/sci/ - Science & Math

>>6923497
I don't know how it is taught. I went to high school from '90-'94. I know that I got As and Bs until I hit precalc in eleventh grade, where I practically failed. So something went wrong since the first quarter of pre-calc was a glorified review. How did I do so well up to that point if I didn't know the material? Well the story has a happy ending but that definitely points to a problem somewhere earlier in the line. I enjoyed math, and apparently was good at it, except that when the time came I was shit. This should not be possible.

I will hazard a guess at the problems I experienced.

1) too many word problems and not enough emphasis on manipulation of terms. "When are we gonna hafta use this for???" Followed up shortly by, "I hate word problems!" Kids are petulant little fucks. To this day people can balance their checkbook but can't handle fractions. That's a big red flag to me.

2) Too much emphasis on tricks and formulas. People in my age group tend to say "cross multiply" like it's a religious invocation and don't even understand why it works or when to use it. People who are shit at math can still recognize the quadratic formula but they can't solve a linear equation for the unknown. This is a bad sign.

3) Not enough actual calculation is done. To this day I am better at symbolic calculation than numerical calculation. To some extent this makes sense but the relationship, for instance, between polynomials and normal positional notation was something I literally discovered on my own even though it's fairly trivial. "Synthetic division" is retarded, it's just the usual division algorithm, only you don't have borrows and carries. Similarly, "FOIL" is stupid, multiply the coefficients like schoolboy multiplication algorithm, just don't have carries.

Anyway. Develop their intuition (practice, not application), shy away from shortcuts, show how algebra is an abstraction of calculation rather than "something you do with eks."

>>6923497
>1st Grade
Basic addition/subtraction/modulo/compliments
>2nd Grade
Basic times tables/fractions
>3rd Grade
Division, Powers, Roots, Primes
>4th grade
Algebra
>5th Grade
Geometry, Logic, Sets, Combinatorics, Proofs
>6th Grade
Higher order Algebra. Trig, Exponential, Logs, Series, Sums, Limits
>7th Grade
Calculus, Matrix Algebra
Chemistry
>8th Grade
Vector Calculus, ODEs
Mechanics, Thermodynamics
C++ Programming
>9th Grade
Linear Algebra, Probability, Statistics
Electromagnetism, Circuits
Digital Logic, Comp Arch
>10th Grade
Real Analysis, Abstract Algebra
Stat Mechanic, Optics, Advance Mechanics and Special Relativity
Data Structures and Algorithms
American Government and Political Science
>11th Grade
PDEs, Complex Analysis, Fourier Analysis
Quantum Mechanics
Numerical Analysis, OS, Parallel Programing
Macro & Micro Economics
>12th Grade
Money and Banking, Finance
Philosophy, Theology, Religious Studies
Electives (Organic Chem, Biology, GR, Astrophysics, Robotics, Comp Vision, etc...)

>>6923930
>C++
stopped reading right there

teach them logic asap, from the most basic forms to advanced forms.

>>6923930
gets me every time

>>6923497
>inb4 overly ambitious, verging on autistic suggestions which fail to take into account that children have lots of other subjects to juggle and may not be interested in the subject matter.

>>6923939
>Supporting C over C++
>2014

Get with the times and stop parroting Linus.

dafaq is "Higher Order Algebra".

>>6924641
Conic sections, Quadratic/Cubic/Quartic equations, Complex numbers, Fundamental Theorem of Algebra, nonexistence of a formula for quints, partial-fraction decomposition, absolute value and inequalities, etc

Basically nonlinear algebra

>>6924692
Is there and official/formal title for this kind Algebra?

>>6924696
Nonlinear Algebra

>>6923770
>"FOIL" is stupid
Fuck, I'm about to get my bachelors and I still don't know what this is.

>>6924696
Algebra II, Algebra III, College Algebra

>>6924759
Something that causes people to be incapable of multiplying out (a+b+c)(x+y+z)

>>6924766
(a+(b+c))(x+(y+z))?
I still wouldn't do it that way, but you could if you needed to foil

>>6924759
It's a mnemonic acronym, and it stands for "First, Outer, Inner, Last," to help Algebra I students remember how to multiply binomials.
(a + b)(c + d)
First = a * c
Outer = a * d
Inner = b * c
Last = b * d

>>6924126
Maybe it is Linus.

>>6924786
most don't realize it and you get

ax+az+by+cz

>>6924792
Yeah, it looks more complicated than just doing a * (c + d) + b * (c + d). But what do I know about middle schoolers.

What bothered me in high school is teachers would scare students out of math, specifically calculus. My algebra and geometry teachers in high school would talk about calculus like it is the hardest thing in the world and you had to have an IQ of 150+ to be able to find a derivative.

When I finally took my first calculus course my freshman year of college my reaction was "this is it?"

The notion that you have to be extremely smart to do anything before and up to calc 1 or 2 has to go

>>6924809
They don't stop using this method in the High school I went to, but they didn't make it mandatory either, like they did in middle.

>>6923770
>>6924813
All true, all catastrophic.

High school math class is a fucking nightmare. These courses should focus exclusively on inarguably applicable geometry, probability, statistics, and only the most basic algebra/trig. Nobody outside of STEM gives a shit about the quadratic formula or trig identites, nor do they need to. Common core math is saturated with these topics because it is designed to prepare students for calculus, a topic that the vast majority of students will never use once as long as they live. High school math courses serve to traumatize far more students than they inspire. As a high school student I learned to detest math because the instruction was so consistently tedious and punitive, to the point that I actually failed Algebra II and had to re-take it, only to pass with a D by convincing the professor that I was already a lost cause.
As soon as I left high school my natural scientific curiosity brought me to lament my horrible performance in mathematics, since I realized that it was actually the most useful topic of all. Now I'm a year away from my B.S. in applied math with 50/50 A's and B's. I'm still not a great student, and while I have learned to love the subject I know that some of those B's would have been A's if my four years of high school math hadn't been so damned esoteric. I ended up learning all the algebra I was supposed to learn in high school in my freshman Calc I course, and it was comparatively a breeze because it had the exciting context of applications in calculus.

>>6923497
No school grades
No homework
No grades such as (first or second)
No mandatory topics to pass,(math,foreign languages)
And lastly, no boring teachers with indulge in topics with boring and mundane details. My god, I feel stressed out in class.
Learning is over by the time one is 14. You get trained in your career by then. Before hand, you're be given assesment tests throughout the years to see which career are you. Nobody will ever work in boring and mundane career ever again.

>>6924958
>mundane career ever again
like a fast food joint

>1st Grade
C++ Programming
>2nd Grade
C++ Programming
>3rd Grade
C++ Programming
>4th grade
C++ Programming
>5th Grade
C++ Programming
>6th Grade
C++ Programming
>7th Grade
C++ Programming
C++ Programming
>8th Grade
C++ Programming
C++ Programming
C++ Programming
>9th Grade
C++ Programming
C++ Programming
C++ Programming
>10th Grade
C++ Programming
C++ Programming
C++ Programming
C++ Programming
>11th Grade
C++ Programming
C++ Programming
C++ Programming
C++ Programming
>12th Grade
C++ Programming
C++ Programming
C++ Programming

>>6924766
>(a+b+c)(x+y+z)

a x+b x+c x+a y+b y+c y+a z+b z+c z

>>6923930
You mean I have to got the whole 12th Grade without doing any pure maths? Fuck you.

>>6924958
I was a lost cause in middle school because i was with a group of kids with canonical high expectations asian parents and the entire thing placed a higher value on that submissive and soul-crushing grinding process of "achievement" over legitimate intellectual growth and development, the kind of kids who were forced to drill the multiplication tables well beyond the point that they lost even the vaguest notion that that's boring and punitive. I resisted it at every turn, and channeled my disillusionment to a productive end as soon as i felt the slightest desire to do so (and succeeded phenomenally.) The very idea that I could have been directed into my permanent. fucking. career. based on how i responded to a shitty environment that fucked with me in my most vulnerable years is terrifying.

If it was within my power, I'd have you shot for posing a serious danger to society.

>>6924984

Still a good foundation for pure math nonetheless.

>>6923930
I wish I had this education

I bet if you did this, you wouldn't hear inane comments like "math is so pointless, when am i ever going to use this?"

>>6924926
That's inspiring as fuck, anon.

>>6925111
it's 100% true, I still don't like going to school though...

In the history of american public education has there ever been a elementary/middle/high school math class that spent a semester focusing on axioms and the history of math?

>>6925183
I never had a lesson in which the history of math was discussed.

>>6924993
I got you get rapped by a dildo
faggot

>>6925183
http://en.wikipedia.org/wiki/New_Math

>>6923930
I am pretty sure 2/3 of all students will be diagnosed with autism by 10th grade

>>6923770
>>6924926
This all the way

I'm still pretty bad at math (and a shit student in general due to admitted laziness), but none of it made sense until I took "Discrete Mathematics" in the very end of highschool and from then on it kind of "clicked" for me.


I knew that the way math is taught is bad, but I couldn't figure out WHY it was so bad until I tutored my little brother with some division and fractions.
He's a smart kid, but he pretty much failed his test. He had no understanding of what fractions even were, much less how the fuck they worked in tandem with one another, he just repeated the formulaic steps the teacher doled out.

After about 30 minutes of me telling him to forget all that shit and teaching him the actual concept of fractions and how to add/subtract/multiply them, he was able to do it in his head. He had the biggest fucking grin I swear.

But that required me to sit down and explain a concept in a few different ways until he understood it, and I'm willing to bet that between time constraints and the teacher probably not giving much of a shit (I know from personal experience that motivated teachers are few and far between), instead of teaching the kids concepts and guiding them through that way until the rest unfolds in their minds, they just opt for these "fool-proof" mass-production methods.

Why take the time to teach kids fleshed-out concepts when you can just offer them a cheap, universal method instead?

>>6924970
But is that really going to prepare them for REAL C++ programming?

I hate they way math is taught. I was never taught what e or natural logs signified until my second year of calculus, and that's only because my teacher was so devoted to this idea of teaching the concepts and backgrounds to every topic, rather than the shitty shortcuts. I asked my Calculus I what the hell e was and why I used it, and he told me it was a constant I needed to use.

>>6923770
>"When are we gonna hafta use this for???" Followed up shortly by, "I hate word problems!"
This always makes me laugh like hell.

>>6925279
That's where "real world problems" are nice. When I was first shown that e was the result of continuously compounding interest, a light went off in my head.

