math-pedagogy

[remote vine]

How can you keep up with so many acronyms?

I find that amazing about the English speakers

What do AP, IB, HL, AICE stand for?

[tidal whale]

Context matters, I'd say

AP is Advanced Placement, American exams handled by CollegeBoard aimed at high schoolers

IB is the International Baccalaureate, which is similar to the APs in that they're special programmes aimed at high schoolers but also different in terms of subject matter and teaching/learning methodology as far as I know

HL in this context means a High Level IB subject

With IBs, you can either take the Standard Level of a subject or the High Level

If I recall correctly, there's a 6 subject compulsion of which three are High Level and the rest Standard Level

Then you have AICE (Advanced International Certificate of Education) which is actually a modified form of Cambridge's International A-Levels

AICE folk take the same exams as A-Level students, but the difference lies in the fact that A-Levels need 3 subjects minimum whilst AICE requires you to take a variety of them to satisfy credit criteria

[remote vine]

Thank you very much

[tidal whale]

No problem

Fascinating that IB is considered great abroad

They've just started bringing it here, but the students currently enrolled in our school's IB programme hate it claiming the teachers are awful

If that's the case, I'd hope it gets better

[lament wraith]

Our IB teachers were very good. I honestly think the IB program overall is much better than the AP

[tidal whale]

mhmm

What I've read is good

We don't have APs here though so I can't say much on those

We're A-Level folk

Hopefully the implementation gets better here

[scarlet perch]

ive heard mostly negatives about ib for us based unis mainly due to unis capping how many credits you can transfer over thru ib

[lament wraith]

Oh yeah, I was talking about the program itself. The unis haven't really adapted to IB's yet

Some colleges still don't even take them

[tidal whale]

Weird

[wind ice]

@remote vine as a native english speaker, it's hard for me too

acronyms suck until you know them

then you just use them and annoy others who don't know them yet

[proper sky]

I heard if you TA you can get some of your debt waived in college. Is this true?

[strange bronze]

TAing is generally a paid gig

relieving debt is one way that payment can be given, but an atypical one in my experience

[scarlet perch]

depends on the program

bio students can TA to get credits towards their major n the like

pre meds are notorious for this and similarly notorious for caring very little about their students in my experience

some times it's paid

masters students get their tuition waved for the quarters they TA here

[brazen pendant]

it also depends on your institution

or, at least, on your country

[turbid zenith]

Anyone up for looking at an exploration I wrote for supernatural numbers?

[unreal ledge]

Sure, show it off

I don't know a ton about them so maybe I'm not the best but eh

[meager bronze]

i will look at it

[turbid zenith]

The idea is that I'm going to be having one group of 4-5 students work on this together and then put together a 5-10 minute presentation showing off the number system and what it's like to the other groups, each of whom will be working on a different number system

They'll have 2 class periods to work through the exploration and make the presentation

(This is for that special summer program for high school kids who love math)

Also I'm working on fixing typos 😅

[unreal ledge]

Neat, the supernaturals have some cool properties

[turbid zenith]

Which properties do you think are cool?

[unreal ledge]

I didn't think to form a lattice with them, but I can see why that works

[turbid zenith]

Yeah!

When I drew it out for the first time a lot of things clicked

And convinced me that adding in the infinite exponents actually did get you something useful

(Also apparently they're really useful when describing profinite groups)

Also I tried to design it so that it does some explaining where necessary, but the majority of it is spent with the students exploring the properties

[meager bronze]

looking at it I think it's got some nice exercises. I don't understand the phrasing of exercise 15. how do you order natural numbers by inclusion? is it somehow related to the divisibility hasse diagrams or something?

also exercise 9 just tells me that the proper generalization is to use ordinal numbers as exponents. then 2^w + 2^w = 2*2^w = 2^(w+1) so there isn't a contradiction ;)

[turbid zenith]

Oops

I meant partially ordered by divisibility

I was trying to reiterate that I didn't mean the linear order, and I instead said the wrong one XD

And good point about Exercise 9 -- I also thought of using ordinals as exponents and wondered what that might do

[tawdry venture]

division will definitely be messed up

[turbid zenith]

Division is already pretty messed up

[ionic dagger]

hi. I often I pretend I am a tutor.

[scarlet perch]

hm, how would one define a function in the simplest terms possible? My first thought was: a function maps values from a domain to values in a codomain

would that be sufficient generally?

i'm thinking maybe saying instead: it takes values found in one group and transforms them to values of another

but i'm afraid that might not be clear and cuts out too much

[ionic dagger]

Technically a function is just a set of ordered pairs of ... anything. (thing, thing's "favorite" color) is the context here. A function is: {(Paul, Red), (Mike, Blue), (Jennifer, Purple),(That Bull In Spain, Red)}

[scarlet perch]

hm, so really it's just a method to find the other half of the pair based off the first?

[misty peak]

Is it not "method" per se, but just general pairing? You can define the pairing with "method" though.

[lost raptor]

@turbid zenith I think it's definitely much more well worked out than the original idea you proposed a while back

@scarlet perch The most generalized simplified form of a function for sets is your domain to codomain, but if you want a more intuitive approach as vincent listed you can consider functions as ways to get from one object to another (or as his example uses, the function g(x) = (x, f(x)) for any function f to create ordered pairs).

you can also get more fun with m o r p h i s m s and treat functions as the paths which can be followed along a collection of sets and functions (since you'd probably not care about all functions and sets, you'd likely restrict that collection)

Rather than as maps from an object in the domain to the codomain, you could just chase the diagram, but that's probably not too helpful for you

[turbid zenith]

Thank you @lost raptor !

