Slashdot Mirror
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."
Yup, today your kid is doing algebra, tomorrow he's smoking crack. Just say no.
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.
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
What? Why the heck is algebra being taught in secondary school? Why leave it that late? I mean, they aren't covering linear algebra, are they? They didn't in my high school. Apart from that, I cannot imagine what else they could be teaching about it. The only time I used algebra was in physics class in high school. Everything else, I had learnt by grade 6 (including geometry and trig, though I'll admit that I did not learn about conic sections until high school...)
So what are they talking about? Linear algebra? I doubt it, I can't see that they have been able to catch up that much. So, errm... what?
Oceania has always been at war with Eastasia.
I've always been a believer that algebra is very important across a wide variety of subjects, one of which is music. When I was younger, I was a subject in a study on how algebra (and maths in general) helps general musical ability. It makes sense - sheet music is a kind of abstract form of math. You've got different length notes in different positions with different intervals between.
I'm sure there were more complete studies out there, but the results indicated a strong correlation between mathematical and musical ability.
Ladies, form queue here -->
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.
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
Cav Pilot's Reference Page
UNIX - Not just for Vestal Virgins anymore
math teachers need to be able to make it more interesting in some way...i don't know how. but it really sucks
How about calculus as a gateway, It's not hard and it's not like making them take Diffy Q's
Course I think Thermodynamics should be taught in HS and be required. Be a lot less stupid people and suckers in the world if people understood thermodynamics.
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.
Who would take out the trash? Not every child 'needs' to learn algerbra.
love is just extroverted narcissism
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.
If you can't see the value in jet powered ants you should turn in your nerd card. - Dunbal (464142)
Please, original answers only. Lets get the obvious ones out of the way...
1) What does it get you? -1=Offtopic, sucka!
2) pr0n
I'd have to disagree. I work as a network administrator at a rather large ISP and am fluent in several programming languages. I also am very fluent in computers and fixing them, however math has never been my forte, and quite frankly I couldn't do an advanced algebra problem to save my life. But it's never ONCE hung me up. Math teachers at my Uni told me time and time again that Math is a key component to computers.. but I have yet to see it. Sure binary and hex and all that.. but only if you're working at the lower levels.. and even then you can do it on calculators.. and that's still really only low level math and just knowing how to do it. But algebra you never use unless you're programming a specific program that does something algebraicly in which case you have the formula. And, as a network administrator I have *never* once needed to know algebra.. just lower level math... I disagree and think the whole "math in the comp sci" thing is politics in the schools.
Most of them don't even need to speak properly- they can get by with grunts, points, and rolling on the ground with bellies up in a submissive posture.
What we call folk wisdom is often no more than a kind of expedient stupidity.-Edward Abbey
that teaches pre-algebra classes... you'd think they wouldn't be needed but there they are.
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
The Revolution Will Not Be Televised
They've always done a crummy job teaching the sciences even back in the 70s for me. Every science and math teacher thinks that everyone sees the world / problem set in their eyes. Alas that is not true. I couldn't for the life of me get a handle on some formulas. When someone showed me that I could just as easily understand this via the visual (ie graphs) then my education in this area finally took off.
Now I work as a programmer supporting people in statistics.
People in the sciences need to take cues from those in the arts. There are many ways of looking at it and they need to find the right way to "reach the student".
The way the indignant parents act about this is the worst of all. If it were up to me, a probability and statistics course on top of trig (including spherical trig) and a C programming course (but not calculus) would be mandatory to graduate high school. The way parents get all huffy about their kids homework, taking their own ignorance personally I suspect, it is unlikely to come to pass.
Are there any other states where it is possible to graduate high school without algebra?
Not all engineering students begin as math wizards but by the end of their degree program are quite comfortable with calculus and transform mathematics.
It's all in the amount of exposure and the level of application availible to the student.
"player 4 hit player 1 with 0 stroms"
When do most people start taking algebra, anyway? I remember that I took basic algebra in 8th grade, then algebra II in 10th. Granted, that was the advanced math track (such as it was; my school didn't offer many advanced classes). However, I'm currently working with the AVID Program (Advancement Via Individual Determination) which takes students "in the middle" (2.5-3.5 GPAs) and puts them in advanced classes; it seems to work fairly well. In 9th grade they actually continue that with matrix algebra. These are the traditional "high-risk" kids; low-income area with a largely minority population.
That said, maybe a partial soluation is to require algebra at the middle school level rather than high school...
Twenties Retirement
Mathematics is pretty important to Computer Science. Its just not important to the system / network administration side which you say you're doing. You're simply managing the programs others have written.
Don't confuse administration with computer science.
The reason public schools do so poorly is because there is no accountability for how good a job schools do. Teacher unions and parents and even school boards fought, and still fight testing standards and complain about how small the budget is while students performance is pathetic. If you cannot tell if teachers are doing a good job or not, how can you tell how much they are actually worth?
All I can say is I am glad that I don't have kids right now becuase I would hate to send them to public school
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.
I aced algebra, but I failed "discrete math" twice in a row. Now this could be becuase this course was only offered after lunch... and my lunch at the time was a 6-pack of beer...
This was supposed to be a "gateway" to computer science thinking. And I have a career as a CS cat, but when 2 times 1 = 97 in a particular universe of discourse it's meaningless...
(Oh yeah, and alebra was a prerequisite of this course.)
Bah.
Some cats swing, and others don't. Don't you be the kind that won't.
Well anyone who's seen the commercial knows the cow can talk, so I bet it's smart enough they can teach it algebra.
Oh wait...maybe I should read the article...
Since when is Algebra advanced math? That sort of attitude doesn't help this country at all. I was going to write Ann a reply letter, but since she was already dead I didn't bother.
Disclaimer: I'm currently working on a Ph.D. in applied mathematics
First Equation is Free...
and not like in speech
Your code without algebra:
10 print "I never learned algebra"
20 goto 10
Your code with algebra:
for (i=0; i<10; i++) {
printf("I learned my algebra!!!\n");
}
-tpg
Hmm, methinks the beer might have had something to do with your failing discrete math, and the extra F's.
Oh well.
Articles like these are exactly why I would rather sell my own organs then put a child in most public schools. Public education is a joke... its more about feeling good and not hurting little Johnny's feelings then teaching them how to read, write and do math. Its shocking that one can graduate highschool without even knowing algebra!
I went to a private, Catholic school that placed you on tracks depending on your performance on their own assesment test. If you did poorly you were placed on track 3 and the best were placed on track 4. Track 5 was reserved for advance students (chosen from track 4) who were given the option of taking the AP exams for college credit after taking more intense courses. After the first year you could change tracks based upon your grades and teacher recommendations -- a few did. Track 5 students took algebra the first year of HS and finished Calculus II by senior year. Track 3 took pre-algebra but had to finish some level of calculus before graduating. Most slackers left for public schools within 2 years and I was happy to see them go. They waste time and energy from the good students.
Most schools in my city (Miami, FL) had their own police force(!) whereas we had a single guy in charge of discipline. His top 3 discipline problems were: hair was too long, didn't wear a tie (dress code was shirt and tie), keep out the porn magazines. My public school friends had to watch out for ethnic tension, gang fights, and walk through a metal detector into halls guarded by police officers. F@ck that!
Oh and my school wasn't for rich kids either. Tuition was $3,700/yr (some had scholarships) but if you were a discipline problem your ass was tossed out cause there were 10 waiting to take your seat.
If you haven't gone through a computer science program, then I can understand why a network admin doesn't need math. As a Computer Scientist math is needed all over. Any program that calculates numbers uses math. Computer Graphics is all math. How about numerical analysis? Cryptography? The point that people miss is that Information Technology is not the same as Computer Science. In fact, not too many people actually know what Computer Science is.
How about we reward the students who fair well in algebra with visits to prostitutes? That might make the lads hit the books.
Maybe i'm goofie, but me thinks more people have troubel with basic english than algabra has done. I'll leeve it up to the reeders to decide about it. How many grammatical erreor can you find in the front page comment was on? I'm not trolling b/c I could give too shits about typos here and their, and lots of grammitical errors, and mispellings in /.'s responses in here, however, if you make the 'front page' you should definetly at least double check your work too make sure everything is good and makes sense and their are no run-on sentences are in your article. Yes, geeks have to know how too write to. Very important.
My old Algebra is was a pothead.
Coincidence?
Music is more "simple math" or "arithmetic" than algebra.
from yourdictionary.com:
arithmetic : a branch of mathematics that deals usually with the nonnegative real numbers including sometimes the transfinite cardinals and with the application of the operations of addition, subtraction, multiplication, and division to them b : a treatise on arithmetic
algebra : a generalization of arithmetic in which letters representing numbers are combined according to the rules of arithmetic.
A quarter note = X BPMs (Beats per minutes), ie a quarter note = 60 BPM is 1 beat per second. (This is the closest you get to algebra.) From there it's division and multiplication. (arithmetic.)
8th notes = quarter notes/2.
16th notes = quarter notes/4 or 8th notes/2.
A dotted quarter note = 1.5 times a quarter note
A dotted 8th = an 8th note times 1.5, etc.
Not so much algebra as simple math or arithmetic.
Actually music is much more complex (listen to jazz) but music notation is definitely math based, but not really algebra.
J.
Some cats swing, and others don't. Don't you be the kind that won't.
I think that Algebra is one of the most important math courses for young people.
I learned Algebra in 7th grade (I had a great teacher). I stopped taking Math courses in 10th grade, and didn't start-up again until my mid-twenties, when I decided to return to school instead of remain working at word-processing jobs by day (while trying to write novels and children's stories by night).
I found that I still understood the Algebra after I returned to school. I was pleasantly surprised. To my mind, it's because Algebra can be learned as a set of ideas, rather than a set of facts and rules to be memorized and forgotten. (I'm not called 'Forgotten Password' for nothing).
Later, I taught Algebra in college, as well as to junior high kids. I've watched a lot of Algebra instructors: I was often disappointed by what I saw, and wondered how any of the kids in the classroom could possibly see the simplicity, or fun, or beauty of the subject by listening to the instructor that they'd been placed with.
Without interest, insight and a little mathematical maturity on the part of the instructor, Algebra can easily be taught as a book-keeping or rule-memorization activity, rather than as a perspective and mode of inquiry. And, if students learn that Algebra is boring, I doubt that it will be easy for them to find the fun in future science or math classes.
Sorry for the rant. I just think that Algebra is an incredibly important subject that should be taught well.
Best wishes,
Forgotten Password
FWIW, when I started high school I failed 6 (yes, SIX!) straight quarters of algebra. That's a whole year, summer school, and another quarter until I pulled a D to pass the next quarter. Was it me or the teachers? A little of both, but I blamed myself mostly.
So then I got into college, got a great teacher, and immediately pulled A's in math. This guy was no joke, he TAUGHT the shit.
Yeah, I blew stuff off in high school, but I'm old enough now to realize I'd been drowning in math since second grade. Where were the teachers?
Smoking in the lounge, of course!
If thou see a fair woman pay court to her, for thus thou wilt obtain love
So, according to media hype, what exactly are schools teaching well?
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~
Algabra...a gateway subject?
Heck no!
That's like calling crack a gateway drug.
I agree that the level of algebra that is taught in school these days is far from adequate. I just finished high school and I am lucky that I studied math on my own before I started college. I believe that the teachers are more to blame than the actual course materials. They don't get paid enough to really give a shit about what they do. Teacher moral is somewhere along the lines of a division of soldiers that were just masacred. Most of them are brought in from other subjects. Most of them aren't even qualified to teach math/algebra/calculus. I for one, was lucky to have the Geometry/Algebra 2 teacher that I did. If it weren't for him, I would not have the interest in mathematics that I do now. We need to fix the teachers, then the teachers will fix the material.
I was lucky.
My father has a masters in math and physics education. Taught me almost everything, mostly how to think about the problem. That's they key. That's what most schools really lack. They teach how to get it done quick, hard, and dirty. Not to really "think" about it.
Then, to top things off I was accepted to a special mathematics program from the University of Minnesota and took Algebra I&II in 8th grade, geometry and Pre Calculus in 9th grade and calculus I & II (essentially) in 10th.
Had I gone further I would have completed most of my required college math courses by the time I graduated high school.
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.
Show that a^2 + b^2 >= 2*a*b for any real numbers a and b.
I taught freshmen engineers Calculus a few years back and these kids were so bad at algebra I almost wanted to cry. Some of them acted like they had never seen a fraction. Some kids seem to get the impression that math is too hard therefore they shouldn't bother. Teachers need to get the kids to understand that algebra may be difficult to get at first but it becomes second nature to those who practice alot. They should just drill the students day in and day out and threaten to fail them if they don't do their homework. This type of approach is taken in many asian schools and I can tell you one thing asian, as in from Asia, students are really good and quick with all of the basic and intermediate mathematics.
Heck even art students need to pass the algebra exam if they expect to get any type of college degree. I honestly think that many High School teachers don not demand enough of their students. As a result some universities see nearly a 40% dropout rate for freshmen.
After dealing with college freshman I really think that our public school system is in need of a serious overhaul. Setting standards higher then they are now is a good place to start.
I learned algebra for real when I was taking calculus. Our math teacher told us that algebra was the most important thing to have down in order to learn calculus. And she drilled us endlessly with it. I remember integrating equations where the first step or two was all the true calculus, and then there were two pages of algebraic manipulation to get the final answer.
Some may point to Special Education and/or Gifted programs as alleviating this, but they are typically under funded, help only the lower/upper 3-10%, and don't have any set way to help, instead focusing on the main weaknesses/strengths of the bottom/top 2-3 individuals.
Example: my HS gifted program was essentially a quiz bowl team. Why? It wasn't because we learned a lot(we didn't), but because we had 3 people who were really good. Everyone else was perfectly happy, because going to the events meant they could hang out with their friends and usually get free food. For them, it was just a bonus to watch the top 3 do so well sometimes.
Why hasn't a solution been found and used? Quite simple: parents don't want their kids labeled negatively, and quite often kids don't want to be labeled positively by teachers because it leads to more negative labels from their peers. Having multiple classes, each for a certain level of performer, and you will have complaints, and lots of them.
In other words, don't necessarily blame the teachers or the buereaucrats for the problems of the system--blame our culture for being too Politically Correct.
I've often wondered how much of it I've lost. I had algebra beaten into my head. Then I got a BS in electrical engineering and had calculus, linear algebra, etc beaten in my head. But recently I've gone through old college text (from 6 years ago) and realized I've lost most of the calculus I knew. At UMich calc was divided into 4 basic classes (calc 1, calc 2, vector calc, and diffy eq). I know I've lost the last two for sure. I could probably do some basic calc (at least I understand the concept still.) But I wonder if I've lost the "basics".
Anyone else wondered this? Have you tested yourself? I took the math section of the GMAT and rocked it, but that's more of a problem solving test.
----- obSig
I have a ten minute time slot to play these pieces.. how fast do I have to play??
Algebra
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
Of course Al-Jebrah is a terrorist group. After all, it was the evil Egyptians who invented the zero. What other purpose could there be, except to spread Radical Islam throughout the world, and destroy the non-believers?
