Elementary School Math Curriculum

If you were in charge, what would elementary school children (that is, grade 7 and below), be expected to learn before going to high school.

Kids should learn algebra in the 8th grade.  So everything leading up to there?

Grades 1 & 2: Basic math (though grade 1 should probably focus more on other things such as language and writing)

Grade 3: Algebra

Grade 4: Sets and propositional logic

I'm serious as fuck. This will get kids learning how to use their brains as early as possible, which will go a long way to help develop critical thinking skills.

Grade 5: Geometry and trigonometry

Grade 6: Calculus I

Grade 7: Physics I

You can take it from there. But of course the public school system in the US is not designed to generate intelligent kids, so none of this would ever work.

It is a shame, however, because I am continuously disappointed in the people I meet in everyday life who don't even have a good grasp at problem-solving skills.

People become impressed when they see someone that can add "big numbers" (3 or more digits) "in their head". No, that is not impressive.

Fuck, now you've made me depressed again.

>>3

Agreed on everything you said.  I barely made it out of new orleans public school system and had to take summer school geometry just so i'd be able to get to calculus before i finished high school.

I could have done so much more, but school systems don't expect you or even allow you to elevate yourself (past all the dumbfucks).  They even wanted to hold me back a grade because I was born late in the year.  Idiot school board.

Bottom line: kids will learn what you put in front of them.  Yes, there are a few that will fall behind, but that's natural selection for you.  Start them early!

The US public school system is not designed to educate.  They repeat lessons in such an obvious way that it's equally obvious that they have another agenda.  That agenda is twofold:

1. Keep the niggers off the street until it's legal to jail them as adults.  Then you can just throw away the key.
2. Since the niggers are already dumb, you don't have to worry about them getting smart.  So, the 2nd part of the agenda is to make most of the remaining, non-nigger kids into drones who largely obey orders.

In public schools across America, math "teachers" are busily repeating the most boring elements of math education, and are trying to obtain the strongest, anti-education reaction from the children.  These "teachers" are merely jailers who are trying to get the inmates used to the sight of the bars on their social cage.

When a school or educational system is freed from this system of propaganda and control (i.e. pre-imprisonment), then real education can happen, and you'd find that pre-high-schoolers (grades 6-9) are perfectly capable of handling strong algebra, and the minority of those (the truly exceptional) are capable of handling "college-level" calculus at such an "early" age.

Poster #3 had it right, and I'm only following-on to what was said.  The public school system in the US would never tolerate this depth of education.  They only want to collect their FAT paychecks, benefits, and retirements ... while they prepare the niggers for prison and the rest of the children for corporate slavery.

Ideally, kids would know early on whether they were going into a math/science/tech field of study or a literature/arts one.  The science kids could probably manage >>3's plan, and the parents of the lit kids wouldn't start screaming bloody murder because their child flunked out of 3rd grade math.

#6, you're proposing placing children into development pipelines at a much earlier age than is done today.  Of course, I approve.

Basic philosophy early on would prepare kids to think logically, and basic numeracy ( number-line concepts, addition and subtraction) pre-grade 2.

For those that show promise with that, progression on to multiplication, division and fractions in line with the ability of pupils.

There should be provision for the brightest pupils to have learnt basic algebra, trigonometry and formulation of proofs by end of elementary.

I'd like to add one more thing to American education in addition to the accelerated learning:

Graduation exams!  I took the full International Baccalaureate (IB) coursework and passed the whole thing (similar to AP, but an entire curriculum).  These tests are so much better at gauging someone's ability to perform well in college (and not suck at life) than SATs.  To do well on the SAT, all you have to do is pay Kaplan a crapload of money and sit through a summer course.  That's crap.  If you haven't been learning your shit and can't pass some AP or IB exams, then you can wait one year while you study your ass off to make up for all the time you wasted.  Then if you still can't pass, then you don't deserve to go to a regular college. 

They would not be EXPECTED to learn anything more than they currently are. But they would be given the OPTION to do whatever the hell they want beyond the basics.

australian maths is a fucking joke
in year 7 -> multiplication/div/fractions

>>8
If you want to teach children logic, why not just have them take a logic course?  In my experience, philosophy classes have not been as objective as they should be, whether through subtle hints in the response to ideas or through selective omission.

>>3

Nice, although you're not suggesting only one subject a year, are you?

>>13

No of course not, that is just a general outline/idea.

Basically, around here, the schools do not even teach Algebra until 7th & 8th grade. This is absurd.

I would like to see propositional logic and introductory calculus become a part of the general curriculum by the 6th grade (hopefully sooner).

