Algebra As A Gateway Subject

Spock the Baptist writes: "The Washington Post started a two article series Sunday, and Monday August 18 and 19 2002. The articles deal with something that the math, engineering, and physics faculties at colleges, and universities have long known. Algebra is a 'gateway subject' for math, science, and technology, and secondary schools in general are not doing a good job teaching algebra."

Comments

Beware the gateways...

[pizza_milkshake]

Yup, today your kid is doing algebra, tomorrow he's smoking crack. Just say no.

Algebra is taught wrong.

[Inominate]

Currently algebra is taught as a "You'll need to know this eventually" kind of a subject. Most of it is forgotten in a few days. Instead of teaching algebra, and then a few years later using it, math classes should be integrated with the science classes in which math skills are usefull.

A skill without a use is going to be forgotten quickly.

Re:Algebra is taught wrong.

[andrews]

How about using it every day?

Do you ever solve for an unknown quantity?

How many pizzas do I have to order to keep four programmers working through the night?

That's Algebra in a nutshell.

I use Algebra, Geometry, Trigonometry Statistics and yes even Calculus almost every day. Cost curves, margins, product pricing, queuing theory... it's all part of every day business life.

Poor math teaching in school ruins people's lives. I have to teach employees the basic math skills they need to do their jobs, and these are people with college degrees.

Re:Algebra is taught wrong.

[foonf]

Thats rather silly. You're basically implicitly conceding that there is no intrinsic importance to mathematics, and it is only "useful" as a means for solving scientific problems. Of course, as far as most students in middle/high school are concerned, what is being taught in science classes is "useless" also, and simply saying "learning X is important so you can do Y" is not a sound argument in the view of a student who sees no reason to understand either X or Y.

I would suggest that this attitude is the main problem, and based on my own experience, it is something that the educational system in general seems to promote. After all, instructors are not necessarily encouraged to promote a real appreciation for and understanding of a given subject, but rather meeting various "standards", increasingly codified very strictly in terms of various new state standardized tests. This environment leaves a student no goal but passing these tests, which whether they reject it or accept it does not enhance their long-term understanding.

Personally, I would rather have seen the intrinsic logic and beauty first, and the "real-world" applications later.

Re:Algebra is taught wrong.

[foonf]

I appreciate what you are saying, and I think it is true that there are many people who will never like math, but I also cannot see how any pedagogical system predicated on the assumption that what is being taught is inherently boring and undesirable to know can possibly result in meaningful learning.

Really, I feel like if a person only likes cars or sports, they should be free to direct their education in that direction, without being forced to study any more math (or anything else) than they want to in order to do what they like. Reciprocally, the only people who would study mathematics would be those people who actually wanted to.

But a system like this runs into tons of problems, I don't deny that, especially when financial success depends on taking a certain educational path during ones youth. The dynamics of education are totally different when things are made compulsory, and the focus becomes "how can we make people like what we are forcing them to do", rather than allowing people to do what they like. And maybe trying to tie it into things which do make sense to their lives will work better (read: higher test scores, or perhaps more qualified engineers in the future) than working under the mistaken assumption that everyone wants to learn.

As an aside: Everything I remember of myself and my friends, from before prolonged exposure to education, suggests to me that children in their "natural" state really do enjoy learning. To paraphrase your comment, I think that most students see learning as a chore because learning in the school setting _is_ a chore. I've known many people who ended up dropping out of school or getting through very marginally, who I must say loved to learn, but simply could not work within the framework of school. There are things (drawing comes to mind) that, because they were forced on me at an early age against my will, I don't think I will ever be able to learn to do or even appreciate. And moreover, when I think about those teachers whose classes I really enjoyed, the one thing that they all had in common was a belief in the intrinsic worth of what they were teaching, and a sort of stubborn insistence that really, the students in the class _did_ want to learn, whether that was the apparent case or not.

Re:Algebra is taught wrong.

[civilizedINTENSITY]

"Personally, I would rather have seen the intrinsic logic and beauty first, and the "real-world" applications later."->math is always presented as primarily being a useful tool for other areas of discipline is simply because that's exactly what it is. Math, at its lowest level, is merely a language to describe things.