Jesus was all right but his disciples were thick and ordinary. -John Lennon
Comment removed based on user account deletion
news at eleven
Many readers are too old to remember the "New Math" of the '60s (for an example see http://members.aol.com/quentncree/lehrer/newmath.h tm). It didn't last long. I was fortunate that I was just ahead of it's introduction in my school system. I was the last to be taught using the "old" math.
In retrospect I didn't learn how to begin solving more than trivial problems until I had to struggle with doing proofs in Geometry. I had to do lots of proofs. By the end of the year I was able to tackle problems that required several steps to solve and prove. Looking back, I now see that this skill came to be used in most of my other classes from history to writing to Physics to calculus. I wasn't very popular because I could take arguments and generalities apart and worse yet, construct counterarguments.
But proofs aren't necessary in Geometry, and likewise, Algebra has been gutted. It appears that the process is more important than the correct answer. I guess this is "politically correct math."
Maybe one day your dorment algebra skills will help you win a yacht race.
pun-foo..
If you disagree then it must be overrated, redundant or trolling.
I guess I had a very different experience from you... I also failed freshman algebra but as soon as I was able to pass it I never took it again. Now I have a successful career as a programmer and I use barly any math. I think its all a waste of time for CS students.
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.
That America's education system took a turn for the worst when it became a public, government subsidised education system? Algebra isn't the only thing that they're falling down on, gateway or no.
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High school graduation tied to an exit exam, that has as one of it's requirements to pass: Community Service.
Since when did the schools become a place to get free student labor and not ( and I know this may sound like a troll) actually a place to educate people.
You can say "well rounded student" all you want but in the end well rounded doesn't teach you how to add and subtract.
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...
MARIJUANA, SHROOMS, X: ONLINE?! - E
I went to public school through High School. A lot of people here are claiming that inadequate teachers and school systems are to blame for students failings in mathematics. I sincerely doubt that is the case. Algebra is just not that hard. I myself was doing poorly in algebra. I never really had my times tables down(and still don't). But it was my parents who got me to turn around. My mom, bless her heart, would go over times tables with me when she got home from work. She was not too good with the algebra so she hired an old teacher to tutor me. After the second session the tutor discovered my problem. I wasn't doing my homework. The tutoring sessions then consisted of me doing my homework. It took me longer to do my homework with a tutor then it took alone and I could watch TV while doing it on my own. Needless to say, I saw to it that the tutor was cut out immedately.
I am pretty good at math but I learned a real lesson that day. In college I was taking Discrete II with my roomate the math major. He was a natural and just got everything without any work. I would slave away at the exercises and eventually figure out how the math worked. Good as he was I saw him hit the wall. The concepts got beyond him. I would try to explain them but do no better than the professor. He needed to do the exercises to keep up. He never had to before and was too lazy. I got a better grade then him all due to my dilligence.
Kids need to do their homework. Parents need to make them.
Every science and math teacher thinks that everyone sees the world / problem set in their eyes
I think that this is a bigger problem than most people realize. Most math teachers in Jr. High and up (I leave out Elementary, because they're generalists) tend to have strong math backgrounds (or so I hope). Thus, it's second nature to them. I have problems helping my kids with their math, because I look at their problems (basic arithmetic) and just know the answer.
Luckily, I am well aware of my limitations, and know that "I don't understand why you don't understand!".
Think about it. Who would you rather have as your basketball coach? Michael Jordan or Kurt Rambis? Me, I'd prefer Rambis... It's too easy for Jordan. I bet he couldn't even explain how or why he does some stuff. Rambis, on the other hand, while talented, wasn't quite as much a "natural" as Jordan, and had to work at it and learn it.
General Relativity: Space-time tells matter where to go; Matter tells space-time what shape to be.
"Gateway Subject"? is that like a Gateway Drug?
Won't someone think of the children?
"Oh my God. This is terrible. This is the end of my Presidency. I'm fucked."; ~ Donald J. Trump
Someone please explain to me, after spending one year on learning algebra, they switch to geometry and let you forget everything you learned, after which, they put you into a year of algebra, where you spend half the year re-learning all the algebra you forgot in the year previous?
Seriously, is there a conspiracy to keep students stupid, or do they just not get it?
I'd advocate spending Pre-algebra and the first part of algebra the first year of junior high, and follow through in eighth grade with algebra/algebra2/trig and a good dose of AP Chemistry. Ninth grade, you get trig/pre-calc with AP Physics. Tenth grade, you get AP Bio with statistics. Eleventh grade, you do 2 sememsters of college calculus (AP calc is weak, for get it). Twelfth grade, you take shitloads of standardized tests, and optional linear algebra with multivariable calculus.
Or you could do basic math and continuously flunk, and have to pass remedial math as a senior in order to graduate...
Don't think I'm neglecting history or english either - the AP Language and AP Literature tests are so similar that you might as well do both and get the extra credits. AP US History, US and comparative government, AP Music Theory, etc. My philosophy is you should be prepared for grad school when you do your undergrad, assuming you've got sufficient maturity to do so. No point spending 4 years of your life taking shit courses (most of them weeders) you should have gotten out of the way when you had the chance as a High School student.
Seriously, how can you explore different career choices if they have you doing the same remedial crap everyone else is taking?
Fortunately I had good 7th -9th math instruction. 7th = "Algebra 1/2", 8th = Algebra 1, 9th = Advanced Algebra 2.
Advanced Alg 2 was probably the hardest math class at my high school (considering that only 9th graders took it). In pre-Calc you could immediately tell the difference between the normal Alg2 and the Advanced class. Basically, Precalc was redundant for us, but it was pre-req to take Calc.
This is a very good topic, and point. Teaching and education is all messed up.
Why does the blame immediately fall there? Here's a clue for all the parents or wanna-be moms and dads out there: Your Johnny many not turn out to be all that bright a boy! In fact, nearly 50% of the population is going to have below average intelligence. While you'd like to assume it'll be the Smiths next door that raise the moron, you'll do your own kid a bigger favor if you assume the coin flip is not in your favor and thus actively participate in their education.
The problem I always had growing up and learning from teachers was inconsistency. I hated it then, and I hate it now.
Clue time for the young student now: teachers aren't high holy men (and women) with any ultimate truth to offer up. At best, they're just guides along the path and you need to get up off your ass and do the walking yourself. Socrates gave perhaps the best phrase regarding education I can think of: "I cannot teach anybody anything, I can only make them think."
I finally got through school by deciding to tune out the teachers entirely, buying my own text-books (after online research), and doing all my homework and papers in class while the teacher was lecturing.
Now that is a worthy solution. Keep it up and you'll end up doing well in life. But don't go expecting everyone in your class to be so motivated, and then don't go blaming the teacher because some who coasted through their first 18 years ends up hating the rest of their life. You learned the lessons of learning early; some never learn to learn. Sucks to be them!
Being a musician and scientist myself, I paid heed to those studies. The most famous and conclusive of these was the study of the Mozart effect, which shows that spacial and temporal reasoning increase for about 15 minutes (by a few IQ points) after listening to 15 minutes of Mozart. Similar indications, specifically in spacial and temporal reasoning have resulted from other musical studies. Spacial reasoning is the basis for geometry, and temporal reasoning is most helpful in Physics, especially mechanics.
I've never heard of studies in which Math in any way was used to benefit musicians, though it would be nice. My personal theory is that strengthening spacial or temporal reasoning either way will help both music and Mathematics.
Mod me down and I will become more powerful than you can possibly imagine!
instead of biology-chemistry-physics, we should teach physics-chemistry-biology.
While I sort of agree with this, and certainly once people are at the University level, there's a big reason why we don't: familiarity.
Most any kid can picture his dog (biology). He can maybe think about what happens when the dog eats (chemistry). There's almost no way he can conceive of what the food is made of, on a level so small it has to be described only with mathematics (physics). Even when talking about classical physics, I don't care how much of a science geek you are - balls rolling down planes are NOT exciting. Physics tends to be either highly math focussed (and a lot of memorization), or so abstract that most people don't even grasp the basics (quantum physics, anyone?).
Biology is an easy course to teach, because it deals with every day occurences. Sure, adding vinegar to baking soda looks cool, but without the biological effects, try explaining to a 10 year old why this should be important to him/her. Why there are so many mosquitoes during rainy years is a lot more relevant, and approachable, to the average student.
Personally, I think we really need to return to a more traditional "Science" type of course, with less division between the fields. I'll never forget the day in chem lab when it occured to me that everything we talked about in physics and bio were all connected - it was an epiphany I'll never be able to top. Yet all through school, it was never really explained that all of this stuff is not only related, but basically THE SAME THING.
Same goes for math (esp. algebra). You simply cannot do physics without it, nor chem, nor bio (unless we're talking the ubiquitous worm disection that really teaches nothing). The worst mistake we ever make in school is the old "this isn't english class, so you can't deduct marks for spelling mistakes". I've seen people get away with horrendous mathematical errors (even in University) because "this isn't a math course".
Abstract concepts like algebra are simply too fundamental for darn near everything, most peope don't even realize they're using it almost every day. Unfortunately, testing understanding of abstracts isn't as easy as checking memorization and regurgitation skills - hence those dozens and hundreds of formulae that almost no one remembers 5 minutes after the final exam.
Endless arguments over trivial contradictions in books written by ignorant savages to explain thunder in the dark.
Over in England, we have a system called GCSE's that you leave school with and are mandatory (then you can do A/AS-Levels and then University).
In year 9 (GCSE's being 10 and 11, I would have been about 12-13) we had one of the most crummiest teachers ever (Her first year of teaching as well - she would leave classrooms crying because she couldn't even control the class), and that was the year we were meant to get a good grounding in Algebra.
Then when I got into year 10, I was put into the top class... and couldn't do Algebra, and had the same teacher who would deride and take the piss out of me because of my fundamental lack of Algebra skills (and didn't actually offer to help).
My parents (at my request) got me private tuition for 2 hours a week for my year 11. And it definately paid off, especially when there was an open day when the GCSE results came out... and wiping the smug smiles off so many classmates (because me being the one in class who couldn't do math) scoring significantly better grades than them... a very satisfying moment indeed.
I agree that a combination of teaching is good, because you are given different enviroments and approaches which can only help in the learning process (rather than dreading going to a certain lesson). And yes, teachers aren't really paid enough over in England as well. My university lecturers were on a semi strike for months because of this, in that they refused overtime, extra paperwork, and just did the required lectures only.
Are you local? There's nothing for you here!
"9-11" is composed of 3 (count 'em, three!) arabic numerals!
In fact, those dirty arabs have pervaded our way of thinking so much I used an arabic numeral without even realising. Look, up there, the "3"!
Dammit, there it is again!
In addition to explaining all that (and TAOCP is the only place I've ever seen it explained), Knuth goes on to give the translation: Rules of equating and restoring.
You cannot apply a technological solution to a sociological problem. (Edwards' Law)
I know several people who were homeschooled (dated one of them for 1.5 years), and they certainly weren't lacking in social interaction.
While most parents teach the "three Rs" at home, there are other classes, like art, which are more difficult to teach unless that's really your thing. I don't know about other homeschooling situations, but the Christian Home Educator's Network (CHEN) has kids get together for such classes once per week, and they also meet for other activities.
Plus, you certainly have the kids who live on your block, any siblings, etc.
Most homeschoolers I know also finished their high school degree in 3 years, and started going part time to a community college before they were done. They then had a nice head start at a college education.
WMBC freeform/independent online radio.
Algebra is boring because the students aren't being challenged. They should increase the pace so that they learn something new every day and force the idiots to repeat it until they get it right.:)
Is this a sigs-optional kind of place? 'Cause I am totally down with that if you know what I mean.
How about planes? Rockets? Planets and
stars? Day and night? That's not exciting?
Perhaps... How about electricity and electronics?
How does a TV work? Or a CD player?
Considered harmful.
dude, these are not reasons to opt-out, these are reasons for you to GET INVOLVED with your public school. get other parents involved too. it is your school, make it be what you want it to be!!
I hate quitters. home schooling is dropping out.
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"
It's psychosomatic. You need a lobotomy. I'll get a saw.
First of all, "Kids these days" are not universally stupid. I base this on myself as a counterexample: I'm only two years out of high school. I'm 21. Does that qualify me as young? Now I'll try to convince you that I'm not stupid - this will also lead me into my main point, which is coincidentally the part where I talk about these lowest common denominator kids I mentioned in the subject of this post.
I teach math - at the same high school I graduated from two years ago. I don't have a degree, so they can't hire me as a professional; instead, they pay me as a $15/hr tutor. But they send me the "lowest common denominators"; they send me the kids the professional teachers can't teach, because I can.
If I said that right, that qualifies me as smart, refuting the point made earlier (in this post's parent's parent) that kids these days don't know jack. It also leads into the point I'm more interested in: that the problem isn't the lowest common denominators. They can indeed be taught. You speak of these people asif they were lepers. We can't cure their disease, and they are hurting us by being around, so just shut them away and forget about them? That's what I thought in high school, too, but not since it's been my job to teach them. While it's true that it's possible for kids to have low natural talent with math (which doesn't matter, if you can get them interested), it generally isn't the problem. The low-end students are almost always normally skilled - their problem is their attitude. For one reason or another, they don't want to learn math.
What you're probably expecting to hear from me now is my theory on why they have bad attitudes. I have a couple idle speculations, but I don't really care; my job is just to get math in their heads. What's important is knowing how to fix a bad attitude, not who to blame for it.
It's literally impossible to make math cool to a high school student. It is pretty much as not-cool as things get by the high-school-popularity definition of "cool." They know better. So do you. Forget about cool. They way to make them want to learn math is to show them what it has done. Since I've started teaching math, I've worked up a repitoire of examples from the real world where people need math. I don't mean the lame-assed examples you get in math classes (what if I am three times more than two years older than my five-year-old niece?) - the kid knows, just as you do, that that'll never happen. You have to come up with something that shows them plainly that math really is useful. Here is an example:
Once, I was given the task of showing a student how to use ratios. I found a scale drawing of a house in the library - basically blueprints. I gave him a ruler and a calculator and asked him to draw the house on a poster, only bigger. It looked like crap. Then I did it, and it looked perfect. He asked me how I did it. He wanted to know. That's all you can hope for. After that, teaching him was a breeze. When he took the final for that class, he got all the questions on ratios right, and averaged 40% on the rest of it - stuff that nobody had ever interested him in.
You can't teach anyone how to do math unless you first teach them why, no matter how smart they are, and any idiot who's motivated can handle high school algebra.
PUBLIC SPLIT ON WHETHER BUSH IS A DIVIDER -CNN scrolling banner, 10/15/2004
algebra is about as much a gateway into science as marijuana is to cocaine, i got into science while in about 4'th grade of public school, this is crap.
Having taught many college math classes, I can tell you invariably (haha :)) that the students have problems with arithmetic if they don't something in class.
Doing arithmetic in your head means moving numbers around in your mind and combining them.
Doing algebra is one step beyond this. So, if you never understood arithmetic, you won't understand algebra.