I've met so many people (even adults) that can't even follow simple "p -> q; p; therefore q" arguments that it isn't funny. Public schools (at least here) don't even teach shit like that! You have to go to college if you want logic taught to you!

And when I was in a logic course in college, the class started with 30 people, and ended up with 5 people left in the end because they thought it was too fucking hard to finish. It really isn't.

I don't mean that this stuff should be opt-in in or only given to kids persuing careers in science, this should be given to everyone. It is that important.

But, again, it will never happen in this country. Too much interest in keeping kids dumb (hoping that they will stay dumb as adults, which they do), and too many parents/kids BAWWWWWWWing that the education is too difficult. Here's a hint: Life is difficult. Not everyone can get an "A" grade all the time.

>>14
you can if you dumb down standards.  then everyone's a winner!

or everyone loses...

doesn't matter, everyones the same! :DDDDDDDDD

>>5
I don't think the system is _that_ overtly racial...

>>6
Also so that the /sci/ kids don't get Cs for misinterpreting Shakespeare.  That one verbose guy really was there just for comic relief... oops.

>>8
I also propose a proper definition of "inverse" (in the general sense, thus also requiring "identity") and "division" (hell, might as well squeeze in a little group theory).  If people properly understood that "division" is the inverse operation of multiplication, then there should be fewer "omg divide by 0" threads.

>>9
Many other major countries have such things.  The US system is soo much easier lol.

>>14
CA just dumbed down standards a few years back with their laughable "high school exit exam".  It only tests rudimentary writing, reading comprehension, and arithmetic.  Despite its trivial difficulty, some 1/4 of the students at my high school failed the first time around (first administered sophomore year oddly enough) (and my high school wasn't even that crappy either [relatively speaking]!).

Back in middle school, they required an entrace exam to Atake PRE algebra in grade 6.  The "standard" was pre algebra in grade 8, followed by algebra in high school.  8 years of learning arithmetic...

oops, I saged it by accident

Oops, you're a gigantic faggot

>>3
that's ambitious

>>11
Yes same in Canada too.  I remember just barely scraping the surface of algebra before leaving grade 7. 

Through grades 3, 4, and 5 though, every year there is a section on how to add numbers, and how to multiply, and how to long divide. I also remember one lesson in grade 4 focusing entirely on multiplying by zero.

I think I would want the average kid to be comfortable in manipulating algebraic expressions and perhaps drawing xy- graphs from equations by the end of grade 7.  That would speed things up about 1.5 years here.

>>18
Jeepers, that was very rude, mister

I agree with #20.  #18, gosh darn it, put a sock in it.  There are ladies about.

Grade 1: predicate logic and naive set theory (inc. discussions of injections, bijections, etc.).
Grade 2: Elementary algebra (inc. arithmatic and some number theory, variables, polynomials, a more concrete discussions of functions and their roots).
Grade 3: Euclidian geometry and proof, trigonometry.
Grade 4: Elementary analysis. (rigorous treatment of limits, continuity, derivatives, integrals, differential equations).
Grade 5: Linear and abstract algebra.
Grade 6: Intermediate analysis (vector calc., Stokes' theorem, etc.etc.).
Grade 7: Point-set topology, category theory, more set theory, a survey of topology and (real) geometry.

All material will be given an informally rigorous treatment.

I agree that more advanced courses should be taught sooner. The way it is now at my highschool, if you don't take algebra 1 your first year there you basically won't be able to graduate on time, which is insane considering how many people just aren't ready for algebra 1 since they're not really exposed to it in middle school.

And not even with just math, other subjects like English too. I was recommended to go into honors english, so I did. I didn't understand anything. I was expecting it to be like my other lame ass English classes, where it just taught you about punctuation and grammar usage. Instead I have all this symbolism and underlying messages and shit that I had never been exposed to before, all thrown at me at once. Lord of the Flies is about society and human nature? I thought it was about some kids trapped on a fucking island! Why was I not instructed about shit like this before being told to go to honors english?

I can't wait till one of you has kids and tries to teach your third grader euclidian geometry proofs.  Seriously.

#24, you attitude is exactly the same sucky one that has led to America's mental demise of today.  Your low expectations are the problem since they lead directly to low exposures upon your kids.  But, I'm sure you have more important things to do with your time other than helping your brood DAILY to become commonly intellectual ... I mean, things like working OT to pay for an overpriced home and car that you don't have time to enjoy.  THAT all seems about the speed of the Average American Parent (i.e. "fucknugget").

when the fuck did calculus change its name to "analysis", sounds queer

>>25

Does the name 'Piaget' sound familiar to you at all?