My BS was in Physics, and I'm currently working on my MS in applied Mathematics. I'm still working my way through the paradim shift, but I can empatically state that your comment would raise issues with my professors. Math is most definitely neither about describing things, nor about being useful. To anyone doing abstract work, the suggestion that they are "applied" is considered an insult. They are better than that. They have generalized beyound the mere physical descriptions and are involved in the essence of mathematical logic. Now one can use math to model, yes. But then much work is done to remove from the proofs any hint of that real world model. The "scaffolding must be removed from the cathedral before its presented to the public". The concept that math works "Exactly the same way that a programming language describes the actions that a program performs" sounds alot like the Computational world view. While I lean towards applied and computational maths myself, this is *not* the world view of the majority of math people. There work is more than "purely recreational", they would say, but it isn't "useful" either.

Re:Algebra is taught wrong.

[philg]

You miss the point. (Well, IMO anyway, I can't speak for the original poster.) Making algebra skills required in other classes has a fundamental practical advantage -- it makes it harder to get any good (or even passing) grades if you don't know a fundamental skill.

Reading is already this way; students that can't read or have trouble are virtually doomed to low grades, as reading skills are relied upon at increasing sophistication almost as soon as they are taught. It is a very obvious red flag that students are missing something very important.

It is very difficult to impart a genuine appreciation for something before someone understands it at some level.While I agree that this approach needs to be much, much more heavily promoted, I also think you need the negative, "look, just learn it" repercussions of an interdependent curriculum, so society can be guaranteed that children emerging from our schools have a known baseline of educational skills.

phil

I'm lucky here in FL...

[NewWazoo]

I was blessed here in Tallahassee, FL, with some really great math teachers, as well as the option to take a "real" algebra course as "early" as the 7th grade. And we're not talking "algebraic concepts" here - I was required to derive the quadratic formula w/o completing the square, which is TOUGH when you're 12 or 13. :)

It disappoints me to see schools lowering their standards to raise average test scores. I'm one of the minority who believes that D should be passing, but that a C truly should be an "average" grade (just like it says on the report card). My H.S. has an average GPA of something like 3.4! That's just silly - there's nothing differentiating the truly exceptional from those who could either kiss a lot of arse or slough through it and do all the extra credit.

I also see a very disturbing trend of schools offering classes that, in essence, "teach the test", be it the SAT, ACT, or the FCAT (in FL's case). Doesn't this skew the results? I'd like to hear some others' opinions on this... :)

Just my $0.02 worth of incoherent rambling...

Brandon

Re:I'm lucky here in FL...

[UncleFluffy]

Oh, and my use of "arse" is just my way of avoiding the apparently-vulgar word "ass"; is it 'just as vulgar' "over there"?

"ass" -> Donkey
"arse" -> The Queen wouldn't use it in public, but that's about the extent of its vulgarity.

Home School

[Grumpman]

I agree that public schools can't do the job. The teachers are told to crank the kids through as fast as they can with little to no support from the board or, more importantly, the parents. It's not their fault. They are among the lowest paid professionals doing a thankless job.

Solution, home school. My wife stays at home and raises our two kids. My 3 year old can count to 20 in English and Spanish (no, I'm not bilingual), do simple sums, and knows her alphabet. I plan on testing her knowledge of the Pythagorean theorem before she hits 10. She will not be rushed, pressured, bullied, or pampered. But we can give her a far better education than some underpaid, overworked teacher afraid to discipline her class for fear of losing her job or his life.

Flying and Algebra

[HerrGlock]

I thought it was an "I'll never need this or see it again" when I was in HS. Problem is, I became an Instructor Pilot. Algebra was life and used every day.

I read in the Washington Post that the Maryland schools are putting BS into the standardized tests and calling it "algebra" and then they wonder why Johnny cannot do anything in real life.

Perhaps we can get back to basic R, R, and R one day and not be as worried about people getting their feelings hurt when they need help in the subjects.