Now I'm working on one for p-adics 😃

[lost raptor]

Yeah, the ordinal thing buncho said would also be what i would say about the addition, but you could just treat it as N U {inf} (plus it still doesn't fix addition for 2^inf + 3^inf xd)

also ooh p adics

If you don't include the inverse limit thing at least in a passing mention i'll be dissappointed

[scarlet perch]

Thank you! @lost raptor

[turbid zenith]

...I don't actually understand the inverse limit thing

[lost raptor]

hence at least in a passing mention

[turbid zenith]

I don't understand it well enough to even mention it. :/

[lost raptor]

just be like
"yeah you can make the p-adics with this cool diagram, but this goes above your heads and mine" or smshit

it looks fancy enough to probably wow them

[turbid zenith]

Infinite decimals to the left and weird absolute values are enough to wow them 😛

[lost raptor]

Yeah but i'd certainly enjoy if my teacher pulled some crazy shit outta nowhere and said "yeees but actually please no" (or other equivalent statement referring to how it's a bit much)

[turbid zenith]

The surreal numbers assignment will have a bit of that heh 😛

Have you seen what multiplication looks like

[lost raptor]

I think so, but in any case refresh me

[lost raptor]

Oh yeah surreals

I thought you said supernatural for a second and I was like "wait was it something weird"

Yeah I took surreals and once played with them a while back and examined what got broke when you allowed * to be treated as a number wrt addition and mult

[turbid zenith]

I'm making four activities total --- hyperreal, surreal, p-adic, supernatural

[lost raptor]

$\eta_z \cdot r = (2-r)\cdot\eta_z$ is certainly something I remember writing, though I forget if it was actually right, for $\eta_z = {z | -z}$ or something

[burnt vessel]

Darkrifts:

[turbid zenith]

Yeesh.

[lost raptor]

It had some weird negation sign that couldn't be distributed because it was as a unary operator, not multiplication by -1, and I forget if the statement I wrote included it or not

It probably has a - in front of the right half tbh, but I can't be bothered to go back and find out

In any case, if one accepts $2* = * + * = * + (-*) = 0$ then that holds somewhat

[burnt vessel]

Darkrifts:

[lost raptor]

@turbid zenith How are you gonna introduce the surreals? I assume you'd not do anything beyond S_omega

[turbid zenith]

Basically start off with the left-and-right-set thing at first, get used to what numbers are created when

then look at what's created on day omega and afterward

And see how you get a lot of ordinal-like numbers as well as infinitesimals

Hopefully also have an aside about Hackenbush

[lost raptor]

afterward
owo

[turbid zenith]

Well so that you get things like ω+1, ω-1, etc

[lost raptor]

yeah

[turbid zenith]

They'll have already seen such numbers because we're looking at the superreals first as a class

[lost raptor]

S_omega^2 probably wouldn't be surpassed by them

[turbid zenith]

Well like

There's no reason to not see why such things would exist if you really can just "keep going" 😛

[lost raptor]

tbh

but I doubt they'd do anything too far like epsilon 0

[turbid zenith]

It's easy enough to see what the number, say, ω² - ω + 5 - 3ε would look like

Yeah I doubt we'll get into epsilon_0

Though I've at least mentioned it before in previous years

[median locust]

Hello

[meager elk]

Hi

[ionic dagger]

hi

[cedar lotus]

Hey doggie

[turbid zenith]

Aaaaaa I leave for the summer program Wednesday and I am hype 😍

[scarlet perch]

that's not how i expected that to be read

[civic tree]

thats how i read it first

[misty peak]

Isn't that how you normally read that?

[warm lintel]

[brazen pendant]

<@&268886789983436800> just above

[wispy slate]

🚔

[civic tree]

wot happen

[warm lintel]

some wtf ad posting

[civic tree]

bad

[scarlet perch]

what happened lol

[civic tree]

lol

[silk moon]

Lol i need a trignometry teacher to stick around in dms

[brazen pendant]

not the place

[kind radish]

How should I handle teaching someone the mathematics behind a Laplacian transformation? The context here is for engineering students that will use it for practical system analysis later on.

I was thinking about giving a background on how to solve the integral for the transformation, but quickly switch to a dictionary style translation of functions between t domain and p domain.

[unreal ledge]

@kind radish
The approach that worked best for me was using it to solve a DE. The transform turns problems of derivatives into problems of algebra. That's likely all they will ever use it for

[urban notch]

any good resources to learn any of this advanced math?

I really wanna know what's being discussed in here lol

[unreal ledge]

@urban notch
Copy-paste a message that interested you

[lament wraith]

Also probably not here

[urban notch]

Where?

[unreal ledge]

Ehh, this is an odd enough request we don't have a channel for it. So, feel free to post it here

Either of the discussion channels works well too

[urban notch]

Alright

Well, nothing in particular stands out

I'm just trying to get a better grasp of the terminology used

especially regarding logic

just wondering if anyone knew any resources I could use

[strange bronze]

I mean

The best "resources" for uni-level math are, by and large, textbooks

You might find videos of lectures on YouTube or MIT OCW

But the textbooks are still good for alternative explanations and as a reference - and, more importantly, to provide practice problems

[scarlet perch]

if you plan on tackling a textbook, consider a study group of some kind for mutual accountability

[civic tree]

i feel like those work better with people you know irl but thats hard to set up initially

as in finding the people

to begin with

unless ur at a place with a bunch of people who are compatible at the moment to study with you

eeek

[round robin]

Just wondering, are lecture notes good to have or is it better to say let the student make their own or maybe email them some noted after the lecture

[brazen pendant]

as a student, lecture notes make my life a lot easier

and I hate it when there aren't any

[wispy slate]

Agree with ᛋᚪᛋᚳᚪ

[brazen pendant]

I like to have the lecture notes printed out and annotate them during lectures

and a lot of students do sth like that

[round robin]

Ah ic

So like lecture notes that contain the important information i guess?