>>6925314
>e was the result of continuously compounding interest
yeah Euler was filing his taxes when he came up with e

>>6925335
I thought it was Bernouli.

>>6925209

I see...that's disappointing.

>>6925345
It's called Euler's number you nigger. What do you think the fucking "e" stands for?

>>6925351
You're a fucking idiot, the relation of e to compound interest was discovered very early

euler's number wasn't even discovered by euler

7/10

>>6925351
according to wikipedia, Bernoulli first attempted to solve for lim(1 + 1/n)n n -> ∞. Leibniz referred to it as b, and Euler just called it e.

https://en.wikipedia.org/wiki/E_%28mathematical_constant%29#History

It is wikipedia, though, so...

>>6925199
I will cut off your fucking tongue and balls and make you eat them while i beat you senseless with all my journal publications and lick the delicious salty tears off your fucking plebian retard faggot face

>>6924803
cz+bz+az+cy+by+ay+cx+bx+ax

Not everyone needs to learn math. that's the plain truth of it.

Frankly I think we need to focus more on teaching kids about the aspects of life they're likely to experience more directly, and give them the ability to be critical of their world.

>>6925396
>Leibniz referred to it as b
Leibniz confirmed for prescient as fuck, seeing as e is the best base. How is that man so perfect in everything he did? Was he actually a time traveler?

>>6925642
If they can't think logically they can't be critical.

>>6925314
I had the opposite reaction. That "continuous compounding" shit was mystifying to me. (in my defense, i had horrendous, shit-tier teachers in middle/high school and never felt engaged by cookbook algebra of the reals.) It wasnt until i found out what calculus was and that e's exponential function is its own derivative that i really understood what it and exponential functions in general was/were.

>>6925642
Everywhere you look there are utter dumbasses. Not everyone needs to learn math in the sense of computing integrals, applying the law of cosines or what have you. Cranking computations and *application* of notable results don't become useful for the majority of us. Mandatory math education should omit anything vaguely "cookbook" after basic arithmetic and become purely abstract. Knowledge and retaining of the theorems in their own right is irrelevant, but the exercise behind the proof is invaluable in saving individuals from a lifetime of complacent mediocrity and learned helplessness.

>>6925209
The Thermidor from new math makes me cry harder than anything i have ever personally experienced in my lifetime. This nation almost doesn't deserve saving.

>>6925272

>>6923930
THIS SO MUCH. Instead we spend the first 5 years doing the stuff you have listed on first grade! We never learn anything in contemporary public school!

>>6925279
mind sharing your explanation of e?

>>6926270
yes every 90 IQ high schooler needs to learn fourier analysis and quantum mechanics in 11th grade clearly you and the anon you are replying to are realistic and reasonable and not autistic or trolling at all

>>6926296
>every 90 IQ person needs 12 years of education
It appears that I have found your problem.

>>6923930
This is the only real aswer.

>>6926297
>missing the point
do you also think letting the average pleb never take a single math class again after 7th grade is a good idea? because they aren't gonna be able to handle ODEs and vector calc in 8th grade even if they somehow manage to survive 6th and 7th, designing an education system that everybody will go through to cater to the needs of the <5% capable of benefiting from it takes a pretty insane amount of autism, the point is to maximize the average level of education not the extreme top end.

you faggots are too focused on preexisting solutions. school fucking sucks, no matter how you alter it. self learning is the future.

You do not need math for most jobs. The world is run by liberal arts people who attend elite schools. Past a calculus based stats/prob math is worthless to 99% of people.

I know two UCLA CS majors that are IT and Apple repair bitches for elite schoolers. One for an Oxford language major the other for a UPenn/Harvard guy; both in the entertainment industry.

Even PIMPCO which employs lots of STEM people has been run by a Cambridge guy, a Duke guy, and a Dartmouth/Harvard guy.

Most of you have not had real jobs, but I can tell you one day you may wind up working for a Harvard grad that majored in art history.

>>6926312
>do you also think letting the average pleb never take a single math class again after 7th grade is a good idea?
I think not making school a requirement is a good idea.

Compulsory curriculum for grades 1 through 8:

>1st year
Arithmetic
Basic problem solving
Basic geometry
>2nd year
More advanced problem solving
Preliminary introduction to concepts of algebra
More geometry
>3rd year
Powers in addition to more in depth problems about stuff taught before
Logic
>4th year
Proper introduction to algebra, mostly equations in 1 and 2 variables
Introductory combinatorics
More logic
>5th year
Roots
Introduction to the cartesian coordinate plane along with relevant applications to geometry
More combinatorics
More logic
More algebra
>6th year
Some instruction in different coordinate systems with relevant geometry stuff
Simple introduction to sets
More algebra
>7th year
Trigonometric functions
Complex numbers
Polynomials
More algebra
>8th year
More complex numbers
Exponential functions
Logarithms
Series (not necessarily calculus related yet)
Function sketching

To be honest, this might be too much for the average kid. Essentially, the aim is to teach a typical Algebra I course over 8 years plus some geometry, combinatorics, logic, sets and the ability to apply these to problems.

Math curriculum not compulsory after 8th year and picks up speed

>9th year
"Nonlinear" algebra
Limits
Derivatives
Introduction to integrals
>10th year
Finish up integrals (probably improper integrals, trig substitutions, numerical computation methods etc.)
Series and sums in calculus
Matrices
Vectors
>11th grade
Linear algebra
Statistics
ODEs
>12th year
Partial derivatives
Multiple integrals
Taylor series in multiple dimensions
Fourier series
Integral transforms

The aim here is to finish up Calc I and II and some of Calc III

>>6926312
>an education system that everybody will go through to cater to the needs of the <5% capable of benefiting from it
aka
>an education system that everybody will suffer through to cater to the needs of the <5% INCAPABLE of learning at the pace of their pears

It's that kind of bullshit that has ruined high school education in the first place and is killing college education now:

>why do we need to take unrelated electives
>why do we need to know all this theory
>why isn't college more focused on job training a practical topics
>why are there majors that aren't job titles
>why do they deny people degrees who fully paid for them
>why spend 4 years when we could do just 1
>we all need degrees to get a job, it's not fair to place obstacles to get it when we are ostracize if we fail

If you only want the equivalent of a 6th grade education, THEN FUCKING ONLY GET A 6TH GRADE EDUCATION. Don't demand that a GED/Bachelors/PhD should be at a 6th grade practical level because you look inferior otherwise.

>>6926821
>>why do we need to take unrelated electives
This is just to steal money. I have learned absolutely nothing having taken 15+ credits of humanities bullshit.

>>6926861
>but if I don't get a degree I can't get a good job
This is what people are paid to get you to believe.

>>6926866
No, ofc not. But it's easy to find one through the university and I enjoy what I'm studying. I wish I could study more of it instead of having to take some asinine literature or theatre appreciation class.

>>6926873
>being reasonable in response to my shitpost
Anon I'm sorry I did that to you. Please continue to enjoy learning.

>>6926312
>do you also think letting the average pleb never take a single math class again after 7th grade is a good idea

The average pleb ALREADY never takes a single math class after calculus if they even bother going that far as most high schools and colleges only require the 5-6th grade for a degree. Why should we pretend to give them 11-12 years of education when they are only receiving 5-7 besides to stroke their ego?

>because they aren't gonna be able to handle ODEs and vector calc in 8th grade

Vector calc and ODEs aren't much more difficult than single variate calculus and matrix algebra.

>even if they somehow manage to survive 6th and 7th

How wouldn't they? Do kids really need to spend a year on addition, a year on subtraction, another year on "big" addition and subtraction, a year on multiplication, a year on division, a year on fractions, and a year on pre-algebra like they do now? A passionate but average kid could even combine 1st and 2nd grade to go even <span class="math">faster[/spoiler].

>the point is to maximize the average level of education not the extreme top end

There's no such thing as one size fits all education. Some kid will just have to deal with only completing 6 grades of math education after 12 years and look for schools targeting that. Others should be allowed to set their sights higher and allowed to advance while leaving those other kids behind. In no case should the different populations be indistinguishable.

>>6926476
>You do not need math for most jobs

Who cares? You don't need a lot of things (e.g. sex, friends, leisure, happiness, beer) for most jobs, but that doesn't mean you shouldn't partake in them.

>>6926861
Because you picked humanities bullshit instead of something interesting

>>6926799
this MIGHT be viable if math took up a way bigger portion of a school's curriculum.

I'm pretty dumb and I managed to B calc I and linear algebra I when I was 17, this curriculum is probably not too rigorous for an average student if they spent way more time on math.

How much time in your elementary schooling was actually math study, /sci/? Not really that much.

>>6926901
The various humanities are many things, but uninteresting is not one of them.

>>6926903
I think it'd be very viable considering my experience throughout primary and secondary education.

Then again, I study at a top 10 university and found math at those levels easy.

>>6926799
Far too much repetition with the topics spread out, (how do you even spend 3 years on logic?), and the order is all over the place. That would be a massive cluster fuck if put into action. Not to mention good schools already have student taking calc III in 12th grade without that "improvement".

>>6926799
Far too much repetition with the topics so spread out, (how do you even spend 3 years on logic?), and the order is all over the place. That would be a massive cluster fuck if put into action. Not to mention that good schools already have students taking calc III in the 12th grade without that "improvement".

>>6923930
How do you modulo before times/division? Maybe the easiest way to do this would be to introduce state as a puzzle/game.

>>6925351
You're so dumb lmao it's called e because it's the base of the EXPONENTIAL function.

>>6923930
The research on Human expressions suggest that many concepts in mathematics and elsewhere can be interpreted as either...
>>A value or extent of a value
>>intensity or extent of intensity
>>magnitude or multitude
>>nesting or repetition
>>state or process
>>bounded or unbounded
>>and so on.

Multiplication,for example, can be thought of as a repetitive concatenation of objects of equal magnitudes. These objects recursively nest themselves in a super-structure that is our new value.

Subtracting from this super structure is a simple as removing a substructure of intended magnitude from our super-structure.

Pretty cool right?

There is a lot of research done on how we develop mathematical intuition.

>>6927112
That's kind of a crucial point: it would be great FOR YOU. imo the underlying problem with the American k-12 school system is, as some have suggested, the one-size-fits-all curriculum being liberally applied when individualization would allow for greater engagement and enthusiasm in academics.