DanH

As a secondary algebra teacher

[Troy]

One of my biggest problems teaching algebra is that my students were never given a firm foundation in basics throughout middle school. The philosophy described by the article is accurate as to what I am seeing in middle school math education, but results in a bunch of students who can only solve linear equations in a "trained monkey" kind of way. They have no real cognition as to what their actions mean (ie. When you add to both sides of an equation, you aren't REALLY changing it.) I was halfway through last year (my first year in a new district) before I realized that most of my [otherwise intelligent] students really didn't understand basic concepts like substitution, the difference between an expression and an equation, why you do things to both sides of an equation, etc etc etc.

Let me tell you how much of a nightmare solving solutions were.

I also think that algebra is pushed on students before they are cognitively ready. The average middle school student should go as far as evaluating expressions, variable substitutions, (MAYBE) 1 step equations and (MOST importantly) reading an expression (ie. 3x + 4 means three times x plus 4). The rest of their time should be spent brushing up and applying their ARITHMETIC skills, such as working with/reducing fractions. Give me a class of students who know how to substitute and know their arithmetic, and I'll give you a class of all stars.

In this upcoming year, I'm dedicating the first 2-3 weeks to an intensive review of arithmetic and bare bones algebra. Hopefully that will smooth things over as we go on.

I really like the suggestion of merging science with math. I would love to see those two subjects team taught over a double period.

Re:As a secondary algebra teacher

[Jucius Maximus]

"and (MOST importantly) reading an expression (ie. 3x + 4 means three times x plus 4)."

I agree with you fully on that point. I am a university student (in Ontario, Canada) and sometimes I hear tales from the really enthusiastic professors about some of the madness when they taught grade school level math.

For example, one kid did something like this:

Question: 6x + (-5) = 63

Answer: x = 8

Question: 3x - (+12) = 15

Answer: No solution!

Now really try to think about the thought process which would have lead to these (wrong) answers. Can you figure out what the kid thought? I couldn't until the prof explained it to me:

The kid thought that the first question read as "sixty-(what) minus five equals sixty-three" ?

And naturally 68 - 5 = 63

Thus you can figure out how the kid thought there was no answer in the second one.

Yes, you are right, and there are too many kid falling through the cracks and with rising class sizes, you can't help them all get the concepts right.

"The rest of their time should be spent brushing up and applying their ARITHMETIC skills, such as working with/reducing fractions. Give me a class of students who know how to substitute and know their arithmetic, and I'll give you a class of all stars."

Once again I think that you are right on the money. Too many people are afraid of fractions. Back in the 80s in Canada, fractions were a real subject in grade 6-8 and the students came out of it with a real industrial knowledge of how they work. Most people in my generation in Ontario are scared stiff of the same things. (But if you take a kid from Alberta, they know it cold because they do it all in grade 4-5 there.) Fortunately for me, I was blessed with a really bad teacher (?!?) in grade 5 who was terrible at teaching fractions, so I just ignored him and actually figured out on my own how they worked.

Even now I see people my age who are half way though a university level engineering program solving laplace transforms and systems of differential equations, and they can't handle fractions within fractions or negative fractional exponents.

I wish you good SKILL in tuning your students into shape. I believe you have your priorities in the right place and know what the real problems are.

Re:As a secondary algebra teacher

[bfields]

I also think that algebra is pushed on students before they are cognitively ready. The average middle school student should go as far as evaluating expressions, variable substitutions, (MAYBE) 1 step equations and (MOST importantly) reading an expression (ie. 3x + 4 means three times x plus 4). The rest of their time should be spent brushing up and applying their ARITHMETIC skills, such as working with/reducing fractions. Give me a class of students who know how to substitute and know their arithmetic, and I'll give you a class of all stars.