Like don’t go through entire proofs but just show the outline

[brazen pendant]

My favourite ones were the 800 page Analysis notes

that contained absolutely everything in it

my notes would just be highlighting important steps, or annotating references with what they refer to (I hate "from 3.1.16 and 4.7.3 it follows, using equation (16) that x=y (compare also equation (5))")

[round robin]

kinda also feel that theres no purpose to the lecture if the notes contained everything XD

[normal bronze]

I've never had a prof that didn't add to the notes somehow through extra explanation or little side-journeys or whatnot, usually the lecture is at least a little better lol

[lament wraith]

In my opinion, I think a decent number of math undergrads are mature enough and responsible enough to decide for themselves whether the lecture is worth it for them over just some notes

[round robin]

hmm thats quite true actually

[wispy slate]

Like don’t go through entire proofs but just show the outline
I wonder about the opposite, namely doing the major points of the proof in the lecture and leaving the details for students to read in their home, with the detailed proof either in lecture notes or in an accessible reference

Personally, I think the plus that lecture notes should have over merely reading a book is that the lecturer explains things in a way not found in books

[lament wraith]

That's an interesting thought actually

I feel like if people are getting lost in classes, it's because there's some long proof with a ton of details that they can't keep up with

But if a teacher just gave a large picture overview of how the proof goes, the students would just believe it and then move on

And then the students could go over the proof in details on their own time and at their own pace so they could fully understand it

[round robin]

ah

[misty peak]

maybe you need study group to study detail of proof for motivation?

[round robin]

as in?

[round robin]

i think the whiteboard really liked it XD

[civic tree]

oh the satisfaction of cleaning that board

i wanna do it

spritz the cleaner and just

wiping it all away

n u t

hhhnnnng i wish my highschool had a whiteboard i could use with my friends whenever

like during lunch in some emptyish location

trying to do math with friends on small paper when i have huge handwriting is annoying

[round robin]

Classroom whiteboard?

[civic tree]

ye but i feel weird asking for it during lunch and afterschool

[round robin]

i just straight out abuse it mdr

[civic tree]

whut

lol

[turbid zenith]

Just thought I'd share this

For my summer kids.

[lament wraith]

shit you're teaching kids p-adics that's sick

[ionic dagger]

Shit is probably what most humans now alive would think p-adics are worth ... so few people care about "real" math ... so sad. Pure math ... the only thing that gets lower poll numbers than Trump :).

[lament wraith]

Sucks, but being sad about it doesn't really do anything

do what Ashura does and make sick lesson plans to get people interested in math

[turbid zenith]

We'll see how it goes!

I tried my best to write it so that you can probably get a good ways in with just precalc

Also, that's just one exploration that one group is going to do. The other three groups will be doing different explorations of different number systems (hyperreal, surreal, supernatural), then the next day they'll reassemble into different groups and share what they've learned.

[craggy verge]

jesus

you're doing a disservice to these kids

this is so awful

[turbid zenith]

@craggy verge Did you really just come in here to say that?

[craggy verge]

don't ping me

[turbid zenith]

lol

[craggy verge]

you should honestly quit

whatever you're doing

but you won't

[turbid zenith]

Nope

But thanks for trying

👍

[round robin]

hmm that’s quite a interesting intro but irritates the part of me seeing a divergent sum casually being equated to a finite value XD

[turbid zenith]

@round robin Any particular one, or all of them? 😛

[round robin]

all of them 😛

Meh the kids probably wouldn’t care much XD

[turbid zenith]

The point is to get them to play with them as formal objects, see that there's some consistency there, and then see in what context it could actually make sense

We've already talked about why convergence matters, so this is kind of a continuation

[lament wraith]

@craggy verge you want to at least describe why you think it's so bad?

[turbid zenith]

I don't think that's necessary. Let's just move on. 😃

That being said I'm up for legitimate feedback on anything that could be made more clear. I'm probably going to be fine creating the other two explorations, but this one took some effort to figure out how to sequence it.

[craggy verge]

@lament wraith sure

the core of the issue is fundamentally the approach to math

the idea of these modules is that math is about coming up with random shit

and doing it for fun

it's stated quite explicitly in the document and is clear from the choice of topics as well

and that's when it becomes a concrete issue

teaching useless nonsense like hyperreals and surreals and supernaturals to kids, who are probably starting to develop interest in math, diverts them completely

it takes their useful interest and sends it into nonsense

and kids at that age need guidance in order to start developing good mathematical intuition and a taste for what math is about

a good format for explorations is to come up with puzzles which have creative solutions that kids can come up with, and which also happen to be an application of some tool of theoretical interest

and it becomes about both creativity and learning about the field of the tool

an example that's widely used is burnside's lemma

I think what this is going to accomplish, is mostly confuse the kids about what mathematics is, make them waste time and effort into pursuing useless topics, and ultimately doing a disservice to young talent

when doing any kind of thing like this, designed to guide young students into math, I think it's crucially important to seek guidance from professionals in mathematics

or at the very least someone like graduate students

to avoid these kinds of issues

and that's how most outreach activities done by universities do it

[turbid zenith]

I 100% disagree with most of your assessment.

[craggy verge]

shut the fuck up

this isn't for you

it's for him

since he asked

you don't deserve any feedback or explanation

what you deserve is a bullet to the brain

[turbid zenith]

Excuse me, but no. You can disagree with me, but that kind of tone is completely unnecessary. Keep it civil.

[craggy verge]

excuse yourself

[cobalt stream]

Yikes

[turbid zenith]

He's banned. It's over with.

Debating cleaning up :P

[misty peak]

Is it wrong to learn useless nonsense?