>>6927935
mod 10, mod 12, mod 24, mod 100, mod 1000

>>6926924
>but uninteresting is not one of them

you're forgetting women's studies

>>6923930
>American Government and Political Science
This is retarded.
>>6923497
>World's standard mathematics education

I don't give a fuck bout america, why would you include it in math education, considering nearly all great mathematicians come from europe.

>>6923497
What all those educational systems seem to not get is, that not all people need the same mathematical knowlede in their jobs/life. Most of them, like 90% dont need something like "completing the square" or "trigonometric functions" and only a verry verry small portion actually need something like Real Analysis, Abstract Algebra
Stat Mechanic, Optics, Advance Mechanics and Special Relativity
Data Structures and Algorithms.

the classes should be divided into 3 groups:
>frist group would be what people now learn from grades 1-7 just over the time of 8-12 years
with an option to only have math every second week or so. (for your art or lingual jobs)

>Second group would learn the stuff from grades 1-10 (for jobs that need basic math)

>The third group is for the pupil who want to study math and use all that shit >>6923930
listed.

(english is not my first language)

>>6928660
political science and government studies are essential to a democracy as political consciousness means the average voter is more informed means the country runs better.

I would introduce common core

Start with algorithms and word problems and writing with units (basically they're just variables; apples and baskets, same notation). Have them translate and solve, also have them work outloud and in groups occasionally, like where one person's answer is put into another person's expression to emulate real-world teamwork; and, this can even be applied to basic addition and subtraction. Just have beginning education focus on how to communicate in math outloud and within their own work or else they're just learning by wrote memory with some singularly prescribed algorithm. These paradigms can be used all the way up into algebra. The only key difference in algebra being the manipulation of 2 or more expressions at the same time and using the Cartesian coordinate system. Learning how to do algebra isn't straight forward, but using games and gameplay analysis would help out exponentially. If games are employed it would be more important for people to work in teams, like as in sports. Working by themselves more than occasionally would end in a lot of discouragement because of the scoring and performance factors. Next up would be geometry which should go hand in hand with art projects having them use rulers, compasses, scissors, and glue (scissors and glue would actually be important for laying the foundations of engineering and conceptually working with error margins) like a mother fucker. They should be ready for a primer in physics at this point, which can then lead into properly into chemistry afterwards. I find in chemistry people have no conceptual foundation which leads them to stumble about blindly through it. Chemistry would be the pinnacle of a general education and it's the absolutely perfect platform to teach them history from the end of alchemy (my education here started with John Dalton, and conveniently he comes right after Newton) and end wherever so long as they understand how scientists played with charges and such to expand human knowledge of matter.

adding to>>6929847
..maybe squeeze trigonometry in with physics, though. idk

>>6923930
Autism speaks

Khan Academy. Nothing else is really needed.

>>6924813
This. I'm not even the average 160 IQ /sci/enlist and I still got an A in Ap Calculus without struggling.

I think parts of algebra 1 and geometry should be introduced during elementary school.

There's no reason to spend 6 years on arithmetic. By the time kids get to middle school, they'll have been doing 2+2=x for over half a decade. Then they start doing algebra and 2+x=4 looks like black magic to them. Tons of kids do the "lol letters in math how does that work" thing after elementary school.

I really like how the common core emphasizes understanding over plug and chug. Elementary school teachers probably don't know math beyond what doing their taxes requires, so there's really no way kids will get a deeper understanding of numbers if there isn't some sort of outside requirement to do so.

>>6929847
>replacing education with mindless group projects and games

https://www.youtube.com/watch?v=NbOqxQUB10A

I don't know about you guys but I was dumb until late highschool. If I had to take the classes suggested in this topic at such an early age I probably would have never enjoyed math as much as I do now. Some people are late bloomers. Maybe you've been looking forward to learning quantum mechanics since you were 8 years old, but I'm sure most weren't. Not even the geniuses who have continued a lot to science and math.

>>6930125
*contributed

>>6924813
>mfw in 8th grade being scared into thinking Pythagoras theorem would be hard

>>6927958
then it would be an x

>there are people this stupid on /sci/

>>6930184
>>6927958
>implying base e is the unique exponential

it should be N for natural exponential

>>6928660
>>American Government and Political Science
>This is retarded.

Not if you want people to have any comprehension of the world around them. Same with most everything on the list.

>>6923497
More first principles
Introduce algebra earlier
Introduce calc much earlier
Introduce vectors earlier

>>6925255
>Why take the time to teach kids fleshed-out concepts when you can just offer them a cheap, universal method instead?
A lot of this is out of the individual teacher's hands. Administration is full of retards who insist on following a script.

>>6932126
Add introduce affine spaces earlier

>>6932361

A lot of teaches would just put on a TV show and spend the day on facebook if they weren't forced into teaching something

http://en.wikipedia.org/wiki/Conrad_Wolfram#Mathematics_education_reform

https://www.youtube.com/watch?v=60OVlfAUPJg

>>6932388
>Wolfram

opinion disregarded

kindergarten
play with these legos
kindergarten senior
smaller legos
grade 1
geometry
grade 2
geometry
sums
grade 3
geometry
extensions
grade 4
counting in base 10
grade 5
fucking geometry
grade 6
geometric integer integration
grade 7
geometry
relations of ten, squares, cubes
grade 8
geometry
grade 9
geometry
grade 10
geometry and logarithms
grade 11
geometry and logic sums
grade 12
theoretical topography

>>6923497
integrate a vocabulary study system to study vocabulary math words and terminologies for each 2 weeks or week

>>6932394
it's his last name. conrad is stephen's brother. less of an egoist.

>>6932388
I disagree with him. calculation by hand may be a pointless thing if you're looking back at it, but it was a crucial example to learn how algorithms work, how numbers work, getting used to the concepts behind logic and math etc. These simple things aren't so simple for a child and if it's not done intensively the child will never get a feel for it. I doubt that typing stuff into a computer where some magic gives you an answer can replace that, although I kind of agree that many things that only "experts" could do can now be done at home or in class rooms with computers and that's fantastic to illustrate that math can be a great tool.

The problem is that Wolfram is a guy who's probably always been great at what he does. He's not an educator and he has (in my opinion) no idea how learning really works, especially in early childhood. Plus he obviously wants to sell his product.

>>6923930
I wish I had an education like this. Damn teachers had me doing algebra in fucking 9th grade!

>>6924766

I multiply:

(a1+a2+a3+...+an)(b1+b2+b3+...bn) = a1b1 + a1b2+a1b3+...+anb(n-1) + anbn

>>6926799

How are you going to teach series before teaching limits?

>>6933786

We usually try to introduce sequences and series on the tail end of Pre-Cal. We can't talk about convergence in a formal sense yet.

The idea is supposed to be that they're already somewhat familiar with them by the time they hit them in Calc.

A more "vocational" approach to math that shows how different disciplines use it and the important of things like statistics when it comes to studies and polices. By the time I had a "holy shit math is everywhere and extremely important" I was already out of high school. None of my teachers really ever talked about you do with math just you must learn this to pass.

>>6929955
In an arithmetic set the goal of group activities would be to get children to routinely communicate in mathematical language rather than purely decoding (or encoding) the same exact symbols over and over again ad infinitum. Those group activities I made mention to but did not describe would have nothing to do with feelings, and everything to do with developing English (example) skills which parallel mathematical information.

It's my theory that math skills do get highly developed in virtually all children in schooling but are routine dissociated from their native tongues. The overkill on the monotonous repetition of (solo-worked) symbolic routines not only cause people that leave school to lose their math skills at an exponential rate over time, they also result in everyone performing horrendously on word problems across the board.

Increasing abilities to solve word problems would be an accurate measure of group and communication activity success and the human-development progress. In my experience word problems emulate real-world skills and real-world problems more accurately; so, not having better math-students is a tragedy we perpetuate by putting up with, allowing, and/or acquiescing to the current state of affairs. The real world with respect to math is more like mountain climbing and the way math is taught (at least with respect to arithmetic and algebra) is like walking up and down stairs until the bottom performs are on the brink of exhaustion. Problems lined up absolutely straight in symbolic and numeric form spoil children by robbing them of work they are capable of doing on their own and are a lie to form math takes on in the real world where they are never already lined up and perfectly accounted for you 'in the wild'.

I'd have to save another post for explaining the algebra group work, but it is a more difficult argument to make. I hope this makes more sense.

me>>6934583
>until the bottom performs
*until the bottom performers

>>6934070
>A more "vocational" approach to math that shows how different disciplines use it

Trivial examples are already in every shitty primary/secondary school textbook there is. Nontrivial examples will go way over the students' heads.

Math is one of those things that you have to have faith in and have that faith rewarded in the next (school) life

>None of my teachers really ever talked about you do with math

Because math teachers come from the bottom most percentiles and don't know why the fuck people learn math in the first place...

>>6933769
did you use foil?

>>6923930
This is great,after this education we can be everything but human!

>>6934851

>Because math teachers come from the bottom most percentiles and don't know why the fuck people learn math in the first place...

I'm actually studying out of Rudin at the moment and I want to go into teaching compared to a phd simply because I'm going to start earning money sooner and because I think the whole education system is fucked in Australia. But also because the phd is a huge investment. Not everyone who goes into math teaching is bottom of the percentile, it's a nice easy profession with a decent pay and plenty of jobs going around for it where if you're passionate for math you can still study it outside of teaching hours.

>>6923930
>Religious Studies
GTFO

>>6935287

>>6935287
Oh no, someone might be educated about the world around him, can't have that can we?

This board has become flooded with underage fedora /b/ trash. Fuck this

>>6935293
>educated about the world
>after hearing QM, PDEs and stat Mech
yeah thats a fucking masterplan to teach them stuff they wont understand anyway and then just waste a year doing fuckall and talking about god and stuff

>1st grade
propositional logic

>>6935301
Religious studies isn't talking about god you fucking imbecile, it's a secular study of world religions.

My god I hate 4chan now.

>>6935330
Still isn't maths. Just b8.

>>6935330
and its as productive as talking about fucking god and doing fuckall.
>My god I hate 4chan now.
get out, you wont be missed

>>6935333
>maths
Oh, your retardation makes all the more sense now. Nevermind, keep at it anon!

>>6935337
http://grammarist.com/spelling/math-maths/

North American much?

>>6935335
>get out, you wont be missed
Of course I won't. I actually contribute quality posts to this board and you shit the place up because you're from /pol/

>>6935340
your inbred islands' vernacular idiosyncrasies are not science

>>6935344
>I actually contribute quality

>>6924970
While I agree, it should switch to haskell in 12th grade

>>6935340
I was insinuating that you are a retard because you're British.

