Why Modern Math Education Is Obsolete

I AGREE burn THOSE math books WHAT AN EVIL plot against humanity!
Fortunately my subconcious reallized that and REJECTED it.

a reply to: StanFL

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.

I think you're entirely missing the point I was making. Learning high level concepts like algebra and linear algebra are exactly what I'm saying we need to focus more on. Learning your multiplication table is not even necessary to know how linear algebra works. Understanding the concepts behind probability theory does not require one to know their multiplication table. Of course if you want to calculate a probability in your head you need to know such things, and I do often calculate things in my head, it's just that most of the things I need to calculate are simply too complicated to be done in the head of most people and so computers are required. As long as I understand the concepts involved, I can write algorithms which implement those concepts, then let the computer do the hard calculations for me.

originally posted by: TycoonBarnaby
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?

Well I've already said twice that not all children could be taught in a way that I suggest. Also, I'm not saying we should totally ignore all the basic stuff, I'm saying we need to focus less and drilling redundant information into students heads. Let me ask you, how often do you actually perform long division in your head? Has that basic operation really helped you get anywhere you couldn't get without a calculator?

Surely, as someone who claims to study advanced mathematics, you must understand the importance of understanding high level abstract concepts, and why that is more important than being able to multiply some large numbers in your head. Being a human calculator does not automatically make someone good at advanced mathematics. It is much more important that they can conceptualize abstract concepts.

Here's a brilliant lecture by Conrad Wolfram where he argues the same point I am making in this thread. He sums it up very nicely with one sentence: "Stop teaching calculating and start teaching math".

From rockets to stock markets, math powers many of humanity's most thrilling creations. So why do kids lose interest? Conrad Wolfram says the part of math we teach -- calculation by hand -- isn't just tedious, it's mostly irrelevant to real mathematics and the real world. He presents his radical idea: teaching kids math through computer programming.

Conrad Wolfram: Teaching kids real math with computers

a reply to: ChaoticOrder

Dividing polynomials, though I prefer to use the more simplified version of synthetic division over long division most of the time.

Multiplication tables help people factor integers. Something that is quite useful to be able to recall without having to look them up or use a computer every time.

Do I utilize computers for many basic things NOW? Yes of course, but having those basics as building blocks in my head has helped me to understand more abstract topics better.

I have seen the new ways math is being taught and it's ridiculous. Not sure if I saw it on ATS or somewhere else. Something about using simple addition to solve everything but it is much more tedious. I am not sure if this is just a viral hoax on the internet or it is in fact new curriculum.

a reply to: TycoonBarnaby

Dividing polynomials, though I prefer to use the more simplified version of synthetic division over long division most of the time.

Ok, but I doubt you have a division table memorized in your head. It's more important to remember how division works than it is to remember every division answer. And I doubt you actually do such division problems in your head or by hand anymore. And that's the main point I am making, we put so much focus into the calculation part of mathematics and not enough into understanding the concepts. Being a mathematician you are one of the only people who really does need to know math inside out and how to do all the calculations manually. But in practice most people will never need to know that stuff, they will just use a computer.

a reply to: ChaoticOrder

I certainly agree that many people do not need to memorize math basics or do calculations by hand after they get through high school. Some do though.

Having taught high school mathematics for a few years, I agree that the current methods are pretty messed up (and only getting worse sadly, which is why I got out of it.)

My main issue with those who claim we should never teach students to memorize mathematics is that they rarely bring up the fact that many other subjects also require students to memorize information and regurgitate it on tests. History comes to mind as an easy example of this.

a reply to: TycoonBarnaby

My main issue with those who claim we should never teach students to memorize mathematics is that they rarely bring up the fact that many other subjects also require students to memorize information and regurgitate it on tests. History comes to mind as an easy example of this.

Well that's true, but it's not like they repeat the same thing 100 times in history class until the students remember it. I can remember back in primary school when we were learning the multiplication table, we probably spent several weeks on it, then we had a test where the teacher would ask us random multiplication problems and see how fast we respond. I remember being quite terrible at it because my brain just didn't want to remember a bunch of numbers. And I was made to look stupid in front of the rest of the class because I hadn't memorized those numbers like most kids had. Now most of those kids probably wouldn't even be capable of understanding the algorithms I write.

a reply to: ChaoticOrder
Its not obsolete, its only obsolete in the way we go about it for about 60% of the population me thinks.

Which again just leads into what you were talking about and saying. But lets face it unless you have a specific interest in it, or any any part of it, well its all just meaningless jumble of data. Its really a question of relevance, is it relevant to you, and for many people the answer is a definite NO.

