to still enjoy learning when its all over?
@Pipenta in comment #14,
The story you may be looking for was written by Isaac Asimov. It is called “The Feeling of Power” and has a wiki entry.
http://en.wikipedia.org/wiki/The_Feeling_of_Power
I’d be mostly ok with removing algebra as a requirement, what little most people use as a practical skill can easily be folded in to classes on their specific field of interest. Even for low level technical jobs, one of the two community colleges I went to had a “Math for Science and Technology” that taught the algebra, trigonometry, and geometry that most low level technical jobs needed.
That being said, the practice it provides in disciplined, rational thinking is extremely valuable even if you never use algebra itself once the class is over.
So, ok, remove algebra, fine. What do you replace it with? The disciplined thinking side of algebra is something that I don’t think we can afford to lose. As loose as so many peoples thinking is, take away algebra without finding some other way to teach the thinking side, and we’ll be screwed. School isn’t just about learning practical skills, it’s also about learning how to think.
So basically, I’d consider supporting a proposal to drop algebra requirements if there was a proposed replacement to cover the thinking skills it practices. Either teaches those skills in a better way, or the attached practical skill has better general applicability. Without such a proposal, anyone supporting this is insane.
No, I don’t really have any idea on what would be a viable replacement. I could think of more widely useful practical skills easily, but not really one that would replace algebra as thinking practice all that well. I’m just open to the idea if someone cleverer than me came up with something.
No, this is a myth. Einstein was always at the top of his class; the myth arose because in 1986 his school changed marking system from 1 being the highest mark to 1 being the lowest mark. A researcher casually looking at his marks, mistook his marks as meaning that he had been failing, and the myth was born.
He “dropped out” of high school early, to avoid conscription into the army, and went to Switzerland with a letter from the principal requesting that Einstein be allowed to sit the entry exam for the Polytechnic, despite being two years younger than the minimum age. He did not have the requisite skills in French or Swiss Geography, and so spent a year studying at a local highschool before entering the polytechnic, still one year younger than everyone else.
For some reason, there is a lot of quote-mining to make out that Einstein was stupid, or at least seen to be stupid. From my reading on the subject (mainly from online copies of primary documents held in the Einstein archives in Israel), no contemporary of Einstein thought that. They did think he was arrogant, and with an attitude that would mean he would never amount to anything. He was not sponsored by any faculty to work as an adjunct at the polytechnic while doing his PhD, and so worked as a patent clerk to bring in some cash.
Oh bullshit. Algebra is an EXAMPLE OF the type of thinking you are discussing. To pretend as though learning algebra specifically is the only way to think analytically is dishonest.
skeptifem:
Because people who are mathematically illiterate are vulnerable. It’s not true that people have no chance of using these skills.
Back in the day, I wrote a program to emulate our housing mortgage contract, and over the years found several instances of “bank errors” in the bank’s favour, which would have left us thousands of dollars poorer had we not picked it up.
I was explaining why math is important to my soon-to-be-entering-high-school son. If you’re going to paint your house, re-do your roof, or fertilize your lawn, you need to know geometry to determine the are you’re working on, so you don’t buy too much or too little of what you need. I pulled an aquarium out of the garbage, and had to figure out the volume so I knew what size filter and heater to get. When I work on my car, I have a torque wrench graduated in inch-pounds that I usually have to convert to foot-pounds. I cook, too, and have to use math to double or half a recipe.
So yeah, anyone who says they don’t need math is a fool.
@3
I doubt they will need a manager, they will just use a computer to do it for them. I don’t see many manual cash registers these days.
People keep talking about how stupid and lazy poor people are for not wanting to count out change and so forth, but have any of you looked at the desktop in a hospital lately? There are applications for calculating all kinds of shit that used to be done manually. I’ve answered my fair share of totally embarassing questions from doctors/nurses about very basic concepts because automation has come so far. I’m not automatically saying it is all a bad thing(I’m sure a pediatric dosing calculator is less error prone than a human calculation), I am just pointing out the world we live in now. I think that there is a more meaningful discussion to be had than how dumb people are for failing to do something that would probably just waste a lot of their time.
Calling people dumb for failing maths is, to my mind, blaming the victims of an failing education system, which includes the anti-intellectual community that surrounds them, so I agree with you in part, at least.
I don’t agree that maths is a waste, but my idea of maths is where the maths is well taught, and not dependent on wrestling with endless problems in the hopes that the student will infer the mathematical principles involved.
The problem with that is it it will remove options for students, and the decisions that will remove options will have to be made when many are not entirely sure as what career they will want to pursue.
Again with the unspoken assumption that simply putting kids in a classroom and telling them something means they will learn it. Assuming Hacker’s statistics are correct, rather over a third of kids who are tested in algebra (at least for those states) fail. Yet they’ve nearly all been in an algebra class haven’t they?
Being able to do algebra is undoubtedly a good thing. I’d like to see a world where lots more people can do algebra. Probably the single change which would bring this about fastest would be dropping compulsory lessons, and the consequent banishment of the stultifying fear of learning which they bring about. Sure it would still be a long journey, but I would love to see even the smallest sign that we are about to begin it.
