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 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
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.
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.
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
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?
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.
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
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
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.
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~
Give me a break. "Standards" is just another way of saying "hey, instead of funding public schools sufficiently let's threaten the teachers".
All these idiotic standards movements have done is make sure children spend all their time preparing themselves for tests. Of course they do better at the tests, but they don't learn anything else.
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.
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.
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
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.
You need a FREE iPod Nano
Not into higher math eh? Just wait until you have to design and implement more effcient algorithms. Having only a passable calculus background (which I had since forgotten), I had to resort to brute-forcing all of my solutions when I was taking programming in school. For example, instead of notating in polar coordinates, I coded in degrees and converted into X/Y coordinates (this was for a X-windows clock written in LISP.) It worked (ie, it got me the grade), but it was ugly, and ate up a lot of processor cycles. At least take some classes on graphing and number theory. Linear algebra too...
and nothing else taught in school is boring.
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
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.
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!
8th grade ? What's that, 13 years old ?
Ouch. We were doing trig by then, moving on to elementary calculus at 15/16. Mind you, things have got a lot more dumbed-down on the other side of the Atlantic too since I did my secondary education. Procrustes, and all that...
What would Lemmy do?
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.
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.
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.
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
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!
"Alpha children wear grey. They work much harder than we do, because they're so frightfully clever. I'm really awfully glad I'm a Beta, because I don't work so hard. And then we are much better than the Gammas and Deltas. Gammas are stupid. They all wear green, and Delta children where khaki. Oh no, I don't want to play with delta children. And Epsilons are still worse. They're too stupid to be able..."
/need/ it for their work.
-- Aldous Huxley, "Brave New World"
If it's all the same to you, I'd hope that even the sanitation engineers are educated, because a) they may vote, b) if they're clueless, their mistakes may plague others, and c) I consider human beings to have substantial intellectual potential, and it'd be a shame to neglect it just because they may not
Only the dead have seen the end of war.
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.
Involved parents also help -- they, probably at least as much as a school, can get their children interested in learning not just as a way to graduate, but in something they should be doing for their entire lives.
Only the dead have seen the end of war.
Good for you. The problem-solving skills are fundamental, but you can usually look up Greene's theorem or Runge-Kutta differentiation or Simpson's rule and its ilk for numerical integration or what-have-you if you need them.
Learn the concepts, but don't be afraid to reach for the CRC Handbooks or other favorite reference book.
Only the dead have seen the end of war.
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
You can't, because it's a falsifiable statement.
a=-1
b=-1
LHS:
2^-1 = 0.5
3^-1 = 0.33333...
Sum:
0.833333.... (5/6)
RHS:
5*a*b =
5*-1*-1 =
5
which is greater than 5/6. If you can prove 5/6 >= 5, then you've either got different definitions of those numbers, or you've got an inconsistent proving system that lets you derive a contradiction.
Only the dead have seen the end of war.
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
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.
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.
--
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.
There's nothing wrong in testing in general, but the standardized tests that the whole standards group likes to tout don't encourage any deep understanding of the subject. It's short-term memorization, and it's no wonder that people forget what they learn.
Those students you had probably learned algebra fine; and could do it for a few weeks after learning it. Then the knowledge is gone.
The result of students doing arithmetic on that $2 calculator is that they have no number sense. Their brains can't make connections between this concept and that because they have no clue what their neighborhood is like. They aren't familiar at all with the "world" of numbers. They don't immediately see the connection between points (1,2) and (3,6) and equation y=2x. They don't see what numbers to use when factoring x^2+4x-21. They have to run the numbers through their calculator.
You say that students already know arithmetic, and really, they don't. They can add and subtract well. Multiplying if they are lucky. Long division is anxiety producing. Fractions are downright scary. Decimals are ok as far as addition, subtraction and multiplication goes, but division is again tough. They get mixed up with negatives and positives -- is -3 - 2 = -5 or -1 or 1...or is it 5, since -3 and -2 have the same sign?
Indeed, the problem is that the dominant philosophy in mathematics education in the past decade has been a bastardization of NCTM Standards. Standards can be boiled down to one [very astute] statement: Most of a student's work should be related to what you are teaching. In other words, (for example) students doing graphing shouldn't be bogged down in long division. This statement got twisted to become "You're in 4th grade now. You can use that calculator for your all of your arithmetic. Look! It even does fractions for you!"
This is what we call a strawman -- misrepresenting a statement so that you can knock it down. If students' arithmetic was all calculator based (which is pretty much the size of it now), and if students' really didn't get substitution (which is pretty much the size of it now), I would be spending 2-3 weeks on both mechanics and meaning.
THAT all said, you're right in that students' (not necessarily numerical) problem solving skills do need to be stretched AND celebrated in math as well (read my previous post about the dyslexic student). You can't go wrong getting a kid to exercise those parts of their brain. Though, you do have finite time and you do have to teach stuff that is explicitly math too, so you have to balance your time that way.
Last year I did a week long project at the end of each quarter. This year I would like to put a smaller logic problem at the end of each chapter to replace half of the larger problems (I have a couple of *REALLY* good projects that I don't want to give up...my group theory project is one of those!)
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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It depends on economy than anything else. If your parents are poor, you have a far greater likelihood of taking out the trash. If your parents are rich, consider a blue collar job an impossibility
And if all the rich kids were smart, how come they make so many dumb choices that the rest of us have to live with?
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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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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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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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.)
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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?
I presume you were trolling for a couple of "Funny" mod points?
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
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.
I Browse at +4 Flamebait
Open Source Sysadmin
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.
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?
let me correct myself, i went to private school.
FYI private school teachers get paid less than public school teachers and supposedly produce better results. That is probably because private schools can pick their students (we did have a 3 track system though), have smaller classes, and GASP require homework from kindergarden on up(i was pulling 2-3 hours a night in 2-3rd grade, which wasn't fun because my friends we all playing outside or watching tv after school).
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
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."
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
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
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.
"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'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.
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.
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.
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
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.
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
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...
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.
No, that's not it. And now that I think about it, Carl Brooks is some one else. It took a bit of googling for me to dig it out. It's Carl (Benjamin) Boyer and the book's actually "The History of Mathematics".
The origian is relatively old, but there are newer editions available and my understanding is that it's still considered to be quite accurate and a classic text book on history of mathematics.
It seems that the finnish translator had been imaginative enough to include a subtle "Queen of Sciences" remark after the actual title. Oddly enough I only remembered that.
1 Earth is warming, 2 It's us, 3 it's royally bad, 4 we need to take action NOW