Why Modern Math Education Is Obsolete

a reply to: TinySickTears

I totally agree. You are not just teaching them math, you are teaching them to think critically of a problem.

I know I won't use a lot of the things I learned about in my electrical engineering courses in college, but it's the process of thinking through the problem and realizing other solutions that makes engineering so difficult.

a reply to: ChaoticOrder

I completely agree and have been ranting about it for a long time. Starting around the time that multiplication is introduced, they stop teaching concepts and start teaching the memorization of equations.

One thing I always think of is "why is the product of two negatives a positive?" Hardly anyone knows the answer, showing they do not understand the concept.

And for the layman:
Like adding numbers together gives you a sum, multiplying numbers together gives you a product.

originally posted by: EternalSolace
a reply to: ChaoticOrder

What I meant was that I don't understand how that complacency teaches math fundamentals. Sure 2+2 is about as simple as it gets. But as the problems grow in complexity, the underlying lesson that "so long as I'm close it's okay" is still there. Everything in me just doesn't like that.

Wonder what would happen if they did that at CERN lol!!!

A algebra professor told me once that Its just a fancy way to show off your intellectual prowess. IF you arent going to be a rocket scientist he didnt see the reason to force students to take it. STraight from the horses mouth its useless to 90 percent of humans who only need to know basic math. Its a educational scam for more cash.

originally posted by: ChaoticOrder
a reply to: EternalSolace

When I watch the clips that a child can answer 2+2=5 and still get it correct because correcting them would lower self esteem, I shudder.

Yes we all should be able to do such basic operations, but that's only because we should all understand the basic concept of how addition works, and adding two units to another two units is not exactly challenging. I can actually do many basic operations in my head, I just don't remember the answer unless I have to do the same operation all the time. Since I work with binary and hex a lot I do remember many of the 2 and 16 multiples.

there are different levels of 'basic operations' for different people. i can't imagine lack of understanding of geometry, trigonometry and many other things, and multiplication table for me is as obvious as different powers of two.

yes, i'm a programmer as well. 3d engines, FFTs, image processing - been there, done that. and while i agree that there are many things that are best left for research on as-needed basis (we can't be experts in every field possible), there are some things that one just should know - and sorry, but i can't imagine blaming not remembering a multiplication table on anything else but lazyness. such simple things that you prefer not to remember have to slow you down quite a bit during your work as well.

also, i think you're quite far from understanding the idea behind math at all. i also prefer to think like a programmer - because i am one. but you can't simply imagine how a stream of particles will move in space just by knowing the rules being the building blocks of their movement. you'll get it simple - but you'll have to perform so many iterations of your simple math and traverse such a tree of dependecies to get to the end result, that by the time you'll get there, you'll forget what was it that you were checking. computer will do it - sure. you won't.

on the other hand, someone able to think like a mathematician will be able to imagine the flow of said particles just by looking at a single, complicated equation. why do you think scientists all over the world use such complicated math? are they a bunch of morons, unable to come up with anything better? far from it - it's just a natural way for them, and a natural way for a human in general. you can of course research new problems using computers, you can create models and optimize them using methods you've described - but that's not how things are done, and it's not optimal.

it's not optimal, because you have to optimize the problem for a computer first, and when searching for new answers, while operating only at the building-blocks level, you won't notice the bigger picture, unless you'll visualize it - and even then, you'll be only able to see what you've included in your visualization. it's not how things are done, because it would be actually backwards - scientists are able to come up with theories that require such a massive computing power to visualize, that without their imagination and ability to visualize it all in their heads, we would be quite a few decades behind with technological progress.

so the bottom line is, i have to disagree. while the education system is far from being perfect, teaching children to simplify problems just to avoid having to look at the bigger picture would turn them into a bunch of idiots lacking imagination, that - as a bonus - have to rely on calculators/smartphones/computers to come up with anything.

and you don't bring your calculator with you when you're going shopping, do you?

originally posted by: yuppa

originally posted by: EternalSolace
a reply to: ChaoticOrder

What I meant was that I don't understand how that complacency teaches math fundamentals. Sure 2+2 is about as simple as it gets. But as the problems grow in complexity, the underlying lesson that "so long as I'm close it's okay" is still there. Everything in me just doesn't like that.

Wonder what would happen if they did that at CERN lol!!!

A algebra professor told me once that Its just a fancy way to show off your intellectual prowess. IF you arent going to be a rocket scientist he didnt see the reason to force students to take it. STraight from the horses mouth its useless to 90 percent of humans who only need to know basic math. Its a educational scam for more cash.

luckily for the governments and corporations behind that scam, 90% of humans won't be able to calculate just how much cash did they loose because of it.

Math eh ! ...Much like most subjects in school ,I was there to learn .Problem is what I was being taught .Just regurgitate what you have been given and the system will place you where they can use you . I became a rebel very early on . It's about what to think, opposed to how to think . A website that really spells out the mathematical errors of our ways is Climate Audit . Very advanced and very much a sore on many of the ones put to the task to deceive us .

The big turn off to anyone wanting to learn is the constant moving of what is proper and right about any of the many subjects . Few escape the trappings of our educational system because of apathy .If you don't get with the program then you will be outside of it and will never be allowed to excel .