And also most people drop into two groups, those who just remember things without questioning and go on from there, they can acquire more knowledge faster as any deep explanation or though need not be required or even exists for some of them for instance 4+4=8, but why does it always equal 8? That does not register in 99.9% of humanity or even why you all can only think in binary and subsequent consequences, but that is not a math subject and would take a whole host of other subject to understand that and it would make no sense in a mathematical subtext unless its under a certain context. Its not a thing in itself its a construct, but the construct is all that is required.

And those who can only remember things after they understand the point of it, being the other half, and likely the way you learn, the meaning of it, or even the use of it, before you can bother with it. Math being more abstract even make believe would be harder for the latter half, as first they would have to figure out the point of it before bothering with all that other things and waste time trying to figure out something completely alien to them especially at an early age. Hence why a majority of kids dont like math, they will never use 90% of it even when learned.

And today's age since you can just literally take 1 minute to look it up online most things become obsolete. So in essence they just learn it or would memorize all that math backwards processing, and by backwards I mean once it becomes necessary for them in a step, or reason to do so, like you said they will go online and check up on it, and after a time they would have used it so much that they would have either memorized it, or it would become a redundant fact kind of how knowing that you dont need to know how the brain actually transmits signals into your body and to your hands to move your index finger when you can just do it.

Its literally reaching the same place by different means eventually. You got to understand that teaching process in school are thought processes, and each teaching process caters to a groups though process, hence why some are good at math or like math, and other don't, they have different though processes going on in there heads at that point and place in time. Basically like learning a language you have and aptitude toward and want to learn to trying to teach somebody a language they dont want to learn and are busy with other thoughts and things in there life.

Understanding the concepts of why for some is more interesting and they can never go anywhere until they get that reason of why? It will bother them, that itch you cant scratch. But for others..The whole why? Is not important and nowhere near to understanding as to how? But anyways math should maybe be classified as art in some instances, in others its merely mental group cohesion tool memetic evolutions.

For instance you could have tools and rulers and and even programming languages all have different numbers and meanings and move them all over the place and change them up. But as long as you have a bunch or group of people all work under the same understanding and mind frame then it will still work no matter how upside down or inside out it will be, so yes even in basic things like lets say measuring or rulers you could make 1 feet twice or three times as long as it is now, and just subdivision that into different numbers and fractions, and measuring things even when making a car or space station will still work as long as all humans involved follow the same though process and understanding.

There is essentially no correct way of doing things even were math is concerned there is only the way it works, and you could go further to say how that way works for certain groups of though processes and even subgroups, but its all just a tool of cohesion.

So ya! Its all for the most part like everything else, a social cohesion effect and tool. Math is not the language of the universe, its a language in a universe, one which if we ever come across another civilization don't be surprised that they may have a different math then us, because math is a language in a lot more ways then one. And not only that but they could have build all kinds of things space ships the size of planets and everything in between and all of it using a different social cohesion program and maths which wold all be nothing but static noise to us even if it used charters and numbers we would recognize, because recognition and understanding are two different things, they are both products of social and mental cohesion.

Math is another thing which is not a thing in self, outside of its prescribed channels it becomes much static noise and meaningless, just like radio stations outside there frequency and locality become just much static noise and meaningless. Its a conceptual language of synchronicity in this ecosystem called earth and society. Outside of it I do not think it would have any meaning or much of a meaning. Especially considering when everything is tied into it including sight and perceptions the filters of our reality could quite literally be useless static to other beings just like math is useless jumble static when trying to learn it in school isto some kids, and to others its there life and code.

Its merely a matter of mental cohesion and synchronicity in there conceptual realities, the many ones, subdivided by the mass of the whole must be in synchronicity, to which all believe becomes context which become reality. And in the whole you do not need to know all the processes of how exactly your brain fires signals to get your index finger to move, you just do it because it works. And why it works or how is not important as long as it works.

I think the reason why they started teaching kids that whole tedious way you seen in the other thread is because there trying to figure out the why? in a whole nation full of hows? Or at least get new generation to understand and break down more concepts instead of just the whole social botlike memorization we had so far, it has created lots of stuff and even wonders but not really. Social experimenting is the stable of all that we have achieved today, including the popularity of math and its effect in this world. That is likely to continue onto future generations as well.

a reply to: galadofwarthethird

Its really a question of relevance, is it relevant to you, and for many people the answer is a definite NO.

Well math is kind of the exception to that rule because it's required for many different things and it's so deeply ingrained into the way society functions, so I can perfectly understand why math education is compulsory. The problem is the education system teaches math in a way that repels many kids.