No way. This is how we end up with a typical math sequence that goes:

• 6th grade: we're finishing up arithmetic now, and then we're going to get you ready for algebra with little fill-in-the-blank arithmetic problems and stuff. Next year you'll do real algebra! Won't it be fun.
• 7th grade: fooled ya! No algebra yet, no, we're doing pre-algebra! Next year you'll do real algebra! Won't it be fun!
• 8th grade: OK! This year we're going to give you a little algebra. But not too much! You'll learn to solve 2 equations in 2 unknowns, but we don't trust you to actually *understand* something so mind-bending, so we'll just give you a bunch of really mechanical drills on this.
• 9th grade: wait! We're not sure you got that! Let's go over that algebra stuff again, and maybe do a tiny bit more.
• 10th grade: you guessed it: more algebra! This time maybe you even get a little trig or very basic analytic geometry or something.
• 11th grade: pre-calculus, which is, you guess it, more algebra....
• 12th grade: calculus, whoop-de-do.

And this is for the super-bright kids. Come on! Even the "slowest" kids want to see something new every now and then!

I know how frustrating it is trying to teach people something when they don't really have the prerequisites down cold yet, but that's life; they'll pick that stuff up when they have to, and you can't let it keep you from throwing the new stuff at them too....

--Bruce F.

math teachers

[NeoSkandranon]

This seemed to be pointed more towards the middle-school level math courses, but I never had algebra that low. I took algebra I, II and precalculus in highschool, and IMHO (this being two years after i graduated) the problem is that algebra classes have to cater to the lowest commmon denominator, since they're almost universally required for graduation. Even in college calc, our teacher had to spend a few minutes refreshing everyone's memory on basic algebra (factoring, synthetic division, etc)because we never really learned it.

Of course, one approach would be to fail the fuckwits that can't hack it, but apparently teachers catch more flak for failing lazy students than passing smart ones.

Bueller, Bueller, Any one any one?

[puto]

Well I can't imagine what school's must be teaching these days cause the younger generation I do run into seems to be completely clueless for many things.

Math, science. But also literature, geography, world events. But no couth is one of the biggest problems.

I admin from home. Sit in my underwear, drink beer, do not shave. See me in public like that? Hell no. I go on an interview for a possible client and I look like the man from IBM in the 80's. The orginal Men in Black

I am 32 and not that old(or at least I dont think so). Here is what I know.

Late 80's schools had gotten so horrid they had to administer tests that had to be taken before graduation. Basic skills tests. You might have passed your exams but still had to take this one. I never took it but I saw one and it was frightfully easy. Along the lines of the ASVAB for the military.

Schools dropped physics and trig to go to things like Alebgra 1,2 and geometry and that was it in math.

Anyone have that physics teacher who used the overhead for the notes? And he had written the notes originally back in 63 and over the years had made corrections to them? But sill used them. Probably still teaching.

TENURE - stay here long enough and we will give you a free cushion for your ass.

I went to a boarding school for my formative years and while I did recieve a fair amount of ass whuppins I did get some great teachers who really got me into science and math and literature. We built a Heathkit Hero in the dorm and fiddled with ham radios, and even had a unix box in '83. A DEC. And I owned your ass playing miner 2049er and Lode Runner on the Apple //.

I then switched to a local school and bam. I saw the wonders of a regular high school. Sure I got girls and booze and had quite a bit of fun, but I did not learn near as much or the teachers did nothing to generate my interest in things. Well, methane soap bubble torches were fun.

Teachers aren't paid enough. Private schools do tend to get the better ones. I graduated in the end from a public school, and had good teachers, but my private school experience was by far superior. And when I choose to lay my eggs I will make the sacrifice and send my little geeks to a private school. For them.

Teachers also need to be recertified every couple of years, just like people in the tech industry. "I had a TRS-80 back in the day so I don't ever need to take a computer class". Teachers get complacent, light a fire under their asses.

Bit of a rant here, but we do need to do something about it. Our world ya know.

And I do not care if you are 18 and can write a script that will control the weather, make Bill Gates give it all to charity, or even make Slashdotters a more level-headed bunch. Education is the the real fucking deal.

Take the time. I had to do it at 32 and it sucks.

Puto

This Al Jebrah sounds like some terrorist group...