Math seems to be something that can be very accurate at it's basic level but becomes less so the more detailed it develops . Take CERN and the level of math that is involved . If it were possible using math to know something then the physical project would not exist .Reality is a fine point where theory becomes the order of the day it seems .Theory then becomes a what ever math you need to push forward the what ever possibilities are part of the fray .

Modern math has only given us the possibilities to over step reality until a time we come to the conclusions that they are just not so . I stick to the simple basic stuff that finds reality in my back yard and leave the rest to the best hoping that some day someone will get it as close to reality as we can appreciate . time for a Bud

a reply to: ChaoticOrder

It depends on the field you are in.

If you're in say finance, it's very useful to have "go-to" equations memorized for use in programs such as excel. Same with actuarial science. You do need to be able to do certain functions from memory to be successful at that job because looking them up all the time wastes time that could be used doing the actual job.

I do agree that things like the multiplication table and other areas that schools focus on is useless. That's more arithmetic though and not "mathematics" per say. In fact most mathematicians are usually bad at average arithmetic.

You see things from the perspective of someone who programs. While I do understand what you're saying I don't know if that would be feasible to teach on a wide scale because it requires competency. The reason most math is taught the way it is taught is because it is the easiest means to an end.

Kind of how most people can write in English but aren't experts on etymology and the history of grammar.

Kind of how I said that in certain fields it's easier just to memorize the equations without necessarily knowing complex theory behind them.

Things are changing though which begs the question as to how to best prepare students for the future of mathematics.

Now in fields such as actuarial science you are far more likely to get a job if you know how to program and model. Things are definitely changing. It isn't acceptable to just know how to do equations but rather to be able to create from scratch what is needed to answer whatever question is up in the air.

I dunno man.

a reply to: pl3bscheese

If you ever lived with someone who was trying to learn your language, you would realize how important grammar is. It is very easy to change the meaning of a sentence or paragraph by using words incorrectly. Why is spelling correctly so difficult for an autodidact? Just memorize the rules and exceptions. Saves time to be correct.

a reply to: ChaoticOrder

There are values to learning abstruse branches of mathematics that cannot be replicated by learning to program. Each branch of mathematics has concepts that enlarge your thinking ability. You mentioned you learned linear algebra. Don't you think you can understand linearity of everyday quantitative relationships better because of it? Same for probabiity, which I think you mentioned also.

Programming certainly teaches you some thinking skills that mathematics doesn't. Knowing both gives you the union of the concept spaces. By the way, simulation doesn't replace knowing the theory of how things interact, it just gives you some examples of the cases you tested.

a reply to: StanFL

Yea , well if only getting very close is all one needs . The term "I am hungry " will ,or should get some response .I guess math is just that ,...it depends on what you mean .

a reply to: StanFL

If you ever lived in the streets you'd realize how important slang is. Proper language is boring, and IMO an indication of low cognitive flexibilty.

How can you not know your multiplication tables? That sounds like you are stubborn. 100% agree with you a lot of what you learn in school is forgotten and not used again, but it's problem solving one, and two it's getting from point A to point B, i.e. K-12, 4 year University, etc... Education is very important and helps you succeed in life.

If I wasn't taught the basics of mathematics throughout my younger years I never could have earned my PhD in Mathematics. Are we supposed to just ignore students who might someday go farther than YOU have with mathematics because YOU don't see the point?

I think that the Math kids are taught now is much more advanced than when I was in school. Though mind you, I have LD in Math and was really really behind the other kids in my class. I didn't understand certain concepts of Math until they started teaching basic Algebra, as long as I had a calculator I was fine with that. Ask me basic math skills and I have no clue what is going on. Show me a Algebra problem today and I probably couldn't solve it.(No practice for almost 20 years...lol.)

Anyway, my son is in 3rd grade and as part of the school supplies they requested Addition, Subtraction, Muliplication, and Divison flash cards. We looked everywhere for the divison cards and couldn't find them anywhere(finally found a set at Goodwill). When his Grandma found out we were looking for divison cards she was surprised that they were already teaching divison, she's a retired school teacher for 8 years and she said they didn't start until fourth grade. Of course she could have just been saying that because she dosen't like the school we are sending him too.

I really wish I knew basic math because it takes me forever to count out change, and half the time I get it wrong, I need a digital clock because I get the hands confused and the digits wrong. I see numbers and they get all jumbled and confused in my head. There's more, but yeah. You don't realize how much you need math skills just to make it.

Ontogeny Recapitulates Phylogeny.

It may not always be exact in biology but in learning it is. If you 'skip' steps, you don't gain true understanding, you are just faking it.

a reply to: noonebutme

Really? I used to be a programmer/developer before i moved into project management and at 44 years of age, I still remember all my multiplication tables to 13 without a second thought.

Good for you.

The way you had it elevated programming languages above mathematics. You cannot have programming languages without mathematics but you do have mathematics without programming languages.