Incidentally, an improvement in world understanding of algebra would be an entirely incidental consequence of voluntary lessons, and should not be seen as any kind of goal. The really fundamental change that I would like to see is an increase in self-determination for children and an element of self-government in their schooling – “schooling” used here in its broadest sense. Real self-government automatically implies voluntary lessons; and in fact it’s the self-government which is most beneficial. It tends to make kids happier and enjoy themselves more. That, combined with an honest approach from adults and easy availability of any instruction wanted, would go a long way to giving us the better-engaged population we’d like to see.
None of this would be easy to achieve; and indeed historically speaking compulsory attendance at school was a great humanitarian triumph since it meant small children didn’t have to work any more. But we’ve got beyond the stark choice between the schoolroom and the mineshaft now… haven’t we?
Even if one doesn’t use algebra itself, learning it can only improve one’s general problem-solving skills. It keeps the mind pliable.
Since most algebra requires the use of a calculator, I see this situation as a failure in how to teach and use technology skills. There are things like iPhone apps for algebra:
http://itunes.apple.com/app/wolfram-pre-algebra-course/id453096829?mt=8
It cost a $1.99! Start with pre-algebra and add $1.99 apps as you improve. This is the beginning. You still need a good maths teacher connecting this technology skill to real-life situations.
Additionally, I see companies like Pearson as the problem. They sell tests, of course, and have convinced enough of our “enlightened” politicians that testing is the key to unlocking the mind when nothing could be further from the truth. These would also be the same politicians that have no problem interrupting the school year with christmas and easter vacations at critical times in the learning cycle. But I digress.
I assume no such thing.
Wait, what? I took algebra in about 1970. I didn’t have a calculator, I had a slide rule. And I never had to use it in algebra class.
it does?
ok, so maybe I don’t understand what algebra is, after all.
Thank you, Dr. Myers. I read that column two times to see if there was a hidden “LOL, only kidding”, but apparently he was serious. I find it very sad that someone in higher education, a person with advanced degrees would question algebra. Algebra, not calculus, not advanced trigonometry, but something as basic. Very like “why teach basic arithmetic, since they can use a calculator”. And where did the “they will not use it in their lives” argument come from? Do people no longer estimate unknown quantities based on known values? Like budget? Or estimate arrival times? Or does he think that is something else, not “algebra”. Wow , just wow!
The arguments seemed so much like “Students find it hard, so lets not teach them that”. Some of my students find the distinction between “their”, “there” and “they’re” hard. I guess they don’t need to be taught the difference!
So if you remove algebra from high school, presumably you’d also be removing geometry, trigonometry, calculus, and statistics because you really can’t teach those without the fundamental knowledge of how to solve problems and rearrange equations. So they seem to be suggesting to remove the entirety of high school math except basic arithmetic. That sounds an awful lot like the education system of small Christian groups like the Amish where people stop formal schooling at around age 14.
I also think the general public doesn’t appreciate where algebra is useful. If you’re shopping, and you want to know what size laundry detergent you should buy. There’s many brands, some are liquids, some are powders, so you can’t just go by which is cheaper per mL or gram. But a bit of basic math tells you which brand is most cost effective. Or you could be math illiterate and just buy the shiniest box, regardless of how it affects your budget.
If we left what subjects should be taught in middle and high school to the students desires, I cringe at what would be chosen.
Parental Unit observation: my kids have ‘calculator active’ portions of their math classes and non-calculator portions so they are well aware that algebra doesn’t really require a calculator.
I’m not sure why you think it does since I took lots of algebra classes and never used a calculator except to explore how to graph functions in one for a week. We hated it, paper was easier.
@echidna
Well, you didn’t question skeptifem’s use of the word “force”. How do you think we can compel kids to become mathematically literate? The usual answer to this question is “put maths in the compulsory curriculum”. This assumes that kids automatically learn stuff by being put in a classroom and fed it. I would suggest that it’s in fact impossible to compel kids to become mathematically literate in any humane way; it seems ironic to suggest that literacy (mathematical or not) would be improved by voluntary lessons but I believe it’s likely to be the case.
If that’s not your assumption then many apologies; but I’d be interested to hear your ideas on how to improve engagement. Given that forcing kids to attend lessons isn’t likely to end soon, any suggestions you have might well be more practicable than any of mine!
The “algebra requires a calculator” remark sent me to wikipedia for a definition.
huh.
(also, you can’t play darts without “elementary” algebra)
Frankly I’d prefer to see the teachers and schools “forced” to actually teach mathematics. Kids especially, and people in general, mainly learn just fine when not actively discouraged from doing so.
I’m pretty sure your last line there is the goal of the religious right-wing. They may all look like idiots, but the guys at the top of that ladder are devious and cunning.
Regarding algebra: never mind whether they can learn science or tech skills, how about going to the frigging supermarket? Just because there aren’t Xs and Ys doesn’t mean it’s just arithmetic. The skill of manipulating numbers around until you solve the unknowns is exactly the skill you use to compare relative costs of different options; and therefore to figure out how many loaves of bread and jars of peanut butter you need to make enough sandwiches to feed your kids lunch this week.
The cumulative effect of two of the right wing’s darling plans is terrifying: First, create a class of people with zero skills to get them through life. Next, when they are unable to gain any useful employment, refuse to provide them with food, clothing, or shelter.
No math requires a calculator.
Calculators just make it easier.