I blame the purveyors of calculators for "convincing" state school boards to give kids calculators from day 1. They shouldn't get calculators until high school at the earliest or they'll never learn arithmetic and they'll never get abstraction and they won't be able to solve problems.
Best. Comment. Ever. Enjoy!
Back when I was at Uni (not that long ago really) our Faculty held seminars for all the Maths teachers in the local School Region (SE Queensland). The Minister of Education gave an address one year and made the following statement:
None of you should ever expect to meet a student who can apply a quardratic equation to a appplied problem
This boggled those of us who had been teaching awhile (17 years teaching Maths in my case).
What I've seen is that very few mathematicians seem to go into teaching. After all, if you have a decent Maths Degree (whether Arts or Science) you will get a much better job in the Computing/Finance/Actuarial industries. So the vocational teacher who is also a mathematician is a rare bird indeed.
So we have all these ppl who are teaching because they had to do something with their degrees. They don't really understand maths, they don't appreciate the beauty or the simplicity of it. These people's approach to algebra is to 'transliterate' things from one side of an equation to the other! Now how we can take anything balanced and transfer bits from one side of it to the other and still have something balanced escapes me. I know that if I always perform the same operations on both sides of an equation it stays balanced though...
It's the same as "the square root of 4 is plus or minus 2" - absolute crap. Square root of 4 is 2. Roots of the equation x^2-4=0 are plus or minus 2.
Until the pecunary rewards for teaching can attract people who feel passionate about the subject as teachers we will continue to see the ongoing slide in Maths Education.
Note that I'm not teaching anymore - I can't afford to. I work in IT now.
Well, duh, I mean they use *Arabic* numerals too!
Why isn't algebra more important than it is? For several reasons. Namely, it hasn't been dubbed a valuable vocational skill by businesses yet.
Secondly, education (and algebra) is presented as content, and not a means of lifelong learning. A credential is now the driving force behind learning, we are driven by economics, not intellectual growth. Pretty soon, society is going to be so fragmented and specialized that people won't be able to see the links between their discipline and other disciplines. They'll know a hell of a lot about their one little piece of the world, but not know how to relate it to the rest of the world.
An education's vocational relevance is the driving factor behind most student decisions- this is what businesses have been telling us and schools for years, that schools are not doing their jobs to make students 'work ready'. It's been a slippery slope from educational setting to corporate training ground. This was supposed to be our answer to economic development. Vocational education. Every peg in its hole. So if a real education itself is unnecessary, why don't we just train for a job and quit pretending we want to educated kids? Maybe because we must leave the masses their illusion of living in a democracy?
I'm not cynical, nope, not me....
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.
It's psychosomatic. You need a lobotomy. I'll get a saw.
And I'm a calculus addict. I've even tried multivariable calculus, offen refered to on the street as "differential" calculus.
It all started in Junior High, when I was introduced to Algebra. I've never felt so high in my life. I was able to figure out what X stood for. It was like reorganizing truth. It was crazy shit.
After awhile, I just couldn't get the same high anymore. I knew what X was without even divinding by both sides. I couldn't get that same high. Then my "teacher" showed my this great shit from some old greek dude called "geometry". Man, that shit fuckin' blew my mind. I could like, create intricate angles, and they all meant something. I could find the length of side C, and I only needed length A and B and the angle between A and B. Crazy shit.
Of course it all spiraled into what I am today. I integrate on the weekends, sometimes before I go to work, but it fucks with my head too much. I've lost many girls and spent a lot of cash on my habit. I have "loans" of over 20 grand to pay off. My name is ferrocene and I'm a math addict.
Most folk'll never lose a toe, and then again some folk'll...
why is it surprising that students aren't doing well in a subject when, first, they have no interest in it, and, second, they are rushed?
my proposals. first, waste as little time as possible forcing students to learn that which they don't want to learn. in the extreme, this would mean letting high schoolers go out into the work force and then go back to school for free when they realized they missed out. less extreme: alleviate the grade pressure in school and also allow students more choice as to what to study. too much pressure can make a student learn the quadratic formula, but it won't make him or her learn why math is such an interesting and useful thing (which i would argue is more critical for our society).
second, it takes a long time to understand something well. creating mandatory tests against teachers' recommendations will probably create unreasonable curricular requirements that can only be met by teaching to the test. if it takes a year of algebra just to learn algebra concepts, without learning any "hard algebra", so be it. teachers generally have good hearts and are close to the problem, hence their recommendations in these matters should be weighted heavily.
As Del said:
Industries rising,
with energy declinging,
People think I am whining?
Really, I don't give a shit.
Because everyone's dying but you all think that is the end of it.
That is why it's so easy to be a Benedict.
Or imitate,
Because they wouldn't teach you algebra when you were eight
As we can see from Del's words, it isn't just science and technology that algebra provides a gateway to, but also to a true understanding of the afterlife.
Hopefully I didn't put any [] around my words.
I got a C in Algebra and took Trig in college a few times and never could pass. So I switched to a different school and sneaked into calc and did okay.
I don't consider myself a dumb person and I do enjoy math, but I just couldn't get through trig for anything. I was stuck with the same teacher every semester but it was probably more my fault than hers.
The man who trades freedom for security does not deserve nor will he ever receive either. - Benjamin Franklin
Public schools have been doing a poor job of teaching algebra for at least the past 30 years. I was encouraged to take remedial algebra in college. The instructor was excellent and I did very well. Math became my best subject, although it wasn't my major. I took math courses as electives. I really should have made it my major but engineering beckoned. Since graduation, I took 3 more math courses. I thoroughly enjoyed all of them. What I like most about it is it never becomes obsolete. Most mathematical principles are pretty old; math just doesn't change all that much. Whereas the half-life of an engineering degree is about 5 years. It's a pity public schools do such a lousy job teaching something as important as algebra.
Wansu, th' chinese sailor
interestingly enough, my computer science classes helped me to understand algebra better. i didnt even like math until i started programming. im sure others here have had similar experiences.
Gyrate Dot Org - "Where high-tech meets low-life"
Preparation is probably the key.
I remember playing addition and multiplication 'games' with my mother before I entered kindergarden. We went up to 12 + 12 and 12 x 12. Years later I found out that earlier generations used to memorize this stuff up to 24 x 24.
By the time I was in grade 4 I was doing square roots by estimating, multiplying and interpolating. No, it wasn't part of the curriculum. But I wanted to figure out transit times between planets at constant acceleration & decelleration. So I figured out a way to solve the equations.
I also think that algebra is pushed on students before they are cognitively ready.
I've learned a lot last year about what students are capable of in terms of mathematics. European kids start Algebra as early as (US equivalent) 6th grade, before they are split apart into different schools. They are capable of learning Algebra, but not with a US mathematics curriculum.
One of the largest problems with US math curricula is that there are too many teachers such as yourself that keep encouraging arithmetic. In today's US curricula, students start arithmetic in 2nd grade and keep studying it in 7th and 8th. That's 7 years of math that can be done on a $2 calculator. Students psychologically develop abstract thinking skills between 11 and 12 years old. The majority of students are capable of understanding symbolism at that age, and are well capable of learning Algebra by 6th or 7th grade.
The problem that too many teachers discover when they run into students who have a hard time with math is that they've not been taught well. Problem solving is one of the biggest setbacks in any math curriculum, a skill that is as essential for Algebra as it is for arithmetic. If students don't understand how to pursue a problem, they'll appear stupid no matter what grade-level problem is presented to them.
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.
Alright, but there's a catch. They've just returned from summer break and haven't cracked a textbook in three months. There arithmetic consists of punching numbers into the calculator as it is presented in the textbook. They can substitute, but they do so without direction. Think you can turn them into stars?
They have no real cognition as to what their actions mean.
Of course not. So many teachers turn math into a cop-out method of teaching: it's purely mechanical. There's no abstract thinking involved but what the book says. If you see
Add.
1) 502 + 582 = ?
It doesn't take a brain surgeon to figure out what needs to be done. So many teachers (especially in elementary school) treat math like it's supposed to be made as understandable as possible. Unfortunately, it doesn't teach them how to think about what they do.
Students know how to do arithmetic, so don't keep beating it to death. Instead, try some problem solving puzzles and let them develop their analization skills.
it was indies not egyptians
That's odd...
Nyquil = Nectar of the devil
Lynette Shields, who teaches math at Washington Irving Middle School in Fairfax County, said there are more students with problems in eighth-grade algebra because an effort to get more children into the course has lowered the standard for admission.
So in other words, some people just plain suck at math.
Your mother implements multi-vendor protocols without synergy
Actually pretty much any word beginning with "Al" has Islamic roots. Algebra, Algorithms, Alchohol. Mind you they might not have been invented there, obviously the greeks had developed algorithms for various things, but the word we use came from the Islamic world.
You know the Islamic world wasn't always a bunch of backwards religious zealots.
At one time Baghdad had the biggest library in the world. If it wasn't for arabic trnaslations of greek and roman works most of it would have been lost.
And only one semester of Probability and Statistics for Engineers? Must be nice...
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...
I don't read or respond to AC posts
Ha ha, you Americans. Can't even handle metric!
Music is the best way to teach analytical methods like Fourier Eigenfunctions and similar spectral techniques! What better way to illustrate the concepts than with a simple 1 dimensional signal? Couple that with the our cochlear frequency analysis hardware and you've got some serious edutainment!
In middle school we went all the way up to intro to 3d geometry.
:(
In 8th grade we did:
Vectors, Polar, Quadratics, 3D Geometry, the 3D Plane, and Trig Functions (SIN/COS amp freq and so forth)
Wasn't until my 4th or so college mat class that we got back to that sort of material. *frowns* H.S. was just all boooooring review.
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Why the hell do they seperate the courses anyways? Why not take everything as one Math class? Algebra and geometry, instead of seperated as eighth and ninth grades, should be half of each grade's class! Therefore, we don't forget and can use the geometric principles together with algebra, in a manner more similar to what we'll do in real life.
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Score 3? For what? Being wrong, at length? - smirkleton
In fact, nearly 50% of the population is going to have below average intelligence.
That much is entirely true. But you're forgetting that to many people who have a clue, that average is at a far lower point on the overall scale than it has to be. You're also forgetting that most of these people, both above average and below the average, are cranked through an indifferent public school system which have the blessing of similarly indifferent parents.
But what happens when a parent actually starts to give a crap about their child's education? I'm not talking about the, "You had better get all A's this semester, young man," crowd. I'm talking about the parents who take an active part on their child's education by inspiring the child to learn and giving them opportunities to experience the benefits of gently pushing them beyond the norm.
Unless said child has a mental disability, there is simply no logical way that the child who has been actively and positively encouraged to learn could possibly fall behind the average if compared to their peers in a modern public school system. Period.
Well, here's my story.
Seventh grade, sitting in the back of a pre-algebra course. Early in the year. The teacher puts a problem on the board and expects everyone to come up with the answer. The goal is to teach order of operations, I think, which is old news to me. The problem is something like (5 * 7 + 3 * 4 - 9 / 3 + 8 - 2 ^ 4) / 2 = ?
So I sit there. As the teacher is walking around, she stops at my desk and asks, "Aren't you going to do this?" I said, "Yeah, it's 18." "You didn't write anything down." And I reply, "No, I did it in my head."
So they move me up to algebra proper. The only thing I remember missing was the idea of the difference of two squares, which took about 3 minutes to explain. They were still using FOIL enough that they didn't need to stop to tell me about that. After taking algebra in 7th grade, I had to visit the high school first thing in the morning to take geometry in 8th grade.
This was in Cary, IL, sometime around 1991. Over ten years later, I'm living outside of Boston, MA. I sure hope they're still as astute as ever.
that's why I'm glad to have never gone to a private school. by chance, the public school i went to is one of the best but even if it were not, i would still not go to a private school.
public schools actually let the student choose their classes and can provide a much better experience with a wider class selection.
it all depends upon the student
Your mother implements multi-vendor protocols without synergy
If I sit down and read a book, I retain some knowledge.
If I rewrite the contents of the book in my own words, I will be able to retain 7 times more effectively.
If I, in addition to taking notes, also apply it to common problems and understand how they interrelate, I develop critical skills of applying raw math to real world problems in addition to understanding things even better than notes alone.
My high school physics teacher would always say, "of course, there's an easier way to do this if you're at the math b 30 level" or something to that effect. It makes more sense that things like derivations, integration, and cos/sine law should be taught sooner, and re-inforced with kinematics and vector theory in grade 10 and 11, rather than waiting for 12. Then I'd have a couple of years to have it reinforced, rather than forgetting a lot of it (because I was out of practice) while I was earning money to attend university.
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Internet Explorer (n): Another bug -- that is, a feature that can't be turned off -- in Windows.
Actually, I'd argue that geometry has more in common with logic and trig than it does with algebra (remember those damn proofs.) It should be taught as a completely separate math course, parallel, prior, or after the algebra/algebra2 class, and should emphasise the ability to do proofs - no point in having to learn that nightmare all over again.
Your country is a great place for a lot of mediocre people. An AVERAGE american really does not need to know a whole of a lot of things to work 40 hours a week, drink beer, shoot guns, watch TeeVee, pay taxes and support the upper classes. It shows in your movies, music and food. It is a country where many people mixed together and tried to make so that many products are liked by a great majority of populace.
algebra is just a fad
Never before have I seen a more fitting application of the following quote:
Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe and not make messes in the house. - RAH through Lazarus Long
Its calculation. 1 + 1 is 2, 2 + 2 is 4.
You want to teach the concept of addition, however most people just tell you to memorize the answers. Memorize the time tables, they give you a list of problems and tell you to calculate the answers, they fill your head up with rules and useless crap, and this is why alot of people arent good at math.
I'm glad i didnt memorize all my multiplication tables, theres the calculator to do calculations. However because all they taught in school was calculations, It makes it harder for a person to understand the real math, like calculus, discrete math, logic, and the theory behind it.
The problem is with how math is taught, if you are trying to get people to use math you teach the concepts, expecting them to remember the rules when they will never use them, well its pointless, as pointless as expecting everyone to memorize every single linux command or every single programming command.
You remember what you use, what you dont use you look up in a book, or a refrence manual.
How many of you people would be able to code in C++ if you were forced to memorize every single peice of syntax and every rule ? Maybe John Carmack can do that but most people have better things to do.
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My physics teacher in high school did all the tests "open book". You could use whatever you wanted. I loved this kind of test. This way you actually get tested on whether you UNDERSTAND what you were taught, and not whether you can memorize a lot of stuff overnight, as unfortunately most other tests are. I don't like memorizing stuff (I tried to get through those king of tests with logical thinking too) and I always understood the phyiscs I was taught (he was a really great teacher, and he was really obsessed with physics {"there are three important things in my life: 1. Physics, 2. Physics, 3. Physics") and could show one the beauty behind it all), so the tests were always a lot of fun for me, since the questions were usually a bit challenging, but I could look up all the formulas and stuff I needed, and usually got a very good grade. But most people were absolutely frightened of these tests, because they usually got through tests with memorization skills, even if they didn't understand the subject matter at all. (Though sometimes the method of getting all the physics tests about that subject from the previous few years and hoping that some of the questions will be the same worked for them as well).
