Comment by reliabilityguy 3 days ago
> Lying to Children reverses and bastardizes this process. It starts with a single useless system which contains equal parts true and false principles (as misleading assumptions) which are tested and must be learned to competency (growing those neurons close together).
Can you provide some concrete examples of it?
I included the water pipe analogy for electric theory, that is one specific example.
Also, In Algebra I've seen a flawed version of mathematical operations being taught that breaks down with negative numbers under multiplication (when the correct way is closed over multiplication). The tests were supposedly randomized (but seemed to target low-income demographics). The process is nearly identical, but the answers ultimately not correct. The teachers graded on the work to the exclusion of the correct answer. So long as you showed the correct process expected in Algebra you passed without getting the right answer. Geometry was distinct and unrelated, and by Trigonometry the class required correct process and answer. You don't find out there is a problem until Trigonometry, and the teacher either doesn't know where the person is failing comprehension, or isn't paid to reteach a class they aren't paid for but you can't go back.
I've seen and heard horror stories of students where they'd failed Trig 7+ times at the college level, and wouldn't have progressed if not for a devoted teacher helping them after-hours (basically correcting and reteaching Algebra). These kids literally would break out in a cold PTSD sweat just hearing the associated words related to math.
I did some tutoring in a non-engineering graduate masters program and some folks were just lost. Simple things like what a graph is or how to solve an equation. I really did try but it's sort of hard to teach fairly easy high school algebra (with maybe some really simple derivatives to find maxima and minima) in grad school.
I'd love an example too, and an example of the classical system that this replaced. I'm willing to believe the worst of the school system, but I'd like to understand why.
The classical system was described, but you can find it in various historic works based on what's commonly referred to today as the Trivium and Quadrivium based curricula.
Off the top of my head, the former includes reasoning under dialectical (priori and later posteriori parts under the quadrivium).
Its a bit much to explain it in detail in a post like this but you should be able to find sound resources with what I've provided.
It largely goes back to how philosophy was taught; all the way back to Socrates/Plato/Aristotle, up through Descartes, Locke (barely, though he's more famous for social contract theory), and more modern scientists/scientific method.
The way math is taught today, you basically get to throw out almost everything you were taught at various stages, and relearn it anew on a different foundation, somehow fitting the fractured pieces back together towards learning the true foundations, which would be much easier at the start and building on top of that instead of the constant interference.
You don't really end up understanding math intuitively nor its deep connections to logic (dialectics, trivium), until you hit Abstract Algebra.
Up to the first or second chapter, depending on the book being used is more than sufficient to cover the foundational concepts. Sets, and Properties such as closure over given operations, and mathematical relabeling which is a function (f(x), the requirements for it (uniqueness of x, and projection onto) along with the tests for the presence of these, and common mathematic systems properties.
This naturally provides easily understood limitations of math systems which can be tested if there is a question, and allows recognition when they violate the properties that naturally lead to common mistakes, as well as providing a space where they can use numbers/geometry/reasoning at play.
Not OP, and it was a couple decades ago, but I certainly remember professors and teachers saying things like "this isn't really how X works, but we will use the approximation for now in order to teach you this other thing". That is if you were lucky, most just taught you the wrong (or incomplete) formula.
I think there is validity to the approach but sciences would be much, much improved if taught more like history lessons. Here is how we used to think about gravity, here's the formula and it kind of worked, except... Here is planetary orbits that we used to use when we assumed they had to be circles. Here's how the data looked and here's how they accounted for it...
This would accomplish two goals - learning the wrong way for immediate use (build on sand) and building an innate understanding of how science actually progresses. Too little focus is on how we always create magic numbers and vague concepts (dark matter, for instance) to account for structural problems we have no good answer for.
Being able to "sniff the fudge" would be a super power when deciding what to write a PhD on, for instance. How much better would science be if everyone strengthened this muscle throughout their educatuon?