How would you design the World's standard mathematics education system if you could?
Starting from kindergarden up till graduation from college.
>Ensure that you are specific and use proper names of topics so people can have a counter argument.
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."
Basic times tables/fractions
Division, Powers, Roots, Primes
Geometry, Logic, Sets, Combinatorics, Proofs
Higher order Algebra. Trig, Exponential, Logs, Series, Sums, Limits
Calculus, Matrix Algebra
Vector Calculus, ODEs
Linear Algebra, Probability, Statistics
Digital Logic, Comp Arch
Real Analysis, Abstract Algebra
Stat Mechanic, Optics, Advance Mechanics and Special Relativity
Data Structures and Algorithms
American Government and Political Science
PDEs, Complex Analysis, Fourier Analysis
Numerical Analysis, OS, Parallel Programing
Macro & Micro Economics
Money and Banking, Finance
Philosophy, Theology, Religious Studies
Electives (Organic Chem, Biology, GR, Astrophysics, Robotics, Comp Vision, etc...)
>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.
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
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
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
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.
No school grades
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.
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.
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?
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.
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.
It is wikipedia, though, so...
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
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.
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.
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.
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.
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
>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 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.
Compulsory curriculum for grades 1 through 8:
Basic problem solving
More advanced problem solving
Preliminary introduction to concepts of algebra
Powers in addition to more in depth problems about stuff taught before
Proper introduction to algebra, mostly equations in 1 and 2 variables
Introduction to the cartesian coordinate plane along with relevant applications to geometry
Some instruction in different coordinate systems with relevant geometry stuff
Simple introduction to sets
More complex numbers
Series (not necessarily calculus related yet)
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
Introduction to integrals
Finish up integrals (probably improper integrals, trig substitutions, numerical computation methods etc.)
Series and sums in calculus
Taylor series in multiple dimensions
The aim here is to finish up Calc I and II and some of Calc III
>an education system that everybody will go through to cater to the needs of the <5% capable of benefiting from it
>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.
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.
>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 faster.
>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.
>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.
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.
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".
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.
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.
>but uninteresting is not one of them
you're forgetting women's studies
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
(english is not my first language)
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.
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.
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.
>mfw in 8th grade being scared into thinking Pythagoras theorem would be hard
then it would be an x
>there are people this stupid on /sci/
>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.
play with these legos
counting in base 10
geometric integer integration
relations of ten, squares, cubes
geometry and logarithms
geometry and logic sums
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.
I wish I had an education like this. Damn teachers had me doing algebra in fucking 9th grade!
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.
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.
>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...
>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.
>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
being a paint-sniffing half-retarded descendent of convicts is not science
Here's a handy list so that you can start ticking off your guesses:
I'm assuming 'trial and error' is your de facto approach to solving maths problems.
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!
>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
Kindergarten-4th grade arithmetic
5th-8th grade-algebra and geometry
10th grade-calculus I/statistics/math of choice
12th-optional:Calc III/Diff Eq
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.