>>26
It didn't. Calculus is a much broader field than analysis.

#27:  No.  Do you mean Jean Piaget, "a Swiss philosopher, natural scientist and developmental psychologist, well known for his work studying children and his theory of cognitive development"*?  Surely you're not suggesting that dumbing our children down (through a process of reacting to diminished expectations) is instead the natural order of development.

* credit: wikipedia

>>28

No, analysis is a much broader field than calculus. lern to pass grade 10

>>23

It's high school; get over it you fag.

>>29

I'm saying that children aren't fully developed and that it's a scientific fact.  And that until a certain age they aren't capable of abstract logical reasoning.  Read moar dumbass.

I felt that I did understand you there, #32, but that you are also avoiding the fact of the dumbing down of America's children.  Has some educational philosopher appeared lately that has lauded said "dumbing down" since America's students were being somehow damaged by learning more abstraction at an earlier age IN THE PAST?

Reserving the Calculus for collegiates is part of the modern crime being committed against high school students.  But it's also become part of the same crime how lesser abstractions like Algebra are being moved upward in the age ranks.

Where YOU are lacking a sound basis of reading is in HISTORY.

I'm not denying that American's are being dumbed down.  All I ever said is that it's futile to teach children at such young age concepts that they CAN'T understand for basic biological reasons.  Piaget's theories have been tested time and time again.  Until a certain age kids simply can't learn complex abstract ideas.

Wth does that have to do with history?   Also, at least in my high school, any student who wanted could take calculus.  I did.

I understood that as well.  What remains to be seen about biological limits is what happens when you push the envelope, not what some ghei-ass ivory-tower type has to say about it.  This "tested time and time again" nonsense is purely an artifact of the dumbing-down system in American schools to begin with.  Who conducts these tests?  Yes, that's right, "educational professionals" ... who are the same EduPros who are dumbing down the schools as we speak here.

When challenged in a supportive environment, children can excel.  Let's find out THAT WAY about how early children can learn certain things, NOT by saying "oh well, Lord Piaget said these 8-yr-olds can't learn that topic".

Can you see why history study is important, now?  Pick up a few of the K-12 (equivalent) schoolbooks for American students in the early 1900s.  Those were some rigorous curricula to be sure.  Compare them then to the so-called textbooks (in reality, webpages-on-paper) we use today.  It's like night and day (and I'm not using the metaphor to imply that the past books were dim and incomprehensible).

History shows that children today can learn a lot more and be more rigorous about their knowledge.  We should suspend your disbelief about the entire matter until we know from actual exposure, support and testing what American children are REALLY capable of.

Wow, you just displayed a complete lack of understanding for the scientific method.  If thats how you think scientific studies are conducted then this whole argument is fairly moot.

This has little to do with scientific operations, #36.  It has mostly to do with CULTURE.  Like I said, we pushed children harder to achieve in the past, but now the gaywads in academia are telling us to go easy on the children ... as if they're devolving or something.  Fuck the gaywads.  They're part of the entire Great Dumbing-Down Machine and they should be summarily opposed.

Parents can put all your gaywad-worship aside and simply push and support their children and then see what happens.  Generally when parents do that, their children achieve greater intellectual capability.  So I don't have to play the gaywad game of predicting failure after trying to make failure happen; I'd rather predict success after trying to actually ACHIEVE success.

>>22
Why do you propose that children learn analysis before linear/abstract algebra?  Given that the latter is far simpler, I'd argue for the opposite.

Punctuation, grammar, syntax, and vocabulary are all critical to a proper understanding of the English language, and all students should be required to know these things thoroughly.  However, the utility of interpreting literature is far less.  This symbolism/allegory/allusion stuff isn't very useful, but it does give one a slightly different perspective on literature.  Harry Potter isn't just a young wizard attempting to defeat a great evil.  At the same time, a working class protagonist tripping over a log doesn't always mean that the log represents the bourgeoisie oppressing him.

>>24
I can't wait either.

>>28
Orly?  I thought it was the other way around.

>>32
I'll read moar.

>>33
Proof plox?

I will read/respond to rest at a later time.

4tran/#38, just go get some of the math books that were used in early 1900s America.  By the 1950s, they really started to get simpler, and that degradation has slid downward until today.

Modern students are dragged though simple mathematics for most of their K-12 career and in comparison to the expectations of prior generations, it's a shameful crime.  They are being intentionally held back since the education system itself is vicious and racist and functions more like a jail than a school.  Part of the viciousness is that it is ruled by "professional educators" who largely achieve their PhDs by demonizing the rigor of past educational norms.  In effect, these pros have a conflict of interest -- if they really taught children to be self-sufficient in their education, they'd be out of their jobs.