I'd really love to see these kind of tests used more widely, and I think it would help a lot to raise the quality of education.
. . .that is my home.
I learned integration in 11th grade at a US public High School.
I also learned that most Americans in college can't handle basic integration and can't even derive the quadradic formula.
I think stressing the practicality of math or science is the problem. It makes it seem like things worth knowing should be easy to know, like sports, beer, TeeVee, etc.
Algebra really has nothing fundamentally to do with quantities or counting. It has to do with logic and mapping sets to sets.
When math is taught using "I have 5 apples and I give 2 to Billy Bob. How many apples do I have left?", it makes it extremely difficult to introduce abstract concepts, and show the true beauty in algebraic constructs.
Schools do not exist to prepare people for the real world, if they do they certainly arent doing a good job because the majority of what you learn in school is bullshit.
What you need to learn for the real word, ethics and morality, critical thinking, creativity (helps with problem solving), finance (this is the only math you ever need to learn), reading, writing, and plenty of technology and science classes so you can understand the world as it is in 2002 and not as it was in the 1800s when people used libraries and typewriters.
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This isn't funny but informative as a two seconsd google research gives off a lot of link ! :
Url
http://www.ualr.edu/~lasmoller/aljabr.html
Quote :
Al-Khwarizmi's most important work, however, was probably the treatise called al-Kitab al-mukhtasar fi hisab al-jabr w'al-muqabala or The Compendious Book on Calculation by Completion [or Restoring] and Balancing. This book is an explanation of the solution to quadratic and linear equations of six varieties. Al-jabr refers to the process of moving a subtracted quantity to the other side of an equation;
C. Sagan : A demon haunted world:
http://www.amazon.com/gp/product/0345409469/
visit randi.org
Option? It was a required course in 7th grade at Millburn grade school in Lindenhurst, IL. Might be for the entire state, but at that time I had *other* things on my mind besides investigating the math lessons taught at other middle schools.
Course at the beginning of 9th grade my father was stationed at Fort Knox, Kentucky, and the local Elizabethtown High School starts Algebra in 9th grade. Kentuckians, being stubborn as they are with the "we are the best" attitude, refused to accept Illinios schools are two years ahead of KY in math, and wouldn't let me start with trig.
Funny thing is two years later they were named a Blue Ribbion School, which is suppose to stand for "excellence", which I find ironic...
John Dewey obviously was ignorant as hell if he actually believed all humans learn in exactly the same way.
Thats why some humans pick up math and some dont. Some people dont learn from repetition, in fact I hate repetition so I hated math all growing up, it was always repetitive as hell, solving random problems, etc.
Making people do slave labor and calculate stuff for no reason does nothing to teach them the actual concepts. I assume some people do learn math well through this, this is why some people do well in math, but not everyone does.
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. And THAT is the problem right there. People learn by asking questions and gathering information. Currently teachers dont do much but give students books, drill and practice sessions, and test them with a quiz.
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.
That is a GOOD point. I agree that the school system is almost mechanic in nature, it prevents people from having any creativity, and does not allow people to think, just gather information, memorize stuff, do drills, and take tests. Like some kind of robot.
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.
This is how it should be.
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...
Well if people were stupid enough to listen to Dewey and not einstien who failed math in school but who claimed the key to his success in math was his imagination and creativity.
It tells you something, the greatest scientists were not great because they could calculate and solve random problems, pass tests and remember their multiplication tables, they did good because they were good thinkers, who had creative minds, also having a bit of logic helps too.
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Then when I need to use the formula i can just look at a little card or pull out my pda and look at the formula you have right there.
Its pointless to teach people to calculate. Teach them how to enter it into their calculator and push enter.
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1000+ on your SAT in junior high? What country do you live in? Our schools arent good enough to produce such scores.
calculator-enabled math is a fucking joke (in my day there WERE NO CALCULATORS ALLOWED.)
This is 2002, before paper was invented, people did math in their head, why dont you try it? You like the challenge of going without a calculator
That we can't even get HS seniors, with the benefit of a supposed 12 years of education to score decently on the SAT is merely a symptom of how bad the problem is. Seriously, why are we wasting money with remedial education for adults when we should have spent that money when they were still minors?
Because people like you are so focused on SAT scores and doing math without calculators that students never really learn to think, they just have to remember alot of useless facts, formulas, and other crap, when you are focused on remembering stuff you arent going to be able to think as well be creative.
The SAT being over 1000? This depends on who your teachers were, unless we drastically add to the school budget, like raise it to 100 billion and spread this money to all the right places, we arent going to be able to teach students mainly because the teachers suck, and the current way school is designed, students are held back by other students, and class structure. I think technology should be used more, so students can all learn at diffrent paces, and to allow the teacher to properly teach 30-40 kids in a class.
Perhaps you went to a private school, but most people did not.
As far as english, yes people should learn english from reading, but the problem is schools force students to read what THEY want them to read and this is one reason students dont learn to read as well as they would learn if they were reading what interests them.
Kids who like video games can learn to read playing final fantasy. Chatrooms and the web can also teach students to read. Allow the student the freedom to read whatever they want as long as it is within guidelines, and then make them write a paper about whatever they read, if it was a video game such, make them write a paper on it.
The main change school needs to make is to stop teaching useless facts, stop making kids learn to spell by giving them a dictionary and making them look up words and instead convince the kids to read more, even if it means creating a web based communication system for students to talk to each other with, have auto spell check built it so it corrects their errors for them, saving them time they'd have to spend doing things the way you did it.
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If you want kids to learn social skills and get a good education you are better off putting your kids in a residential private school where they'll live on a campus like atmosphere.
They will learn how to deal with people their own age by living with them as this is the best way. Also they would get a better education because they would always have a teacher around to help them at any time of the day or night.
Parents are supposed to help with teaching but in this day and age, parents often have to work 2 jobs and dont have time, I think residential schools would solve alot of problems.
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- Very basic job skills - enough to get hired in safeway and avoid being homeless. Personal hygeine, respect for your manager, showing up on time, looking for cheap housing etc.
- Dating. Sure, slashdot crowd is suffering from lack of skills in this area in particular, but for most people that's what makes difference between just surviving and real happiness. Meeting people, balance of getting what you want and making sure the other person is happy too, raising children, handling a divorce if it has to happen, etc, etc. Even a very happy relationship could be more happy in some area and that's the happiness that counts most. Teaching something that might help at an age when you can understand it would be super cool.
- After basic survival and interperson skills are taught, students should be offered a sampling of subjects that are currently in hot demand or are likely to be soon. If they happen to have a liking/talent for one of these subjects, they should be taught skills that would help them land a job that pays well.
- Finally, students should be taught how to be good citizens in a larger society beyond their family - volunteering, donating to charities, conservation and so on. Of course it's important but people are not likely to do it until they are satisfied with their own life.
Only after someone has mastered all these things, it makes sense to teach abstract enjoyment of math, physics and so on. For most people, this will only happen after 30. There is a small minority though which is critical to the society. A reasonable number of people will trade high-paying job for the one they intelectually (or physically for that matter) enjoy. This is a large percentage of slashdot I guess. Several people I know will give up dating to do what they are doing. And really gifted people will rather be hungry than give up their quest. It's important that the school keeps the door open for this kind of people, because they will contribute much more to the society than most of us who are happy to sip a beer and sit on the couch with a date. Perhaps offer small samples of each subject and encourage students to study ones that fascinate them. But it's equally important not to torture the majority of us that just think about a date and a beer (hopefully in this order) and expect us to enjoy the stupid math.You do realize alot of parents work 2 jobs dont you?
For low income families, residential education would be a perfect solution.
I suggest we build more residential schools, it would have the benifit of both worlds.
A 24/7 education. 24/7 social interaction. Students could be home with family on weekends if they want or stay, students could go home at any time with parents permission etc, this would be perfect for middle school aged students.
I dont think as many highschool students would benifit from this, although some might.
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You see, its good to have social interaction when its with intelligent peers, but when you are surrounded by ignorant peers, you'll get picked on, harrassed and bullied.
Social Interaction is good when its with intelligent people. Social Interaction sucks when you get your ass kicked every day by bullies, but for alot of kids growing up, thats what they have to look forward to when going to school.
"hmm which bully is going to kick my ass and take my lunch money today?"
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Reading the story and the comments, I seems that "algebra" encompasses everything which is remotely mathematical, but is not directly linked to the set of real numbers (or calculus). That's a bit funny because the technical meaning of "algebra" is rather different (and in other languages, "algebra" has largely retained this rather specialized, technical meaning).
Unless you are around alot of intelligent peers who are social in a GOOD way.
Your kid will not learn to be social, if other kids bully him everyday and kick his ass. Your kid wont be social if by being social people tease him, make fun of him, and humiliate him every time he ever tries.
So believing public school will teach you to be social, its a dream, in a perfect world were everyone smiles and is nice to everyone else yeah, but in the real world people are mean and cruel, especially young people. So expect your kid to pick up alot of wounds and scars because you wanted him to be social, and it could backfire, your kid could end less social like I did, or your kid could go insane like those two kids from columbine, theres alot of possibilities.
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I guess the article and most posts in this Slashdot topic are referring more or less to calculus (which is closer to analysis than algebra) and linear and second-order equations solving (a mostly insignificant part of algebra IMHO).
:)). Anyone tried the reverse? You could learn a major part of the definitions and theories first, and then apply them to solve equations. That would need quite some maturity, which you can get through learning english (or french in my case) and some philosophy first.
In France, you cannot enter state approved (the so-called technical elite) engineer schools without first passing school-specific competitive tests for which you prepare for two or three years after graduation.
Their you get mostly math and physics high level courses where I got taught what was called algebra: group theory, rings, fields, vector space, etc... (More info available at Eric Weisstein's world of mathematics)
In the business field, I don't have to use much maths whether theoretical or applied. I find what's more important is how you express your ideas and how you communicate with your co-workers, your boss, the customers.
Obviously, I had to go through high level science and tech courses for which math is a life-saving requisite. However, my day-to-day job is not, unfortunately, to find new undiscovered tools and theories for my field, but just to use abacae and tools of the trade. And yet I've co-authored some patents.
Math is quite an interesting subject. It's a shame that it's taught entirely bottom-up though (eh, I was taught base conversion before multiplication, bare with me
English is the #1 required skill everywhere anyhow.
And to think we are horrified at slipping standards here...
Chapter 1. Transformations, Matrices and Determinants
Column vectors. Transformations in two dimensions. Matrices. Multiplication of matrices. comparison of transformations. Determinants.
Chapter 2. Further Transformations
Vector product. Transformations of three dimensional space. Inverse transformations. Inverse matrices. Solution of linear equations by systematic elimination. Calculation of an inverse matrix by reduction. Vector spaces. Linear independence of vectors. basis sets and spanning sets.
Chapter 3. Mathematical Proof
Statements. Direct proof. Proof by induction. Proof by contradiction. use of a counter example.
Chapter 4. Functions
Even, odd, periodic functions. Continuity. Singularities. Logarithmic function defined as integral of 1/t dt from 1 to x. Hyperbolic functions.
Chapter 5. Polar Coordinates
Polar curve sketching. Area.
Chapter 6. Series
Comparison tests for convergence. Ratio test. Maclaurin's expansion. Expansions of exp(x), ln(1+-x), sin(x), cos(x). Taylor series.
Chapter 7. Differential equations
First order exact equations. Integrating factors. Second order linear differential equations. Particular integral. Complementary functions.
Chapter 8. Complex Numbers
De Moivre's theorem. n'th roots of unity. Exponential form e^(i*theta). Relationships between trigonometric functions and hyperbolic functions. Loci in the Argand diagram. Transformations of the complex plane.
Chapter 9. Polynomial functions and Equations
Remainder theorem, factor theorem, homoegenous functions. Relationship between the roots and coefficients of a polynomial equation. Complex roots. Quadratic factors with real coefficients.
Chapter 10. Further Integration and some Applications
Reduction methods. Improper integrals. Mean values. RMS values. Area of a surface of revolution. The theorems of Pappus. Curvature.
Chapter 11. Numerical methods for the solution of differential equations
Polynomial approximations using Taylor series. Step-by-step methods.
Chapter 12. Curve sketching and inequalities
Rational functions of x with a quadratic denominator. The curve y^2=f(x). The cycloid. Tangent at the origin. Points of inflexion. Inequalities of the form f(x,y)>0 and their interpretation as regions of the xy plane.
Chapter 13. Coordinate geometry.
The parabola, ellipse, hyperbola and rectangular hyperbola. The line pair. The existence of asymptotes.
Chapter 14. Groups
Symmetries. Definition of a group. Integers modulo n. Permutation groups. Isometries. Matrix groups. Subgroups. Isomorphism. The order of an element. Direct products. Cayley's theorem. Lagrange's theorem.
Chapter 15. Matrix algebra
Matrices as transformations. The transpose of a matrix. Symmetric and skew-symmetric matrices. Symmetric matrices and quadratic forms. Diagonal matrices. orthogonal matrices. Eigenvectors and eigenvalues. Diagonalisation. Interpretation of diagonalisation. Proofs of the algebraic laws.
This on a first year Calculus test. At one point the answer had reduced down to 16/64. One student just cancelled the 6's.
After we saw that we wished we had used different numbers, and we wondered how many other students had mentally done the same thing and just not marked it for us?
Looking through the posts there seems to be 2 issues here, I am currently taking my 3rd year in a degree in AI and maths at edinburgh university so I know a little about this.
Firstly I know it would have helped me if instead of wasting half the maths course teaching statistics (which are trivial if you have a good grounding in maths) I was taught a lot more solid grounding in calculus and different proof structures, techniques etc. My last year was spent doing pretty much exclusively complex analysis and multivariable analysis as far as maths goes. Basically this is hard core calculus all the way and as a result of not being taught enough basic calculus at school it is quite different. I dont think algebra is the problem, most people are quite adept at manipulating equations by the time they reach uni.
The second issue is that maths IS required in computer science. Those people saying I work as this or that sysadmin or network programmer are simply not doing computer science at all.
It's like the difference between an accountant and a mathmatician.
Most of computer science is underpinned by proof structures, measuring time complexity etc. Just setting up your companies LAN is NOT computer science.
My experience is that most people who say they are good at anything actually suck. Particularly when it comes to computers.
Or, as Alexander Viro put it, Now, _I_ won't use the stuff I don't have a source for unless I have exceptionally good reason to believe that authors of that stuff are among the few percents of programmers who *can* find their arse without outside help. But that has nothing to do with licensing or any moral considerations and everything to the fact that I know what kind of crap most of the software is.
Indeed. And network administrators are no better in my experience than anyone else. A network administrator without the math skills necessary to understand in his gut why chatty protocols on a flat network will lead to packet-storms particularly doesn't inspire confidence.
You have never read Dewey.
Dewey's first insight was to argue that learning by rote was a bad -- poor -- inadequate -- way to learn.