And those who can only remember things after they understand the point of it, being the other half, and likely the way you learn, the meaning of it, or even the use of it, before you can bother with it.

Exactly, different groups of people tend to think in very different ways, and I think a huge part of the problem is that they don't really care about the people who truly want to understand and conceptualize the problems, well not until we reach higher education anyway.

originally posted by: ChaoticOrder
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.

as for lazyness, a programmer lazy in a sense implied by Larry Wall, would remember that damn multiplication table - because reaching for a calculator and checking the result on it is not only slower, but it's also a much bigger waste of energy than getting the result from your head.

as for particles, you cannot visualize it in your head without understanding the complex equation behind it. you can either focus on the building blocks (each of the forces you've mentioned), calculate each separately, sum the results, and do so step after step, just like a computer would, just thousands times slower - or you can imagine the forces at hand translating into function graphs in three-dimensional space, as long as you can imagine those functions.

the education system you're proposing would produce people that would be only able to imagine basic operations - because those would be the only ones they would be able to perform.

also, knowing the value of a sinus for a particular angle isn't equal to understanding what a sinus is. calculator can only give you the first thing - and you'll need a good one using symbolic notation to avoid getting lost in a forest of square roots. if you can't comprehend what i'm saying, it only proves that your theory and understanding of the problem at hand, is flawed.

and last thing, if you think that every programming language is clearly defined, you probably never coded in anything else than C or java. the whole comparison is completely pointless, there are far less differences between different fields of mathematics than between different programming languages and philosophies behind them. ever tried forth? lisp? tcl? ocaml? haskell? perhaps F# or at least clojure? do you have any idea what kind of flexibility a language like forth, or even tcl, gives? judging by your posts, doubtful.

a reply to: jedi_hamster

as for lazyness, a programmer lazy in a sense implied by Larry Wall, would remember that damn multiplication table

No, they would remember parts of the multiplication table they actually use regularly. Even if I did remember the entire multiplication up to 12 or x13... you do realize there are about an infinite number of larger numbers which I will often need to multiply at some point. And in practice most of the multiplication problems I need to do are with very large numbers, some so large most people wont even encounter such large numbers in their life time.

as for particles, you cannot visualize it in your head without understanding the complex equation behind it. you can either focus on the building blocks (each of the forces you've mentioned), calculate each separately, sum the results, and do so step after step, just like a computer would, just thousands times slower - or you can imagine the forces at hand translating into function graphs in three-dimensional space, as long as you can imagine those functions.

I'm not exactly sure what you're saying here. My whole argument is that understanding the equations and being able to visualize them is far more important than simply remembering them. Clearly it is much easier to understand how something works when you break it down into its component parts, by visualizing each force separately instead of trying to combine them all into one equation or one function graph. It also happens to be the best way to write code, so that's it's clear what the program is doing, instead if trying to combine all the forces into one programming function.

the education system you're proposing would produce people that would be only able to imagine basic operations - because those would be the only ones they would be able to perform.

In the education system I propose people would be able to imagine the complicated 3D function graphs you talk about because they could be visually represented by a computer and they could play around with the variables in real time. On a related note, obviously the education system which produced your grammar and punctuation skills did a very poor job.

do you have any idea what kind of flexibility a language like forth, or even tcl, gives? judging by your posts, doubtful.

Regardless of the flexibility those languages offer, there is nothing ambiguous about the syntax, because if there was the compiler wouldn't be able to interpret the code. That is not the case for mathematics, complicated equations often do require some degree of reasoned guess work to figure out the real interpretation.

a reply to: ChaoticOrder

Internalizing and memorizing those basic math facts lets you concentrate on the higher concepts like algebra when you get there.

Basically, it sounds to me like you are totally OK with making kids completely dependent on calculators to do all the basic calculations?

What happens if they are ever in a situation where they don't have a calculator?

I was in 9th grade in 1971 and had an algebra class which was taught with "new math", I was not getting it. My father was an engineer who learned algebra before "new math". He showed me a logical approach and I did well "his" way. I in turn did the same for my daughter in 1995... just one 1/2 hour session and she no longer had any trouble with algebra.
I am convinced that "new math" and "look-say" (memorizing entire words as opposed to phonics) for teaching English are part of an intentional "dumbing down" of America.

a reply to: ChaoticOrder

I saw a thread the other day about how kids are learning ridiculously tedious methods to do math and it got me really thinking about how flawed the overall way we teach math actually is.

I think you answered your own question with that lengthy thread.