It even gets worse ... for exampmle, children today are tapping out math problems on calculators, ill educated on how such answers are arrived at.  In that manner, slide rules were better instruments since they allowed the student to see how imprecision is intrinsic to the calculation.

>>37

Alright, I'll explain the concept to you one more time as slowly as possible and then I'm done.

When a baby is born it's brain is small and underdeveloped.  This baby is not capable of abstract reasoning.

As this baby grows up it's brain develops in a biological, measurable sense.  This development is completely independent of culture or education; it is completely physical/biological.

At some point in this child's development it will become able to understand and reason abstractly.  Before this point it is physically and biologically impossible.

This age has been determined to generally be between the ages of 7 to 11 in the average child.  The methods for determining this have been scrutinized and developed extremely well over the past century.

These methods are designed to remove all exterior influences except for the biological development of the brain.  Independent of culture, sex, race, education, et al.

Theres a reason this stuff is taught in every single child development course at every single university.  It's because it's not about culture, it's about the biological development of the child.

#40, you were done before you even started.  You're still pushing educational agitprop since you're still denying the past ... which is well evidenced to the contrary to your assertion.  I never said to teach the Calculus to a fucking TEN YEAR OLD, you immense donkeycock!  I said repeatedly that with the dumbing down of our society we've removed rigorous mathematical instruction from children of all ages.  Instead of seeing where children can naturally absorb Algebra, we push it off into the late teens on average.  Too many children who SHOULD BE addressing the Calculus, simply pass it by during the grades 9-12 entirely.

Vicious fuckos like yourself have already CONDEMNED children in this magical 7-11 age group.  Your contempt for their abilities (unknown until tested by trial, since Humans are different in how they achieve) is leading the tsunami of ghei-instruction which afflicts American students today.  It's all watered down and nearly useless.  The sheer repetition itself makes us the laughingstock of the civilized world.

Stop holding children back with your Neo-Regressive mentality and start expecting them to TRY TO PERFORM.  Remember, fuckwad, that children are by law forced to attend some form of schooling for about 12 years while they are minors.  Their time is already going to spent learning.  Why not drop Piaget's cock, wipe his nasty cum from your mouth, and insist that children actually learn something during that period of time?

(I'd ask where stupid fucks like you become so heavily indoctrinated.  However, I already know the answer:  COLLEGE.  American colleges prefer to manufacture obedience rather than critical thinking.  Obedience is obviously much more controllable and fulfills America's rising Fascism.)

I've asserted nothing other than before a certain age children are incapable of abstract reasoning. This is indisputable since a newborn is clearly incapable of this type of reasoning, whereas a fully developed adult is not.  Therefore somewhere between these two ages a child must develops this ability.  I didn't even go as far as to draw a single conclusion from that one fact.  Everything else that you think I said is a product of your own insane delusions.

#42, as long as we both recognize there is a line, but that we're not sure where it's drawn, then sanity has been achieved.  What all I've criticized American schools systems for, is still true.  The danger of your attitude, is still true.  Despite your assertions, you really don't know where any individual child lies on the spectrum of capability, UNTIL YOU SUBJECT THEM TO ACADEMIC TRIAL.  An academic trial presumes to instruct.  Only after they FAIL to achieve, do you have any rational basis for claiming said child is too young for the subject matter he was exposed to.

Of course, modern ghei-Liberal thinking demonizes any hint of passing on the concept of failure to children.  Again, American children handled the concept of failure perfectly OK.  It remains as an obvious conclusion that the modern population is simply coddled and mis-served thereby.

Bother to challenge your children, and with your loving support and intent, they'll be better off for it.  Continue instead to follow some egghead's highly restricted ideas on child development (mental note:  people usually enter the field of child development since they hate children!) and you'll end up undermining what your children are capable of.  It's fucking elementary and it applies to all ages of people -- challenge is GOOD, pre-judging incapability is BAD.  EPIC DUH!

>>36
Assuming he conducted his experiments well, it still only places a statistical limit on humans.  Unlike iron spheres, humans have quite a large distribution of non negligible characteristics.  It's rather hard to conduct the same experiment with the same 100 kids repeatedly.  Each time the experiment is conducted is with a new batch of randomly selected children.  Another variable you failed to consider is the possibility that early exposure can lower the age limit at which they can understand abstractions.  On top of that, there are tons of other behavorial variables that can affect the outcomes in a very non linear fashion.

