I don't remember hating math in school as much as I do now. The internet is partially to blame. I bought a used math dictionary and "encyclopedia" to see if they help, and they do, so part of my problem was the crap on the internet on websites like BestEasyJoyMath101.crap. Crap should be a mandatory TLD for crap. It makes me want to teach math the proper way, after I dig in and finally figure something out. But I decided to try writing math instruction before I realized how bad things were.
About six months ago I was almost finished creating some math instruction and now I'm trying to pick up where I left off but I can't really do that. I have to dig up the right definition for some terms because I forgot. At least I have notes and books now.
I've been wondering whether specifying imaginary/real numbers even matters since imaginary numbers seem like impossible numbers or impossible solutions to impossible problems when you read certain instructional material about them AND when you get an "invalid input" error from a calculator when trying to find the square root of -1. One definition of "PIECEWISE-DEFINED LINEAR FUNCTION" begins "Given non-overlapping intervals on the real number line..." Could there be an imaginary number line? In my digging I found there's a way to express different imaginary numbers, so maybe there can be. It depends what you read.
IMO, someone with aptitude for math who wants to get concepts could be turned off by all the crap out there.
I've been wondering whether specifying imaginary/real numbers even matters since imaginary numbers seem like impossible numbers or impossible solutions to impossible problems when you read certain instructional material about them AND when you get an "invalid input" error from a calculator when trying to find the square root of -1. One definition of "PIECEWISE-DEFINED LINEAR FUNCTION" begins "Given non-overlapping intervals on the real number line..." Could there be an imaginary number line? In my digging I found there's a way to express different imaginary numbers, so maybe there can be. It depends what you read.
I never really got imaginary numbers, but knew the rules. I haven't had to deal them them in a long time. But how I understand them is that the real number line is like 1D, and imaginary/complex numbers give you a pseudo-2D. So you can describe things about 2D shapes like circles using them. Probably they get so much flak because they're called imaginary. All numbers are somewhat imaginary though.
Traditional sadistic math pedagogy I'll worship like a dog at the shrine of your lies ... take me to math class! Shout out to Hozier!
"My favourite song from one of my favourite albums, Nena asking you to please, please let her be your pirate. So smooth and joyful, I have to listen to it three times if I listen once" - ashi
I kind of like math for its efficiency in learning it, as long as I can consult written instructional material at my own pace (reread a sentence, refresh my memory, regular study stuff, unlike what you get from a teacher). I hate stuff like reading a novel and memorizing as much as you can because you don't know what will be on the test. I also like that good math work is easily proven to be good. The equation clearly works. Good novel writing...what even is that? Good written instruction is more substantial. People of all kinds could tell you if it's better than the competition. You don't need qualified reviewers.
I never really got imaginary numbers, but knew the rules. I haven't had to deal them them in a long time. But how I understand them is that the real number line is like 1D, and imaginary/complex numbers give you a pseudo-2D. So you can describe things about 2D shapes like circles using them. Probably they get so much flak because they're called imaginary. All numbers are somewhat imaginary though.
This is quite a good video on where they came from. The tl;dr is that when solving quadratics you didn't need to care so much as you could dismiss them as artefacts of physically impossible solutions as the OP says. The thing is when you got to about the Renaissance era and mathematicians started working out how to solve cubic equations - that actually have physical analogs too - there are real solutions that come from the cancellation of square root of minus 1 that are valid in the real world but come from a process that temporarily throws up these imaginary numbers. That is what gave them a kind of semi-legitimacy as a temporary problem solving tool. It took a lot longer until people accepted them as a self-consistent 2d number system in itself.
In some sense they are no more unnatural that negative numbers or zero both of which were also considered unphysical abominations sometime in the past but that which are now widespread in their use. As I understand electrical engineers use them a lot too in terms of calculating phases, impedance etc in circuits.
That said, for all I have tried, I have never yet fully got my head around quaterions as a number system in 3d graphics. I suspect this is why many game devs still prefer to think in Euler angles despite their shortcomings.
I got enough of a handle of where I left off in the instructions I'm writing that I'm not procrastinating like I had been, but I encountered something in the material that's given to teachers of common core algebra 1 that refers to something that I can't find, which got me daydreaming: I think it may be a good idea for math teachers to play a video of a really good teacher teaching, then just stop it along the way to answer questions, or replay sections, or give a quiz, because I see that teachers aren't told exactly how to teach certain things which could be a big problem.
They’re actually doing that now. I saw a post where a student find out the teacher had died the previous year. She was taking online university courses, and the university owns the recordings of classes done in prior years. I imagine this will become more of a standard practice post-pandemic.
While it could be done well, in the states at least it’s likely to lead to further injustice against workers. Someone who is alive will be teaching that class, but they won’t give them fair pay because of the use of recordings.
Anyhow, math thread. Right.
I’m still all about set theory and group theory tyvm.
Attention is the rarest and purest form of generosity - Simone Weil
I found no index to help me find when certain things are taught. I wanted to find when imaginary numbers are taught and had a very hard time and almost gave up. Turns out "imaginary number" is used in a definition that's introduced in Algebra 1, but the term isn't actually taught until, well, by that name maybe never, but the italic i is referred to as an "imaginary unit" and taught in Algebra 2. So, in explaining the technical definition that includes "imaginary number" in Algebra 1, I have to teach a little Algebra 2. But it will be very little and I have an idea. When I submit this I think suggest an index to help find when things are taught.
*graffiti's a horizontal 8 to the tune of "rock 'n roll high school forever and ever"
"My favourite song from one of my favourite albums, Nena asking you to please, please let her be your pirate. So smooth and joyful, I have to listen to it three times if I listen once" - ashi