[NoMoreNicksLeft]

My goverment has informed me, a patriotic citizen, that I should be especially aware of anything arabic sounding around me. They like to sneak things in to try and destroy our beautiful country, and this could be one of the very plots that brings about 9-11 the sequel!

Why, filling our kids heads with islamic math propaganda is the last thing we need right now. Will it help us build bigger bombs? No, I don't think so. Counting to 10 is enough, and if you forget a few numbers in between, that's alright by me. President Bush himself can't count to 10 without his advisors helping, and I bet none of them know al-jebrah either.

Al jebrah is a tool of the devil! It might help when you're trying to decide how many camels to give away to marry off your daughters, and it might even help to figure out how to build those crazy pointy towered mosque thingies. But as americans, what good does that do us?

Besides, they come right out and say it. It leads to godless science, teaching us that we're the grandchildren of monkeys. Yes, cousin Cletis kinda looks like a chimp, but by god he's a good 85% human. Keep your godless atheist algebraic satanic brainwashings out of my kids skulls!

(stupid lameness filter won't even let you do a *** seperator bar)
Dammit. Spent 20 minutes writing one of my best trolls ever, and I can't bring myself to click 'submit'. It wouldn't be a big deal, but I know people like this... ugh. I'm wimping out.

Science-Math connection

[MacMasta]

Pardon if this is a repeat.

I remember reading somewhere, and, after much thinking, agreeing with it, that science is currently taught in backward order.

That is, instead of biology-chemistry-physics, we should teach physics-chemistry-biology.
The reason for this is that to really get chemistry, you need a strong grounding in why all those little particles do what they do. To really understand biology, you need to have a strong grasp of chem.

Students today have a very hard time with math - and that's crazy. They shouldn't.

One way to make math more "real" to students is to apply it to science - perhaps if they aren't math-nuts, they'll be science nerds, and the connection will draw them into both.
The problem with this, of course, is that physics is classically taught as a calculus-based course, (although it's perfectly possible to do it with trig and algebra - my AP test 5 can vouch for that)

Chemistry "needs" algebra - at least it works a lot better with it.

Biology (at least at the high- and middle-school level) needs very little math at all.

Therefore, we teach them in reverse order.

As to not teaching algebra, there is no excuse.
I explained the basic principle behind algebra to a bunch of fifth-graders and had them doing "x+59 = 226" in about fifteen minutes.
Everything else is derivitive of that - if the textbooks can't get that across, blame them.
(Note - I would not suggest blaming teachers in the slightest - teaching from books works, even bad books, and teachers, at least in my district, are required to teach from a book - they were good teachers with bad material)

So damn the torpedoes and shut down Houghton-Mifflin!

~Mac~

As a teacher

[Quill_28]

I taught math for exactly one year. My biggest problem with teaching was not teaching algebra but fractions!! They were never taught how to add and multiply fractions, except by using a calculator. Some of these kids were quite intelligent and had no problems with
x^2 +6x +8 =0 but (x+1)/2 = 4 and they were lost. All the blame can't be laid on the jr/sr high some of it also falls before they get there.

Actually it is al-jabr

[Brian_Ellenberger]

Interestingly enough, our word Algebra comes from the book Hisab al-jabr w'al-muqabala written by a Middle-Eastern man named Abu Abd-Allah ibn Musa al'Khwarizmi around 830.

Brian Ellenberger

Re:Actually it is al-jabr

[thopkins]

I thought it came from Vice President Al Gore, because he invented problem solving, by using Al-Gore-ithms. This was before he invented the internet.

Comment removed

[account_deleted]

Comment removed based on user account deletion

A Primer on "Fuzzy Math" or the "New New Math"

[matroid]

In an effort to overcome our country's mathematics woes, the National Council of Teachers of Mathematics (NCTM) put together a monumental group of standards and principles revolutionizing the way that Mathematics is taught at the High School level.

The NCTM-based curriculum is different. Some teachers and college professors believe it to be weak on mathematics because it doesn't look like the curriculum they grew up with. Traditional curriculum (teacher does a couple examples, students practice solving 30+ problems similar) has not been good enough though.