Your description of Dewey's thinking is exactly the opposite of what he said and wrote.
My highschool (private) had quite the Math Program. I never had problems in Algebra, Algebra II, or Pre-Calc. (Nor Geometry and Trig). However, when I hit Calc in college, it seemed as though my math ability hit a brick wall. Up until that point, I never had a single problem with math, concepts, etc. Everything came really naturally (including mind math, I can't give you horribly complex, but I seem to do better then all of my peers). Calc ate my cookie and made me go from a CS major to a Spanish Major. I am taking Math 111 because its the only required math class for a LAS degree. I took the placement exam in 10 minutes and got more then enough right to qualify(I would have gotten more, but I forgot a few things in the 2 years since a math class).
So, in a semester I will be able to tell you how well one University does...
PS - My university has an issue. Namely foreginers teach Math. I have nothing against anyone's nationality. However, if there is one accent that I can not understand, it is the Apu'ish middle-eastern accent that populates the halls of the Math building. For weeks I thought they had a meth lab in the building, then I realized no - it was a math lab. Again, nothing against foreginers -- but I want a profesor who I can understand. If english was my second language, I could take special ESL classes where they slow it down for me. However, I have just as hard of a time understanding a prof with a BAD pakistani accent as a mexican does with a british accent. (I speak English and Spanish, start Italian this semester I hope, and will eventually learn French as well, so I fear not language, just accents that are HORRIBLE.)
The ultimate network admin tool needs HELP!
I just took a placement exam which consisted of 25 multiple choice algebra problems. There was a 30 minute time limit on the exam. It takes a little longer than a minute or so per question for me to shake the cobwebs off of what I learned over ten years ago, but it is still there. The point is that all of us taking the test were pretty much in the same boat, and the time limit didn't do anything to "test" our knowledge of the subject, other than to point out how little we use it. Given all of the time needed to complete the exam, I'd estimate 45-60 minutes, I would've probably aced it. With the time limit, I will most likely be told that I should take a remedial math course. Hey, that's another three semester hours in the coffers of the university. Anybody see a conflict of interest here?
What is it, exactly, that they are calling algebra?
1 + 2 = x, solve for x?
3x + 2 = 14, solve for x?
ax+by=m, cx+dy=n, solve xy in terms of abcdmn?
x^n+y^n=z^n, n>2, xyz integers, solve for xyzn?
Which of the following could be a zipcode?
The choices listed included a 123-45-6789 ss#, a 456-7890 phone number, a (321) area code, an actual five-digit zip code, and - I don't know - a six-character license plate combination.
At this point, the Honors students were actually snorting from laughing so hard... but yes, students failed this exam. Some more than three times, so that they couldn't graduate.
Testing might not be the solution after all. Alas, common sense can't be taught.
I presume you were trolling for a couple of "Funny" mod points?
In other news:
THE SKY IS BLUE.
Why is this even news? High school algebra teachers have always been nitwits. At least mine were.
'nuf said.
I briefly attended the University Of Bahrain and from firsthand experience I can say the average student was at least three years beyond the average American HS student upon entering college. I'm not sure how representative these students were of the general populace since the students very well may have been the cream of the crop students among Gulf countries.
"God fights on the side with the best artillery." - Napoleon, Marshal of France - speaking truth to power
Since I'd rather not reopen old wounds by talking with my personal former math teachers, I'd like to ask you as a math teacher a question. Why is the "Fundamental Theorem of Algebra"(emphasis mine(duh)) reserved for Algebra 2?
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I could not help seeing quite a few postings about how "boring" algebra is. Algebra is boring in proportion to how boring the person is who is teaching it. It IS important, and it IS required for all sorts of mathematical subjects later on.
For anyone who has object orientation sussed out, think about containers... what are they? They are (abstract) algebraic structures with certain operations that can be performed on them. You can only get a deeper understanding once you know algebra!
This might seem like a trivial example, but there are many similar examples where a sound mathematical basis helps considerably in software design (because you can approach the problems differently)
Oh and of course I have not even started on the importance of math in engineering (but I am not an engineer, so I'll leave it at that).
Moral of the story - the moment that the standard of mathematics drops, the entire IT industry will feel the blow of ineptitude.
"I hate people who fabricate unintelligent quotes to add to their work seemingly by some 'anon' sage" -- anon
I hated algebra, not because it was boring in itself, but because I had homework every damn night. Regardless of how well I understood the subject, it was required to do a crap load of redundant problems and you MUST show your work. Screw that, I'm not stupid, I don't need to work out 50 problems before I understand what's going on. Just give me the test and let's move on.
Everyone is entitled to their own opinion. It's just that yours is stupid.
"It doesn't add up," Loveless said. A D.C. schools spokesman did not respond to a request for comment.
They sent me to a classroom where 7th and 8th grade students were (theoretically) preparing to take the SSAT (Secondary School Aptitude Test) to try to get into some of the East Coast boarding schools. Apparently, those schools have some programs to try to increase minority enrollment, but candidates have to take the SSAT and have results above some threshold.
They told me I would be helping the students review the math that would appear on the test, including algebra. But within the first two days, I discovered that even the best students among them had a very weak grasp of algebra. Most had no idea what was going on. So I started from the most basic-- what the "equals" sign means. I wrote "3=3" and asked them if that was right. They understood and responded correctly. I wrote "3=5" and asked them if that was right. They understood that it was not and responded correctly again. I then showed them that if you do something to one side of the equals sign, but not the other, you go from a true statement to a false one. For example, take "3=3," which is true, and add 2 to one side. Then you get "3=5," which is nonsense. But... if you do the same thing to both sides, you end up with another true statement... For example, take "3=3" and add two to both sides... then you get "5=5," which is perfectly valid and correct.
I then introduced the concept of variables and using them to represent unknowns. When I felt that they were pretty comfortable with variables, I started writing equations with variables. Since they already knew the rules for messing around with equations, I showed them how to mess around in a way that would isolate the unknown variable on one side of the equation.
These kids were like sponges. Every day when I left the school, I left knowing for sure that they had learned something they didn't know before. It was extremely rewarding. And by the end, almost every one of them (there was one I couldn't really reach, no matter how hard I tried... but even she did start to get the basic concepts) could solve any linear equation, even if it was "disguised" by having the unknown in the denominator of a fraction. They also learned how to convert crazy word problems I invented into equations to solve.
These students were clearly ready for Algebra. Only one of about 25 students ended up not knowing what I considered "enough" by the time I finished, which really wasn't that much time. I spent two periods of about an hour and a half or two hours each per week with them during a few months. But whoever had "taught" them Algebra before didn't teach them a damn thing. One thing that I think made a big difference was that I praised to high heaven a student who refused to just say "got it" and move on when she didn't understand what I had done. She insisted that she didn't get it. So I put a problem on the chalkboard and started going through it one step at a time, showing her why I was doing each thing. I was in the middle of doing this when I saw her face light up. I stopped and said that I could see that she had understood. I erased the problem I was solving and put up a new equation. I passed her the chalk and stepped away. She quickly and easily solved the equation for the unknown. I then made a big deal about how great it was that she didn't just say she understood it and move on without really understanding. After that, all of them were more willing to say when they didn't understand and not just say "got it" and move on. I think the people who "taught" these kids algebra had just presented the material and asked if everyone understood without really "digging" to confirm that everyone had understood. I know that when I arrived, students were in the habit of saying they understood things, even when they didn't. Just curing them of that ill left me feeling satisfied with the work I had done.
I hope some of these students continued to study math and science and have the same kind of success they had when I was teaching them. If my algebra "review" served as a "gateway" for one or more of them to take more math and science, that would be great.
"It is nice to know that the computer understands the problem. But I would like to understand it too." --Eugene Wigner
He was the epidemy of a geek - short, skinny, coke bottle glasses, greasy black hair. He was a "brother" (not a priest, but someone pretty much living by the same rules) and wore the long black robe. He was brilliant and spoke at a hundred miles an hour.
We learned algebra out of pure fear, because you see, he would physically punish those who made it clear that they weren't paying attention or didn't do their homework. He'd box people's ears in, pull hair, grab you by the back of your neck, knock your desk over with you in it. I'd even seen him punch a kid in the chest and heard the infamous story of how he'd thrown a kid out the first floor window into the snow. I'd tell my mother that Brother McCaully dragged me to the blackboard by my earlobe and she'd say "good, you must have deserved it". There was little anyone could do about it (and this was not the 50's, it was the late 80's).
But we didn't need fear to learn of course. At least I didn't. The big complaint I've heard from people about algebra (and all it's silly trains going in different directions type problems) was "when will I use this in real life?" Well, all anyone could have told me at the time was that algebra is the quintessential skill to mastering computer programming and software development. Without a strong base in algebra, you really cannot be successful as a programmer.
I've since gone back to my old high school for Career Day. I gave a talk to about 50 of the 400 graduating seniors who wanted to go into software development. I explained the importance of algebra as well as the other applicable fields of math, but made it especially clear that if they didn't like algebra, they might want to choose another related field in computers aside from programming. Of course when I asked for a show of hands, 95% of them wanted to be games developers (which too is what had darwn me into programming back when I was 10 years old), but explaining the reality of the chances of success in that sector of the market was difficult. They'll learn on their own just like everyone else ...
BTW - It seems that good old Brother McCaully, the violent nerd, had since been forced to "retire from teaching in order to write textbooks" after one too many a violent incident.
Yes, I'm OT. So sue me.
:(
The most amazing math revelation I ever had was how math was invented to describe and talk about phenomena that we had no way to discuss before. I didn't get that until I studied the invention of what we now call "Calculus" by Newton and Leibniz.
Our math, the math we know, isn't fundamental. The logical concepts and universal laws it attempts to describe are fundamental. It is quite possible to describe the same phenomenon with two different maths.
I feel sorry for those who will never get enough math to see that. But then again, there are plenty of truths _I_ will never see.
"We reject as false the choice between our safety and our ideals." --The American President (20.1.2009)
For the same reason your parents lifted you by the arms and dragged you while your legs found out the wonders of walking. Teaching you by moving each foot in front of the other would leave you learning to walk but completely incapable to maintain your balance, because those skills are usually learned at the same time. And for good reason. I might think about which direction I choose to walk, I depend on a simple routine to move my body in that direction, but I must react in a split second when I slip on a wet floor or trip over a step in a stairwell.
Now I also noticed that when children learn to speak articulately in detail about something before they have a more intuitive understanding of the topic they are incapable of insight, epiphanies, imagination, nor the ability to see themselves in the mirror, to step out of a problem and see the mountain of spilt milk for the molehill it really is.
My 8 year old knows so much detail about things that annoy him that he forgets how much time wastes on them and cannot conceive of being in error when he has such a mass of details for his supporting evidence.
That is I'm supposing that to learn to move your feet forward in absence of the need to keep your balance will put you at a disadvantage. And I would bet with mathematics as well.
The message on the other side of this sig is false.
In a way, I agree that teenagers need time to socialize, but I disagree that school is the time or place for it. Public schooling is 7 hours of being talked at, with 3 minutes passing period. Theres no time to talk and interact with your friends like you want to, and there should be. A serious look at how teaching is needed. Lecturing is not equal to learning. I think we could get away with less school hours, and give more time to children for their own social interactions, like playing street football with the kid down the street that doesn't go to school with you for some reason.
I used to think that homeschooling was only for religious wierdos, and by and large, it still is. But now I think of it more as an act of rebellion against the instutional education system. Public schools really dislike this stuff happening right under their noses. Gatto has more to say on the failings and realities of public education; if you liked the article google for more on gatto. Whether you dislike homeschooling or not is not the question; the number of dissaffected students graduating with no hope of self-actualization demands the question, "What are we going to do to fix it?" Or perhaps, this was a semi elaborate trolling.
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Maths have always bored me, before I got to know what mathematics actually entailed. Thing is, the maths I got tought in secondary school was boring. All we did was functions, integration, differenetiation and the like, without ever being told wtf it was good for. The actual application of it was only being tought in the two final years of physics. By which time about 3/4 of the class had already dropped maths. And even then maths was boring. Now however I know a lot more. And if I knew then what I know now, I would have been a lot more interested in mathematics. Maths actually has a romance attached to it, as well as being somewhat philosophical at times. If only I had know about non-euclidian maths, Fermat's theorems, quaternions, different models of space etc, etc etc. What it boils down to is that the teachers never had the time to go into the more interesting aspects of math; they where only allowed the most basic, boring bits for the curriculum. And that is the reason why most people hate maths; they don't know how much more there is to it. And so they drop the subject asap, before they get to the good stuff. Truth be told, I regret having been so bored with mathematics (I got a 5/10 on my final report card, and am nearly a mechanical engineer now; reason being that physics WAS fun). If I knew then what I know now, I might of even have studied mathematics...I didn't know there was all this controversy, all this exiting stuff. Because of the curiculum, I was never told about it. And I still wouldn't if it wasn't for sites like /., Kuro5hin et all.
I believe that if we were taught more about the people, the history, behind mathematics, more about the 'fuzzyness', the challenges, contradictions and wierd things to be found, as well as being told the actual applications, more people would be interested.
And who cares that at that young age you might not fully understand what you're told. Just give it as background info, leave it off the test. But at least let the kids know that there is so much more behind it, instead of saying "integrate, differentiate, this will be on the test...just do it how I tell you".
-- Waht? Tehr's a preveiw buottn?
It seems like the fear of algebra that the article thinks many people have has a simple cure. Just keep on doing algebra bit by bit, grade by grade, like they do in other countries.
In Poland, I remember we did the distributive law in grade 2: we were told to use it to do calculations like 47*4=(50-3)*4=50*4-3*4=200-12=188. They didn't teach us long multiplication until grade 3. I also have vivid memories of being taught how to write an "x" (a letter that doesn't occur in Polish) in grade 2 or 3 maths, so I think we must have done simple symbolic manipulation.
One could easily introduce solutions to linear equations like 4x=8 or 5-x=3 in grade 3 or 4, and then more general linear equations in grade 5. If one did these things step by step, building from year to year, instead of the endless arithmetic that is done in the U.S., there would be no need for algebra as a special subject, set apart in a fearsome manner from the maths done all along.
ARP
At one time, being a scientist meant either being arab, or at least reading arabic. The single handedly rescued it, when christianity waas trying to burn it to the ground.
There was a period of 100 years or so, when the most complete astronomical charts, the best observatory, and the most knowledgable astronomers were all in... Afghanistan.
I may be a troll, but I'm not stupid.
I took algebra in 7th grade, and I consider my experience to be pretty good, in the sense that we actually learned a lot of algebra.
What I remember about algebra was tons and tons of homework. We had at least an hours worth of algebra homewrok every single weeknight every single week. And it was graded. I can't quire recall, but I think we'd pass our homework one seat over, and the teacher would write down the answers on the board and we'd grade our neighbors papers. Then we'd hand the graded papers in. There was probably some cheating, but the teacher knew who graded the papers, so it worked pretty well, actually.