The fact that you responded to it by confirming your nationality just proves me right.

Checkmate limey.

>>6935351
Unfortunately you are fully fucked my retarded yank bud.

>>6923930
i agree with this except way too much math. replace those with physics and comp sci.
also remove chem. chem is a joke

new age of god-tier engineers incoming

>>6935351
Such amazing use of logic.

"...maths is preferred in the U.K., Australia, and most other English-speaking areas of the world"

Guess again.

>>6935354
being a paint-sniffing half-retarded descendent of convicts is not science

>>6935360
Here's a handy list so that you can start ticking off your guesses:

http://en.wikipedia.org/wiki/List_of_territorial_entities_where_English_is_an_official_language

I'm assuming 'trial and error' is your de facto approach to solving maths problems.

>>6935353
>autist sticks undergrad courses, most of which he's probably never taken, under a grade school curriculum
>taking it seriously

>>6923930

just replace C++ with C and assembly and it will be perfect

We need to drastically improve the standards of education by dropping the insane idea that everybody should have a high school degree.

We must also make sure to teach maths using PROOFS. I remember in my first year of uni we proved loads of results we blindly used in highschool and it made so much more sense. I couldn't help but ask myself "why didn't they teach us these proofs in the first place??"

The answer is obvious : some students are too dumb to understand proofs, so to cater to that dumb minority it was decided to drag down the level of maths education to achieve "equality".

I mean, in my country (France), my dad told me that in his days (before the leftist reforms of the 80s), high school students learnt lineral algebra and a bit of group theory. Nowadays, the hardest thing learnt in high school must be derivation of functions!

>>6935407
>The answer is obvious : some students are too dumb to understand proofs
i think they simply dont care. you dont need math in your everyday life anymore because we have calculators or some nerds who do it for free.
why should sally fuckface learn to solve quadratic equations if she plans to become a nurse?
i think we should make highschool math more rigorous but fags who think they dont need it should be able to drop it after they learned the basics

>>6923497
Kindergarten-4th grade arithmetic
5th-8th grade-algebra and geometry
9th grade-trigonometry
10th grade-calculus I/statistics/math of choice
11th-optional:Calc II
12th-optional:Calc III/Diff Eq
The fundamentals

>>6935439
*8th grade being linear algebra
>implying you need calc II

>>6935432

Dividing up the high school classes such that the students who want to do well can take classes with basic proofs in them.

Classes should also be there if sally fuckface ever decides that she needs to learn how to deal with ratios and whatever else so she can give properly dosed medicine to old people when she becomes a nurse.

>>6934851
>>6934851
>Math is one of those things that you have to have faith in and have that faith rewarded in the next (school) life

None of my teachers gave me any reason to have such faith. Even if students don't understand the equations used in things like finance or engineering showing them how math is used helps understand the importance of it. Things like statistics play a huge role in deciding government policy. Math is power and students should be learning how to harness that power. I didn't learn about the power of proofs until I was way out of high school.

>>6935287
>if you do not listen to Theology, that will not mean that you have no ideas about God. It will mean that you have a lot of wrong ones

>>6935439
That's basically the UK system.

no mention of the 7 classical liberal arts?
https://en.wikipedia.org/wiki/Liberal_arts_education
>be the quadrivium
>teach people pure number, number in space, number in time, and number in time and space
>blaze dank space-age memes for your lord jesus christ
ya'll illiterate as hell

>>6935373
C is outdated and there's hardly any reason not to default to C++. Stop listening to /g/nu/drones bashing it when they've never actually touched C++

>>6935407
>I mean, in my country (France), my dad told me that in his days (before the leftist reforms of the 80s), high school students learnt lineral algebra and a bit of group theory. Nowadays, the hardest thing learnt in high school must be derivation of functions!

That was back in the days of "new math"

>>6935439
That's already what is in place at private schools and good public schools. Also, 4 year of arithmetic is too slow and 4 years of algebra+geometry is way too slow.

>>6936157
C is still used in some industrial robotics applications. They mostly use proprietary languages though.

>>6936157
I agree about c (to an extent)

But learning assembly is an incredibly enlightening experience

>>6936178
4 years of arithmetic is not too slow for 90% of students, don't be such a fucking autist, the point of an education system is to educate the majority of society not the top 1% like that autistic retard >>6923930 and the dumbfucks going along with him. The earlier you push subjects back, the more time students are going to need to be able to handle it, you should be able to cover algebra 1+2 and geometry and trig in 2 years if the kids aren't starting til 9th or 10th grade but if they're starting in 5th grade when they're fucking 10 years old you need to give them some more time. And middle schoolers aren't going to be able to handle calculus on any reasonable scale.

There's a reason it's the system already in place at good schools, they have actually done research and figured out the way students respond to best instead of just making up a curriculum that is leagues beyond the abilities of most students because if you thought classes were easy when you took them in college clearly they would be just as easy if you took them in middle school.

>>6936200
>the point of an education system is to educate the majority of society not the top 1%

Ladies and Gentlemen, I present to you pure communism incarnate! Not even the Soviets and Chinese in the peak of their revolutions <span class="math">\underline{dared}<span class="math"> to make education exactly the same for everyone like we are now.

There's no point in unified education if the top 50% rots while they wait for the bottom 50%. It's just common sense that the bottom should be separated out and allowed to complete grades slower for their 12 years of education and graduate with middle school or elementary school degrees instead. A high school (as well as a college) diploma should signify nontrivial achievement and not a right of passage based on age. If you can't cut it, you shouldn't get one.

>And middle schoolers aren't going to be able to handle calculus on any reasonable scale

Plenty of totally average kids that were allowed to go at their own pace have already successfully done calculus by the 7th grade. It's not unreasonable by any stretch of the imagination for most of the population to follow suit.

>they have actually done research and figured out the way students respond to best

No, that's just what we have right now when kids can skip pass the redundant 1st and 2nd grade math levels.[/spoiler][/spoiler]

>>6936180

It's not like a C++ programmer can't figure out how to limit himself it the C subset and quarks.

>>6936200
>the point of an education system is to educate the majority of society not the top 1%

Ladies and Gentlemen, I present to you pure communism incarnate! Not even the Soviets and Chinese in the peak of their revolutions <span class="math">\underline{dared}[/spoiler] to make education exactly the same for everyone like we are now.

There's no point in unified education if the top 50% rots while they wait for the bottom 50%. It's just common sense that the bottom should be separated out and allowed to complete grades at a slower rate for their 12 years of education and graduate with middle school or elementary school degrees instead. A high school (as well as a college) diploma should signify nontrivial achievement and not a right of passage based on age. If you can't cut it, you shouldn't get one.

>And middle schoolers aren't going to be able to handle calculus on any reasonable scale

Plenty of totally average kids that were allowed to go at their own pace have already successfully done calculus by the 7th grade. It's not unreasonable by any stretch of the imagination for most of the population to follow suit.

>they have actually done research and figured out the way students respond to best

No, that's just what we have right now when kids can skip pass the redundant 1st and 2nd grade levels in math.

>>6936167
I know that new maths has a bad reputation nowadays, but was it really such a bad thing? I'd rather math be too abstract and difficult that too watered down and simple.

>>6936317
>Ladies and Gentlemen, I present to you pure communism incarnate! Not even the Soviets and Chinese in the peak of their revolutions dared to make education exactly the same for everyone like we are now.
Funilly enough, the soviet education system was far more selective and elitist compared to the west

>>6923497
math education is a waste of money since 'math' is just made up anyway.
why waste money on that when we can use the money on paying off the entire debt instead?
what has 'math' ever done for anyone anyway?

>>6936335
Epic XD

>>6936335
keeping you alive is a waste of money since 'yourself' is just made up anyway.
why waste money on that when we can use the money on paying off the entire debt instead?
lets just harvest your organs for the benefit of everyone else.

It's been interesting reading people's thoughts on this. My two cents to all the comments about either allowing people who don't like maths to drop it early, or introducing advanced concepts earlier is that it would limit a lot of people. I did compulsory maths until I was 15/16 (It's an elective after that in NZ) so like algebra, trig, pre calc. The thing is that until I left high school I wanted to be an illustrator or a kindergarten teacher. If I had advanced stuff pushed on me I would have rejected it, but if I hadn't had the basic education I wouldn't have been able to pick up calc once I decided to study chemistry at uni. So I would say that to some extent the system works. However I would like to see more emphasis on logic, proofs, and examples of why maths is useful, as opposed to the rote learning that happens. I don't know what it's like in America though.

>>6923497

Common corea is best korea.

>>6923930
>Brain developmentally incapable of rational thought
>Vector Calculus, ODE's

>>6937255
you don't need to be logical for either of those, its just learning how to do calculations and the basic proofs behind them

>>6937255
>>Brain developmentally incapable of rational thought
>buying into Piaget's stage theory of cognitive development

You're an idiot and Piaget was a quack that didn't "believe" in statistics, past work, the scientific method, or even the very principle of cause and effect. Ordinary 12-14 year olds are capable of learning vector calculus and there are schools that do teach it to them.

>>6923497
There's a huge dichotomy between mathematics and language and reading; they need to integrate so that learning to read and speak is learning math and mathematical concepts.
The average kid also watches hours of moronic babbling on tv every day, eliminating something like that could improve learning regardless of what system

>>6923930
Great plan. New question: How to find teachers that can teach calculus to non-autistic 12 year olds LOL.
Also, the intro to Weeds. (TV show)

>>6924926
Keep fighting the good fight. Knowledge is power.

>>6937335
>implying language should be altered for your plebian attempts at scientific discovery and industrial propagation

do you even quantum grammar

>>6924958
Your system is shit.

>>6930125
I am also a late bloomer.

>>6937851
Postdocs; supply is already 7 times the demand for them.

>>6938473
>teachers that can teach calculus to non-autistic 12 year olds
>supply is already 7 times the demand for them.

I know how bad teachers can be, and I'm fairly certain that most of them are too sour to be able to do this without losing their temper/exaggerating.
I know.
The IB is kinda new to my school and the teachers are all like: "Well ACCORDING to the IB CURRICULUM you are supposed to KNOW all of this COMPLICATED stuff." or "You are going to FAIL if you don't do ALL of your homeworks. The IB isn't a JOKE"
Replace "IB" in both of those with the name of this new change our savior proposed and you'll see our future maths teachers.
We were learning about cell parts (nucleus, cell wall etc.)