[inland kayak]

It depends on your definition of useless

[misty peak]

OK I admit I don't have precise definition of useless, but I suppose it's something that doesn't seem to be immediately useful, like calculus or "real" math, whatever that's called. Maybe to go to the extreme it's like abstract symbol manipulation, with your own prescribed rule?

[wispy slate]

@Pear#5283 ye 100% correct

math education is shite these days

[lament wraith]

@misty peak yeah I feel like if it at least is interesting to kids then that's all that matters

Not them actually learning something that's relevant? I mean they're high schoolers like they'll have plenty of time to learn relevant things

I do get the argument that people will mistake what pure math is actually about

But I'm not sure you can make that argument for the p adics which literally come up all over the place in many different fields

@wispy slate lmao

[brazen pendant]

good riddance

[round robin]

Personally i would like to start with axiomatic foundation but that’ll probably scare people away haha

[brazen pendant]

I feel like it makes sense to first give some motivating examples and first properties

starting directly from the axioms just feels too unmotivated

[long loom]

I'd start off by giving someone/people a problem, asking how they'd go about it, and then trying to take previous knowledge to solve it (to some extent.) Atleast for more advanced classes.

For more basic classes/young children, I think one of the best ways to teach math is, by far demonstrating that you really can do anything. So long as it "makes sense".

(obviously there's more to it than makes sense)

I feel that, from looking at my peers, many people don't understand why the things we do can be done because they were taught fundamental in a poor manner for their taste.

It's really crazy to see someone even within a few years of my age try and explain what exponents and multiplication represent.

[turbid zenith]

I agree with lots of y'all.

In particular one of the things I keep saying is this --- mathematical foundation does not mean pedagogical foundation.

Just because mathematically you need to start with x to get to y doesn't mean that's how you should teach it.

[wispy slate]

What do you mean? You don't teach high schoolers the axioms then present proof after proof and don't tell them the underlyong motivation? (I am kidding.)

[brazen pendant]

well, no, you don’t actually present proofs to high schoolers

you just tell them the results and then give them 50 mindless tasks that are all the same thing but dressed up differently, to teach them that you don’t acutally need to read the entire exercise, only pick out some numbers

from When Good Teaching Leads to Bad Results: The Disaster of “Well-Taught” Mathematics Courses (Schoenfeld), which is a great read: http://jwilson.coe.uga.edu/TiMER/Schoenfeld (1988) Good Teach Bad Results-2.pdf

[civic tree]

wow

why are you putting this here

wrong channel ???

also yeah i agree with sascha

that way is pretty dumb

formulaic is sad and its prevalent in the usa

but showing proofs to highschoolers doesnt work either bc kids arent really prepared to deal with logical arguments

its gonna have to go wayyyy back some

sow the seeds of logic somehow

on an unrelated note

do yall think the number of kids in a class affects how well they learn?

i would think that it does affect it, because maybe fewer kids in a room would reduce the pressure to engage in class discussion... but

maybe a good lecturer could explain things well enough

and could answer questions in and out of the class period well

regardless of the size of the class

[brazen pendant]

is the wrong channel stuff regarding some deleted comments or was that directed at me cause my stuff relates to the above “teaching today” stuff

do yall think the number of kids in a class affects how well they learn?

so in Switzerland school classes cannot have over 24 students (and even that is considered exceptional, our classes were usually 17-20 students). during high school I went to brazil for a year and the class I was put in there had some 30-odd students. teachers had zero control over the class, and students didn’t learn anything. this is surely not soley because of the class size (seemed more of a cultural thing, tbh), but it certainly didn’t help either

at university, we have tutorials (which I give myself as well) which are intended to have about 10-20 students, but I’ve been in much larger and much smaller ones too

I found 10 to be about the sweet spot

if it’s much smaller, then it gets more personal, but it also often seemed less instructive just cause less people ⇒ less questions. but the 30+ classes were much worse too, because at that point it has to be restricted to only frontal lecture and silent work, but the tutor doens’t have the ability to answer everyone’s problems at once if multiple people get stuck on a problem

also I found that I’m more motivated to teach if I have more students

[wispy slate]

it depends on your self discipline

some people can manage in 30+ just fine

some people need to be manually put back on track

[grand laurel]

if it’s much smaller, then it gets more personal, but it also often seemed less instructive just cause less people ⇒ less questions

I had the exact opposite experience

Small classes always meant that the classes are more a conversation and not normal teaching

You go through material slower, but I learned much more

You can e.g. discuss definitions with the lecturer and other students

I.e. "Why don't we define it like that?"

Currently I TA a class set up kinda like that

People discuss questions in small groups and I'm there to listen to their ideas and modify them if they're stuck or give tips if they don't know how to start

Also give additional insight into why we do things and why I think they're interesting

It is the best teaching experience I had so far

[brazen pendant]

Small classes always meant that the classes are more a conversation and not normal teaching
yea, that does happen too, but it also derailed much more and in the end you learned less. the other thing I had happen twice was that the tutor liked to go a bit more in-depth. then students who didn’t like that left. now there’s about 5-10 students left who are actually interested. but then the tutor goes too far in that direction, because he actually gets interesting questions asked. and in the end you didn’t get anything but fluff out of it anymore

[grand laurel]

That's why I like my current setup

Groups that are not that good, I can help with the basics

But if someone wants to know more in-depth stuff I can talk with them kinda in private

Because I help each group of students individually

Obviously you can't design a lecture like this, this is just additional exercise classes

I'm actually surprised it works so well this semester, I tried doing it in the past

Had the first half of classes be normal teaching, and second half students work on problems and small group and I offer immediate help

But more than 50% of class left, once I stopped writing things on the board they can just copy

[brazen pendant]

yea that’s how it went with my classes a lot too

I had some success sometimes when I made the problem-solving stuff
a) not at the end but in the middle and
b) more interactive, breaking it down into subtasks and occasionally bringing everyone up to date on the last subtask

[civic tree]

@brazen pendant it was some deleted stuff

ok cool answers from yall

thx

yeah about the point about the more interested kids seeing the teacher later and talking about it

i like that a lot

[solar fiber]

What if we taught radians right from the start, and left out degrees?