It was miserable, having that much damn homework, and I hated it, but we really learned algebra. And I'm pretty certain that algebra is one of those subjects that requires lots of practice.
than some underpaid, overworked teacher afraid to discipline her class for fear of losing her job or his life.
Underpaid teachers? Teachers fearing losing their job? You obviously don't live in New Jersey.
The teachers' union literally runs the state government in NJ. In NJ teachers are grossly overpaid, nmany retire with 7+ figure pensions.
A teacher has to just about kill somebody before they get fired. A few years ago there was a teacher who was convicted of some crime (don't remember what), and the school board had to pay them several hundered thoudand dollars to get them to quit (with full pension).
I actually taught algebra to high school freshmen in rural North Carolina, and I can say, with confidence that the problem secondary schools are having teaching students algebra is, largely, that students are coming to high school completely unprepared to learn the subject. I spent the vast majority of my time in the classroom teaching my students such esoteric branches of mathematics as LONG DIVISION, and FRACTIONS.
Sorry folks, but the fact of the matter is most of your peers are NOT getting math, even basic math, the way you are, and nobody is taking notice of the fact until it's far too late.
My kids worked hard--I made them work hard--and all but a very few passed. The other math teachers in my school failed NO ONE. If you want the real culprit here, look to the self-esteem Nazis running our schools and the egregious damage being done to their chances of a meaninful education by social promotion.
-- The Sage does nothing, and nothing is left undone. --Lao Tzu
You're definitely right in saying most people don`t see what algebra is good for. But by the same token there is such a fear of math out there that when people encounter a problem algebra could solve they tend to avoid it. They do this by either not concerning themselves with the answer or relying on guesstimates.
* If I'm coming home from work down a road that I usually travel at 60 MPH but traffic is going at 20 MPH, when should I say I'll make it home?
* I have only so much money to spend for gifts this christmas. I went to spend amount twice as much on the kids than on the adults.
Everyday we encounter life's little word problems and things are so much easier if we are willing to use the tools to tackle them.
Unless you are around alot of intelligent peers who are social in a GOOD way.
Even then, public schools do not teach social interaction, unless you expect a child to only interact with people who are the exact same age for their entire life.
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?
427 hours work of work to be done in 3 weeks, how many compentent programmers do you need
This question was asked on Slashdot's servers in the United States, and United States law states that a full-time week equals 40 hours. Thus, one pair of programmers can do 120 hours of work in the alloted time. Let n = the number of pairs of programmers. Then 427h = 120h * n, or 3.56 = n. Round up to four pairs of programmers, and you can give them nearly an hour of free time to unwind at the end of the day (Quack 3: The Duck Mod).
Will I retire or break 10K?
This is very similar to what happened in our school back in 1985 or so - our senior-year "math" teacher wanted to offer a Calculus class - a full-blown freshman-year calculus class, but the rest of the school district wanted to each some sort of watered-down "pre-calculus" or some such thing. In the end, he got the go-ahead and taught us, using the same textbook and class outline that the local Purdue branch used in the their first-semester calc class.
Once we all excelled at the class, he was fortunately able to prove to the schools that it was the right thing to do. I will always thank him for that - not to mention the 10 credit hours that I was able to test out of before starting college - saving me time and money down the road.
People have to realize that if you push kids to excel at something, they will rise to the occasion to do it. You don't have to dumb everything down.
This story reminds me of one of my frequent getting-to-know-you conversations:
Stranger: What do you do?
Me: I'm a mathematics professor.
Stranger: Oh, math. I was pretty good at math in school, until they started throwing letters in there. I kept asking, "What is X anyway?" and they wouldn't tell me.
I think that one reason students are suffering in algebra is the "rush to calculus" phenomenon. High schools (or maybe parents, or maybe the students themselves) are trying to force students to take a year or more of calculus in high school when most of them aren't ready. The result is that nothing is learned well, not the algebra which needs shoring up, and not the calculus which is now a house built on sand.
I teach calculus to college students, and the two biggest problems I face are (a) students who think they already know the subject and try to coast until it's way too late and (2) poor algebra skills. I think that although algebra is not "needed" for calculus (as you can learn and prove every theorem without it), it becomes such an obstacle for doing homework that I wonder if that's the reason calculus is considered hard.
Students complain that algebra mistakes should be overlooked when they have some understanding of the concepts, and that's partially true. But if you build a bridge and it fails, the people on the bridge die whether your mistake was in calculus or algebra.
If the majority of college-bound students spent high school learning algebra, geometry, trigonometry, and analytic geometry (the last two are now called "precalculus"--but why?) well, then they would enter college ready to excel in calculus. Not only would they have a solid grasp of mathematical expressions (and better geometric thinking skills), the first strokes on the calculus canvas would be painted by a college teacher who has a better handle on it than an average high school teacher does. Instead, they are fundamentally unsound and overconfident because their high school transcript has the word "calculus" on it. A little of everything is a lot of nothing.
im from new jersey and agree, they spend around 10k per kid in new jersey. Thats probably around 200k per classroom and plenty of money. I'm not sure though how they rank nationally though. I went to public school. Property tax values up there are very high though to pay for the school system.
People complain about teachers salary's but keep in mind they only work 9 months out of the year(look at your own salary and take 75% of it and compare it to a teachers salary, a teacher making 30k would make 40k etc), you can easily supplement that income during the summer with tutoring, summer school etc.
Bring back the old version of slashdot.
Let me quote from this page
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.
Hopelessly pedantic since 1963.
Sorry, but the arguement that rote learning is evil and useless is bullshit. Rote learning isn't good for EVERYTHING, but in some subjects, it's neccessary, especially for young minds. It's got it's place. In most of the countries where schoolchildren regularly beat the piss out of US children in math and science scores, rote learning is the preffered method of teaching, at least in most of the math classes. All learning is NOT going to be fun and fascinating. There are neccessary things to learn in ANY education that are going to be just plain boring and tedious. We've gotten this idea that all classroom instruction should be creative and "personaly fullfilling", when a lot of the bedrock knowledge neccessary for things like theoretical physics must come from hard, repetitive memorization. I had both kinds of instruction, and it seems the class always did better when we had to memorize the principles first, then "drill till it kills". Once that solid foundation is laid, THEN you can better understand the theoretical.
Life is hard, and the world is cruel
This is exactly the sort of thinking that John Dewey advocated. He was a socialist, like most of the elite were in his days. This guiding principle of education is about as democratic as any socialist regime.
This is merely a different kind of learning by rote, that is differentiated through equivocation, not by true fact. What Dewey advocates is learning not JUST the facts, by their relative value to others. It is classic relativism, the essence of 20th century humanist thought.
This is the same system of thinking that gave birth to the insane multiculturalism and ebonics of the late 20th century.
I do not believe Dewey was a complete fool in his writings, nor are they as blatant as I describe. The real problem is that Dewey's ideas were taught in the halls of academia for the next fifty tears, and were contorted into perhaps the extremes of what Dewey wanted. Whatever the case, the system we have today is the essence of the very quote you have given. Children are taught that no piece of fact has any intrisic value. This IS nihilism, the nothingness of value. This is what makes a human go from the "renaissance man" to the beast, of which I speak. When we teach children that nothing has intrinsic value, we remove a valuable skill that is not easily learned again. That is what creates the Cattle Culture.
I don't have the time at the moment to get you actual quotes, but I suggest you read all of Democracy and Education as we as How We Think in particular to gain insight into what I am saying.
One can take a short quote of any work, and gain the opposite impression. Its not like any published philosophy actually preaches to turn man into a mindless slave. If it were, we would not be having this debate.
I don't read or respond to AC posts
Algebra never seemed interesting to me the way it was taught in public schools. I took it in two different states (Vermont and California) and the method used to teach it never worked for me. Our public schools seem to teach math in a "follow this trick and get the correct answer" type of way. I was always left wondering *why* it all worked. I never did well in mathematics untill I took Calculus in highschool. Math then started to seem interesting and my algebra skills improved. I did not realise of how much I had been robbed by having math taught in the way it is untill I took math in college. Proofs! Everything laid out consistently, logically, and everything argues for and proven rigorously. I loved it. If I were to change majors from history, it would be to mathematics. I'm sure my skills in mathematics would be much improved had I always been taught math as a set of proven theorems from limited axioms instead of as tricks to get the same result as the back of the book. It seems to me the way math is taught has some advantages and disadvantages.
Advantages:
1) Some people *hate* proofs. They don't care why it works, just that it does. These people might have more trouble learning a very usefull skill set (algebraic manipulation) if math were taught differently.
2) Some people aren't smart. This is different than (1), in that 1 indicates a different style of learning rather than potential for thought. These people need to learn basic math to do jobs in the real world. Teaching math in a more complicate manner may compromise their education.
3) Teaching math rigorously is time consuming and requires well trained teachers.
Disadvantages:
1) Some people are turned off by the way math is taught.
2) Some people have trouble dealing with the change in approach in higher level mathematics twoards proofs.
I'm not an education proffesional, and I don't know how resources are best spent teaching math. In my particular case, I'd say most of the resources thrown my way in math were wasted.
The preceding passage has been checked for spelling, you will find no sentence without at least one mis spelled word
Every now and then I read broad sweeping claims about how we could fix our secondary education. Let us look at some of the reasons why it is so hard to educate our children properly.
I have a Ph.d. in mathematics. I work as a software developer and I have not even used simple algebra in over 5 years. That does not mean that my job is boring or lacks the need for reasoning skills, but it does imply that a lot of my education has less relevancy than many people would like to believe.
This is a general problem. It is very hard to pursuade students that their education has relevancy and to some extent the students are right. Our education establishment is focused on properly preparing students to be ready for the late 19th century. Many teachers in secondary education are teachers because they were not clever enough to get an education that made them relevant to the work needs of our current generation. It is very hard for such teachers to pursuade students that their education matters.
Many of the teachers who teach math never had the "ah ha" experience that is vital to true understanding. Such teachers are unlikely to generate any real understanding in their students. Since I taught myself mostly from books, I always thought this business of having teachers and classrooms as being overrated. The books did a much better job in explaining the material than the teacher.
Although I hate the type of teaching that standardized testing inspires, I also hate teaching that has no accountability. Given the choice between two evils, I tend to choose the standardized tests. Over the years there have been many attempts to bring "creativity" or "understanding" back into our classrooms. Except for a few model classrooms with very motivated and bright teachers, these "innovations" have usually been an excuse for teachers to create an even more muddled and useless experience for their students.
In particular the "new math", that was being taught when I was in middle school, is especially brain dead. Students would end up stripped of any mastery of the basics of math and were not sufficiently compensated with any "deeper" or "creative" insights into mathematics. When I got to college, I saw some of the point of teaching students about "sets", but only a really inspired and talented teacher could have communicated the deeper ideas in "new math" to a standard classroom of kids.
I see no easy fix to our secondary education problems. But with no way to hold our teachers accountable for the educations they provide, there is no way to know if a particular idea is actually helping or hurting.
Now that I'm in college, we spent a couple days reviewing algebra that we were supposed to learn in high school. We only learned basic algebra like 10x + 5 = 2 (ok, well a little more complicated than that, but you get the idea), and then we went straight to gerometry and trig.
Algebra was treated like a subject that would never be usefull and was taught for the test, not permanent skill.
I feel that this has more to do with the trouble in the educational system, because in countries like India, China and Korea, school children are taught much much tougher concepts at a young age, and they comprehend it.
For Americans, education is being made cumbersome because you can very well live without it. But in a developing country, it becomes a necessity. Also, lack of "comforts" propel you to spend more time to go through what's been taught today in class rather than go off to play that "cool game".
Hell, these kids are taught calculus in the 8th/9th grade, and co-ordinate geometry in the 7th grade. Most of them are bilingual (English + their mothertongue) and extremely smart. I'm sure that most American kids might do this too, if they were guided properly.
Sometimes it takes seeing things more than once, or from more than one teacher, before it makes sense.
Agreed. The first year I took algebra, I had a teacher who was really stubborn about requiring all work to be done in pencil. I, of course, was really stubborn about doing all work in pen (I still hate pencils.) She failed me, forcing me to take algebra in summer school. I cursed her at the time, but it was the best thing that could have happened to further my understanding of basic algebra. My summer school teacher (great teacher, btw) actually asked me why I was there since I seemed to know it all already, but it was that second viewing that allowed all the pieces to fall together.
~~Galen~~
Sure, why not?
Specious argument. The education level was quite high in recent times before the introduction of the current educational system. Standard of living is irrelevant unless you can demonstrate that our current standard of living would not have been better under another educational system.
Depends on what you mean by modern schooling. If you mean the usual public/private school system, this is wrong, as demonstrated by many homeschoolers. If you just mean "a broad education in many subjects", then your statement is nothing more than a tautology: "You can't learn more than a small amount of knowledge, without learning more than a small amount of knowledge".
Also, arguably, the current curriculum is rather harmful in terms of "what you need to know". The current system of education in the U.S. (largely Prussian in origin) was good at churning out factory drones for the Industrial Revolution, but in light of today's automation, that's no longer what our society really needs. It's more efficient to direct your studies into the subjects that you intend to pursue, rather than a homogenized scattershot. Most people forget the vast majority of what is taught in schools, simply because they are not interested in it, and don't use it. It's more effective to pick up the bits and pieces that you do need to know as you go along, rather than memorizing random subjects in the hope that some of them will someday be useful.
Higher. For instance, in Massachusetts, the literacy rate was at 98% immediately prior to the introduction of mandatory education (circa 1850). Since then, the literacy rate in that state has never exceeded 91%.
Most people learned just the math they needed, because they needed it, and no more (unless they had a particular fascination with the subject). There is nothing wrong with that.
Unless you're trolling, can you elaborate?
In my experience, it's difficult to ask question. In my classes, people got annoyed when I wanted to go more in-depth on a topic because they were just there to take in what they needed to get a good grade. I've never cared for that type of education and I still don't, but it's the fantasy of an open, welcoming classroom hasn't existed for me since kindergarten, and while it should be better in college, at least in the UCLA Physics department, it's hard enough to find a teacher that speaks clear English, much less a Feynman (what I would've given to study under him...)
I have to disagree: I found mechanics to be quite exciting (and no, I'm not a physics major either ;-). I was frankly fascinated by the idea that a few simple principles would allow you to compute the position of any object from an accelerating car to a planet orbiting the sun (absent friction, relativistic effects, and other real-world complications, of course). That was cool.
Biology is an easy course to teach, because it deals with every day occurences.
Uh, what did your high-school biology courses teach? I recall mine spending large amounts of time on evolution, genetics, mechanisms of cell division, the ATP cycle, and so on. Those are only "everyday" things insofar as they provide the foundation for the macroscopic lifeforms that we observe -- but the same could be said for physics.
It sounds like you are equating biology with about something more like "life sciences", which I agree is an important foundational course, perhaps at the middle-school level. And I think it's absurd to assert that physics can't answer the same kind of macro-level questions: mechanics, electricity, magnetism, and optics are all things that we exploit on an everyday basis.
The worst mistake we ever make in school is the old "this isn't english class, so you can't deduct marks for spelling mistakes".
