Why Modern Math Education Is Obsolete

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. Back at school mathematics was actually my worst subject because the way it was taught just didn't seem to click with me like it did for some other kids. I was always terrible at remembering the multiplication table and it always seemed like useless information to me because I could just use a calculator. And a lot of the time the methods they'd teach us were unnecessarily complicated. Even though I was terrible at math I had an odd sort of intelligence. I remember one time in primary school when we were doing geometrical problems, I suggested to the teacher a much easier and quicker way to solve the problem, and he was completely dumb founded.

Now I'm a programmer and I've done things like create a crude 3D graphics engine from scratch, which involves a lot of math. I still cannot remember most of the multiplication table though. The reason I can do stuff like that is because I have access to a thing called the internet, and when I need to know something I don't know, I can just look it up and find all the information I need. I'm not going to remember every physics equation in my head when I have almost instant access to it whenever I need it, especially since I will most likely never need to use 90% of those equations in practice. I also have a thing called a computer which can perform calculations billions of times faster than I can do them in my head. The most important thing is that I can understand new concepts and convert those ideas into algorithms, that's where real intelligence is required.

When you think about it, mathematics is a language, and it's actually very similar to programming languages, because both are based on raw logic. When you write an algorithm it only does exactly what you tell it to do because the rules are explicitly defined just like in mathematics. However, mathematics is actually more limited than a typical programming language. For example, in most programming languages, I can do things like dynamically allocate memory and then come back and read or update the memory at a later time. I can reuse code with the use of functions and I can even create custom classes in object orientated programming languages. It's not clear how to do many of those things with the language of mathematics, and when we try to do those things, the equations become a complicated mess which only mathematicians can understand.

Those same equations can often be written very simply in powerful programming languages and they are much easier to understand. One reason is because there are numerous sub-fields of mathematics, each of which often use the same symbols in totally different ways, so in order to interpret the equations, you need to know what field of mathematics the equations relate to, and even the personal tastes of the person writing the equations. We don't get those sorts of fuzzy definitions in programming languages, when you write some code, others will know exactly what it is supposed to do by reading the code. The round() function will always round a number to the nearest integer, etc. Also, it's much easier to conceptualize complicated programming code than it is to understand complicated math equations.

If you can understand what the code is doing then you can understand the flow of information and the way the algorithm solves the problem. For example, I'm a fan of cryptocurrency, so I've taken time to understand how it works. I understand the algorithms involved and how they work together to produce a decentralized money system. I can actually conceptualize it inside my mind, I can see how the different parts function and how they interact with each other. If Satoshi had of tried to describe how Bitcoin works using only mathematical equations it would've been a nightmare for him and nearly no one would understand exactly how it works. It would be impossible to conceptualize if you were trying to understand it with only equations.

Like I said, the real trick to being intelligent is being able to conceptualize complex systems. If you can picture how it works in your head, then you can write computer code to simulate your ideas. In fact, in the field of complex systems, the systems being studied are so complicated that it's often impossible to develop equations which describe the behavior of the system. However it turns out that we can often describe complex systems through much simpler rules of interaction which are easy to conceptualize, and we don't need a single equation to do it. For example we can model a flock of birds or an ant nest just by understanding how the birds or the ants interact with each other. We can find simple interaction rules, and then use those to create simulations.

The result is that the complex behavior, or what we thought was complex behavior, will often naturally emerge just from those simple rules. The flock of birds will start doing very complicated things as a group, even though the rules dictating the behavior of each bird are not that complicated. It is easy to conceptualize such behavior when you think of it like that, and it's easy to implement those models in computer code without needing to be good at math. This is the core reason you'll often hear many programmers who say it doesn't really matter whether you're good at math or not. Of course it helps to have a wide knowledge of different mathematical concepts so you can create innovative and efficient solutions to problems, which is what math education really needs to focus on.