The rest of your post missed the point entirely, so there’s little value in discussing it. This, however, is just ripe for some tearing apart. Firstly, the objective of education is not to foster anything, it is to endow students with the tools necessary to be productive members of society. Secondly, you are aware that your exact point can be used against any subject, yes? The vast majority never need English lit, or art, or PE, or any of the science courses. They may not need keyboarding, math, CS, or foreign languages. This does not render them useless. Likewise, while the subject itself may be esoteric, its applications may not be. In the case of programming, you learn to break a problem down into components, and to solve them individually. It teaches you to think, in other words. The same works with calculus and formal logic. I am certainly not opposed to including/excluding other subjects from the required list. It’s simply that those happen to be in my area of expertise. Now there’s the matter of the word “force” you used. I once again direct you to the actual mission of public education. I do not consider the use of “force” to be misguided, and certainly not the cause of the current problem. If anything, the lax attitude described in Hacker’s article (which I was also privy to during my high school days) is to blame.
I’m one of those fuzzy “social science” types, and I see two problems with this argument. The less important one is that I didn’t know I was going to do that – I was halfway through a computer science degree before I decided I’d really rather study people than bits. The more important reason is you use algebra every freakin day! Sure, you might not sit down to prove that 2x^2=34, but you work out tips, make change, figure out how much something is without the tax or how many cucumbers you need for x people for a salad, and that’s all before you ever do a thing professionally. If large numbers of children are struggling to pass a standardized test, maybe the problem’s the test.
Roland72: How about developing a skilled, engaging teaching force?
I know my motivation and enthusiasm for various subjects in school was pretty much 100% dependent on the teacher. I loved algebra because Mrs. Levinson was awesome. I hated chemistry because Sr. Whateverthefuckhernamewas was a horrible bitch. I was soured on calculus by an incompetent pre-calc teacher, but thanks to Mrs. Levinson, I already had a self-image of being good at math, so I fought through it and eventually got through three semesters of calc plus linear algebra.
I hated history with a passion until I had the right professor in a mandatory history class and fell in love with it. What a difference it makes to view history as a narrative, and to look at the causes and effects of event, rather than just a list of names and dates and dry facts! I ended up getting my degree in history.
We don’t pay enough to attract the best people to teaching. Maybe if we did, we might get better results for more of our students.
point: while I agree in concept, many math CLASSES require the use of a calculator and basically train in how to input the numbers to get the correct answer out.
And someone upthread said algebra requires the use of a calculator?
Must be a child. I’m of Generation X and I didn’t get to use a calculator for math class until calculus, and it wasn’t a programmable calculator. It just did the complicated arithmetic that would take too long to complete during a timed exam (e.g. square roots, or division of long decimals into each other).
I hope this helps clarify the topic of math teaching –
1. Estimation in math is important. It should get more emphasis. Everyone using a calculator or computer for a calculation should know the approximate expected answer before hitting the enter key.
2. Students of parents with professional jobs are more likely to see the importance of math. Students of parents that never use math are more likely to not see the importance of math.
3. Private secondary schools only appear to be better because they can select the ‘successful’ students. They send the discipline problems, slow learners and learning disabled packing to the public schools.
4. In the large upper socioeconomic suburban schools many students take math every year and many of these take a year of calculus and even get college credit for it. Require every student in every school to take math and science every year. The fast and slow learners don’t have to master the same courses.
5. One can teach and understand evolution (and a lot of good science) without algebra. See Richard Dawkins, The Greatest Show On Earth. Don’t blame the math teachers for the general students not learning science.
6. The Republican Party is trying to debunk, starve and dismantle public education. The rich erroneously think they don’t need public education.
Again, commenting as Parental Unit here: my kids are in public school in a super-not progressive place and they have never taken a math class that ONLY used calculators. The teachers have to have “calculator active” and “calculator inactive” portions of the class so the students actually understand the math. They train them to use the calculators, that’s true, but they have never had a class that was exclusively calculator because that would completely fubar the “test”, the EOGs have calculator inactive as well as calculator active portions. Teaching for the EOGs requires the teachers to teach how the math works as well as how a calculator works.
This is public school so I can’t say how private schools operate about maths.
@Pteryxx
Quite so. The effective teaching of maths is hindered because teachers have to be responsible for discipline, which is a direct result of compulsory lessons. This means that many potentially effective teachers are dissuaded from teaching because they are no good at classroom discipline. I cite myself as an example – had a great time teaching at Summerhill, got several kids through GCSEs in languages and history – but, later, as a teacher of a music group in a compulsory environment was a horrible failure.
It’s also hindered by the presence in any compulsory class of a substantial proportion of kids who are not interested. Even the most amazingly inspirational teacher in the world isn’t going to interest *everyone*.
I agree that kids learn fine when not actively discouraged. I can’t think of a more effective way of actively discouraging most children from learning than making them go to lessons. Those of us who were privileged by being academic cannot understand the incredible pain and confusion which is caused by the prizing of academic attainment over practically everything else in regular schools. Listen to people who have been affected by it – it’s pretty sobering.
@frog
I agree that having a good teaching force is a great idea, and that spending lots of money on this and on school facilities in general is an excellent idea and would undoubtedly improve everybody’s experience of education. Compared to what I’d like to see I’d say it’s a lot more likely to happen as well, so perhaps a better thing to campaign for in the short term.
But stuff is worth learning for its own sake. To develop on Pteryxx’s point, kids learn fine when not discouraged – and they really do find genuinely interesting things genuinely interesting. You can trust them! If something really does interest them they will go at it like a dog at a bone – we can rely on the inherent interest of the world to inspire kids, so long as we make instruction in it available, inform them it’s there, and don’t kill interest stone dead with compulsion.