The new curriculum, based on psychology and education research from the latter half of this century, focuses on understanding in addition to the traditional acquisition of skills. It is mathematics rich with connections to other areas, and deep in content. Students start in 6th grade learning basic algebraic concepts, number theory, geometry, probability, etc. Obviously mastery of all these concepts does not happen in a single year. In fact, the curriculum spirals around the same concepts, building new understanding and making new connections with each pass so that, ideally, when students graduate their skills AND understanding will be better than that of previous generations.

Sometimes this math is called "Fuzzy Math" or the "New 'New Math'". Some educators, professionals, parents, and children feel the curriculum is weak on "real math." My concerns were similar before I started teaching the Interactive Mathematics Program (IMP).

Between 9th and 10th grade, students master basic algebra, learn the basics of the trig functions, work with standard deviation and the chi-squared measure, build and solve and maximum profit linear programming (something most math majors don't do until grad school), derive and prove the pythagorean theorem, work with exponential and logarithmic functions, do all sorts of number-theory related problems, and so much more. Still IMP and other standards-based curricula have their problems. In my opinion, although there's plenty of problem-solving and understanding-based activities, there needs to be more traditional skill work. I supplement my lessons with such work where appropriate. Any teacher worth their stuff would do the same. Additionally, the curricula is very wordy, which is fine for middle-class suburbanites, but when you're teaching in a city where 25% of the students don't speak english as their first language, and 75% are in poverty (typically correlated with smaller vocab and weaker reading/writing skills), a wordy curriculum is just one more thing making it tough to teach/learn math. In sum, there's a lot of hostility from the non-math-teacher world toward this new curriculum because it's so different. But, with the abismal performance of American mathematics when compared internationally, it can't be business as usual. The curriculum is already working well in the classes I've seen. And the research points to positive improvements after curriculum implementation (no large study has been completed as far as I'm aware). NCTM-based curricula is no panacea, but it's a definite improvement over the more archaic traditional curricula.

i don't know what is better...

[edrugtrader]

all through middle school and high school i had a ~40% homework average in algebra through calc 2. i also had a ~97% test average to make my B- or C+... i got the whole "you aren't applying yourself speil" but i DID know the material. i was just a lazy fuck and didn't do homework. then i go on to college... homework isn't graded and suddenly i have straight A's.

can not grading homework WORK for a middle school student? or will they all just not do homework and fail?

i have always hated the learning process in math for that very reason...

math more linear= more chance of getting derailed

[call -151]

Moreso than any other subject, mathematics has more of a linear structure- meaning dependence upon previous material.

If you have a bad teacher for 7th grade English, you may never quite be the greatest at diagramming sentence grammar, but the chances are high that you can overcome that shortcoming and still learn to compose good essays, read literature for more than just content, and so on. Other subjects also have the potential to recover from a bad teacher or missed material.

But mathematics has much more of a reliance on prerequisite material. If you have a bad instructor and don't develop good algebra skills, you will struggle and have a great deal of difficulty in algebra 2, trig, etc. When people find out that I do research in mathematics, (a casual conversation-killer if there ever was one) they often have a story, something like "I was always good at math until Mrs. Crabapple in 10th grade" or something like that. One bad experience leads to poor understanding in that subject, and, unfortunately, is rarely overcome and years of struggle result.

I've seen people get derailed at all levels and it really is a problem that needs addressing. At the undergraduate level, sometimes it is particularly painful to witness when a student passes a class (such as first-semester calculus) without learning the material. This can put them into a hopeless limbo- they have no chance of passing the next class, and will probably fail it a few times, but they cannot take the preceding class since they already passed it (sometimes even with a reasonable grade.)

There is a unfortunate stigma to taking something a second time, and that stigma undermines healthy mathematical learning. Sometimes it takes seeing things more than once, or from more than one teacher, before it makes sense. Passing students who just barely have a grasp of the material does them little good and may doom them to years of floundering.

Until there is more recognition of this fundamental aspect of mathematical learning, there will be way too many people who grow up dreading "story problems" and "meaningless algebra"

algebra the key to abstraction

[call -151]

One of the things that seriously separates humans from other animals is our ability to think, and to think abstractly. Too often the comments are made about algebra- "I'll never use this..." "What is this good for?"