>>6938507
>I know how bad teachers can be, and I'm fairly certain that most of them are too sour to be able to do this without losing their temper/exaggerating.
Which is why all teachers should be purged and replaced with mathematicians/scientists that know and care about their subject.

Many PhD holders want to research and teach but they simply can't find positions even though they are applying to universities on every inhabited continent. A perfect solution to the problem of educated professionals truly desiring to teach and research and the problem of terrible uneducated unmotivated teachers failing to teach students is obviously to replace high school teachers with professors. They can perform research activities at nearby university while satisfying their teaching obligation and earn their paychecks by teaching high school students on the state's dime.

More research gets done, there's reduced "publish or perish" pressure that will improve the quality of the work done, and students get better educated and inspired to go into STEM. 3 birds with 1 stone.

>>6938792
Goddamn, that's a great idea.

This would never fly though because >muh unions.

Fuck 95% of public school teachers.

>>6936317
this

http://youtu.be/aaFAUeftTKs?t=5m2s

>>6938792
I take it you've never tried to lead a group of children, or had any interaction with a postdoc

>>6939139
>children
>15-18 year olds

Yeah, no.

>>6935439
This is what some of the really smart kids I knew did. Except that my school didn't offer anything post calculus 2 (I think thats AP Calculus BC?).

>>6936317
Top autism. The smart kids do take more advanced classes. It's not my fault you were one of the bottom 50% and was stuck taking shit classes and convincing yourself that you're actually smart.

>>6939225
>The smart kids do take more advanced classes

Pretty much only in the 11th and 12 grades. And even then, it's quite limited and not really much more advanced.

>>6939225
Honors classes are not "more advanced classes"

>>6939241
There were people in my public school who started taking Calculus in 10th grade. That's pretty good for an unranked public school who never met CA standards. And then there were people taking Algebra 1 in 12th grade. The point is that people don't get equal educations. Smarter people take more advanced classes anyway. If you couldnt even take Calculus in early high school, when chances are that if you did good enough previously you would have had the option to, what makes you think that you'd be able to handle infinitely more difficult topics at that same age? You already had the opportunity to take more advanced classes, but you weren't deemed ready. It makes no sense to say that you should have been taking even higher level classes.

>>6939572

see >>6939117, 4th grader can pass the Math SATs but still forced to take the same times tables classes as his peers and must wait 6 years to learn something new.

Grades 1-6 do not have a choice beside the rare student that skips a grade and that is where most of the time is wasted in math education. Students only get to differentiate themselves in high school and only in a very minor way.

>Smarter people take more advanced classes anyway
>had the opportunity to take more advanced classes

No. they <span class="math">and[/spoiler] their parents have to fight tooth and nail to get the school the cave in and let them do so. It's rare because schools <span class="math">\bf{ \underline{ HATE } } [/spoiler] to do so.

>It makes no sense to say that you should have been taking even higher level classes

It does if you have already mastered lower level classes.

>>6939225
In highschool I certainly wasn't even in the top ten with respect to gpa or IQ yet I was only one of three (500 student school, ~90 people in grade) that were allowed to go to another school to learn AP physics 1. The highest we had at our school was honors, this was in 2009.

>>6939139
If they're old enough to sneak drinks and steal cars, then they're old enough to be abused by postdocs.

>>6939572
And after finishing Calculus in the 10th grade they're SOL because the school is out of math courses. They might be able to do the commute to a community college (at their expense) thing for 11th grade and do Vector Calculus and ODEs but they still are going to be left with nothing to do in 12th grade.

>>6940740
linear algebra and differential equations in 12th grade? i'm taking those next quarter along side vector calc, so if we split them into 2 years for highschoolers i don't see what is so bad.

the thing is though, very few kids would ever get so far.

>>6941813
** note: im taking vector calc 1 and linear algebra, then differential equations and vector calc 2

2 quarters, not all in one, sorry if confusion

>>6941813
Vector calculus doesn't need a whole year and matrix algebra can easily be combined with ODEs.

>>6938812
Teachers Unions want a total monopoly and value decades of mediocrity over fresh teachers that actually understand the material they teach
Left Wing wants to abolish all private schools, bring back busing so suburban kids are put in danger at ghetto schools and gang-bangers can run wild in hereto crime free schools so people will care and then their money will solve everything, and remove any program, aka advanced programs, that don't the have perfect racial mix because clearly calculus professors everywhere are racist since nearly none of their students are black.
Right Wing wants to eliminate all public schools for private schools only so that they can then later defund any system to make private schools affordable since people shouldn't be entitled to education.
Parents demand that each of their children be top of their class and any exam or class that shows they are not be abolished as unfair and that teacher fired long before they dare consider their child might be an idiot.

No matter who gets their way or what compromise happens, education is only going to get more fucked.

>>6944168
>education is only going to get more fucked
General theory of tragedy of the commons, or what?

>>6944168
>remove any program, aka advanced programs, that don't the have perfect racial mix because clearly calculus professors everywhere are racist since nearly none of their students are black

Reminder that this is already happening everywhere

>New York City school cuts popular gifted program over lack of diversity
>http://www.washingtontimes.com/news/2014/jan/30/nyc-school-cuts-popular-gifted-program-over-lack-d/
>http://www.nytimes.com/2013/01/13/education/in-one-school-students-are-divided-by-gifted-label-and-race.html?pagewanted=all&_r=0

>>6944250
I don't think this is related to the tragedy of the commons.

>>6944250
More like the four horsemen

>>6945611
It's not.

>>6936157
>C++
>>>/web developers/

If you don't use FORTRAN, you shouldn't even try talking about science.

, Counting, Arithmetic, visual math (algebra but with computerized images) Calculus, Geometry and Trigonometry all in 1 2 and 3 classes. Learning the trigonometric applications where pertinent to other things. Higher Maths 1 might be Geometric proofs, + Basic trigonometry, accelerating from there.

>>6947016
But also with like basic Calculus functions. When Alg is still hot on the mind.

>>6947006
>> FORTRAN
>>Science

Yeah. Fuck your bullshit. C, C++, R, and Julia are our new standards. Only legacy systems run on FORTRAN

Even the groups that develop mission critical software, or expensive research have made the leap from Ada and Fortran to the 21st century.

>>6947006
>C++
>web developers

You're fucking retarded

>>6947016
>>6947025

.... what?

>>6924926
I'm becoming like this anon. I never really understood the importance of math until my algorithms course where comp sci and math started to click for me. Now I want to take more math classes and possible double major math and comp sci.

I believe the issue lay within the difference between two mindsets, the first is "i don't believe i'm good at math" the second being "I believe the teacher taught me wrong, or i just missed a concept due to being absent".
The first mindset discourages people from actually trying, while the second encourages people to try again even after failing because they believe they can change.
The solution to the first mindset would be to discourage teachers/parents/whatever to not say "ayyy ur just not gud at math ur probably good at other shit."
>>6947006
COBOL 4 lyfe bro

>>6935407
In the US, the standard methods of teaching proofs are simply retarded and get in the way of understanding. Kids are taught to memorize some shitty formulas and vocabulary words, and it's left up to them to construct an argument for why something is true. If we're going to teach proofs in high school, there should be more focus on the method of how you prove something and less on the cargo cult of "Theorem 2.1, Definition of Angle Bisector, Multiplicative Property of Equality, etc." as if those phrases mean anything to the average kid and are actually a rational way of proving anything.

>>6949707

And there's a third mindset: "I don't believe I need to know any math past multiplication and division for high school or life". And it's spreading...

>>6921547
>http://www.chieftain.com/opinion/3121748-120/students-mathematics-diploma-district
>School to reduce by one the mathematics credit requirement for students pursuing a diploma
>“The principals shared the graduation requirement regarding math is not serving students well,”
>In the grand scheme of things, it may well be that for these non-collegiate students, it’s not the quantity but the quality of the mathematics education that counts. And as long as the students are proficient in the basic mathematics functions — addition, subtraction, multiplication and division — are properly equipped to take the next steps in their lives, perhaps the reduction is for the best.

>>6925255
Discreet mathematics should be taught in middle school and high school
Took that in college and holy crap I swear I could read math like it was English

>>6926885
That's why they have private schooling magnent schools and home schooling

>>6950031
I think the real issue lies within the answer every teacher gives regarding most subjects: 'it is the way it is, just read the text book and memorise it.'

People don't like that answer and all it does it make kids who are good at memorisation prevail, whereas those with good critical thinking but subpar memory get discouraged from asking questions for long enough and they stop caring. A good amount of my friends had/'ve this issue and now they rot away in retail wishing they did something else.

This is of course, ignoring those who have no wish to learn anything which is not a cause of the education system.

Yes memory is important, but not nearly as much as it used to be.

>>6950139
>That's why they have private schooling magnent schools

They often don't start early enough, they tend to not try hard enough, they are not very common, and they're completely out of pocket.

>home schooling

The lack of peer interaction is terrible for kids. Also, who's got time to teach their kids everything?

>>6950112
>Discrete mathematics should be taught in middle school and high school

Way too late. It should be taught near the end of Elementary school at the latest.

It's trivial enough for any child to fully understand it.

>>6951081
most computer scientists I talk to say discrete math is the hardest subject they have ever taken

>>6923497
As far as I understand the only reason we have children take exams at the same time is so that they don't get the chance to cheat off each other and ask what the problems were. But these days we can easily make computer generated tests that are randomly unique to each student.
1. Have each child self-learn the material at his own pace
2. The children just take the computer generated tests when they are comfortable with the material
3. Each child gets to focus on what he needs to learn instead of being stuck in the purgatories of being too far ahead or too far behind
4. Everyone graduates 2 years earlier because they don't waste time on things they already know and/or things they can't understand
5. PROFIT

you guys are seriously overestimating the average kid's intelligence

>>6951106
Most kids aren't dumb, they are just unmotivated. If you can trick the kids into learning, they are damn good knowledge sponges.

>>6951093

Because CS majors are fucking retarded

Give the child 6 books to read.
Algebra by IM Gelfand
Functions and Graphs by IM Gelfand
The System of Coordinates by IM Gelfand
Geometry part 1 and 2 by Kiselev

Then send them off to university.

>>6951155
Oh, I forgot Gelfand's Trig after the Geometry.

>>6951155
>>6951157
This
math is way simpler than educators make it out to be.

>>6929294
Yeah, but it's not part of a mathematics program.