When teaching fractions to year 4, tell them right up front that every single one of them *will* succeed. Tell them they *can* learn what’s required. They *will* be able to do the work set at the end of however many weeks it is.
Just make sure you’ve got the teaching materials and the personal skills to make it happen. You *must* be able to explain clearly and to elaborate those explanations for students who don’t get it at first. You must also have the personal skills to hand out lots and lots of praise – for demonstrated competence or improvement. Students might be ‘stupid’ but they always know when praise or reward is undeserved. They don’t value it and they don’t respect the person who hands it out so cheaply.
None of this “everyone wins” because they tried nonsense. Every student *will* be able to do equivalent fractions or addition/ subtraction of fractions. Noone fails. Noone is laughed at. Everyone who needs help will get it. And because of this they will try. They already know a lot more than they think they know – stress and tension just gets in the way of good performance. Remove the obstacles and learning moves right along.
I recommend John Mighton yet again. This is part of his approach and it really does work.
Damn, didn’t see this on PZ’s RSS until this morning.
Anyway, as Jules might say, allow me to retort (as a grad student in math with a background in teaching both high school and college):
I’m pretty sure this was the first electronic calculator that I used.
http://en.wikipedia.org/wiki/Sumlock_ANITA_calculator
@mildlymagnificent
These sound like really good ideas to me.
This is the difficult bit. I would like to think that people with the personal skills to accomplish this are easy to find, but I don’t think they are. Are there ways of learning personal skills like this? Absolutely sincere question; it’s something I’d love to be able to do.
I think the high development of personal skill required here, particularly as it relates to discipline in the classroom – while a good thing to have – is a product of the compulsory environment. I would argue that in a voluntary environment we would not need to ask so much of our teachers, and that perhaps they would therefore be easier to find. Teaching is tricky in any environment – but compulsion makes it needlessly trickier IMO.
I think also we need a broad definition of “teaching materials”. I think this should include the quality of the building and the support given to these methods by the whole school and by the education authority.
But with proper funding and application your suggestions sound good. Thanks for posting them.
I actually enjoyed calculus, but really, it’s useless outside the hard sciences.
Bullshit. Economics, for starters, requires calculus, and a whole lot more. My mom is an economist, and you know why I couldn’t read her PhD thesis? Because the math was so far beyond my college-level courses.
Basic algebra really is very useful stuff, one of the four or five basic competencies needed in a majority of jobs as has been verified by surveys of workplaces(Murnane and Levy 1996). Thing is, though, to ensure that students learn particular mathematical skills like algebra, the solution has always been to make them study the next level of mathematics. For example, a lot more people actually use the content of a second-level algebra course than will ever have to use calculus to find the area under a curve; but the only way to survive a calculus course is to finally master the algebra and trig you faked your way through in high school. And so on up the line all the way. By this logic, the predictable effect of removing basic algebra from the curriculum will simply be to produce more graduates who can’t do arithmetic either.
Calculus is also needed for statistics.
I once tutored a neighbour’s kid in trigonometry. She knew the various trig rules OK, but had trouble actually doing the problems. Once I figured out that she hadn’t got the algebra to get from the word problems to setting the equations up so that thing you want is on one side and everything else on the other I stopped tutoring her in trigonometry and started tutoring her in algebra.
My mum had problems with it I remember her saying, where to me it seemed fairly easy, certainly at the basic level. Whatever you do to one side, do to the other. Keep doing this until you have only one variable on the left. Preferably the one you want to solve for.
And I am still continually growling at third year tertiary students for not solving the equations as much as possible before putting the numbers in.
(I wasn’t so fond of Partial DEs though. The bit where you had to guess which of the several options might work, tried it and if it failed tried another seemed inelegant to me.)
And in those societies where monetary exchange was important, the majority who were innumerate or barely numerate were pretty much at the mercy of those who were not. The same is, of course, true today. Understanding practically any of the really important political issues we face require a facility with algebra, and at least the basic concepts of calculus (e.g. the difference between absolute and proportional rates of change).
As for abandoning compulsory schooling, that would work just fine for the children of parents with the means and motivation to assist and encourage their children in their independent learning. For the children of those who are poor and themselves ill-educated, not so much.
Well, I used one for passing college algebra around 1982. They were especially useful with the quadratic formula, Fogs and Gofs and since they are useful tools, why not employ them?
I was also distracted by periodic religious festivals required by my parents so I obviously didn’t hone my skills as well as you, PZ. Embrace app evolution. Lolz.
I see what you did there. :-)
And without a well-informed citizenry, democracy cannot work.
In an absolute monarchy, it’s enough if the monarch knows what he’s doing; if everybody else just follows orders and the monarch happens not to screw up, everything’s fine.
In an aristocracy, it’s still enough if the noble class knows what they’re doing. As long as they manage to put important things above their privilege, everything’s fine.
In a democracy, more than half of all adults need to know what they’re actually voting for. When they do, the advantages are manifest – the more people participate in the discussion, the less likely is it that the outcome will contain avoidable mistakes; officers up to and including the head of state can be gotten rid of without bloodshed or other drama; people will actually support even difficult decisions, because they know they’ve been heard and compromises have been sought; and so on –, but when they don’t know what they’re actually voting for, Athens destroys itself by causing the Peloponnesian War or McCain bomb-bomb-bomb, bomb-bombs Iran.
