There is a lot of evidence that the educational establishment is full of idiots. Alternatively, for the conspiracy theory that it is trying to create compliant peasants rather than educated citizens.
It’s very different from the dreadfully boring memorization-based curriculum I had to endure.
Understanding is well and great, but instant and effortless arithmetic recall is table stakes.
I find it astonishing that term rewriting systems are considered esoteric mathematics that you don't see unless you work in a very specific and niche fields of mathematics or computer science.
Plenty of college students are doing multiple pages of derivations for their coursework.
$$ \frac{\frac{a}{b}}{c \times \frac{d}{\frac{e}{f}}} \times \frac{\frac{g}{h \times \frac{i}{j}}}{k} $$
And watch 98% of them fail to bring it to normal for a simple fraction.
Likely you misunderstood something here, not the people you talked to. Do you mean they get confused with that notation? Not understanding specific notation doesn't mean you can't do the thing.
In three classes totaling 43 students exactly one got it right and he was a double major from CS.
This is Latex, it renders nicely to: https://arachnoid.com/latex/?equ=%24%20%5Cfrac%7B%5Cfrac%7Ba...
Which is the question I posted all those many years ago.
Doing real algebra without something like the Kunth Bendix algorithm is somewhere between pointless memorization and the equivalent of a mathematical lobotomization.
That it wasn't invented until 1970 shows us just how poor we are at mathematics.
You get what you pay for.
Pennsylvania attempted to put minimum standards on teachers; a big chunk of the teachers failed. When faced with the huge amount of money the state would have to shell out for teachers who could pass, Pennsylvania dumped the standards and never tried again.
Pay in education is garbage relative to all the other jobs a teacher is qualified to be doing instead.
And then we complain that education is dominated by the unqualified.
And so it goes.
Yes, school management has to genuinely document an "underperforming teacher". There is a full legal process that has to be followed and it takes time. Too bad, so sad.
However, the problem is that school management doesn't want to produce that "documentation". It is genuine work and has the downside of maybe exposing that the teacher isn't underperforming and now a countersuit is incoming. In addition, attempting to fire a teacher almost always causes a kerfuffle in the community unless the teacher is complete garbage. And, see, if you, as a superintendent cause a kerfuffle, that is going to hit the local news and the Internet and is going to be a negative mark when you want your next job (superintendents tend to move on while most teachers do not).
So, what your little shibboleth is advocating for is unlimited authority by the superintendent to punish anybody they deem a "troublemaker"--which is any teacher with the temerity to do something that might get in the way of their next promotion. And that optimizes for teachers who simply don't rock the boat under any circumstances irrespective of any teaching skill or educational results.
Not unless it is coupled with accountability for results.
A tutor can do trial and error and eventually find a way that helps the student understand. School system has a needlesly specific curriculum that is decided a priori, and it's not optional.
I work with a lot of curricula. There are degrees of specificity. Common core is, notably, absurdly specific, and dense. It’s the US at its best, which is to say its worst. Including the fact that CC hasn’t ever really been touched since. This is seldom how curricula in actual developed jurisdictions are built.
There are also degrees to which a teacher can ‘play it by ear’ in their classroom. This is informed by their ability to do so competently, and the freedom allowed by their school, school system, etc. The existence of a curricula, even in a public education context, doesn’t inherently disallow a teacher from attempting different teaching styles to get through to a kid, or changing what they focus on in order to teach to their students’ zone of proximal development.
Schools “adapting to metrics” is very much moreso informed by the undeniably reality that, with any sizeable group of kids, and realistic constants on resources, you quickly need to start doing “formative assessment”, and doing assessment well is really hard.
Above all though, schools adapt to metrics because it’s what’s demanded of them by their bosses. By that, I don’t mean ‘educational bureaucrats’, I mean…parents, taxpayers at large, etc. ‘Hold hands under a rainbow and nothing bad ever happens’ individualised education is simply very hard to monitor, it’s very hard to hold anyone to account. Stakeholders hate this. They want measurement. They want numbers. And numbers invite systems, and putting people into boxes. We get exactly what we deserve here. Nothing more and nothing less.
The world is full of people who are not smart and don't want to feel inferior. No conspiracy needed, we've collectively decided it's best to dumb down to a common denominator to make everyone feel included. That's what you're seeing here. To a degree this is part of a good society but it also removes incentives to escape mediocrity.
Perhaps attempts to abolish gifted and talented programs in schools?
In the metaphorical galaxy brain comic of this situation, “GATE programs fell out of fashion because of tall poppy syndrome” is the first or AT BEST the third frame.
It’s the line of thinking held by the ‘uninformed self-described smart guy’ contingent, that knows nothing about education, yet think that they can intuit their way through it. It’s unrealistic, naive, and utterly condescending. It’s no surprise that I see it so much in tech people.
Are you an educator or pedagogy researcher? You certainly act as if you are.
I've seen this firsthand. Kids who think they're gifted and talented, and coast with B's through high school. Then college Calculus hits and they realize they don't actually know math or how to reason about it - they only know the surface level of the pieces and how to apply them in a test.