I agree and was lucky to have teachers who took exactly the opposite approach. My physics teacher would absolutely mark you off if you had misspellings or grammatical errors in your lab reports.
"Biped! Good cranial development. Evidently considerable human ancestry."
Do you mean Discrete Structures?
It's listed as a CSC course, not a math course.
Twenties Retirement
Are you insane? The apprentice system died with the industrial revolution because most skilled craftsmen became obsolete. The first European Universities were born around the time of Columbus and worked much the same way schools work today (except for the beatings and forced labor) Dewey is not to blame. Public education for most people has been a blessing not a curse. The American system helps more kids succeed then it leaves behind and is argueably the most successful in the world. No country in the world produces as many college graduates. In Europe the system is more selective and most people never even have a chance to go to college. In Russia you have to pay bribes just to get into a college! I just graduated from highschool I took 6 AP classes including Calculus BC. Im going to NYU this September, and have already been awarded 19 credits! Not bad since I havent even started classes. The system is only as good as the kids. My mother taught me well, paid for tutors and books and is now rewarded because Im going to College for virtually no money! I only pay $2400 in tuition each year or 1200$ a term. Work hard and you will be rewarded 9 times out of 10. Slack off smoke pot cut class (like some of my friends) and you will find only 1 carreer open to you cleaning shit up in Mc Donalds. Everyone in this country can succeed it just takes effort. My father is a machinist my mother cuts hair for a living. My older brother goes to Columbia (his tuition is a lot higher). Slam the system all you want but it works for us.
I just moved to Florida, and couldn't get into the college I wanted to, because even though I had a 3.5 GPA and had successfully transferred to 3 other large colleges (I move along to help with my parent's pet store busines), the incoming freshman class pushed the requirement for a transfer student just above that!
There's something wrong with a system that has the average above a 3.0. I got many of the folks at admissions on my side after months of phone calls, but by that point, it was just too late to get in. I've met and talked with a lot of these new students too, and they aren't notably more or less knowledgeable or talented compared to the hundreds of similar students I've met over the years.
It's rather annoying being at the upper 10% of most of your classes at other colleges, coming to a new state, and then being told to go to a local community college instead, so you can take advantage of special rules to be admitted in aother year.
So now I'll be graduating from another college further away. Fortunately, I'm a computer science student with quite a bit of real on-job programming experience (DSP, assembly, MFC, DirectX, etc.), so the college name won't matter that much on a resume as long as the information and skills are there - but this whole adventure took FAR too much of my time and money.
Ryan Fenton
Not 100% accurate but you drove the point home. AMEN!
There is no longer anything that can be done with computers that is nontrivial and clearly legal. -- Paul Phillips
The system doesnt stop you from thinking. You can ask your teacher whatever questions you like, but chances are the answer is already in your book. What new question can you possibly ask that someone hasnt already asked. Chances are that if its a real question the answer is in the book. Teachers teach by example, by solving practice problems on the black board not by making you solve problems you dont understand. When was the last time you people went to class.
The system doesnt stop you from thinking. You can ask your teacher whatever questions you like, but chances are the answer is already in your book. What new question can you possibly ask that someone hasnt already asked? Chances are that if its a real question the answer is in the book. Teachers teach by example, by solving practice problems on the black board not by making you solve problems you dont understand. When was the last time you went to class? Sometimes learning cant be fun, sometimes you have to do the boring questions to understand the topic and to memorize the concepts. Learning is work. Its not all fun.
Did students ask questions too? Sure. And *gasp* -- they can now too.
Not really. So many teachers are incompetent that students' questions would be offensive to them.
I once had a teacher so terribly incompetent, that she made things up to answer my questions rather than admit ignorance. Another teacher just kept avoiding admiting ignorance by asking questions back. Yet another teacher was so convinced of rote learning that homework assignments were dozens of variations of the same problem. It wasn't until college that the average quality of teachers was acceptible.
I find it excrutiatingly sad that teachers, somehow, have been delegated to the bottom of the economic food chain in the U.S. They are not paid well, yet they hold the second-most important responsibility outside of basic parental care: education.
The quality of public schools and many private schools makes me think hard about home schooling. I haven't decided, because I really don't understand all the tradeoffs, yet. The ability to better control the quality of teaching, however, is an enticing aspect of home schooling.
Do you know what literacy rates were prior to mandatory education? How many of the illiterate learned basic math, much less algebra?
This is all fine, but the real problem is that the current education system has already peaked, reached stagnation, and is falling behind in most aspects of maintainence. It is pretty clear that things can be better. Unfortunately, I don't see big improvements on the horizon.
The issue is not how much better we are now than before; it is that progress has stalled.
Healthcare article at Kuro5hin
I wasn't raised in an American School System, where on TV you guys are portrayed as having lines of desks from front to back of class and all students being preached at by their teachers.
Where I studied, in the UK, our desks were hexagonal and students sat together in groups, we were encouraged to talk to each other about the work, to learn from each other and to question each other. It seems to me that in the states, the format tends to be "Teacher lectures --> Teacher poses question --> Teacher nominates student --> Student answers"
In the UK, the teacher will involve the class in the lesson, will ask questions and invite the class to quiz him on why things work, regularly, we would pose questions to our teachers and have them kept on their toes answering us.
Then they would set a series of questions to be answered by the end of the class and the class was encouraged to work on the questions individually, but to discuss them with others on the table if they got stuck, the process of the discussion actually helped us to learn better (or it did me anyway) having things explained in different ways always seems to help the clarity.
Also in the British school system, the subjects were taught in parellel, we started using algebra when we started doing experiments in science class that involved using equations, not only that but once we had learned algebra, we were basically not taught a lessons afterwards which did not involve some aspect of it.
The way our maths is assessed is probably different too, I dont know what happens over there, but over here we are given a worded problem and the student is encouraged to find a mathematical way of solving or optimising the problem, usually we are expected to come up with an equation or method which will solve the problem for any input. We are then graded not by whether or not we solved the problem, but by the method we went about trying to solve it, which avenues we explored, what algebraic method we tried, etc. In this case we are expected to write down the avenues which we explored and any conclusions we made during our experimentation.
When I began studying my A-Levels, I had an american join my class, he had moved back from Chicago to start with us at the beginning of our first semester. I remember him knowing practically no algebra at all when he started, on the other hand, his mental arithmitic was perfect and he could do alot of things alot quicker than we could. However, when he was forced to think of anything in terms of X and Y, he stumbled and fell flat on his face, in the end he dropped out of the class because the maths involved was too complex and not having the grounding that we had in algebra, he found it too difficult.
When he was in the states, he was actually advanced 2 classes for maths, he came to the UK, and he was probably the equivelant of 2 years behind in some areas. A testiment to the different ways in which people are taught across the world.
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.
I just graduated from HS and had absolutely no problem with math/science. I probably have a bit more foresite than most the students in my graduating class, realizing that I'll actually use math as a CS major, but that had nothing to do with good/bad teachers.
/.ers, but currently this is the situation. Most likely it's in more than just my area. All of you who say it's just being taught incorrectly, which may be true in some cases, also have to realize the effort is two fold. If you have an excellent teacher, but poor students it won't work, or vice versa with poor teachers and great students. Hell, I'd wished more than anything now I could have taken Calculus in HS rather than in college just because of all the extra help I could have gotten when I had difficulties.
I live in Colorado, and from what I've been told, and what I've read, we have one of the better educational systems right now. At least, as far as stardardized test scores go (if that means anything). All my teachers were excellent, they really did try to get one immersed in the subject which they were teaching. Even when I was in 7th+8th grade, my teachers were involved with how the students learned. It's the students themselves that need to improve things. No matter how good the teacher is, if the student doesn't want to learn it, they won't. I watched it happen numerous times throughout my education thus far. I mean, they'd offer after school help, during lunch help, one-on-one time for the kids, anything to help them succeed here. The losers just wouldn't hear of it. Unfortunately they wanted to go smoke pot or do something else "constructive". (Unfortunately Colorado is the #1 state in America for teenage marijuana use.)
I'm not sure the age of the majority of
Try actually thinking for yourself. It's quite refreshing.
"It's like asking why Beethoven's Ninth Symphony is beautiful. If you don't see why, someone can't tell you. I know numbers are beautiful. If they aren't beautiful, nothing is."
Paul Erdos, Hungarian mathematician
I started learning fractions in grade 4 and by grade 6 I could add, subtract, multiply and divide fractions easily. In grade 7 started learning basic equation solving and pythagorean theorem. By grade 9 I could factor simple binomials and do simple trig (find the length of the other side of a right angled triangle when you know an angle and a side length). I took 5 math courses in high school two of them calculus courses. I wrote the American College Board Advanced Placement Calculus BC exam and scored a 5. I'm entering the faculty of engineering at the University of Alberta and my first two calculus courses will be pretty much review. Im gonna laugh when some prof starts talking about Polar equations and Taylor polynomials and no one has a clue to what he is talking about. Here in Alberta once you hit high school we have two math streams one for those interested in going to university which teach algebra and trigonometry. The other is for those not going to post secondary or entering lower level trade or technical schools. I've heard that in Germany they take it a step further and aroud grade 9 those we are going to university take courses to prepare them for university and everyone else begins to learn a useful trade like woodworking or welding.
I'm working on my MBA, and algebra is most definitely a big part of doing business math. In fact, the people in the program who don't have strong math skills are really struggling.
Funny, when I was in high school, I thought algebra was a waste of my time (silly me). I couldn't imagine at the time how I would use it in the real world, now I use it almost daily.
I know of a high school teacher who was asked by a student how the trig tables in their handbooks were calculated. The answer was a series expansion. But the teacher didn't know that, so he just made up an "answer": he told the student that machinists fabricated triangles with specific angles, and then, with sensitive rulers, the ratio of edge lengths were measured.
Please tell me where this "real world" is located. I would like to visit it sometime.
By the way, you should have taken IS (info science), CE (computer engineering), SE (software engineering), or EE (electrical engineering) as opposed to CS (computer science). Computer Science was born from research in metamathematics such as: proof theory, lambda-calculi, and automata theory. So its not just "a few people" that think CS is a branch of math. Many people actually know the history of computer science and realize that it is a or at least was born from a branch of mathematics.
Just because you ordered something you don't like to eat doesn't mean the chef or the dish is anything less. The world will always need more plebians like you - leave the "useless" theory to the rest of us.
Whats funny is that you are right about the large number of plebs that don't care for theory. I saw another software company claiming to be able to achieve a level of compression that the "useless" theory proves impossible. I wonder how much money, time, and effort will be wasted on that business. Those "useless" (economic) theories also fortold the economic disaster known as the dotcom-bomb. Its funny how useful those "useless" theories are.
But hey, I like plebs like you, so let me give you a little idea I was going to patent. Instead you can patent it. Its a program that checks another program's code to make sure it doesn't get in any infinite loops. The program takes the filename for your source code, and it returns "Safe" if the program source code has no infinite loops and it returns "Unsafe" if the program source code has at least one infinite loop. The beauty of this program is that it will save millions of dollars for software developers because it will catch "lock up" bugs before test time where it is more expensive to catch them. Go gather some of your pleb friends and start a company on that piece of IP. I mean, how long do you think it would take you and your superior friends to develop a program to solve such a simple problem?
(* How do you know which 3 will use it, numnutz? *)
You did not read it very carefully.
(* Do you hate your job? Well, now you know Algebra wasn't busy work. *)
Are you saying algebra busywork prepares you for the real world just by being busywork? That may be true, but there are *other* competitor subjects to supply busywork for, as decribed in another message.
Why give 1000 hours of algebra busywork but zero of logic busywork? Wouldn't it be more balanced to give say 400 hours of logic and 600 of algebra?
Table-ized A.I.
I dunno about high school, but in college I asked questions that nobody had asked before (at least according to the professor, who was the world expert in the subject). It's not that hard to ask good questions. (It's much harder to find good answers!)
That's hardly true. A single textbook can never touch more than a tiny fraction of the knowledge in a field.
Just for the record the Dewey Decimal System was created by Melville Dewey NOT John Dewey.
I doubt the veracity of this testament to your success... But the issue here is not whether or not people today are intelligent. The point is with all the degrees, all the education, and all the opportunity, people are not living as they should. New York City is a different story, that is why I live there myself. You don't see the millions of fat, TV watching fast food munching pornography addicted fools walking the streets. You are also living in a city that is basically a shell of what it once was. When you marvel at the beautiful parks, the architecture, even the efficient and fast subway, remember all of it was created before these educational ideas took hold.
You will understand once you are in school. I went to NYU myself, and I can tell you that you are in for a big surprise. You are one of the token few who got a scholarship like that if you did at all. Most NYU students are misanthropic rich kids who are more interested in piercing their nipple than any ideal of human existence.
If you live on campus you will be surrounded by people far more wealthy than you, and they will be just as closed minded as you are now. The moment you present a dissenting view you will be tagged as a lunatic, a fascist, a madman. Instead of rational debate to further humanity, it will be insults and lies.
I can also say, without a doubt, that you did not go to a public high school in New York.
Part of the problem of education today is apparent in the incessant dishonesty of the day. Would a person, very much aware of the connection between truth and virtue fabricate such a story such as this purely for fun?
At any rate kid, I will be a Flannery's multiple times a week on 14th street and 7th avenue. See you there. Since you are so poor, I will even buy you a drink.
I don't read or respond to AC posts
You are right! When I took the SAT about 6 years ago, I was confused when I sat down and saw a problem where you were supposed to think "x" meant "blank space for a digit". While it only took me a couple minutes to figure this out because I worked the problem as soon as I saw it, realized the answer didn't match the multiple choices, reworked it, realized I was right but misunderstood the problem... anyway, it cost me time on a timed test.
Such an example is why SAT like standardized tests are bad. It would be like using the word "cat" in the analogies section, but using "cat" to mean "Computer Aided Teacher". Don't teach us one definition and then implicitly use another in a time limited standardized test. I mean, at least the SAT could use canonical symbolisms for algebra, as opposed to using that kind of crap.
The apprentice system is still alive and well, just not recognized as such: on-the-job training is still responsible for teaching the majority of what most employees actually use on the job -- NOT the "general purpose" coursework found in college.
So? Numbers say nothing about quality.
While I would argue that the American system does have one of the highest quality university systems, I don't think that the overall quality of university students the U.S. puts out is that much better than, say, the European nations. We have a few top-notch schools putting out a few top-notch students, tons of average schools putting out average students, and a fair number of poor schools putting out poor students. The European countries have fewer people graduating from university not because their pre-college education system is inferior, but because employers there do not require so many people to have degrees. America graduates more college students simply because employers here value that piece of paper more, so more people go to college, and colleges make it easier to get the degree.
commie_pig rightly said:
"Moral of the story - the moment that the standard of mathematics drops, the entire IT industry will feel the blow of ineptitude."
We already are, but its not a lack of math (yet). My profession, programming and system admin., is overrun by people who say 'I ARE A PROGRAMMER' with BS on their resume and willing to work for next to nothing.