Oh, BTW, Austria’s school system assumes you have a passion for either math and science or languages.
Being a slow math learner and wanting languages, I took the latter branch and managed to get some extra science…
But even so, I had both calculus (differential and integral) and basic statistics and probability.
…See, where I come from, that’s all taught in highschool, and passing the graduating exam at the end of that school type gives you the right to study at a university.
I had those for the first 8 years. After the first 4, though, we had to choose between “technical” (shop) and “textile” (handicraft)… so I haven’t crocheted or knitted in *calculate, calculate* 20 years and a bit over a month.
Poor is the new black.
What – are these separate subjects in Germany??? In Austria it’s all just “math”. After all, in geometry, you draw less and less and calculate more and more over the years, till the drawing is either reduced to a sketch for anchoring the imagination (optimization tasks, vector geometry…) or tacked on at the end pro forma (after calculating all properties of a function).
That is just stupid. It would teach kids that math is a ritual, performed for the sake of tradition, if not explicitly for tormenting them. Everyone in the real world uses calculators, and the kids know that!!!
Especially in the later years, plugging the actual numbers into the equation you just derived and getting the numeric answer isn’t even the interesting, important part. That part is how to get the equation, and that’s not something a calculator can do in the first place.
It’s true that many can’t tell if the answer they get is in the right ballpark or was produced by a typo. Teach them estimation better. I was taught some.
Sono pazzi questi Romani.
Three!?!?!
…
I’m doubly and triply culture-shocked.
Over here, kids are afraid of being mocked for being a brainer ( = showing any interest in anything school-related), and it’s taken for granted that math is hard. Those who repeat classes are never looked down on by their peers for being stupid, because that would be an act of sucking up to the teacher, where “teacher” is short for “enemy”. ~:-|
This, on the other hand, happens a lot. It manifests in different ways – extroverts yawn “I can’t doooo thaaaat”, introverts freeze, try to sink through the chair, and count the seconds till the lesson’s over –, but it’s very common.
“Fuckwit” isn’t a replacement for proper English, it’s an enlargement.
“Mars-or”, on the other hand, is just jibberish. I stumble over such shit when I read it. Learn to use dashes, fuckwit. ;-)
That’s true, but only in English – and it makes no sense whatsoever.
:-o
I’m pretty sure that meant you were telling them they were completely incapable of learning anything more advanced than whatever simple thing was giving them a headache at the moment. *headdesk* *headdesk* *headdesk*
Please explain what I’ve misunderstood and save me from my own headache.
Oh yeah, that’s common. Only music teachers are even worse.
Er, what? Addition and subtraction are equal in precedence, because they’re the same thing – subtraction is the addition of a negative number, and addition is the subtraction of a negative number. That means 5 + 5 − 5 + 5 × 0 = 5 + 5 + (−5) + (5 × 0) = 5 + 0 = 5.
How I’d actually do it is I’d see “+ 5 − 5” in there, drop it because it’s 0, be left with 5 + 5 × 0, drop 5 × 0 because it’s 0 again and “dot before stroke” (multiplication/division has precedence over addition/multiplication), and then only 5 would be left standing.
You won’t, because there simply aren’t enough such jobs in the entire world.
o_O How would that work when someone unpopular is bullied?
Not quite; he got a 4 in math. In Switzerland, where that happened, 5 is best.
In Germany, the numbers go in the other direction: 1 is the best grade. Hence the myth that “Einstein almost failed math”.
No. When you stop making it compulsory, its reputation as boring and useless will by no means automatically go away. The few students left in the class will like it and will excel, but everyone else just won’t take the course, or (more likely) will only very late.
When is summer vacation in the US?
The trouble in teaching is not that the subjects are hard, but the students are convinced that they are either difficult or useless. I used to teach a math class for students who wanted to become teachers. I had one student who was sure that they best way to do math was to memorize the kind of problem, so that she could repeat the solution on the exam. She had every intention of becoming a teacher and telling her students that this was the best way to do math. She would (at best) ignore my lectures on how to understand the principles, and (at worst) interrupt them to ask how to do certain questions on the assignment.
@101: Of course! Which is exactly why we abbreviate “economics” as econs.
Or, I mean…
Oh balderdash.
No student is genuinely “afraid” of being perceived as smart by his peers.
Having an “I’m smarter than you” attitude around friends and classmates, on the other hand, is a completely different can of worms.
Big difference.
Stop being a snarky, disingenuous twit, and I might waste a few more words on you.
Wait till you see it in action. When kids have real power over decisions they are pretty wise. How you could introduce democracy in a publicly-funded school situation – where it would necessarily start in a pretty immature state – is indeed an interesting question. But having lived in a mature democratic school for 3 years I can assure you it works. I gave a talk about it some years ago which expands on this – google “think twice summerhill” if you’re interested: it’s the first result.
So in this scenario, a few kids will learn algebra well and others will not. I don’t think this is very different to what happens now; but with the improvement that the teacher has not had to waste time and energy keeping discipline, and the uninterested kids have probably done something more productive with their time and have not been put off learning algebra in later life.
And don’t you think that algebra’s reputation of being boring and useless (along with that of history, Latin, any number of other subjects) might actually be *because* it’s been forced on the unwilling? I don’t remember maths ever having that reputation at Summerhill.