>>6951155
And Polynomials by Barbeau

1st grade:
Beginning Addition, subtraction, division, multiplication

2nd grade:
Advanced addition, subtraction, division, multiplication with an intro to Algebra

3rd grade:
Algebra with beginning Geometry and Trig

4th grade:
Geometry and Trig

5th grade:
Calculus I
C-Progamming

6th grade:
Calculus II
Linear Algebra
C++ programming

7th grade:
Calculus III
Physics I
C++ Programming advanced
Intro to Java

8th grade:
Differential Equations
Physics II
Advanced Java

9th grade:
Physics III
Python
C++
Java

10th grade:
Accounting
Chemistry

11th grade:
Review of Calculus, Algebra, and Physics

12th grade:
Second year of review of Calculus, Algebra, Physics

End of 12th grade final where you must show comprehension of these subjects to pass high school.

College:
Remove remedial courses of Algebra, Calculus, and Physics.

>>6951638
Education doesn't work like that.

>>6924970

Within two generations we'll become literally transcendent.

>>6951667
Yes, a bunch of programmers using the worst language in existence with no math background.

>>6951106
>you guys are seriously overestimating the average kid's intelligence

You are seriously overestimating the average math class' difficulty and underestimating the tremendous amount of time that's wasted in school.

>>6951674
>worst language in existence

Clearly you've never coded in it and have no idea what you're talking about

>>6951675
Forcing kids to do that much work on math at that age would cause a lot of problems. The best course of action would be to create AP courses at younger ages. Not all kids have the motivation to go at such a fast speed.Most kids don't even like school.

>>6951684
It's a convuluted mess.

Kids should just learn C while learning Algebra. Not C++.

>>6951093
>most computer scientists I talk to

There's your problem.

>>6951638
>Java
>needing multiple years to learn coding
>no math past 8th grade
>calling ODEs "Differential Equations"
>review year
>review yearS

I just vomited a bit

>>6951687
It's the same fucking thing. You can just code in a limited subset of C++ in the beginning and expand it when you're ready and want to. C is outdated for 99.95% of programmers.

https://www.youtube.com/watch?v=KlPC3O1DVcg

>>6951695
Of course the autist who created it is going to say that.

>>6951688
>implying it doesn't take at least 10 years to be a great coder
>implying this isn't setup to get every kid ready for college
>implying everyone needs higher level Math than Calculus

Grade 1:
Math 1
Physics 1

Grade 2:
Math 2
Physics 2

Grade 3:
Math 3
Physics 3

Grade 4:
Math 4
Physics 4

Grade 5:
Math 5
Physics 5

Grade 6:
Math 6
Physics 6

Grade 7:
Math 7
Physics 7

Grade 8:
Math 8
Physics 8

Grade 9:
Math 9
Physics 9

Grade 10:
Math 10
Physics 10

Grade 11:
Math 11
Physics 11

Grade 12:
Math 12
Physics 12
Literature

Hello Alpha Centauri!

>>6951827
>>implying it doesn't take at least 10 years to be a great coder

>implying time in class can substitute for experience after your first 1-2 courses

>>6951105
>Having the resources to teach each individual child

>>6925351
Euler claims it doesn't stand for his name, but we all know he's lying. And dead.

>>6925721
>Thermidor
What? Never heard of it. Care to explain more?

>>6952176
>Thermidor : a moderate counterrevolutionary stage following an extremist stage of a revolution and usually characterized often through the medium of a dictatorship by an emphasis on the restoration of order, a relaxation of tensions, and some return to patterns of life held to be normal

Parents couldn't understand it and demand it be removed. The counter movement won. Their theme song:
https://www.youtube.com/watch?v=UIKGV2cTgqA

>>6923497
1addition, subtraction
2multiplcation
3division, modulo
4algebra
5 algebra
6 programming in python
7 matlab
8 calculus using computers
9 linear algebra using computers
10 objective oriented programming in Java
11 digitial logic
12 microprocessor design


computers can do math for us, why do it by hand

>>6952202
Ah, I see, thank you.

>>6952212
>12 microprocessor design
wow, way to make >>6923930 look like a normal well-adjusted not at all autistic individual

Really important is to get children used to numbers and letters at an earlier age than 1st grade. Lots of videos (muppet style singing with stars) that the kids can sing/dance along to.

Get number counting inside their heads as a melodic pattern..

'12345, once i caught a fish alive.. 123 o' leary...'
They dont have to learn by rote in nursery, but to associate numbers with fun.

I think this is important anyway...

>>6923967
>inb4 overly ambitious, verging on autistic suggestions which fail to take into account that children have lots of other subjects to juggle and may not be interested in the subject matter.

I think the idea is simply to advance math curricula at the expense of other subjects. It blows my mind that the average adult cant differentiate an exponential equation yet can quote Shakespeare.

Protip: knowing Shakespeare is the most useless skill in the universe. Knowing math is not.

As for OP's question, quite honestly the way I'd do it is to go through the tax numbers, and see what kinds of math generate the most tax dollars. So I'd imagine that math for business and accounting would be really the first subject you'd want to nail; which would probably be a lot of simultaneous equations and expected value calculations. Then you'd need math for engineering and science that makes the businesses possible, so probably a bit of stats, calculus, advanced algebra. I'd probably have a rule that you can't do the science until you've passed a prerequisite math course. A lot of the other subjects I'd quite simply slash to make way for math.

The fact is I'm not just some autist with a hard on for math. I'm actually a biochemist; and consider myself an ordinary mathematician. I was horrified to find as an honours student, in a department full of tenured professors that I was the only one capable of basic calculus. We're failing on the math front guys.

>>6923930
huehuehue

>>6952489
B4 anyone gets their nose out of joint because of the hiding I just gave the english curriculum, I should point out I DO believe in teaching english up to a level of basic literacy. It's just the literature side of things I believe has no place in school. Likewise for art, drama, music, history and geography.

I know /sci/ is a predominately left wing board, and sometimes my right leaning politics gets me into trouble here; but I'd really like to see a bit of economic rationalism applied to the curriculum. The entire edifice of scholarly historical study probably hasn't made enough economic impact to pay for a single nations high school history teachers. The Haber process on it's own would have paid the salaries of every high school chemistry teacher on the planet for their whole careers many times over. I think that makes it clear which subjects should be taught in our schools, where our educational interests should lie, where our tax dollars should be going. If kids don't like it, tough. No one ever said you had to like school.

>>6952494
Being well read and versed in history <span class="math">is[/spoiler] important for society

>>6952489
>>6952494
>>6953397

Learning English and History is very important, but they should be subjects that you learn quickly and get out of the way.

1st grade to 5th grade:
Basic to intermediate History and English

6th to 8th:
Selected topics of English and History that are fundamental to society as a whole.

9th-12th:
They shouldn't even be required to graduate or learn.

>>6953397
lol

>>6953516
>English
>Muh Storybooks
It's 2014 bro, no one looks to storybooks as the medium that defines the age.

>>6953528
>implying reading doesn't expand critical thinking, helps with creativity, and makes you a better person

>>6953531
>This is what plebs actually believe.
That's what mathematics is for you plebby pleb pleb.

>>6924970

>>6937274
>>>>you don't need to be logical for a subject rooted in logic i.e. math

>>6923497
I don't know man, I never studied once for math through highschool. It all just seemed to make "sense" to me.

My friends used to joke that I was autistic, long before it was a meme on here. Thankfully I'm not.

>>6923770
>Too much emphasis on tricks and formulas. People in my age group tend to say "cross multiply" like it's a religious invocation and don't even understand why it works or when to use it. People who are shit at math can still recognize the quadratic formula but they can't solve a linear equation for the unknown. This is a bad sign.

THANK YOU jesus christ this is the fucking problem.

>>6923930
I wish I had this...

Kids I think are totally capable too but there's so much of a concern about hurting peoples feewings, kids might think they are dumb

but they are not dumb, america just has a laziness, don't-give-a-shit culture.

I am still fiucking pissed to this day about how I was held back in math a year. I wanted to take precal (which I already knew a lot of the fucking course material) in the same year as algebra 2 (which was a trivially easy class) and they wouldn't let me because alg2 is a prerequisite of precal.

Like fuck you too.

>>6924798
>successful people post on a mongolian throat-animation fetish rehabilitation messageforum

>>6953929
>Linus
>successful

HAHAHAHA

>>6951695
not that I am nay good or belong in any of the smart boards

but I think that with C, like in ASM, you have to think about talking to the computer. Less high level math thinking like haskell, more pointers and shit.

So maybe both of these things are useful

Haskell and C live in perfect harmony

>>6953516
>1st grade to 5th grade:
>Basic to intermediate History and English

Terrible Idea. English skills take much longer to learn than the 5th grade and history above "Columbus sailed the ocean blue in 1492" level is meaningless to a child with limited exposure to the world and people.

That said, less in-class time could be spent for high school English where kids can be responsible for keeping up with the readings on their own by having only 1-2 classes a week to discuses the literature as a group. The extra time could then be spent on more history or math.

>>6953397
>Being well read and versed in history is important for society

Says you. This is such a glib statement, you've just said it and left it with absolutely no corroboration or citations whatsoever. Why should I take you seriously, or indeed, why should any of us give your smug little one sentence post the time of day?

Quite apart from that, lets say its true. Lets say that being well versed in history is important for society. What has that got to do with anything?? Lets understand what school is. As a parent, there are institutions which can legally kidnap my children for 6 hours a day, five days a week. We let this slide, because we like the effects of raising the next generation of taxpayers; in order to get my free police force, I have to send my kids to school to pay for it. I get it. But that's the deal, and no more. You ONLY get to teach them that which turns them into good taxpayers. That's it. Not one second more. Whether or not it's good for society is irrelevant, and quite frankly none of your business- that's my business as a parent.

The consensus ITT seems to be that we need to spend more time on math. So really, the path to reforming the math curricula is really a path to reforming the entire curricula to make way for better subjects.

It's easiest to start with english. One should only do english up to the point they can read and write fluently, after that point english could be limited to a single comprehension class a week, where students would dissect say, a margazine article of a technical nature. Everything else goes.

After this sport. I'd have it as 3 45 minute sessions of powerlifting per week, followed by 15 minutes of HIIT. Many students are going to be going straight out into labouring jobs, knowing how to lift heavy with correct form would be an excellent employable skill, being fit enough to do it all day would be better. You could achieve this with 3 hours a week.

Then you'd have vocational training, which would be a class devoted to training students to use the most commonly used tools in industry. I would expect students to learn how to drive a car, how to touch type, use a drill, etc in this class; essentially a trade class. Maybe devote 10 hours a week to this class, perhaps more for talented students that are failing math.

