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Anonymous Wed 13 Oct 05:33:10 2021 No.13745552 View Reply Original Report

Quoted By: >>13746822 >>13748036 >>13749568

Which math concept do you wish you were taught differently, and summarise how you want to be taught it.
I'll start, It took me ages to learn linear equations because I was taught to solve 3x + 5 = 8 by 'moving the opposite of + 5 over' or 'move the thing closest to the equals sign to the other side' and we had to memorise tables of doing +/- then x/divide then indices. It should have been taught more freely like the two sides of 3x+5 = 8 is like a balance scale and what you do to one side you do to the other to keep them balanced. From there teach them how by doing the certain operations (like -5) makes the 5 cancel out and creates opportunities to put x by itself.

Anonymous

Anonymous Wed 13 Oct 2021 05:47:48 No.13745585 Report

Quoted By: >>13745658

algebra in general was a fucking nightmare and it turned me off math from a young age.
I wish it would have been taught as a "language" with the operations as "grammar".
Instead of learning strange, esoteric algorithmic processes like "Cross multiplying" and "remember to flip the denominator when (rule that I still can't fucking remember)" and shit like that, I would rather have had it introduced as "you have multiplicative terms and additive terms. If all you have on one side of the equation are terms multiplied together, you can freely move one or more of those terms to the other side by moving it to the denominator (or numerator, you get the point) of the other side. If it's an additive term, you can freely move it to either side by moving it to the other side and changing the sign.
A denominator is a multiplicative group, even if it's just terms added together. You cannot (in basic algebra) separate any terms in the denominator and you have to treat it as one unit..."

etc. I was so terrified of fractions because they were never explained well. Only once did I figure out how you could actually manipulate them algebraically did they make sense.

Anonymous

Anonymous Wed 13 Oct 2021 05:54:50 No.13745594 Report

Quoted By:

also fuck whoever decided to call them "random variables" when they're fucking functions

Anonymous

Anonymous Wed 13 Oct 2021 06:00:18 No.13745602 Report

Quoted By:

Linear algebra only focusing on the reals really pisses me off.

Anonymous

Anonymous Wed 13 Oct 2021 06:18:16 No.13745634 Report

Quoted By: >>13747741 >>13749392

I think a lot of confusion in electrical engineering stems from the ubiquitous Ohm's Law First approach. It gives the impression that voltage and current are, in general, functions of one another which is just patently false. It leads to tons of instances where the equations become self-referential (in a "solve for 2 unknowns with 1 equation" sort of way), and where the actual real experimental results directly contradict what ohm's law would predict ("If I'm increasing the current then why is my voltage dropping???")

All of this is solved when circuits are instead given in terms of a constant power, as most real life circuits are. P=V*I, and P is constant. Instantly, you can see how V and I are related. "If P is constant and you boost current, your voltage must necessarily decrease, and vice versa". "Why does a op-amp unity gain buffer let me supply so much current, if V=I*R?" "Because V=I*R is irrelevant. If the op-amp output's voltage is the same as the input voltage, say, 1 volt, and the op-amp is being supplied by a much stronger power supply, say 100 watts, the voltage is constrained to a practical constant and so you have ALL of that I term to supply as much current as needed, in this case between 0 and 100 amps."

You can see *why* real life circuits act the way they do, and quite honestly it puts ohm's law to shame. Why then they treat P=V*I as secondary to V=I*R is beyond me.

Anonymous

Anonymous Wed 13 Oct 2021 06:29:09 No.13745658 Report

Quoted By: >>13748014

>>13745585
True, I feel like the foundations shouldn't be taught with shortcuts but in a way that you can follow what your taught for future concepts. And by doing that everything you'll learn in the future will fall in place with the foundations (since you learnt the real deal) so you'll have a stronger understanding because everything links to each other.
> I wish it would have been taught as a "language" with the operations as "grammar".
How you're taught english is like: speaking/writing --> obvious grammar like writing sentences that make sense --> learning that you've been using adjectives, verbs, proverbs the whole time and you can basically add that knowledge on top and so on...
I wish math setup the same way where you don't have to fix your foundations in future years.

Anonymous

Anonymous Wed 13 Oct 2021 13:47:31 No.13746822 Report

Quoted By:

>>13745552
I wish we were taught more how and when to use those math tools, instead of just spending all the time solving random ass exercises by hand without rime nor reason.

Thanks to that shit I only rememeber like 5-10% of what I've been taught. My brain logically saw math was only about solving exercises and not solving actual problems, so it all ended in the trash. All that time wasted for absolutely nothing.

At least if we spent more time in making us use our brain to see where those things could be applied, I'd remember what I need to use for X case.
Alas.

Anonymous

Anonymous Wed 13 Oct 2021 17:38:28 No.13747741 Report

Quoted By:

>>13745634
oh wow

Anonymous

Anonymous Wed 13 Oct 2021 19:14:45 No.13748014 Report

Quoted By:

>>13745658
>True, I feel like the foundations shouldn't be taught with shortcuts but in a way that you can follow what your taught for future concepts.
I feel the same. So many times you are tought needless specializations or outdated model concepts, just because they are maybe simpler at the moment (or maybe because it has always been taught this way). But that means that you have to relearn all this stuff later on almost from scratch, and often you even need to unlearn old ways to understand the new stuff.
I think chemistry is big offender, with orbital theory often delegated to university.

Anonymous

Anonymous Wed 13 Oct 2021 19:22:16 No.13748036 Report

Quoted By: >>13749396

>>13745552
Differential geometry and tensor calculus since I was introduced to it when learning relativity.
My book didn't motivate or even properly define what a tensor was, just "hurr durr transformations", and when it came to the covariant derivative and parallel transport, it would have been insightfull to learn the motivation behind it from how it's used on surfaces both intrinsicly and extrinsicly.

Anonymous

Anonymous Thu 14 Oct 2021 03:23:01 No.13749359 Report

Quoted By:

bump

Anonymous

Anonymous Thu 14 Oct 2021 03:35:20 No.13749392 Report

Quoted By:

>>13745634
the confusion stems from not starting with maxwell's equations and deriving circuit theory as an approximation

Anonymous

Anonymous Thu 14 Oct 2021 03:37:13 No.13749396 Report

Quoted By:

>>13748036
my notion these days is multilinear map. this works great for finite dimensions, although some math sperg can probably come up with better definitions for infinite dimensional vectorspaces

Anonymous

Anonymous Thu 14 Oct 2021 04:22:04 No.13749516 Report

Quoted By:

I feel like a majority of shit I was "taught" in school was presented as some sort of stupid game or metaphor. I would have been able to understand it a lot better if it was just presented straight forward and with the intended application stated plainly.

Anonymous

Anonymous Thu 14 Oct 2021 04:48:34 No.13749568 Report

Quoted By:

>>13745552
>Which math concept do you wish you were taught differently?
Nearly everything. There was just something in the way math instructors taught that made me not able to grasp the material.
Easily aced every other subject.

Now all I do is think of an equation and the answer almost intuitively comes to me. Like I barely need to think at all.

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