This attitude is absolutely revolting. Clever kids *are* bullied for being clever, and you’re telling them it’s their fault. Stop it please.
Also all kids are “he” are they? That’s not going to wash awfully well round here, and I say that as a relative newbie.
WTF!
Algebra! Not that I can currently solve a trinomial equation, but seriously algebra! Maybe not everyone is up to the task but when I had to face the challenge it was with pencil, paper and brain. I didn’t even have a scientific calculator!
Is it any wonder that America is falling behind in science? Seriously folks. Our country is falling to pieces, bit by bit. America is becoming the next serfdom empire. A land of servile workers and the financially endowed elite.
Maybe the “Hunger Games” and “A Handmaids Tale” are not that far off.
But, but.. what about horrible, obscene, rebellious adolescent poetry attempts? Writing your first sci-fi story? “Love” poetry at 15? Being crap at writing is the *perk* of education!
Also more seriously PZ, forget biologists and physicists – the single most prominent growing means of employment is IT – programmers and computer engineers. Algebra is a cornerstone of what is becoming the major means of employment and production. With robotics even the basic professions: mass-produced furniture, vehicles, utensils – essentially a majority of consumer goods are not made by craftsmen, but the product of a human-machine interface controlled by lines of computer code.
If you don’t learn algebra, forget being employable in the 21st Century.
Shut your piehole.
Kids are afraid of being bullied. They are not afraid of being considered smart, because intelligence is a positive attribute, in any context. They are afraid of idiotic bullies who use their own insecurities to justify their bullying. They are afraid of morons, essentially.
nohellbelowus
roland72
nohellbelowus
And they often target the ones perceived to be smart.
My husband works at a prestigious liberal arts college. He has told me the students are not ready to handle calculus, even though many have taken Calc 1, 2 or even 3 in high school through AP or similar courses. Why? They teach formulas, not concepts. Why?
Well, according to the NSF article America’s Pressing Challenge — Building a Stronger, that “Nationally between 17 percent and 28 percent of public high school science teachers, depending on field, and 20 percent of mathematics teachers lacked full certification in their teaching field in 2002; the problem was proportionally higher for middle grades. Although most mathematics and science teachers hold a bachelor’s degree, many are teaching subjects for which they have had little or no training; this “out-of-field” teaching is most prevalent in rural[16] and urban districts and high poverty areas. These districts reported difficulty acquiring and retaining well-qualified mathematics and science teachers.[17]”
Wow. Guess it’s hard to teach a subject you know nothing about. There are many reasons why students have problems with learning math, and this is one of them. Another reason is fear. Students are told from the time they are small that math is hard hard hard and only those who are naturally smart can understand any of it. Therefore, it’s OK to not understand. This, of course, is ludicrous. Numbers is not math, especially in lower courses. Math is critical thinking. It’s like how a novel is not just words–it is ideas about culture and exposing readers to different ways of viewing the world.
Teachers and counselors can be great hinderances in learning math. When I was in 8th grade (1988) and struggling with algebra, my teacher (the basketball coach) told me I was a girl and wouldn’t understand it anyway, so he wasn’t going to bother trying to explain it to me. I wanted to become an anthropologist, and had no realization that taking that advice to heart meant my future dreams were already destroyed. The school counselor agreed with my teacher, and told me I had a “block” against math and could never hope to understand anything above basic math. How many others are told the same thing, over and over? I went to a rural Wyoming school, and wonder how many other secluded school districts find this type of thinking attractive.
Hacker forgets that most people who have learned something (& forgotten) will relearn it faster when next exposed to it. So on the off chance that one forgets how to do ratios, proportions, or manipulate polynomials. It’s okay: it won’t take all day or all week to re-instill these principles. But if we wait to teach everybody anything until the moment they will need it, they will be spending months learning basic facts.
I think the main reason algebra hurts high school graduation rates is that it should have been covered prior. Math seems to progress at a steady rate until about 5th grade, where it stagnates for 3-4 years before students are exposed to anything new (Algebra & Geometry). And then all of a sudden these things (apparently) have steep learning curves that throws all those poor students off track. We need to simply plant the seeds of algebra & geometry sooner and stop emphasizing the difficulty: it wouldn’t be such a big deal & students would do better.
Hacker also conveniently leaves out the price tag: Trade schools & colleges will happily charge big bucks to teach their students the things our high schools should have taught with tax dollars; businesses will waste more of their time/money teaching “new” skills rather than simply refreshing older ones.
On the “force” issue. During my childhood I (I think rightly) considered the whole of education being making children who want to play in the streets, run around free of authority, kill bugs and pick their noses actually learn something. Education is painful, but the reason its compulsory is that, similar to vaccination, the net benefit overweighs the costs by several orders of magnitude. A majority of the things I learnt at school I felt I was being forced to learn, all the while
Er, no. I’m not exactly sure what you mean to achieve with this remark.
I would recommend you give this a little more thought. The second sentence of this quotation is not consistent with the other three. Also not all bullies are stupid.
Storytime!
So I went to a small (US) school, and when I was in seventh grade I was skipped ahead in math along with another student to eighth grade, wherein we learned the Dreaded Algebra (TM).