I know it wouldn't work in the same sense as metric wouldn't work in the US, as it is so well established in people's lives, but what if?

[round robin]

It’s kinda nice to work with whole numbers mentally tho working in fractions is kinda cumbersome for eyeballing purposes

[inland kayak]

I've seen well known geometers use degrees instead of radians, I don't think using one over the other is a big issue

[brazen pendant]

I personally prefer to think in fractions of a circle

which easily converts to either, multiplying by either τ or 360, depending on what you need

that’s actually also my main motivation for liking τ, you can just think of the symbol as meaning “turns” or so

and ignore that it has a numerical value until you need it

[misty peak]

That's interesting take.

[turbid zenith]

Finally finished my other two explorations.

Holy fuck I'm exhausted.

27 pages of writing

[lost raptor]

smh

[turbid zenith]

WHat's up @lost raptor

[lost raptor]

not much

still floundering about

Might have fixed some issues I had with a nasty F function in something of mine

[round robin]

teaches ε=-dφ/dt
we don’t know calculus

rip

[civic tree]

lol physics

wait

what is that

is that even physics

i just saw φ and thought of physics rip

[topaz blaze]

Looks like faradays law

Physics without calculus is

[hazy agate]

apparently at my school physics with calculus is easier than physics without calculus

AP phys is easier than phys Honors

[meager elk]

ive had physics with literally 0 calculus usage

[hazy agate]

algebra-based calculus?

[round robin]

i just crash courses calc mdr

[frozen cypress]

I just did the ASVAB math practice test

damn that was some easy stuff

[lost raptor]

it's the asvab, did you expect something crazy?

[frozen cypress]

I don't know lol

I'm going for Navy Nuke due to my love for numbers, physics, and legal policy

I think I'll have the right type of skills for the job.

[tidal whale]

A-Level Further Mathematics class here was 1h30min long and just three students - was pretty fun

We could cover an entire unit on the course within a day's work of discussion and example

Teacher also spent time proving whatever we encountered using math we knew

Probably the greatest math class I've sat in

Plus the conversational approach just seemed better

It wasn't a board with him writing away, it was all of us messing around on a notebook to see the point

Heck he even went out of his way to explain properly how Root-Mean Squares worked when we got to the mean values of functions

Root-Mean Squares was on Physics but never explained with any math or something

There it was a magical process where dividing peak voltage by √2 always yields the answer

I hate the Physics course for this lack of math...

[lost raptor]

What was it on?

Was it just like furthering other math used in your other courses?

[frozen cypress]

Algebra and Geometry basics

mostly prealgebra

[lost raptor]

For you, nice

[tidal whale]

@lost raptor
We had Pure, Mechanics and Stats components

Pure
→ Viete's root formulae applied to polynomials
→ Summations of series
→ Further Differentiation & 2nd Order Differential Equations (Homogeneous and Nonhomogeneous)
→ Polar Coordinates
→ Further Integration - Means, Centroids, Curve Lengths, Surface Area of Revolution and Reduction Formulae
→ Complex Numbers & DeMoivre's Theorem
→ Further Vectors - Cross Products and their uses
→ Matrices & Vectors - Dimension, Rank, Null Spaces, Range Spaces, Eigenvectors and Eigenvalues
→ Mathematical Induction

[lost raptor]

what was De Moivre's?

[tidal whale]

(Cos(x)+iSin(x))^n = Cos(nx)+iSin(nx)

[lost raptor]

ah, that

handy thing

[tidal whale]

Aye

[lost raptor]

of course, all the stuff that went into it originally is kinda trivialized by the whole euler thing

[tidal whale]

Yep

Still, definitely a useful identity

Trivial or not

[lost raptor]

of course

it's not trivial in deriving it (though a little bit since you know the answer already), it's just kinda trivialized

most of that seems fairly nice, the diff eq one is interesting

[tidal whale]

The 2nd Order Diff Eq stuff was probably the easiest to tackle

Hardest stuff on the tests was always Complex Numbers and Matrices

[lost raptor]

I assume it was probably mostly in methods of solutions seeing as diff eqs get very nasty very quick

[tidal whale]

It was just using the auxiliary equation to determine the complementary function, then summing it with the particular integral if possible

Then finding the particular solution if possible

Coefficients were constants

[lost raptor]

probably with laplace mentioned somewhere in there

[tidal whale]

Nope

[lost raptor]

really?

[tidal whale]

I wish he was but alas

[lost raptor]

huh

[normal aurora]

black box

[tidal whale]

read the earlier convos a tad bit late

but one thing I've noticed in lower classes and helping out my sis

none of the early kids get how things like the distributive property work

weird

like, they get it once they're told about it and all

but until then they have no idea why taking a common works

just do

they can't apply things like commutivity

don't see where associativity works

boggles my mind

like, how can kids cover quadratic equations but not know why each step works

they just treat it as rote algorithms

then there's this weird bit about memorizing "algebraic identities"

nobody ever sees why sin²x+cos²x=1 is just pythagoras

they never make that leap even in the class with the unit circle

[lament wraith]

Saying that nobody ever sees that is a bit

[tidal whale]

I'm not sure how the school handles classes, but I am somewhat scared - not sure if it's irrational or not

[tawdry venture]

sounds like a byproduct of a shitty teacher or rushed syllabus

[tidal whale]

probably

[lament wraith]

Yeah, not super representative of math education as a whole

[tidal whale]

mhmm

seems to be common among private school kids here now though

that and the dreaded "the exam technique outweighs the knowledge" thing

[round robin]

^^^^^^

so many kids are just training to be professional exam takers

without actually understanding

[civic tree]

it is tragic

but that's how they wanna get thru it quickly :(

also might be a money thing ??? if better scores lead to more funding

[round robin]

hmm maybe?

quite bad tho

[solar fiber]

Not Maths, but my High School Physics lessons were always on the idea and understanding, and nearly all syllabus material (memorisation bit) was learnt as homework. I think it worked really well.