I now understand many complex mathematical subjects which I was never taught in school, including things like imaginary numbers, linear algebra, probability theory, information theory, etc. And now I'm much better at math than pretty much anyone I know, even though I still don't know most of the multiplication table. And it's because I simply took the initiative to research those subjects when I needed to. If I forget a specific aspect of anything I can just go look it up again when I need it, but I'm unlikely to forget if I understand the fundamental concept instead of just remembering it. The human brain much prefers to remember information we can imagine/conceptualize as something meaningful, it doesn't like remembering raw data. This is how a lot of memory techniques work (eg turning a list of words into a story).

In conclusion, I think the way we teach math today is quite obsolete and hasn't advanced much since we started teaching it in schools. We need to place more focus on understanding the concepts involved rather than being able to remember a bunch of useless numbers or equations which take up precious space in our head. Children are not drones who can just have endless streams of data shoved down their throats and be expected to regurgitate any little factoid on demand. They will enjoy the learning experience a lot more and get more out of it if they weren't taught in such a bland and unimaginative fashion. I understand it wouldn't be the best approach for all children but I feel like there are many kids like me who have hidden potential but they are repelled by the way math is presented to them.

It's not obsolete, but there is more going on than a half century ago to where it's not as relevant for many. I'd agree that it would be ideal if kids could grasp the concepts like some others do, but don't think this could be realistically attained in my experience.

I excelled in mathematics and sciences from a young age, and it was because I visualized the manipulation of forms in my mind. Once I could see the concepts, the end result emerged. I could usually work backwards, else short cut a linear sequence superior to the standard teaching. We're autodydacts, and most people aren't. I learned early on who to bother spending my time on teaching my techniques and the concepts behind the "lessons". It was anywhere from 0-3 of my "peers" per class. That was in advanced classes. Most simply can't hack it.

edit....smart ass


and yeah, the internet is here for all to reference but kids coming up need to be taught these subjects. if we get to the point where we rely in the net for answers we are going to be in trouble.

originally posted by: pl3bscheese
We're autodydacts, and most people aren't.

just not at spelling.
sorry, couldnt resist.

education in the states is in a sorry state all around

a reply to: TinySickTears

Or grammar? Spelling was never important to me. It's incredibly besides the point. We are transferring information, and you grasped what I was getting at, so why bother?

originally posted by: pl3bscheese
a reply to: TinySickTears

Or grammar? Spelling was never important to me. It's incredibly besides the point. We are transferring information, and you grasped what I was getting at, so why bother?

i was just being a smart ass.
it just gave me a laugh... kind of an inside joke i have with someone.

i used to use the term autodidact all the time and then he started using it.
i just got a chuckle when i read it and made a smart comment. i dont hear or see that word used often.

to be fair, i cant spell well and my grammar sucks. i often look up a word before i type it out cause im not sure how to spell it

They still teach basics to have it in mind. Like learning to read, once the basics are established, then you can go anywhere.

When I was being taught math the transition from long arithmetic to calculators wasn't clear yet, so some years we were expected to learn ye olde and some we were allowed to use early calculators.

Problem was, we never knew when they would change their minds about it and suddenly not allow calculators on tests.

Same with drafting, I learned it in elementary school, then was told in 7th grade they were switching to CAD, then back to drafting, it was hard to learn anything.

Even in college in a machining class they couldn't make up their minds if they were going to let us use calculators on the final until the last moment. I had to retake a class twice because of it.

originally posted by: TinySickTears
and yeah, the internet is here for all to reference but kids coming up need to be taught these subjects. if we get to the point where we rely in the net for answers we are going to be in trouble.