As for this "math handicap" our country has, its root cause is the attitude of most of the of the public that "Math is SOOOO hard". That's a half-truth. EVERYTHING is hard if you WANT to make it hard. After being beaten over the head that "Math is hard" crap, no wonder many of the kids have a mental block!
Most suburbanities don't go around and spew out crap like "READING IS SOOO HARD" or "SOCIAL STUDIES IS SOOOO HARD" and the numbers show that kids read and know the testing social studies pretty well.
Expectations are half the battle.
I did the same think in high school (blow off the homework, study a little, make A's and B's. This *killed me* in college when it was apparent that practice was important in being able to pass exams. In high school, topics were beaten into the ground -- you had to be asleep not to let it all seep in. In college, new concepts are introduced at each class period and its up to you to work enough problems to be proficient.
I had this problem in physics, also. I read a lot of science books and I understood most of the physics concepts so well that I didn't work many homework problems. Come exam time, I would be trying to re-derive basic principles since I hadn't learned the practical way of solving the problems.
My daughter is in the 6th grade. Most of the time, her homework is basic drill and practice and occasionally I have to teach (or reteach) basic concepts. Sometimes it is just busywork (make a poster about the rules of divisibility -- graded more on neatness and artistic concept, since the text of the poster (the rules themselves) is printed in the textbook). These "touchy-feely" busywork projects annoy me, since a good portion of *my* hometime is spent helping the kids with homework, or at least looking over their shoulders to make sure they do it and do it right.
Which leads to the final problem with homework -- I am sure that my wife and I spend much more time with our kids on their homework than most parents do (my wife teaches high school).
-- stream of did I lock the front door consciousness
One more thing you implied that highschool math teachers may not be as up to the tasks as college professors. Horse Pucky.
My highschool trig/precalc/calc teacher was many many time more qualified than several of the profs Ive see in college.
Anyway, I am not trying to flame you. I think the best solution is to have small student/teacher ratios, and many different classes for different abilities and interests. Educate students in what they are interrested in learning.
Funding for this you say? I dont know, thats a problem for people in Wasington.
Scott.
It's Socrates, not Dewey, who popularized the method of teachers asking students questions. The idea is to use the proding of the questions to get the student to formulate the right answer (the teacher's answer) on his own. (Or to get the student to remember the right answer, since he is timeless and eternal and already knows everything. See Meno.)
... Google? I don't think this is a respected notion of how to teach.
The idea that it's important to get students to ask the right question to the all-knowing teacher is most attributable to
Go read what qualified as political discourse in the 1700s---Common Sense, the Federalist Papers, etc. Then go listen to what qualifies as political discourse today. Draw your own conclusions.
There are reasons why democracy does not work nearly as well as capitalism.
-- David D. Friedman
I think that for young students, a good connection with the real world is a requirement for coming to an understanding of the math. I've taught CS at the graduate level, and was always utterly disappointed in the degree of math understanding of the average student. My wife researches grade school math education, is us utterly disappointed with the manner in which it's taught.
Algebra isn't that hard, really. I like to claim that any sixth grader who can figure out what he can get for lunch with the money in his packet has a basic grasp of it already. Part of the problem is that students are encouraged, from a very early age, to believe that they won't really understand math. "Just do it this way", and you'll get the right answer. They aren't usually taught why that way works, or what's going on. They just push numbers around the right way, and write down what you get. There's a definite lack of connection between the "real world" that the students live in and the way it gets talked about in math class.
I also agree that there's far too much repitition in the math curriculum. From my own experience, we learned "fractions" in third grade, did them again in 4th, reviewed them in 5th, went back to them in 6th, etc. By this time I had already dropped out, and started doing algebra and trig as a way to keep myself occupied. Many other students just stopped paying attention, not because it was hard or they didn't get it, but because it was clear that it wasn't ever going anywhere. What a sham!
--tsw
Sure it can be done in your head, all math can be done in your head, but not everyone wants to or will store the formulas in their head, alot of people have other focuses in life and unless a person focuses on math, they arent going to remember that stuff.
If you use Linux, please help development of Autopac
Is this the book you're referring to? If so, the author is Eric Temple Bell and it is a fabulous book. I didn't see any books on Amazon written by a Carl Brooks that dealt with math.
Methinks maybe the primary failure of teaching is the idea that there is one right way to do it. And that's what the student had better reproduce on quizes and exams.
There is no such thing as a "minimum" tip. A tip is to be given when one receives service above and beyond the norm. A tip is a reward for outstanding service, not an entitlement. I'm sick of people in the service industry thinking that people "owe" them a tip, even for shitty service! As for me, if you give outstanding service, I will give an appropriate tip, but if you give average or below service, you get nothing.
"I'm just here to regulate funkiness."
The article's image, "Algebra or Not?" includes two example problems (one from each of the mentioned states exams). Look closely at the answer to the first one and you'll find the REAL problem with the students coming out of this school... the tests aren't even correct!
My SIG is a SG-552 Commando
Well, I went through junior high and high school in Southern California; it's been a while, but let's see what I can remember about my math and science classes. Algebra, algebra II, trigonometry, geometry, calculus I and II (for the AP calc tests AB and BC respectively), electronics, chemistry, AP chemistry (for the AP chemistry test), biology, AP biology (for the AP biology test), physics, AP physics, and an extra semester of independent-study physics (I blew the EM part of the AP physics test the first time because we didn't have enough time to cover it properly, so I went back to study EM physics and did the AP physics test over -- Halliday & Resnick was a fun textbook). I went into college with 30 units of advanced placement credit. There are good high schools in California that give a damn about the students and try to teach them to learn, not just memorize, and there are teachers who make the effort to get their students to want to learn.
I didn't post the original comment but, for the sake of learning ;-), I googled on "Dewey theory education". Here are a couple of choice links ...
l
y .htm
...
http://lrs.ed.uiuc.edu/students/janicke/Dewey.htm
http://home.capecod.net/~tpanitz/discussions/dewe
Of particular interest is the following quote from Dewey's 1916 Democracy and Education
"While books and conversation can do much, these agencies are usually relied upon too exclusively. Schools require for their full efficiency more opportunity for conjoint activities in which those instructed take part, so they may acquire a social sense of their own powers and the materials and appliances used."
I think it pretty clearly states Dewey's advocacy of learning by doing rather than learning by rote as was originally asserted.
After the sixth grade, however, I think social interactivity simply takes over. Kids typically begin to show interest in the opposite sex around this time. They begin to struggle with deeper issues related to maturing physically, mentally, spiritually. They aren't going to receive theorems and rules for comma usage like they would have before. For me, everything between the seventh and twelveth grades was circumstantial education where some topical introductions to trade skills or apprenticeships could have been beneficial.
It is for this very reason that I thank Cliff Hillegas, creator of Cliff's Notes for helping me buy needed time away from the curriculum. I was asked to read Bronte's Wuthering Heights and James' The American at the same time I was discovering my penis. And English was my favorite subject! Seriously. I graduated from college with a degree in English. How was I supposed to maintain an interest in sappy literature and the Pythagorean theorem when girls were walking around with tits all of the sudden?!
No, there's simply a point when formulae and dipthongs fade into the background and an interest in people pegs our attention. Even if you hate people, people are the fascination, and that's where creative, enlightened interests should be focused. We're doing ourselves a disservice locking down kids in classrooms when they should be out engaging the public and discovering what it's going to take to make it in a field or fields of interest.
And FYI, I recently bought a copy of James' The American, gave it an earnest read, and I liked it. I have several "important" works of literature on my shelves now, and I've rekindled my interest in geometry at least since I've started drawing for fun. Time well spent.
Linear is not the word you want. If math were linear, after learning one concept, there'd be only one direction to go, only one choice for the next concept. Nothing could be further from the truth. The correct word for the concept you're using is cumulative, meaning you have to understand the last concept before you can understand the next. Cumulativity and linearity, in this context, are sort of chronological reverses of one another: linearity dictates the next concept, cumulativity dictates the previous.
The original Howling Frog is a fictional character and has no UID.
Most people who know alot of random facts and who know alittle bit of everything, end up not knowing anything very well. An intelligent person can afford to be lazy and should be lazy because you cannot focus on what you want to do, if you are always focused on doing useless tasks and memorizing random facts which you dont REALLY need to memorize just so you can not be lazy.
Why should I learn all the formulas when I can write them down or store them on a PDA or calculator? Why should I calculate in my head when a calculator can do it? Why should I fill my brain up with formulas, steps, rules, and other junk just so I can calculate random math problems a few seconds faster?
Its not worth the investment in time and effort in my opinion. Its not a matter of not being capable, I'm capable, but I dont think its worth the time and effort I'd have to put to get myself to remember that junk.
People rememeber what matters to them, thats what it comes down to, what matters to you might be these formulas, what matters to me might be something else.
To stress my opinion so everyone can understand the logic behind it. Time is valueable, you can invest your time which could be months or years learning a bunch of formulas, steps, rules and other esoteric math garbage just so you can calculate a math problem in your head and save a few seconds from having to pull out a calculator.
What you have here is an investment of say a years worth of time(at least), to save you seconds of time in the future during rare moments when you dont want to pull out your calculator, or when you dont have it.
Or you can invest your time actually thinking about stuff that matters.
Time is the constant, the information is the variable, and the pointer is the link to your brain. Just as a computer program doing a bunch of tasks it doesnt have to do, ends up being a bloated slow program, the human brain works the same way, when you invest your brain on things you dont have to think about, you slow your brain down overall.
So have fun filling your brain up with formulas, I'd prefer to keep mine on paper, while you were learning some silly formulas to calculate with, and investing all that time and effort into remembering how many atoms is inside gold, I used my time to learn things which matter such as computers, programming, windows, linux, computer hardware, how TCPIP works, how the internet works, how quantum computing works, how nano technology works, and alot of other technologies, because this is what is interesting to me.
Should I tell everyone who uses a computer that they should fill their heads up with all this information just to use a computer? Hell no, let them use dumbed down windows, let them pay me to do stuff for them.
They arent Lazy, they just spent their time doing other things, like being social, going to parties, and getting drunk.
If you use Linux, please help development of Autopac
Make them memorize the programs instead of learning how to write them, see how good of a programmer they are lol.
So you teach them to memorize hello world ?
#include
int main()
{
printf("Hello World");
return 0;
}
Yeah so they memorize that and they are a programmer?
If you use Linux, please help development of Autopac
"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."
Yes, and this is why the first two years of an undergraduate degree program virtually mirrors the last two years of high school. Any reputable undergraduate program goes on the assumption that a student has take at least 2 semesters of calculus at the high school level (I had 4). That provides the "additional perspective" most undergrad students need. The real problem at the algebra level of teaching is the size of a class. If you have 30 students, you haven't got nearly the same ability to teach as when you have a class of 10, you simply can't give the indivual attention needed.
Heh, I conceded defeat when when went into the AP exam after starting the EM portion of the physics course just a scant week and a half previous (why is it they don't teach this stuff concurrent with the newtonian stuff when it's HALF the damn test???) It's one of the reasons I didn't become an engineer - that and my inability to add/subtract numbers properly...
Oh, and why are public schools on the semester system? Forget everything during Winter break, waste 2 weeks of the new year cramming for exams. Might as well go quarter system if they're going to keep us in school till June. And why 6 periods a day? Why not take fewer courses per quarter, and make them a quarter long - at least then if you're going to flunk a class, you don't waste the rest of the year.
Nothing I know about public schools in California makes sense - and this from someone who sat on one of those School-Based-Management showpieces as a student rep, to try and get teachers to publish a syllabus at the beginning of the year, so the student could evaluate, for him or herself, that this class would teach what they wanted to learn. I got a whole lot of flak from the teacher's reps, although the parents and community reps were behind me. The resolution was passed, but I'll bet it was dropped as soon as I graduated...
You are far too generous to John Dewey. Modern schooling is patterned after public schools in Prussia. They are deliberately designed to provide a steady supply of low level employees, corporate cogs, and mindless consumers.
For background, you can read http://www.primenet.com/~afhe/gatto3.htm
More related articles are at http://www.primenet.com/~afhe and
http://www.johntaylorgatto.com
Enjoy.
++PLS
If someone had said, "this has INTRINSIC VALUE!" I'd have laughed. Not even advanced pure mathematics is done because of its "intrinsic value". It's done because some humans enjoy deep, abstract thought -- that is all. The very fact that humans are not slaves means they will make value judgements and act most effectively on their own volition.
And yeah, sometimes people enjoy helping others. That's why you have people answering questions on Slashdot, or helping out at the local homeless shelter. They have found a value important to them that just happens to include helping others.
"Intrinsic value" simply means "I consider this valuable, but I'm going to transform my personal value judgement into metaphysical fact." The end result is dictatorship (after all, if there are intrinsic values, there is no room for judgement), which history has shown does not fare well with the population.
There's more than content to literature?
Until you get to Analysis and Abstract Algebra (and of course all the courses leading up to them), you don't know squat.
Once you get to these courses, everything else is easy.
It is absolutely true that math is a "gateway" subject. I've been tutoring math on the high school and college level for a number of years, and algebra is the single biggest problem area. As you might expect, the majority of my students are taking calculus, and this is often the first time they've had to apply their algebra knowledge intensively to another subject. They generally fail miserably.
However, there are a number of other skills that are also lacking. Basic arithmetic. Estimation. Problem-solving. I can't tell you how many students get confused doing (-5)(-6) = 30. If a car is traveling 58 mph for 3 hours and 2 minutes, how far has it traveled? Quick! If you don't get "about 180 miles", you haven't learned to estimate. Estimation is extremely useful in checking the validity of your answers, and in guiding you where you want to go.
Lots of kids don't even know how to use a calculator, and that's a shame. I have no problem with giving kids calculators if it's going to help them. As long as they don't become a crutch, that is. (Common line to my students: "Don't use your calculator to figure 6 times 5, dammit! You're wasting its time!") The real shame is when kids are using them for the right reasons, say to reduce a complex numerical expression with radicals to a single number... and then they forget the order of operations rules and get the wrong answer because they computed 2/(sqrt(3)+sqrt(5)) by typing 2 / 3 sqrt + 5 sqrt =.
Even many of my smarter students, who had no problem learning the rules of calculus, used to stumble on the algebra. We don't have enough rote learning of these subjects, not enough practice, and not enough incentive to make it interesting. Meanwhile, my artist wife, who's from Bulgaria, doesn't know a lick of calculus but can wipe the floor with most of my students in algebra. It's a real problem for a future generation of engineers and scientists.
...following the principles of Heisenburger's Uncertain Cat...
My younger brother in 5th grade related to me the following...
His teacher's lecture that day had been on how "All non-living things are made of atoms." A student in the class offered "But I thought all things, both living and non-living are made of atoms." His teacher replied that "Oh no, living things are made of cells."
I didn't know whether to laugh or cry.
I have to say, I have never fully studied educational theory to the extent I would like. Much I have learned is from talking to folks pursuing their doctor of philosophy degree in education, simply because there is nothing else for them to do in this world.
These links have given me some new perspective. So often, criticisms of my owns posts are never thought provoking. Thanks for the links.
I don't read or respond to AC posts