[round robin]

Idl to teach physics without the math tbh, it spoils the physics for me

[tidal whale]

I didn't like Physics without the math

It worked in early classes sure

But at higher classes it felt like we weren't evolving much from old material

It is especially misleading as well

Since higher physics is math heavy

Physics without it feels pretty limited in how derivations and interesting questions can be designed

Plus the lack of math means failing to explain certain practices because "it just works"

No Uni-level professor likes what they've done to high school physics here at least

[dusky shell]

high school physics where?

in uni then yeah physics should be math based, but the level of math most high schoolers know isn't really enough to actually do much of anything

even physics C is pretty basic

[tidal whale]

Pakistani Private High Schools that use British A-Levels

[wispy slate]

Hello

Does anyone here study pedagogy? math ed in general?

[turbid zenith]

I do!

Or did

But at least I still read about it

[woven sigil]

I'm training to become a math teacher

[tiny mulch]

😶

[round robin]

how does that work actly

[brazen pendant]

probably depends a lot on your country.
In switzerland, if you wanna become a math teacher at the high school level (which here is generally speaking the earliest level where you study to become a math teacher and not a teacher who happens to also teach math) you do a master’s degree in mathematics followed by a 3-semester teaching diploma (includes an internship and stuff) and then you’re considered qualified to be hired as a teacher

standards are pretty damn high, but salaries are very good too

I reckon about half my teachers had a phd too

[tiny mulch]

In India many teachers have fake degree .

[vestal quiver]

O_o

[wispy slate]

@turbid zenith

Did/do you have a particular focus?

I'm trying to find more resources on textbook/course/lesson design for linear algebra AND also approaches for communicatic geometry/linear algebra/spatial concepts to people who are blind ( and possibly also deaf )

[turbid zenith]

I really want to look into variations of mastery based grading in undergraduate math

[noble phoenix]

@brazen pendant that's incredible. I don't think I had a single math teacher in highschool who knew more than multivariable calculus themselves

[round robin]

same tbh

[brazen pendant]

I can’t find the document rn but there’s a document somewhere that explains why you need a master’s degree

and it basically boils down to “yea, with a BSc you’d have all the necessary knowledge to teach the curriculum, but high school teachers don’t only teach the curriculum. You also have to supervise semester projects and teach advanced classes where you can bring up your own interests”

(one of the mandatory things to get a high school degree in switzerland is writing a project over the course of about a semester. for all intents and purposes this is another subject. you can do more or less whatever you want, in math that tends to boil down to researching some undergrad level topic and writing up a thingy about it. a friend of mine did sth about julia sets, another one looked at the mathematics of shuffling cards, yet another one studied the differential equations governing the motion of a non-mathematical pendulum)

(one friend built some measuring device. forgot what exactly but something something light frequencies. another programmed a simulation for colliding objects. another composed a song. not everyone’s a mathematician ^^)

[meager elk]

maybe someone here knows a good book with problems AND ANSWERS TO THEM from introductory group theory/abstract algebra?

[turbid zenith]

@meager elk Look up Contemporary Abstract Algebra by Joseph A. Gallian

[meager elk]

will do, thx!

[round robin]

me doing a math project
my teachers actually understanding it

once i did some partition function analysis for liquid crystals and my teacher was like
Ah number theory
just cuz a jacobi theta appeared XD

wait you can compose songs as projects .-.

[brazen pendant]

well yea, in music

they let you do just about anything as long as you can find a teacher who’s willing to supervise it

someone built an alphorn

a few years back someone painted a large mural

every year there’s a few people who write a book

one of my classmates studied the salt levels over time in a river that was situated below a dam

another retraced the history of a relative of his who left switzerland to fight for the nazis through letters he had written to his family

I constructed a language

[buoyant oasis]

Your highschool is a cultural hub lol

Once my teacher took us out for an ice cream

However there are some similarities here for math teachers, like maybe qualifications required
Salaries are not included in the similarities though, I suppose xD

[brazen pendant]

my highschool has 1200 students and 160 teachers, it's quite big

only high school that offers the full program in three languages, afaik

[meager elk]

wtf thats a huge amount of students and teachers...

[brazen pendant]

only public high school for a huge region

we’re talking some students come from places four hours away (by public transport, about two by car but they can’t legally drive at first)

the school is accessible to everyone ni the red area (about 70k people live there, it’s extremely mountainous). there’s other schools but they’re much smaller

this is the only Kantonsschule in that region (“state school” i.e. government funded)

(note of those 70k, about half live in the town where the school is)

[grand laurel]

wait, how do the logistics of that work

do students commute to school for 4 hours every day?

or 8 with way back

[scarlet perch]

oh my lord

that commute

[brazen pendant]

dorms

it’s not a plausible commute

and I meant 4h each way

it’s only 3h actually

now, I commuted more or less from Chur to Zürich (top left) and that segment takes 1h15

such is the power of mountains

[round robin]

wow those projects actually sounds pretty fun

[jagged thunder]

switzerland

[shut osprey]

Best time to visit Switzerland ?

[meager elk]

5 pm

[exotic frost]

You missed it, it was yesterday

[civic tree]

lmao

[grave gyro]

second best time is RIGHT NOW

oof looks like you missed that too

[dusky shell]

is it true tho

[turbid zenith]

...maybe?