Even if algebra problems per se never occur in whatever "real life" people end up having, the ability to think quantitatively is essential for an reasonable person. Thinking more abstractly about problems of many kinds is essential- for developing efficient code, for having a reasonable business plan, for managing one's person finances, for voting in a responsible way, and basically for being a productive member of society. The evidence for poor critical/mathematical thinking is everywhere- people falling for Ponzi schemes, short-sided economic policy, unwise credit-card debt, bad laws, ridiculous jury decisions, and the list goes on. The proper perspective about mathematical reasoning is that it is fundamental for most productive people, and essential for all citizens.

Unfortunately, this perspective is usually not instilled by our current generation of underpaid, frequently under-qualified (more than half of the math and science teachers in CA have "emergency certification", which can be extended indefinitely since there is no adequate supply of properly trained and willing math and science teachers.) Instead, students are often exposed to math teachers, who, to be honest, don't actually like math or understand its central role as a foundation for science and modern reasoning. Kids are smart- if a teacher doesn't like math and is just going through the motions, they pick up on that. And given the sympathy that students get from parents, teachers, etc for the horror of "word problems" it isn't a surprise that mathematical reasoning skills are a consistent weak point of students at all levels in the US.

Everyone agrees that more resources should be directed at education, but people have been agreeing on that for at least 30 years with much of the same problems enduring. Good education is more expensive an investment than many decision-making bodies are willing to undertake, and that shows in the wide disparity in education between the "haves" and the "have nots". Until there is a significant change in how much energy and money people are willing to invest in education, it seems that these phenomena will continue.

Re: You can thank John Dewey

[benzapp]

For this spectacular collapse of education, we have the renowned professor John Dewey of Columbia to thank. Yes, the same amazing mind behind the Dewey Decimal system also flagrantly defied centuries of knowledge about the way humans learned and decided that in fact, humans do not learn by experience, but learn by rote.

Men used to learn as apprenctices, learning while doing for years at a time. The educated labored over Socratic dialogues written over two thousand years before, learning that wisdom and knowledge comes only in knowing to ask the right question.
Many students used to take great pleasure in practicing Socrates' dark art by befuddling others into realizing their own ignorance.

But then, the powers that be at the great school of Columbia looked at the masses of the great unwashed in the masses of tenaments of the South Bronx and decided that man was in fact a machine, ready to be programmed at any time. One must merely sit, listen, and learn from those more knowledgeable than he.

And that is when the transformation took place. Instead of teaching children to ask the right questions, it was the teacher who asked the questions and the student who answered them. Critical thinking was no longer a necessary aspect of learning. One could merely develop the inhuman ability to memorize on end without any care as to its purpose. And then succeed. Some can do this, no doubt. Most likely, the abundance of Cocaine in numerous remedies for uncooperative children in the 1890's probably led some to believe humans could practice such tasks better than they otherwise could. Those complaining of stimulant use by children today are sadly ignorant of a tradition going back 120 years.

But there is a limit, all the stimulant drugs in the world can't teach a child to think critically.

The human being is different than other creatures in that we solve problems creatively, by using our heads, not our bodies. The dog when attacked, knows it will fight back. It cannnot imagine any other way to do this than by using its teeth. When it is hungry, it cannot imagine any other way to get food unless that food is right in front of it.

Humans possess the spark of imagination that is wonderous in its abilities to do and create like never before. It is unfortunate when I see anyone creating the false dichotomy of beauty, art, and science, for they are all the same. We must teach children from the beginning to solve problems, to create what has never existed before, and help them along the way. Algreba should not be a subject in and of itself, it is the most basic form of deductive logic that should be a part of a simple logic class. Math in general should not be a stand alone subject, but taught as a tool in the course of study.