That's not really what I was trying to say. I said that teaching an understanding of the concepts (especially high level concepts) is more important than just remembering raw data and other useless information. For example I was once taught long division, a fairly tedious process as I recall, and I've never once used it for anything in my life. Ok well to be fair I did create a string based math algorithm once and used the long division process for one function, but even then I just looked it up online because there was no way I was going to remember something taught to me once like 8 years prior.

a reply to: intrptr

You make a decent point but I think now our computing technology is well enough established and widely used to not involve so much guess work. I think any school who still doesn't allow the use of calculators on tests is living in the stone age.

originally posted by: ChaoticOrder

That's not really what I was trying to say. I said that teaching an understanding of the concepts (especially high level concepts) is more important than just remembering raw data and other useless information.

to be fair you said a lot.
i agree though about teaching the concepts.
in your next post you said you think schools are in the stone age if they dont allow calculators.
i dont agree with that.
i think kids coming up need to know how to work problems. in their head. longhand.
chances are post school they will never need to use this as calculators are everywhere but i would rather not chance it.

a reply to: ChaoticOrder

That was a while ago, but I suspect they don't teach well enough generally these days. Aren't we all disturbed by the level of education being produced in kids these days?

Most professional contractors use tape measures, squares and plumbs during the day, and figure things in their head. I meant that kind of basics, those are good to have 'handy". I don't see many of them using calculators on the job.

You're a programmer, thats different.

My history teacher used to say that there is a difference between being bright and being clever. Bright kids will listen to what you teach and repeat the information from memory. Whereas, clever kids will research and come up with an answer, regardless if they've been taught or not. He believed the clever kids would do better in life. I liked that idea and it made sense to me.

He was wrong.

As an adult, I now see that society prefers conformists over thinkers.

a reply to: intrptr

Most professional contractors use tape measures, squares and plumbs during the day, and figure things in their head. I meant that kind of basics, those are good to have 'handy". I don't see many of them using calculators on the job.

You're a programmer, thats different.

Well I did say not all kids would be able to learn that way, but that is still a very good point, I wasn't really thinking about it like that. It seems to me there are really two groups of people, those who need to be able to perform basic mathematical operations in their head at work, and those who have jobs where they can use computers to solve the problems. But it's not even so much that I have access to computers, it's really more that the sorts of problems I need to solve are so complicated that only machines can do them. I am often modeling complex systems and creating code with countless mathematical operations. I don't have time to be doing simple math problems in my head, I need to be putting math problems into code form.

a reply to: ChaoticOrder

I worked in computer engineering, hats off if you write algorithms…

originally posted by: SlowNail
He was wrong.

As an adult, I now see that society prefers conformists over thinkers.

Lmao well that's a depressing outlook on life. In all seriousness though, he was correct, many of the successful innovators are a bit "out there" and very free thinkers, and they are really some of the only non-conformists that society will accept and even praise as genius. It's just that not many of the thinkers actually think up something new and worth while and then take all the necessary steps to make the idea succeed. They will usually just get bored and move onto the next idea.

originally posted by: ChaoticOrder
...those who need to be able to perform basic mathematical operations in their head at work

That's what I have to be able to do, on the fly, without a computer or calculator. 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. Stuff like that doesn't fly in the real world. Accuracy is key, just like I'm sure it is when you're modeling computer algorithms.

I'll never fully understand why things have gotten so complacent in school today.

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.

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.

originally posted by: ChaoticOrder
Now I'm a programmer and I've done things like create a crude 3D graphics engine from scratch, which involves a lot of math. I still cannot remember most of the multiplication table though.

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.

When you think about it, mathematics is a language, and it's actually very similar to programming languages, because both are based on raw logic.

Actually, I think it should be the other way round :

When you think about it, programming languages are very similar to mathematics, because mathematics is based on raw logic

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.

But to your point, i think maths need to be taught differently -- use some of the more modern ways of multiplying and dividing as opposed to what i learned 30 years ago!

a reply to: noonebutme

Agreed the multiplication tables are drilled in my head, more so because I constantly encounter situations where basic calculations are required. People around me guess or waste time with their smartphones, I know the answer instantly.

Programming is very similar to mathematics. It's simple logic is all. Didn't get what the OP was talking about. 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. Maybe he sticks with languages coming from similar roots, like someone who knows Latin based languages.