[round robin]

meh bell curve it

[shadow basalt]

Ok but why did you post this here

[wispy slate]

(Deleted a message that had nothing to do with the channel and was already posted on several other places.)

[turbid zenith]

Ok bell curve would be true evil

Grading on a bell curve should be a crime

[round robin]

tbh i prefer bell curve grading😛

[shadow basalt]

Bell curve grading is awful lol

Percent-Grading is kinda dumb in general imo

[normal aurora]

if you had to grade using a curve

which would you use

[turbid zenith]

I would find another school.

@shadow basalt What do you mean by percent-grading? Like saying that a particular percentage of A's are available, etc? Or something else?

[shadow basalt]

Well the former is def silly to me, I think curving makes no sense because it’s very possible to have an unusually gifted class

I’m more against formal exams

I’ve had a few discussion based / oral finals for math

I found them all to be more interesting, and I never lost points on silly mistakes because professors could point them out live and I could fix the@

[turbid zenith]

Ahh gotcha. Yeah I'm with you.

[shadow basalt]

I also am a big fan of like, research projects being a decent chunk of a grade or something

I did a cool TDA project for algebraic topology and it was cool to think about

[turbid zenith]

TDA?

[shadow basalt]

Topological data analysis

[turbid zenith]

Ahh interesting 😮

[normal aurora]

all these initials

[turbid zenith]

Yeah, lots of TLA's in education

😛

But hey that's cool to hear about alternate assesssment methods being talked about in higher education

That's something I want to investigate a lot

Anyway, I do think that grading on a percent-based system is stupid 😛

Like what's the real difference between a 79 student and an 80 student?

[shadow basalt]

One mistake

[turbid zenith]

Well yeah but you know what I mean.

[shadow basalt]

No that was my point like

Is one mistake indicative of a difference in skill?

Or chance?

[turbid zenith]

Ahh yeah. Exactly.

It's entirely within statistical variation, but we use it as a cutoff point between "good" and "meh"

And GPA's are calculated with them to the hundredth or thousandth of a point

[wispy slate]

do you want to do this dm

[turbid zenith]

Like

Kinda

[whole veldt]

[tidal whale]

Why even grade on a bell curve

[scarlet perch]

weeder courses tend to do bell curve

mainly bc they wanna screw over as many people as possible

[turbid zenith]

It looks bad if too many students do well, supposedly

Everybody wants to say their program is "rigorous"

[tidal whale]

doesn't that ignore the case of just having a good class though

[brazen pendant]

my school couldn’t actually afford it if everyone passed

but the philosophy is very different

cause it’s nearly trivial to get in

and then really hard to stay in

[meager elk]

lol that's such a bad system imo

[brazen pendant]

it’s a requirement for swiss universities to allow everyone with a swiss high school diploma (which I must emphasize is nontrivial to get and while I don’t know the statistics, out of my secondary school of 20 students, only 5 went to high school and this was considered a relatively high number)

I personally think it is a much better system than having to fight your way into a college, often with ridiculous competition

[wispy slate]

Huh, where do the rest go?

[brazen pendant]

learn jobs

[wispy slate]

Pragmatic

[brazen pendant]

I mean quite literally, switzerland strongly supports apprenticeships

[wispy slate]

Much better system than the academic bloat that we have in the rest of West for the sake of "securing a job"

Another reason to like Switzerland

[scarlet perch]

honestly, i love trade schools

[brazen pendant]

basically the choice is between:
-do you want to learn a specific job right now, make money as young as 16yo and have a qualification at 20 or
-do you want to go to school until you’re 20 to get a paper allowing you to go to school even more only to then, eventually have a chance at a better-paying or more prestigious job

[scarlet perch]

also, interestingly enough, a lot of jobs like garbage collection and construction often pay higher in the us than many that require a degree

[brazen pendant]

it’s a choice between stability/security and a much riskier but potentially higher reward

and the majority go for the former

[scarlet perch]

mainly bc everyone's gone to college to get college jobs so demand is high

[brazen pendant]

often times with the intention to work your way up the slow way while working

[wispy slate]

Yeah, a lot of people go to college for the secure lifestyle - which ironically doesn't always pan out

[brazen pendant]

e.g. my father learned electrician

then got a bunch of extra educations over the years while working

[wispy slate]

And get yourself into a fuck load of debt while you blunder through unessential education

[brazen pendant]

and now has a high paying IT job working for the cantonal (state) government

[scarlet perch]

it's just a lot of unfair societal pressure in the us now

and also some rather deceptive stuff by the universities as well

[wispy slate]

Oh big time "college is supposed to be the best years of your life"

You mean your honeymoon isn't?

[scarlet perch]

they said the same about high school

[wispy slate]

Fucking riperoo

[brazen pendant]

high school was trash
university is just fucking stressful

[scarlet perch]

id honestly rather the majority went to trade schools, because the amount of bullshit competition and the horrible ways the uni tries to handle bloat just deceives the students

[wispy slate]

Hey man, if you're in somewhere like ETH Zurich and you want to keep on trucking academically - you are in a very nice position

[brazen pendant]

that is exactly where I am

[scarlet perch]

like. how is it in any way reasonable to allow students to get a major, and then try to fail them out of it in the first few months

[brazen pendant]

dunno if I’m gonna go down the academic route tho

[wispy slate]

And saddle them with debt that is actually collectible in the process?

Its insane

[brazen pendant]

I’ll do my master’s and the teaching diploma

[scarlet perch]

ooh nice

[brazen pendant]

and then decide whether I wanna apply for a phd position or go straight to teaching

[wispy slate]

It isn't for everyone, does that teaching diploma let you teach undergrads?