The progression was: 8th-Algebra, 9th-Geometry, 10th-Algebra II, 11th-Pre-Calc, 12th-AP Calculus. There was an option for “business math” instead of pre-calc, if I remember correctly (pre-calc was basically trigonometry, btw).
However, after this one other student and I were skipped ahead, they changed the whole math regime, so that 8th grade was “pre-algebra” and so forth. The end result was that now no one could take calculus if they followed the standard math progression.
Surprisingly when I took AP calculus as a senior (12th grade, because I studied abroad my junior year and ended up taking calculus in Spain and having NO IDEA that “derivadas” were calculus lol) I had several people from my grade and also the grade below taking the course! Why? Because they had attended summer school because they wanted to take AP Calculus because they wanted to go to college and as everyone knows, AP classes only help you when applying to universities.
Now the school I went to was public but it was small (high teacher:student ratio) and also very well funded. It was quite expected that everyone would graduate and almost everyone would go on to college. So there is that. But the thing is, that making math “easier” for people only ended up quasi-punishing the students with drive, because they had to come in during the summer just to catch up with the original progression. Plus, this was just AB Calculus, so taking the second more advanced AP Calc test wasn’t even possible for those in my grade (the juniors that worked ahead actually got the BC Calc to be taught when they were seniors, I think).
My point is this: if you don’t require learning Algebra, what’s going to happen is that there will be fewer opportunities for the students that really want to learn, and you’re just shooting the other students in the foot, because what the hell math are they even going to do in high school? You can’t do “business math” for four years! And what happens when those students hit junior year and go “oh snap what the hell is this crap on the SAT test I have never solved for this mysterious x before!”
I mean they do still have algebra on the SAT test, right? Are we going to rewrite that whole exam, too?
It comes down to what do you have to do to earn a high school diploma. If you can find an arts college that will take you for studio art with crap math grades, have at it, but outside of the fine arts you’re going to need basic reading, writing, and math skills for every major field of study, due to science distribution requirements. Or, you know, just go to a school that isn’t accredited. No one is forcing you to go to college, you know. Universities are not just diploma factories where you put in money and four years and then get a hat and a shiny piece of paper. You have to, like, know stuff. And universities DON’T have to accept you, especially if there are other applicants that, say, know algebra.
Also as someone who teaches general chemistry at the university level I would like to point out that one of the indicators for success in a general chemistry course is having previously taken *calculus,* although you don’t need calculus in gen chem. (link: http://onlinelibrary.wiley.com/doi/10.1002/tea.20082/abstract although it is behind a paywall, thanks, Wiley) Why? Because if you can do calculus then you really know your algebra. I am sick of students that can’t do dimensional analysis, I’m a chemistry teacher not a math teacher, ugh. /whine
@ =8)-DX
Do you think that children who are playing in the streets are not learning anything? And again, why do you think that putting children in a classroom who would prefer to be outside will automatically impart information to them?
Why must education be painful?
I don’t agree. I think that the emotional damage done to children by authoritarian education, particularly in respect of their relationships with adults, far outweighs the benefits they gain, dubious at best, of learning a lot of stuff many of them don’t understand and most of them forget.
I always thought of algebra as the beginning of an understanding of math, at least in its modern formulation. The idea of it being as an endpoint, or not even being reached is very weird and setting the bar shockingly low.
I have TAed quite a few physics courses and labs, as well as computer science courses and in all cases I have been stunned by how many students lack basic mathematical skills. Basic algebra has to be retaught at the university level in many cases and it really should not be required. It is frustrating.
Calculators are the bane of my teaching existence. So many of my students immediately reach for them the moment any sort of calculation must be done. When I was in school in the 1990s (ok, late 80s as well) we barely used them. In fact, I remember we had a box of them in my early school days and bringing them out was a treat, something only done on a rare occasion. In my high school calculus classes we also pulled out the TI graphing calculators once and a while but for the most part everything was done by hand. I think this usually leads to a better understanding of the material. Calculators are wonderful tools once you have the basic idea and want to move to problems that are more complicated but I think there is an urge to use them far too often and before students really know what is going on.
This.
Arithmetic boils down to algebra.
1435
+234
———
———
Is the same as:
x = 1×10^4 + 4×10^3 + 3×10^2 + 5×10^1 + 2×10^3 + 3x`10^2 + 4×10^1
You can solve the whole thing using basic techniques of algebra. And when you do, it becomes readily obvious how those techniques are where the whole ‘carry the one’ part of rote-learned arithmetic came from in the first place.
Algebra is the understanding of arithmetic. Without that understanding you’re not doing math, you’re just a slow and inaccurate calculator.
By the way, I’m not denying the usefulness of algebra. All I’m saying is that imposing it on kids is counterproductive.
@189 and 190
I heartily agree, algebra is really just the start of learning about mathematics. It affords the student a conceptual foundation for mathematics and general problem solving.
Just as we require students to learn to read and write, we should expect basic math skills, such as algebra, to be learned at a minimum.
PS: when do students learn algebra in the states? I imagine the curriculum must vary for each state. From the comments here it sounds like high school… Which seems far too late (we were taught algebra in middle school when I was growing up in New Brunswick, Canada in the 1990s). What are students being taught between elementary and high school?
Of course, now that Mr. Hacker has published his article, an old friend jumps back in the fray to add his $0.02.