If you want to get kids excited about mathematics, it's shouldn't be so bloody boring. When I was a kid there was an audible groan from the class when it came to revise long division.

a reply to: ketsuko

Another way to look at it is like this:

When you are learning to read, it used to be that you started with basic phonics, the building blocks of language, and from there, you learned that the phonograms went together to create the words you see. You learned to decode the words, and once you got really efficient at decoding, you starting learning what the words actually meant and how to figure out meanings from context.

Meaning and context are higher level skills like the algebra of language.

Unless you really internalize your basic phonograms and decoding skills, you are still spending way more time and mental energy just decoding what each individual word means when you should have long ago moved on to the higher level language skills.

Math is the same. You start with the basic number skills of internalizing base ten. Then you move on to your basic math facts. Once you have those, you move on to the higher level skills. If you miss any of the basics, you spend more time and mental energy still fighting those basic steps than you should making the entire process much more difficult than it ought to be.

a reply to: ChaoticOrder

No, they would remember parts of the multiplication table they actually use regularly. Even if I did remember the entire multiplication up to 12 or x13... you do realize there are about an infinite number of larger numbers which I will often need to multiply at some point. And in practice most of the multiplication problems I need to do are with very large numbers, some so large most people wont even encounter such large numbers in their life time.

example: 7x57 - it's 7x50 + 7x7, which is 7x5x10 + 7x7 - and that's something you can solve in seconds at most in your mind, by only knowing the answers for up to 10x10. on the other hand, a lazy programmer won't bother. he'll let the compiler optimize it or just write it off as a constant.

I'm not exactly sure what you're saying here. My whole argument is that understanding the equations and being able to visualize them is far more important than simply remembering them. Clearly it is much easier to understand how something works when you break it down into its component parts, by visualizing each force separately instead of trying to combine them all into one equation or one function graph. It also happens to be the best way to write code, so that's it's clear what the program is doing, instead if trying to combine all the forces into one programming function.

my point is that visualizing the components doesn't equal to being able to see the bigger picture. you have to be able - at some point - to wrap your mind around the whole problem, and letting the computer visualize it for you just because you prefer to operate on a simpler level isn't the answer. it's the right way, sure, but it's not the answer - it slows down research, because then you have to do countless visualizations just to find the path you want to follow.

In the education system I propose people would be able to imagine the complicated 3D function graphs you talk about because they could be visually represented by a computer and they could play around with the variables in real time. On a related note, obviously the education system which produced your grammar and punctuation skills did a very poor job.

i'm far from saying that computers shouldn't be used more in the education - quite the contrary. but they should be used as a tool to teach people how to understand complex problems and how to solve them ON THEIR OWN - not to free them from thinking about the complexities. as for my grammar and punctuation, if you're referring to the lack of capitalization of sentences and so on - mea culpa. i tend to write like i've used to on IRC or in unofficial e-mails, it doesn't affect the overall readability and makes it that little bit faster to write (i also tend to prefer text terminals than GUIs). on a sidenote, english isn't my native language, so i guess my english skills aren't that bad - at least i don't confuse "your" and "you're", like so many - native english speakers - do.

Regardless of the flexibility those languages offer, there is nothing ambiguous about the syntax, because if there was the compiler wouldn't be able to interpret the code. That is not the case for mathematics, complicated equations often do require some degree of reasoned guess work to figure out the real interpretation.

some languages let you redefine the syntax - or almost anything actually. tcl is flexible enough so that there are several object systems (the main language didn't have one originally) written for it, in pure tcl - no changes to the underlying interpreter. in forth, well. in forth you would be hard pressed to find things you cannot redefine.

ok> 1 1 + .
2
ok> : 1 2 ;

ok> 1 1 + .
4

nothing ambiguous, right? comments, constants, control structures - all those are defined in forth itself, and new control or data structures - with their own syntax - can be, and are, defined by forth programmers in their code. granted, no other language comes close to that level of flexibility, but many are a lot more flexible than usual suspects like C.

the readability depends on the quality of the code, and i guess the same is true for mathematical equations. take C++ for example, constantly abused beyond belief. is it truly flexible? quite the opposite, it just pretends to be, by adding complexity, layers over layers. is it readable? bad C++ code is a clusterf... no math equation can match, that's for sure.

a reply to: jedi_hamster

example: 7x57 - it's 7x50 + 7x7, which is 7x5x10 + 7x7 - and that's something you can solve in seconds at most in your mind, by only knowing the answers for up to 10x10.

What you've shown here is that knowing how to break down a problem into a set of simpler problems is a good way to solve problems in your head. It's the type of thing I'm saying should be more important to math education. But I don't really think it would be quicker to solve problems like that in your head compared to just using a calculator, especially when you start having more than 2 digits. In fact I cannot afford to waste mental energy on such calculations, I have much more interesting and high level problems to think about.

my point is that visualizing the components doesn't equal to being able to see the bigger picture. you have to be able - at some point - to wrap your mind around the whole problem, and letting the computer visualize it for you just because you prefer to operate on a simpler level isn't the answer.