>>40
Somehow I'm not convinced that the ability to reason abstractly is a binary capability.  Children are not going to wake up one day and suddenly be able reason in such a fashion.  It almost certainly takes time for the progression from 0 capability to acceptable capability.

If it's a purely biological thing, please indicate the brain sections that are not properly formed/lacking in neurons/lacking in neuron activity/not chemically in the right state/etc... or is active research still necessary?

>>41
History shows that people were teaching children more rigorous stuff, but that doesn't necessarily mean they understood everything they were taught.  Do you happen to have statistics on comprehension rates?

>>42
Your conclusion, or at least statement of current trends, is that all children should be taught according to the stastical average age of developing abstract reasoning.

>>43
You were probably better off not posting >>41 and instead just posting >>43.

Another added bonus is that teaching everybody a standard curriculum is far cheaper and easier than adjusting standards according to a child's capabilities.

Spare the rod and spoil the child.

Conclusion: >>43 wins.

calculus

>>38

For the same reason university students do calc before group theory or lin. alg.: it's a little more work, but it's less abstract and gives them the experience in dealing with functions that they'll need for algebra: more of a comfort thing than a theoretically required pre-req.

um i hope you know that the maths curricula is more demanding in other countries, and is successful.

that said, one can only lol at some of the ideas on here. algebra should be started in the final year of primary (elementary school). i think, at least in the uk, the key is to do more once kids are in secondary education. it could easily be more demanding - a sensible target would be to properly start calculus by at least year 11, and preferably year 10 (grades 10 and 9), rather in the final two years. anything else is unneccesary dilution of the curriculum.

>>47
Yes, we do know that; that is part of the reason we are condemning US educational policy.

I had calculus in grade 10 and got As in the class by playing Phoenix on my calculator during lectures lol.

This is anecdotal, so grain of salt and all that, but there is NO. FUCKING. WAY. I would have been able to do some of the shit you're talking about at those ages.

It's nice to say, "Oh, 4th graders can take algebra no problem! Hell, throw some trig in there! They can take it!" Thing is, I remember seriously struggling with fucking long division in 4th grade. I just didn't get it, and there's no way I could have handled full-on algebra.

>>49
Trial and error.  If the kid can take it, give them something harder.  If they are phailing, then give them something easier.

Long division is just a mindless algorithm.  Nobody ever explains WHY it works, which might contribute to a lot of people struggling over it.

Well, #49, that's too bad.  Humans are intrinsically fairly bright and in supporting environments they can generally achieve strongly.  In your case, you may have been incapable, or the environment was poorly supportive, or your teachers were not good, etc.  But in all those cases, the idea of letting achievers ACHIEVE has not been falsified.  We can change our educational systems to stop classifying and limiting so much, and become more enabling and unleashing.  Stopping the monopoly of the public schools in America is a good way to move towards such an organization.

The entire idea of challenging students to thrive (and FAIL, if necessary!), left the public schools in America about a generation ago, if not longer ... which has all been well enough documented by Charlotte Iserbyt and John Gatto.

Let's see if more students can accept higher reasoning by trial and error, not by resolutions crafted by a professional class with a large conflict of interest.

Sorry, 4tran, I was composing my reply while you were posting yours.  You've said the same thing in a more succinct form than I did.

>>51
Unfortunately, we're still uncertain about the real average capability of humans (I'm not very optimistic), but you are right that everybody deserves a chance to prove themselves capable.  Assuming stupidity is a little too contemptuous of children.

If politics is relevant, http://oldamericancentury.org/14_pts_2.htm
#9 in the middle column this dumbing down of Americans fits pretty well lol.

>>52
lol, it's all good.  Coincidences on 4chan are rather rare these days.

>>49
>Thing is, I remember seriously struggling with fucking long division in 4th grade. I just didn't get it, and there's no way I could have handled full-on algebra.

That's because you're an idiot.

VECTOR CALCULUS

>>54
More likely because he hadn't been taught it correctly or wasn't sufficiently prepared, or forgot what he had been taught (which is common because of how we're taught now.)

>>56
49 here.

I think what you're saying is on the mark. Looking back, the way that it was taught was abysmal.

I don't remember if I was taught why it works, but since I explain it often to others, I eventually figured out the whole rationalle myself and how to move from a basic principle to the common algorithm when training others.

To begin, note that multiplication can be understood as repeated addition, and so division can be understood as repeated subtraction -- once that idea is solid, no one should have to ask, "I don't remember, what do I do in this step, add or subtract"

I can't tell you how many times I've seen people forget that the long division algorithm has subtraction in it.

>>1

This resources is how young students should learn mathematics : http://do2learn.com/academics/Mathematics/index.htm