It all somewhat depends on how we define “teaching.” If a teacher is a guide to finding your potential and knowledge on your own terms- then yeah. Let people do it however works for them. If a teacher is someone who’s job it is to instruct you how to fit a place in society- well....
We can distill that down to two types of people really- people who create new ways and people who follow what others create. You’re building a mission to colonize Mars right? You and the smartest people on earth are all in on it. What chance do you think it has for success if every single one of you is following your own direction? If every one of you is doing the best work you know how and innovating new things no one else is familiar with?
Collaboration requires people work together. A project doesn’t have to be “perfect” or even revolutionary to be a success- sometimes it’s better to do something less than “the best” so that you have something. So maybe your teacher is overworked and/or doesn’t want to deal with individualized educations for every one of their 30-300+ students. Or maybe you’re smarter than them and they just can’t follow your brilliance so they need you to do it the way that they can understand it.
Regardless- people who have the skills to break rules and make new ones- who are so smart that when no one else can follow their ideas they can just make it all happen themselves- aren’t that common- and if they are as smart as they think and their ideas have the merit they think- they tend to become the norm.
So really you have to decide, and I recommend honest self evaluation here: are you a towering genius on a path to make major changes to some aspect of the world and how things are understood... or are you maybe better off just learning to follow the path that other people set out?
And there’s no shame in that. If you look at executives- even ones in art, film, music, and technology or science- they don’t tend to have strong technical backgrounds as the norm. They tend to have business and finance and management backgrounds.
The person making technological decisions for a Fortune 500 has foods odds they couldn’t set up their own router at home without help. They generally know this. They surround themselves with people who know the details and mastery of the technical things and their strong suit is finding and implementing ways to use those things to make money or grab market etc.
So maybe it’s a good life lesson. You have to know when to conform to standards of society and conventions, when to concede to the superior subject matter knowledge or experience of others, and understand when your position is strong or weak and you simply have to do what someone wants even if you think it’s pointless or stupid because they have the control and you want something from them.
As you get into more complex math HOW you find an answer becomes crucially important. Being able to show it- and having peers be able to confirm and reproduce it becomes critical. When you you get to higher concept math the numbers and operations don’t even reflect reality anymore. You can’t go pick up a bunch of marbles and use reality to prove your point because your point proves reality. Higher math is increasingly theoretical.
Currently on our system- your teacher is doing one of 2 Jobs and no one knows which one they’re doing- even them- for maybe 20-40 years. See- what you learn depends on you. They say there are no bad students only bad teachers and well- maybe no one is bad or everyone can be- but the best teacher in the world isn’t going to be able to make a low functioning autistic kid or downs kid into a rocket scientist. Some percent of your education is what you bring in and what you decide to take out.
So your teacher is either preparing someone to retain the most basic of things but likely have to learn most lessons the slow painful way through life- or they are preparing a successful professional or even a historical figure of note. No one will know which until you have lived your life- so they have to find a balance between getting you ready for Grad School and getting you ready for minimum wage. That second one doesn’t require you get too much out of school in general.
For the other kids though- teacher doesn’t know if you’ll be a world class chef or a lawyer or a porn star or a Rocket scientist. So they’re just gonna teach you “math” in the most generic and pure sense and let you decide what to remember or forget, what to build on and use for your future and what was in hindsight a “waste of time.”
If you’re going to be an innovator or a doer then you’ll be fine even if you had to suffer through school. If you’re going to be someone who follows the oath laid by an innovator or doer- or cleans up after them and serves them- then learning the math isn’t even that important- they just need you to get used to following directions when the person in authority gives them. Customer says no pickles- doesn’t matter if you think pickles are better. That’s a matter of position in society. If you can’t figure out how to deal with a problem like a teacher wanting to see work done a certain way.... at least eventually... that doesn’t bode well for the possibility you’re going to change humanity.
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TLDR: Teachers have to teach to the average, not the individual. You have to learn both how to find creative solutions to problems AND how to follow directions and tested ways of thinking.
@lolcats121 :')
In specifically math it's often a bad thing to use a nonstandard method for finding the answer because it might not always work right and it might not mesh at all with more advanced lessons later even in the same class.
TLDR: Teachers have to teach to the average, not the individual. You have to learn both how to find creative solutions to problems AND how to follow directions and tested ways of thinking.
@lolcats121 :')