This is just complete nonsense. Being able to visualize the equation and manipulate variables in real time gives an extremely deep understanding of how it works. Some times just looking at the equation isn't enough, especially complex equations. You may have to see what it outputs and graph those outputs, which is exactly what a function graph does.

i'm far from saying that computers shouldn't be used more in the education - quite the contrary. but they should be used as a tool to teach people how to understand complex problems and how to solve them ON THEIR OWN - not to free them from thinking about the complexities.

I'm saying that computers can be used to free them up from doing tedious and redundant calculations so that they can in fact focus on the more complicated high level topics, not to dumb it down for them. When I write an algorithm I have the advantage that I can focus on very high level concepts, and those concepts will be far more complicated than any basic math calculations. I highly suggest you watch the Wolfram lecture I posted near the top of this page, he explains the point I'm trying to make very well.

some languages let you redefine the syntax - or almost anything actually.

Even if it's hard to read and understand for a human it's still not ambiguous to the compiler, so my point remains.

bad C++ code is a clusterf... no math equation can match, that's for sure.

Well written C++ code, even if thousands of lines long, is still easy to interpret and understand. Thousands of lines of math equations is not easy to understand by any standard. When it comes to complex and length equations, it's just not easy to digest for most people. As an example, when I need to learn a new mathematical concept, I will often start by reading the wiki page on the subject, and a lot of the time, the page will contain some complicated equations that I can barely understand. However, that's never really a problem, because by reading the text on the page and looking at the useful charts often sitting to the right of the text, I can usually understand what the equations are doing without even fully grasping the equations. Then I can write some code which does exactly what I want, just by understanding the concepts involved, I can turn those concepts into code, which solidifies my understanding of how the math work.

a reply to: ChaoticOrder

This is just complete nonsense. Being able to visualize the equation and manipulate variables in real time gives an extremely deep understanding of how it works. Some times just looking at the equation isn't enough, especially complex equations. You may have to see what it outputs and graph those outputs, which is exactly what a function graph does.

your reply is a complete nonsense. you're not able to visualize the equation and manipulate variables in real time - computer software is. a software someone has to write, and if it's for a visualization of something that may be the wrong path in the research at hand to follow - it's a massive waste of time. when thinking like a mathematician, one is able to choose a path that is most likely correct, and then write a software to visualize that specific path. if you can't understand that, any further explanation is a waste of time.

Even if it's hard to read and understand for a human it's still not ambiguous to the compiler, so my point remains.

it does not. this thread isn't about the readability of code vs math for computer software, it's about their readability for humans. my point is, when programming language is so flexible that it allows a programmer to change the syntax on the fly to better match the problem at hand, knowledge of the language itself won't be enough for any 3rd party programmer taking a look at a random piece of code from such project, whereas mathematical equations are nowhere near as scary as you paint them to be.

Well written C++ code, even if thousands of lines long, is still easy to interpret and understand. Thousands of lines of math equations is not easy to understand by any standard. When it comes to complex and length equations, it's just not easy to digest for most people. As an example, when I need to learn a new mathematical concept, I will often start by reading the wiki page on the subject, and a lot of the time, the page will contain some complicated equations that I can barely understand. However, that's never really a problem, because by reading the text on the page and looking at the useful charts often sitting to the right of the text, I can usually understand what the equations are doing without even fully grasping the equations. Then I can write some code which does exactly what I want, just by understanding the concepts involved, I can turn those concepts into code, which solidifies my understanding of how the math work.

there's a line between thinking like a programmer and thinking like a mathematician, which you're drawing as far from yourself as possible, and that's a bad thing. you can mimic the equations, you can even calculate the same thing those equations represent, but without deep mathematical understanding of some problems, you will never be able to come up with solutions that won't seem obvious from your purely-programming-driven point of view.

you will never make a leap similar to discrete fourier transform - fast fourier transform with such attitude towards math, and without FFT and similar things, we wouldn't have any decent audio or video compression these days, at all. do you think FFT was invented by programmers? far from it, we didn't have any computers back then.

you can do with additions, multiplications and wikipedia pages for writing simple software that does things that were done thousands of times already, but to code something truly inventive/well optimized, math is your friend. and yes, i'm all for teaching kids programming, but not at the cost of teaching them math.

because if you can't visualize a problem in your head, without your computer, then you're pretty much useless for any serious research team.