We have followed John Dewey's advice for nearly one hundred years, that a child's brain should be poured full of knowledge. It is false, and destructive. We now have a nation of zombies, unable to question anything or solve any problems. They are hardly human, other than form. is it any wonder they merely stuff their faces with food and vicariously live out there sexual fantasies on television? They know nothing of humanity, they feel only the urges of animals. Eat and fuck, eat and fuck. Is this all life is? Of course, they cannot even ask THAT question...

Re: You can thank John Dewey

[Zathrus]

Ah, so in other words we should go back to the old days of apprenticeship and merely allow the curious to move forward.

Sure. Go for it. After all, the last 10000 years of human society clearly had a far better education level and standard of living than we do today.

Or, hell, we don't even have to go back that far. Go look at some of the areas of the world that don't have mandatory schooling. They're top notch. Just last week I was thinking of moving to sub Saharan Africa because they have the best quality of life in the world.

The reality is that you're completely wrong. Even as far back as Socrates and Plato the teacher posed questions to the student. Did students ask questions too? Sure. And *gasp* -- they can now too. If you want to bitch about the (US) educational system, bitch about the funding. Teachers work harder than just about any other profession (hrm, an 8 hour day with no breaks plus another 4-8 hours of planning and grading after school hours), pay them relatively little, make them pay for class supplies out of their own budget, and expect them to educate and morally instruct our children at the same time. With little or no parental backup.

The other minor fact you forgot to mention is the expansion of knowledge in the past 150 years. The concept of a Renaissance Man is dead -- because there is no way for one person to hold the sum of human knowledge now. You can (and should) have a broad base of education, but "jack of all trades, master of none" is becoming increasingly true. Without modern schooling it's impossible to tutor our youth in even a small amount of the knowledge base. Do you know what literacy rates were prior to mandatory education? How many of the illiterate learned basic math, much less algebra?

John Dewey was against rote learning

[admiralh]

Though your criticisms of modern education are valid, they have nothing to do with John Dewey.
Let me quote from this page

Dewey believed that school should teach students how to be problem-solvers by helping students learn how to think rather than simply learning rote lessons about large amounts of information. In Dewey's view, schools should focus on judgment rather than knowledge so that school children become adults who can "pass judgments pertinently and discriminatingly on the problems of human living" (Campbell, 1995, p. 215-216). Dewey also believed that schools should help students learn to live and to work cooperatively with others. In School and Society he wrote, "In a complex society, ability to understand and sympathize with the operations and lot of others is a condition of common purpose which only education can procure."

You can find Dewey's book Democracy and Education at this page.

The problem in our system is not that Dewey's arguments prevailed, it's that they did not.

Algebra Teaching

[Artagel]

First of all, teachers can't serve as the sole source of motivation for students. Parents and communities have to do that too. The transition for fractions to algebra is one of the hardest on young people. As noted above, one problem is that students that did not have a good grasp of fractions just become more lost in algebra. A second problem is the motivation to learn this new, hard subject.

Students need to understand that "the future is now." This is part of a runup to calculus in college (if not sooner), and that what you can or cannot do in math can and will shape your future. If you do not know algebra II and trigonometry, you are going nowhere in Physics I. No Physics I, no engineering, no chemistry, likely no computer science, etc.

Second, we have to face the fact that many students in math want to get through the class with a decent grade, but have no ambitions to actual understanding. They WANT to be trained monkeys. Their parents often have uncritical aspirations too, and will be happy with trained monkeys.

Thus, they do not want to understand the associative and distributive properties. A trained monkey type of student can solve problems while not fully grasping the properties. A student who understands these properties will have an important intellectual tool available. The idea that certain types things can or can't be related in certain well-defined ways is an important idea.

To those who want to teach math only in the context of solving science problems I say: foo. Mathematical training needs to be broader than the known scientific problems to be solved or you encourage inside-the-box thinking. Where in a physic experiment does someone like Godel become relevant? What about Fermat's last theorem?

Gear the teaching to allow the best to be the best. The crank-churners who don't want to excel will find a way to get a B or C on the test. That's why they call average grades "mediocre." The system has to tolerate the mediocre accepting their lot, but it doesn't have to discourage virtuosity in doing so.