That is certainly a valid point, I was going to write a little bit about how math can be more powerful in some areas, especially when it comes to abstract ideas like infinity. Math isn't really what I would call a computational language, because clearly we cannot compute infinities, but we can still manipulate them in equations and reach meaningful conclusions. We can also have infinite precision numbers in mathematics, whereas we cannot save such numbers in a computer because we have a limited amount of memory. Advanced math is more about working with abstract ideas than it is about doing simple computations.

a reply to: pl3bscheese

For instance when he talks about syntax meaning different things in different fields of mathematics, the exact same thing happens when you switch programming languages.

That is also a valid point, except every programming language is very clearly defined, it's not even exactly clear how to distinguish each field of mathematics from each other, and like I said, even the personal tastes of the person writing the equation can be important, even the placement of symbols, especially superscript and subscript symbols, can be ambiguous. There is just far too much uncertainty for my liking, I would prefer the language of math to be much more universal and clear cut. It's also just hard trying to pack complicated ideas into small equations, the notation gets very messy and I just cannot bring myself to try and understand such gibberish. I find it exceptionally easier to read a computer algorithm which is stating the exact same thing as the equation.

When I was in school, slide rules were an incredible tool. It really taught lessons in relationships and scaling. The scientific calculator of today of course, replaced it. However they hide the relationships and scaling and just produce the final result.

I think it is important that the instructor take the student visually through the entire calculation, but perhaps only once, and instead dwell on the concept of how that function appears in many other types of calculations. A more modular approach is needed in our schools instead of tedious exercises that prevent students from seeing the bigger picture, and thus producing interest in what mathematics is.

a reply to: jedi_hamster

yes, i'm a programmer as well. 3d engines, FFTs, image processing - been there, done that. and while i agree that there are many things that are best left for research on as-needed basis (we can't be experts in every field possible), there are some things that one just should know - and sorry, but i can't imagine blaming not remembering a multiplication table on anything else but lazyness. such simple things that you prefer not to remember have to slow you down quite a bit during your work as well.

Yes I am lazy, I am a completely lazy programmer. Laziness is often cited as one of the most important traits of a good programmer. See: The Three Virtues of a GREAT Programmer or Why Good Programmers Are Lazy and Dumb. The fact is, I cannot remember the last time I needed to calculate 7x12 in my head, so I see no reason to remember a table of numbers I'll hardly ever use, especially when I have a calculator handy 99.9% of the time. Of course I can remember many of the smaller multiplication answers, but that's only because I do tend to multiply smaller numbers in my head often. I remember what I need, nothing less, nothing more.

also, i think you're quite far from understanding the idea behind math at all. i also prefer to think like a programmer - because i am one. but you can't simply imagine how a stream of particles will move in space just by knowing the rules being the building blocks of their movement. you'll get it simple - but you'll have to perform so many iterations of your simple math and traverse such a tree of dependecies to get to the end result, that by the time you'll get there, you'll forget what was it that you were checking. computer will do it - sure. you won't.

Of course you can understand how particles will move through space simply by understanding how particles interact with each other. First of all you just need to know how they gravitationally react to each other, and as we know the force of gravity gets exponentially stronger as two particles move closer together. Then we also need to take into consideration the electric forces and the nuclear forces, etc. Of course we can use equations to help us understand all those different forces but it would be extremely complicated if we tried to combine all of those equations into one equation which described everything about particle movement.

on the other hand, someone able to think like a mathematician will be able to imagine the flow of said particles just by looking at a single, complicated equation. why do you think scientists all over the world use such complicated math? are they a bunch of morons, unable to come up with anything better? far from it - it's just a natural way for them, and a natural way for a human in general. you can of course research new problems using computers, you can create models and optimize them using methods you've described - but that's not how things are done, and it's not optimal.

We often start with mathematics because it's the most fundamental way to describe complex systems. By studying such equations and manipulating them we can often make other important realizations. Like I said in my previous post, math is much more abstract and is better at conveying abstract ideas. Clearly it wouldn't make much sense to start by describing physics in C++ and then convert it into math equations at a later point in time. We start with the most fundamental mathematical descriptions and then we can implement those ideas into computer code by quantizing the equations into finite computational problems.

a reply to: OrphanApology

If you're in say finance, it's very useful to have "go-to" equations memorized for use in programs such as excel. Same with actuarial science. You do need to be able to do certain functions from memory to be successful at that job because looking them up all the time wastes time that could be used doing the actual job.

There's no denying we should remember information we need to use all the time. And that will happen naturally, usually after I look something up two or three times, I wont have to look it up anymore because it will be ingrained in my memory. The point is, we never really know what we're going to need in our job until we're in that job, so it's pointless trying to remember as much as you possibly can when most of that information will never be needed in practice.

Kind of how most people can write in English but aren't experts on etymology and the history of grammar.

Kind of how I said that in certain fields it's easier just to memorize the equations without necessarily knowing complex theory behind them.

Yes this is exactly the point I'm trying to make. It's more important to understand how the equation works than it is to simply remember the equation. If you understand how the equation works, you are very unlikely to forget the equation, and even if you do forget it, chances are you'll be able to recreate the equation just from your understanding of how it works. We need to focus more on the high level concepts and less on the basic repetitive stuff.