That settles it, algebra is indeed useless :-)
– RM
So much pain to be a teacher. I was horrified to discover that I was hired to teach an Ecology class to freshmen because it was assumed that Tech students could do this. After all, Ecology doesn’t require math…or science. It’s just…well…hiking. WTF? Ecology is statistics heavy…and I teach science, not new age hand holding and Gaia hippie stuff so they can laugh at the silly hippie teacher. I spend an inordinate amount of time in the dean’s office explaining that, yes, there is a need to require students to learn actual science in Ecology – and that Environmental Science is more than bringing me your recycling. One of these days, they’ll probably declare my science class too full of science, and get rid of me.
nohellbelowus –
I predict this is not going to end well.
You need to apologize to David Marjanović for being an asshole towards him (completely without justification, as of course DM was being neither snarky nor disengenuous) Apologize not for DM’s sake – I’m not sure he’ll notice, or care – but for your own sake, because if you don’t I will do everything I possibly can to make your stay on FtB hell for you.
You are a pissant troll and I don’t like pissant little trolls. Your kind is not welcome here.
David Marjanović –
That means three years of highschool math, which must include at least a year each of geometry, basic algebra, and intermediate algebra. Or other more advanced class (if the student entered high school from a prep school that already did basic algebra, so they can’t “repeat” it in highschool). Three years within a four-year highschool education.
Sadly, high schools offer even-more basic math classes, like “Pre-A;gebra”, because not all students enter high school prepared for algebra. But in that case, if they hope to turn around and apply to University of CA, or CA State University, then they’ll have to take four years of math to get as far as the intermediate algebra.
Calculus is given at (all? most? some? dunno) CA public high schools, but is an elective for students, not required.
I’ve never heard of a CA public highschool which offers statistics/probability as a full subject. There might be some that do; I’m not curious enough to try to search it. There’s a little tiny bit of statistics stuck in with other math classes somewhere. And stuck in with highschool science classes, too, of course.
So it’s still a bit of bad news, compared to your school system which can get most learners through calculus and statistics before applying to college, but it’s sort of good news that at least a decent grasp of algebra is needed before college
nohellbelowus,
You best be trollin’, ninja.
I think I like the analogy of compulsory education and compulsory vaccination.
I am a community college Biology professor in California and the level of most basic skills are very low. When I teach some principles in microbiology that require some math skills, such as calculating CFU/ml, I will get true tears and fear that it will be on the exam. Most students will openly admit that they took their math on-line and that it was an easy “A”. When I teach basic genetics they get lost because you need a basic understanding of fractions and ratios, which most still do not understand after high school. I have noticed that this generation of students coming up tend to be rather good at memorizing random points of data, but critical thinking skills are rare, especially in math.
Another sad condition is vocabulary. During every exam students will as me the definition of words that I would consider junior high level.
It is interesting to me how often some of my worst students in the areas of math and genetics are also the ones that will argue the most with me when it comes to evolution. When they try to argue with me I try to politely warn them that it is evident they are over their heads.
Fractions? Did anyone say fractions? Students need fraction skills to be introduced at around the end of yr 3 and consistently, routinely, developed and reinforced from then on. Not understanding fractions (and how the ordinary language concepts link to their specific mathematical uses) means that students will have chronic problems with decimals and percentages and many straightforward “word problem” calculations.
Lack of familiarity / competence in manipulating fractions for calculation processes means that algebra will be beyond some students. Not for want of ability, but for lack of skill. It’s much the same as musical skill – you may have perfect pitch and accurately keep rhythm – but being a wonderful singer is little help in playing cello or flute. Having a quick and clever understanding of some mathematical concepts won’t help you with fraction calculations or the related algebraic skills if you’ve not acquired the precise skills needed.
stewartt1982: Math requirements & the teaching of algebra vary dramatically by state. My state required 2 years of high school math when I graduated a decade ago, at least one of which had to be algebra (pre-algebra could fit the bill as the second I think). They just now added in a 3rd year to the state requirements that includes geometry.
So anytime between 7th & 9th grade we could start algebra–but you could take basic arithmetic yearly until 8th grade & sleep for two year before trying algebra. Many students in my (rural) area were ready in 5th & 6th grade for algebra but the schools didn’t want to offer calculus so they intentionally wouldn’t allow anyone to start that young.
We also had a middle school gym teacher/math teacher like mentioned above. She regularly made mistakes on the board, didn’t like being corrected, and allowed students to vote on the best answers to the problems. I have hunch she taught math mostly because math had higher job security than being a PE-only teacher.
Another side story, I was flunked from algebra in 7th grade because the teacher didn’t think I was “mature” enough for geometry (despite never getting lower than a C & maintaining a B average). My parents never contested–though I did convince them not to let the same thing happen to my younger sister.
I recently visited one of those “alternative” schools where high school kids get to pick their own curriculum. The principle assured me that they teach to the standards and that every kid gets geometry and algebra. And then he said, “Although truthfully, I don’t know a single person who ever needed the quadratic equation after the class.”
I did. And I told him so. As a sometimes chart hacker, the quadratic equation is really necessary for those little aesthetic effects when ars come together; you need to derive points and lines and rays and all than nice stuff to make clocks and other circular charts pretty.
So, kids, if you want to write video games, learn algebra.
The average person on the street does not understand the algebra that would allow them to understand that you can mathematically prove how change occurs in a population. Without that basic knowlege you have to go with the only other logical conclusion. You don’t need no learn’n to believe in god.