The remaining 11 hours of the school week would be all math and science, teaching students how to maximise their income and tax generating potential. All other subjects get cut.

>>6954627
Take your autism meds

>>6954627
jesus christ anon

your entire view of reality is backwards

sending your child to school is not paying your dues to society for providing you with your autismbux and police protection by allowing them to be brainwashed into good little taxpayers

it is in no way an imposition on you, if you dont want your kids to go to school there is absolutely nothing stopping you, you can homeschool them or send them to private school the absolutely only requirement is that you give them some kind of education and dont let them grow up as ignorant as you

public school is for your child's sake, it is so even if a child has the misfortune to be born to hopelessly autistic parents like yourself who are too insane or just stupid to care about his education, he still, at least, has a chance to learn the basics and maybe if he has a good teacher or finds some really good self motivation might be able to go to college and succeed despite getting no support whatsoever from his retard dad

public school isnt an education but it is a necessary condition that allows students to access real education and history is a part of that, it is certainly not mandatory brainwashing to turn students into profitable taxpayers considering it is not mandatory

>>6954671
>talented students that are failing math

You're baiting way too hard

>>6955827
>You're baiting way too hard

You missed the context. I was referring specifically to vocationally talented students. I remember a lot of kids at school who would've made great mechanics but couldn't pass math if their lives depended on it. I would refer to these children as "talented students who are failing math".

>>6955350
>it is in no way an imposition on you, if you dont want your kids to go to school there is absolutely nothing stopping you, you can homeschool them

Illegal here. So no.

>as ignorant as you

I have a PhD in molecular biology. I am extremely educated. Many things I have been called in life, ignorant is generally not amongst them.

>hopelessly autistic parents like yourself who are too insane or just stupid to care about his education

I care very deeply about my children's education. That's why I don't want their time at school wasted on subjects like english literature.

>a good teacher or finds some really good self motivation might be able to go to college

My daughter has an IQ in the 70-80 range. She has buckley's chance of making it to university no matter how good her motivation. My son, maybe, but I doubt it. He doesn't really have the temperament, and seems generally academically uninterested. The other two are not school age.

>it is certainly not mandatory brainwashing to turn students into profitable taxpayers

I would never refer to turning my children into productive members of society as "brainwashing". It is however a job I'm simply not qualified to do myself; however, I do insist that not a second of my childrens time is wasted on useless pursuits like english lit. We read at home.

Also, for the record, can we end this 4chan obsession with using the term autism as perjorative? I am actually mildly autistic. It in no way effects my parenting.

>>6923497
>K - 1st Grade
Addition, Subtraction

>2nd - 3rd Grade
Multiplication, Division, Fractions, Roots

>4th - 5th Grade
Algebra and Basic Logic

>6th Grade
Geometry

>7th Grade
Higher-Order Algebra, Combinatorics, Basic Statistics

>8th Grade
Trigonometry

>9th Grade
Linear/Matrix Algebra

>10th Grade
Limits and Series

>11th Grade
Differential Calculus

>12th Grade
Integral Calculus

>People keep on continuing this mindset that in order to educate the population better in math we need to improve how math is taught or delivered.

Kek, ask any teacher, you need to change society and how it views education before you can even accurately decipher how that education is truly being recieved by them.

Change education anyway you want but until you change the parents and students mindset of learning, it won't matter how well it's delivered.

Oh wait, we can't blame the parents or they won't vote for a certain politician that told them they're being retarded and shouldn't have had a kid in the first place.

>>6923497
Inspired by a Simpson's episode.

Put everyone in hexagonal learning pits where food is dispensed as a reward for solving problems. People end up in their ideal jobs, including systems analysts, who perpetuate the system.

>>6955855
>It is however a job I'm simply not qualified to do myself; however, I do insist that not a second of my childrens time is wasted on useless pursuits like english lit.
You don't get to insist though.

Because as I just explained, and you seem too autistic to comprehend, schools do not exist to serve you, they do not exist to impose on you, they exist to serve your children, and since we live in a democratic society the content taught in schools needs the approval of the majority of society.

Now, this is gonna be difficult as your autism clearly makes understanding nuance a challenge for you, but here's the thing, most people don't give a fuck about educating their children, don't give a fuck about reading, will never have their kids read or appreciate literature and if left to their own will raise a generation of complete illiterates. However they have, at least, basic awareness that this is the case and that having a generation of complete illiterates is undesirable (that's a different discussion, don't argue with me, take it as a democratic decision by the majority of society that is binding because of its democratic approval regardless of whether you disagree or not). So, to avoid raising a generation of illiterates, schools have to teach some form of literature and language appreciation.

It must be very difficult trying to raise children with high-functioning autism, the way you view the world is just perpetually at odds with the way everyone else does and it's a constant balancing act to push your autistic views on your children while not taking it too far and subjecting them to social ridicule, you sound like you're at least making an effort and I wish you good luck.

>>6955861
>Splitting elementary calculus over 3 years

Why?

>>6923770
I'm a tutor at my university.
I tutor College Algebra, and Pre-Calculus.
(Basically, 2 of the easiest basic courses)
I see this a lot. People have no idea how problems work, and when stuck they start reciting random bullshit tricks, like cross multiplication, or cancelling terms that don't cancel. Some of these people even try to take numbers and terms out of parenthesis like idiots. And these are university students, mind you.

>>6955902
Vector calculus, differential equations, and other higher maths aren't necessary for 99% of careers. Hell, even calculus isn't needed for most.

I still think it'd be nice for students to have learned basic calculus by the time they finish high school and that being the case I'd rather they take their time with it.

>>6924809
It's just a mnemonic to help students understand the basic principle - when you multiply two binomials you multiply each combination of terms, and that this carries over into higher order problems (though not as simply).

It's the same principle as using "xyzzy" to help students remember the basic format for taking cross products.

>>6955855
>molecular biology
>extremely educated

lel

>daughter has an IQ in the 70-80 range

I see it runs in the family

>I am actually mildly autistic

And it shows

>It in no way effects my parenting

If I knew where you lived, I'd call child protective services myself.

>>6955861
>>6th Grade
>Geometry

What for? If you already learned logic in the 5th grade, then there really is no reason to spend much time practicing pure geometry as many better tools have been invented since the time of Euclid to solve actual geometric problems: i.e. Analytic Geometry, Trigonometry, Linear Algebra, and Calculus.

>>8th Grade
>Trigonometry
>>9th Grade
>Linear/Matrix Algebra
>>10th Grade
>Limits and Series
>>11th Grade
>Differential Calculus
>>12th Grade
>Integral Calculus

Those subjects can be done in half of a school year tops and shouldn't take more than 2 years to finish together.

>>6955911
Then let them finish math early; they won't forget it as their HS science classes will now, hopefully, use it and offer constant practice. Why would punish everyone else by taking 3 months to 'learn' the chain rule?

>>6955867
>ask any teacher
They're part of the problem: >>6944168

Teachers will never support the idea of separating out the intelligent kids for higher learning and viciously and vigorously fight against it. Smart kids in unchallenging classes just mean all the less work for them while providing more options will mean the need for more teachers and thus less money coming their way.

>>6955991
>What for? If you already learned logic in the 5th grade, then there really is no reason to spend much time practicing pure geometry as many better tools have been invented since the time of Euclid to solve actual geometric problems: i.e. Analytic Geometry, Trigonometry, Linear Algebra, and Calculus.

I'm not that guy but synthetic geometry has come a long way as well and all of the things you listed are really only useful for models of Euclidean Geometry, only a tiny part of synthetic geometry. Consider for example finite geometries or projective geometries (which can be finite, infinite, discrete, or continuous).

http://en.wikipedia.org/wiki/Finite_geometry
http://en.wikipedia.org/wiki/Projective_geometry
http://en.wikipedia.org/wiki/Synthetic_geometry

Regardless, if you're only interested in Euclidean Geometry (sad), then I still definitely agree that teaching Euclid isn't a good use of anyone's time. Nowadays, there are much better axiomatic systems that don't have glaring holes like Pasch's Axiom.

>>6923497
Start top to bottom, not the other way around. First topic in kindergarten: explaining an unresolved problem at the state-of-the-art. Work downward from there. Points are given when a student can truly decorticate the complex problem into smaller problems (which is a clear sign of understanding) rather than by doing rote learning. Exams also don't need to be designed based on the curriculum anymore, since the problem was started back in kindergarten. After the downward pass, it's easy enough to work backward to the initial problem and yield a solution. As a bonus, it can serve as efficient, distributed problem solving for the math community (i.e. no one person needs to poor out decades of their time on a problem they have no interest in, kindergartners will solve it).
In college, the students will have all the material they need to actually perform real research already.

>>6956031
I would call a class studying projective/inverse/hyperbolic/elliptic geometries, "college geometry" or "non-euclidean geometry", and it's not something students would be ready for after only simple algebra.

>teaching Euclid isn't a good use of anyone's time

It's great for practicing reasoning and logic visibly but shouldn't be treated as the go to problem solving tool for geometry.

>that don't have glaring holes like Pasch's Axiom

If it was so glaring, it would have been discovered centuries earlier. It's not like Euclid an obscure text...

>>6951155
HOly fuck i got the algebra book by gelfand right on my desk right now, didn't know it was so good.

Whats the best book for trigonometry and precal by respective authors?

>>6956024
There are quite a few problems with the core idea anyway. For one, much like better schools are easier to get good grades in (thus, if you start in a shit school, you can cascade into being unadmittable at good colleges), advanced classes could entail such things as more interesting topics and better teachers, which are both conductive to improved performance. You're forcing good kids into the dirt because some asian kids cheated in their exams and you didn't notice.

>>6953587

This would be a nice gif if I were an ant.

>>6926799
>some of Calc III
I think you have all of Calc III if you are including basic vector Stokes' stuff in "multiple integrals".

>>6926885
Have you ever tutored high school kids in math? I have, and let me tell you: *some people just don't get math*. It doesn't matter that vector calc is just calc with indices, because some people don't GET regular calc!

>>6932368
Any child knows what a basketball is. Simply generalize the basketball to the open ball on R^n. Boom. Manifolds in middle school.

