Anyone who has attended public school will nearly unanimously tell you that “school sucks.” Or, as I prefer to say (and Evan Chen prefers to say), “school is broken.” What does that mean? This means there are fundamental roadblocks to the learning of students and the teaching of teachers set up by the system, and incompetency by those in charge is the reason it remains.
To address this obvious issue, we must first ask ourselves what the point of teaching is. I argue that “teaching” in the traditional sense is not even remotely necessary for motivated kids; and for unmotivated kids, they do not learn anything or learn very little from this public schooling system.
We accept the point of teaching as to hasten the growth of or develop understanding of connections in a particular subject and to develop specific and general intuition/problem solving skills in motivated students.
There are a variety of methods for this. Books, online classes, handouts, problem sets, and traditional teaching all place different emphasises. This means that only going through handouts/problem sets will be challenging (but still possible!) to develop higher skills in motivated students, only going to traditional classes will be very lackluster, and a union of traditional teaching and going through material may be an efficient method for most motivated children. (The “motivated” condition cannot be dropped!)
So what is a traditional class about? Well, traditional classes are limited resources; they require immense amounts of time and effort to set up, and motivated students will only absorb a fraction of the information. (Better to give too much to absorb than to bore your students with not enough!) Traditional classes are about pushing regions of math students have not explored before; traditional classes make new ideas more accessible for motivated students. What of the unmotivated students? Trying to teach unmotivated students is pointless, because they will not care about absorbing the information. So we should not be focused on getting unmotivated students to learn; first and foremost, we should be getting them to be motivated. Let’s make a note of that.
It doesn’t make much sense to try and teach unmotivated kids, so we should be trying to make them motivated. However, motivation isn’t black-and-white; a student motivated in maths can be unmotivated in science. It is nearly impossible to find someone who cares about all of their classes, especially keeping in mind the existence of PE.
The “point of teaching” as described in Postulate 1 is non-trivial to achieve.
We proceed via contradiction. Let us assume that “the point of teaching” is trivially achievable. Then this implies that teaching is meaningless. However, teaching (when done right!) has been shown to nontrivially improve the performance of students. Teaching being pointless and teaching being meaningful contradicts each other, so the premise we started with (“the point of teaching” is trivially achievable) is false, proving Lemma 1.
Effective teaching is hard to achieve.
This follows directly from Lemma 1, otherwise it would be trivial to achieve the point of teaching.
But can we really get everyone to be motivated in everything? I doubt it. We would’ve already solved the problem of the lack of girls in STEM if we could’ve done so this easily. This leads us again to the distinction between anyone and everyone. Yes, anyone can become a USAMO winner, but every year there are only 12 USAMO winners. We clearly cannot have everyone be a USAMO winner. We can pique anyone’s interest in maths, but it is ridiculous to assume we could even get close to getting everyone interested in maths.
Theorem 1 applies for students and teachers.
This should make intuitive sense; a teacher needs to teach well and a student needs to learn well. Again, this is different for every subject; I would make a pretty worthless PE teacher, and in all honesty, I am a pretty worthless PE student. This leads me to a very controversial statement: “Math class should be optional.” Lockhart does a better job of saying this than I could, so I’ll be referencing him. In essence, if a student is already motivated for math, then they would be going to math class; if they are not motivated yet, it is a waste of the teacher and student’s time to go to math class. This applies for any class.
So far we’ve laid out the obvious; don’t make unmotivated kids hate the subjects they are unmotivated in. (I feel it’s important to emphasise this isn’t black and white; most kids are unmotivated in some subject or another.) But why are so many kids unmotivated in the first place? This comes from a combination of two factors; kids are penalized for being motivated and are discouraged from pursuing their motivations, instead wasting swaths of time, and kids have been incorrectly taught that hard work equals success.
Kids are penalized for being motivated.
Motivation happens in a long period of time (say a couple of hours) rather than sporadic bursts that can be cut off. School frequently cuts off motivation; this is why we have “settle in, kids” for block and “warmups” for math. Additionally, any second working on a personal project (say, my book) is a second that homework piles up.
Students don’t do their homework for this reason exactly; they care more about personal projects, aspirations, and the like to be doing homework.
This is exactly why students are so lazy; they’re used to their work being useless despite the school teaching them “hard work = success.” This is not the case; you have to learn to do hard work despite the fact that you are likely not to succeed.
Kids are taught hard work = success, which is false. This sets kids up to not work unless they are guaranteed success (which we all know a more accurate descriptor for that condition; this is called “never.”)
How many times have you heard the mantra “hard work is success?” This is setting kids up to think that they cannot do anything, and that they are just failures, when the case is that success is never guaranteed.
We live in a society where the mantra is, “Get good grades in middle school to create a habit for high school! Get good grades in high school to get into a good college! Get good grades in college to get a good job! Get a good job, and… get a good life?” Where does the mantra end? This is completely false! School is setting up these students for a world of disappointment, and is not “preparing students for the real world” as they claim they do!
School is broken. (Refer to the definition of “broken” I gave above!)
Direct result of either Lemma 2 or Lemma 3.
Notice how I was careful to say either. This means that to fix school, we must at least fix the problems that have been referred to in Lemma 2 and Lemma 3. (This result should be very obvious; it is only here to highlight the problems, aka Lemma 2 and Lemma 3.)
How we fix Lemma 2: We make longer classes, and significantly longer classes. (“Longer classes” means longer than 2 hours and certainly no shorter. This could work on a weekly rotation basis.) This also gives us a lot of quality of life changes, particularly in Science; no longer do labs need to be split into a “Part 1” and “Part 2;” this simply emulates actual science. Scientists don’t sit around waiting for the next “work period” when they have found something. Additionally, we can have longer tests that don’t need to be split up; I think this is also a very important quality of life change. (A quick note: Why do the administrators think FLEX has any chance of helping kids make up a test? This basically makes FLEX pointless… because kids can just work in class! Yes, I know a teacher who regularly gives 30 minute tests… what a childish notion!)
How we fix Lemma 3: This should be obvious. Stop telling kids to “try, try again” because if you don’t care enough about something, you will “fail, fail again.” Even people who do care don’t always succeed, and I argue (this is taken from Evan Chen once again!) that it is more beneficial for your growth if you fail.
“It’s hard to do a really good job on anything you don’t think about in the shower.” These words spoken by Paul Graham ring true; the natural question to ask is, “Why on earth has nobody figured this out yet?!” I refer again to Evan Chen, who does a better job explaining than I could hope to; he talks about this in “Diversity and Neg EMH.” In essence, it is very likely that if you think enough about something, you will get a big “a-ha!” moment that should seem obvious to everyone, once you think of it. This is true for nearly everything; even in maths, we have examples of people making obvious mistakes, or obvious oversights (how did it take people so damn long to think of Gaussian elimination)?
Then I present a question: How many fundraisers have happened? Perhaps you have not been very aware of them, and they only took up a small figment of your thoughts (I know this is the case for me), or you have been constantly aggravated when you heard, “Another fundraiser?” Again, this really depends on what position you’re in; for me, it certainly is not a big thing. But for the administrators? Their job has become running the fundraisers, which is ludicrous to me. How can they expect to fill the dual role of fundraiser and making the school better? For a fundraiser to succeed, you need to think about raising money in the shower, and this means you can’t think of making the school better in the shower.
This does explain why the school is run so childishly; the people in charge are focused on raising money, rather than improving the school.