For reference, I'll post how I was taught. I'm a senior in high school at the moment (18) so it is very current
The American Educational system, ladies and gentlemen:
>Kindergarten
No math at all. Colors and shapes and alphabet.
>1st Grade
the numbers. Up through thirteen. Was basically told nothing came after that srs
>2nd Grade
handwriting drills on how to write the digits
>3rd Grade
TI just remember these cool ass sheets and speed quizes that tested how fast we could add and subtract
>4th grade
multiplication/division
long division raped me I cried in class once lol
>5th Grade
area and volume of shapes
>6th Grade
coloring in graphs and plotting points on a graph. No functions yet.
>7th Grade
More work on volume/area
>8th Grade
Algebra I (I had to test into this, most took Math 8)
>9th Grade
Geometry
>10th Grade
Algebra II
>11th Grade
Pre Cal. Mainly Algebra II plus trigonometry
>12th Grade
I'm in Calc BC (like Calc 1.5)
Most are in Calc AB (Calc I). They spent a whole semester learning derivation.

there you go, /sci/

>>6932399
>theoretical topography
Topology?

>>6956041
This is complete idiocy. You'll have a bunch of kids trying to figure out what fucking Hausdorff space is but can't divide.

>>6955909
I tutor as well. People have so many problems with word problems. "I wasn't taught this" is the worst thing in the world. Also people thinking 1/(a+b)=1/a+1/b. That one gets me every time.

>>6956082
>You'll have a bunch of kids trying to figure out what fucking Hausdorff space is but can't divide.
>I tutor
Maybe you shouldn't.

>>6956078
Don't say derivation when you are talking about differentiation. They are related yet distinct concepts. (Think square vs. rectangle.)

Did your school offer AlgII/Trig? Its AlgII + 1 semester of trig. When I was in BC, we concluded that it was the hardest class in the school. Looking back, it was really easy. I think the people here forget that in hindsight everything is easy.

>>6956088
Explain. It seems to me like you want to show little kids something like the Riemann hypothesis and then let them figure it out?

I'm confused by "unresolved problem at the state-of-the-art".

>>6956024
Teachers are all FOR segregating kids into those that are motivated and those that aren't. The problem? NO ONE WANTS THE SHIT KIDS.

>>6956072

Which is why:
>Some kid will just have to deal with only completing 6 grades of math education after 12 years and look for schools targeting that

NOT EVERYONE SHOULD GET THE <span class="math">SAME[/spoiler] EDUCATION. Forcing this kind of educational communism, where something not everyone can do is dropped and everyone must succeed, is fucking retarded.

>>6956090
>It seems to me like you want to show little kids something like the Riemann hypothesis
Correct, for instance.
> and then let them figure it out?
Inaccurate. The point of a teacher is to teach. You would first explain the concept at a high level, then cover the immediate prerequisite concepts again at a high level, allowing a slightly lower view of the original problem, and so on and so forth.

This format does let students who care actually research something useful, but it's not a prerequisite. It also always keeps a tangible goal in mind instead of teaching things which are inherently meaningless. Some anon posted an article by someone lamenting the current state of math education effectively for this reason. Anyway.

A tutor who is not able to explain a concept without getting bogged down in the details is a very poor tutor indeed.

>>6956109
>not believing in the survival of the fittest
I bet you're bayesian, too!

>>6956050

Synthetic geometry approaches all of those using an axiomatic approach. It is often used as an introduction to axiomatic systems, logic, and proofs. Personally I think it would be easier to teach than geometry the way it is currently taught.

Go pirate Venema's Foundations of Geometry and skim the first couple chapters. The material is very approachable.

It wasn't discovered because until the last few centuries mathematics was considered as just a way of describing the real world. People believed that it could only describe the real world and that anything else (like non-euclidean geometries) had to be inconsistent. Logic wasn't formalized till the 1900s and people didn't really start looking at the bigger picture till the late 1700s. Basically what it comes down to is that mathematics was too touchy feely back then and axiomatic systems weren't approached nearly as formally as they are now.

>>6956112
>implying education isn't aimed at lowest common denominator

I got some bad news for you

>>6956110
I don't tutor the Riemann hypothesis. I can't see how it is possible to explain graduate mathematics at a high level without getting bogged down by details.

I don't know any number theory. If you do, do you mind writing a few lines on how you would introduce the Riemann hypothesis to schoolchildren? I'm quite interested in your response.

>>6956054
>You're forcing good kids into the dirt because some asian kids cheated in their exams and you didn't notice

Cheating Asians only come here for college. AA are normal

>>6956107
>Teachers are all FOR segregating kids

Nope. See >>6939117

For comparison to the American course, this is what I studied in Australia.

>kindergarten
Shapes, counting, and so on
>Prep
Counting, addition, shapes
>Year 1
Subtraction, addition
>Year 2
Multiplication, chance
>Year 3
Multiplication, Division, Fractions, Decimals
>Year 4
More fractions, decimals, order of operations, area and volume, powers, roots
>Year 5
Very basic algebra, long division, plotting coordinates
>Year 6
Simultaneous equations, the Cartesian Plane
>Year 7 (start of high school, here I was placed into an accelerated class so things go faster than normal)
Algebra, introduction to functions, area and volume, ratios
>Year 8
Introduction to trigonometry, more algebra, angles
> Year 10 (skipped year 9)
Trigonometry, functions, polynomials, radians, indices

In Year 11 maths split up into three classes. Further Maths (for tards/normies), Maths Methods (middle ground) and Specialist Maths (extended). The gap between Further and Methods is much, much wider than the gap between Specialist and Methods. I was an idiot and only did Methods and not Specialist as well.
>Year 11 (Methods)
Functions, polynomials, trigonometric functions, limits, differentiation of polynomials, indefinite integrals, discrete probability, matrices, logarithms
>Year 12
Matrices, more calculus like definite integrals, chain rule, quotient rule, continuous probability, binomial probability, Markov chains, the normal distribution

If I had done specialist as well, something like this would be added on:
>Year 11
Calculus, complex numbers, linear algebra, geometry, Newtonian mechanics
>Year 12
Complex numbers, calculus, differential equations, linear algebra, Newtonian mechanics

>>6955909
>Vector calculus, differential equations, and other higher maths aren't necessary for 99% of careers

That's not the issue. The issue is does the 1% of kids for whom it is useful make back enough tax to pay for the other 99% learning it. There's quite a lot of maths for business and maths for engineering and science where that is precisely the case. I'm also in favour of teaching children to lift weight correctly, as those skills will be extremely useful in the labouring jobs that a lot of early school leavers end up in. A large number of students who don't end up in labouring jobs would be short changed by this policy, but I think it should be part of the curricula nonetheless.

>>6955895
>You don't get to insist though.

Yes I bloody well do. They are my children. You only get to decide whats best for them over me if they come to school with bruises on their legs. Look, I think it's wonderful that you think the humanities are so much fun to study, and are such important subjects. I share your view in many ways, my major form of self expression is by playing chess, a completely useless pursuit. I would never ask chess to be studied in school.

>autism

Calling me this is like calling an actual homosexual a faggot. It just doesnt work as an insult when it's a statement of fact.

>that having a generation of complete illiterates is undesirable (that's a different discussion, don't argue with me

I'll argue that point if I bloody well please.

>>6956232
Leave.

4chan is for asspies, not hardcore autistics.

>>6955895
>So, to avoid raising a generation of illiterates, schools have to teach some form of literature and language appreciation.

I would also like to point out that the word illiterate is incorrect here. I'm very literate, I read constantly. I haven't read fiction in many years. Kids that can read a technical journal are literate, regardless of whether they can quote Shakespeare or not.

The fact is that I'm not completely unsympathetic to your point of view. Subjects like english literacy are important (although I'm somewhat ambivalent about the study of history). However, I think the reason you hold those views is you've never been on the other side of the equation. My daughter is 10, and barely literate. A lovely, vital, energetic little girl who seems completely normal until she attempts anything academic; at which point it becomes clear how poor her reasoning skills really are. At this rate, she is unlikely to be able to read at a year 6 level by the time she finishes high school and has to enter the job market. Teaching her Shakespeare would take up valuable time that could have been spent honing her literacy. When she's 18, the school system walks away and washes their hands, but she will always be my daughter. The issue is that we have to somehow get this kid into a trade where she can earn a reasonable income and get some quality of life. Knowing the facts of European colonisation of the americas, or Hamlet, simply doesnt achieve that.

>>6956109
This is actually a really good point. I'm on here arguing for an economically rationalised curricula, where subjects are included based on the amount of tax dollars they generate; obviously biasing education toward math for business, engineering and science. I'm getting the obvious pushback you'd expect from such a right wing position, but a more obvious retort is that what is economically rational for one student may not necessarily be economically rational for another. Quite a lot of students probably would be better served by dropping some math in favour of doing a trade.

Of course, I still can't see the economic rationality of teaching english lit, history and geography to kids though.

>>6956258
>I haven't read fiction in many years. Kids that can read a technical journal are literate, regardless of whether they can quote Shakespeare or not

Which is why you can't communicate with people for shit and will doom your kids to the horrors of autism.

Fiction is how people learn about how others think and view the world around them. If you ever read fiction growing up then you might not have become such a worthless sore to humanity.

>>6956321
>doom your kids to the horrors of autism.

None of my children are autistic.

>Fiction is how people learn about how others think and view the world around them. If you ever read fiction growing up then you might not have become such a worthless sore to humanity.

I read fiction constantly growing up. I spent 90% of my childhood with my head stuck in a book. It's only as an adult I tend to eschew fiction. I watch film as my main source of fiction.

>>6956358
>>None of my children are autistic.

Just because you adopted doesn't mean they'll be safe from it...

>>6956126
You would decouple the zeta real and zeta imaginary parts and describe the riemann hypothesis as being that everytime one curve (i.e. the imaginary one) touches the (drawn 0) axis, the other curve touches the (drawn 1/2) axis beyond +10 on the positive side. The +10 is to remove obvious trivial 0's, and the positive side is initial simplification. You don't actually explicitly say it's on the positive side, you just only draw the positive side.

>>6956840
What's an axis? What is real? What is imaginary? What is a negative number? What is a zero? What is 0?

>>6957267
>implying you have to specify the nature of the curves
>implying children don't know what 0 is
>implying children don't know a line is a line
Just because you are deficient does not mean children are.

>>6957281
I'm amazed you think these are trivial questions for kindergartners.

>>6957311
I'm amazed that you're not too dumb to be able to browse the internet.

>>6957396
I'm quite confused. You seem to think those questions are incredibly unreasonable and totally trivial for 5 year olds. And then you call me an idiot for no apparent reason.

>>6929321