[scarlet perch]

i assume it's like. hs right

[brazen pendant]

the teaching diploma is for becoming a high school teacher

teaching undergrads is a professor thing

[wispy slate]

Ah gotcha, gotcha

[brazen pendant]

never seen an important class taught by a phd student or sth

[wispy slate]

Its only recently that we've required people to have PhDs and professorships to teach

[brazen pendant]

minor electives sure

but not like, mandatory classes

as for TAing

I’m in my 4th semester and have TAd already

[wispy slate]

Noice

[brazen pendant]

they let you do that as early as 3rd semester

just gotta have good grades

[scarlet perch]

ive seen like. a weeder sorta class taught by a phd student

weeder in a loose sense

discrete math functions as a weeder class for many cs majors, and i remember multiple of those classes being taught by students

[brazen pendant]

we don’t actually have weeder classes

our classes are always in blocks

[wispy slate]

So what accounts for the drop outs?

[brazen pendant]

overall difficulty

[scarlet perch]

not specific classes

just long term?

[brazen pendant]

you can’t get through unless you’re actually diligent

a lot of dropouts happen because people are lazy in the beginning and never manage to catch up

[wispy slate]

Oof

[scarlet perch]

ah

[wispy slate]

Meanwhile in UK universities first year isn't even taken into consideration with the final degree grade

[scarlet perch]

thats why tutors get hired tho

[brazen pendant]

of course you can repeat but many students choose that it’s not for them

and change majors or even universities

[wispy slate]

Could you change back into an apprenticeship?

[brazen pendant]

a priori yes

there’s nothing stopping you

except the hiring process

[wispy slate]

Right

[brazen pendant]

but you did just waste four years in high school

and then another one at uni

[wispy slate]

Oof

[brazen pendant]

if you do that

I assume most people who fail the first time round try again at a different major or university and succede, having learned from their mistakes

[wispy slate]

Gotta communicate your value over a gullible 16 year old

[brazen pendant]

and some never learn but I like to believe idiots aren’t that common

(slash can’t pass high school)

it should be mentioned that our high school education is deliberately broad, so that you can pursue any direction in university

[scarlet perch]

enough people cheat that I'm afraid the latter hope does not hold well

[brazen pendant]

e.g. one of my best friends (and one of the best math students I know) actually focussed on latin in high school

and then almost at a whim decided to study physics (and we both changed majors to math after our first year)

[wispy slate]

Watching a Chinese kid google translate an assignment and then get a distinction for his thesis was all the proof I needed that the game was rigged.

[brazen pendant]

tbf, that only worked because you didn’t rat him out

[wispy slate]

I was sleeping with him, so that wasn't exactly on the menu

[scarlet perch]

wait

what. google translate huh

that's p amazing

[wispy slate]

Dude came from rich ass family though, so there's some weird going on there

[scarlet perch]

is that more of a statement on the people who reviewed the thesis than him?

did a new building show up the next year due to an anonymous donation

[wispy slate]

The Tong Institute

No unfortunately not, but there's definitely some greasy stuff going on at my last uni - esp. when it came to the Chinese

[brazen pendant]

said friend had to do some catchup to do (because she was e.g. not familiar with differential equations and physics 1 kinda assumed you’d either seen them somewhere or could pick it up) but it pretty much just proved that it’s like 90% diligence if you wanna get through a math degree at ETH

I’ve also seen the opposite, sadly

[scarlet perch]

well, that's rather impressive and motivating!

[brazen pendant]

another good friend of mine has some learning problems - can’t focus for long enough to get enough work done. extremely motivated, but it wasn’t enough :(

[scarlet perch]

one of my friends works with my unis math department and some local schools to try to make sure students who are going into stem majors have some decent math background before coming so they dont have to catch up as much

[brazen pendant]

she’s changing universities now to one that lets her do part time study

[scarlet perch]

aw

well, i wish her the best!

[brazen pendant]

I’d just like to know if she got accepted already (due to not having passed her first year within 2 years she was technically banned from ever studying physics again in switzerland but due to medical issues that got kinda revoked but she had to go through a special application process and they’re slow af to answer)

so she actually still doesn’t know whether she’ll be starting physics or chemistry in september

[wispy slate]

That's kinda nuts

I guess no system is perfect

[scarlet perch]

jesus

[brazen pendant]

it’s to stop people from wasting too many years of taxpayer money on something they can’t do

[scarlet perch]

how do they justify banning someone from a

ugh

still

ig it's different bc it's not like us private unid

*unis

where u pay to buy extra tries

[brazen pendant]

like, the thing is, you almost have to actively try to waste your time to get banned

which she of course did

because she thought she could do it

the second time round

and that’s essentially what they don’t want to see

people who think they can do it, but can’t, and keep trying

[wispy slate]

Harsh

But fair

[scarlet perch]

still saddening to hear

[brazen pendant]

I do think the two year limit on passing the first exam block is a bit overly harsh

but I think that’s more to deter people from postponing their first year exams and continuing their studies regardless

and then it has unfortunate side effects sometimes

usually what kicks people out is failing an exam block twice

(you can only retake exams once, so if you fail a mandatory exam twice you lock yourself out of graduating)

[wispy slate]

I guess you gotta draw a line in the sand somewhere, a policy will always have casualities somewhere

[brazen pendant]

yea. and they do consider the individual

she has a medical/psychological condition, and this is taken into account and she is likely gonna be given a blank slate

[wispy slate]

One more try

[scarlet perch]

hence why she wasnt banned by the country

from physics

?

[wispy slate]

I think so, yeah

[brazen pendant]

well it’s more like… she is but they’re probably gonna ignore it

and pretend she never studied anything

[wispy slate]

Well that's a lot more elegant than the British system which kinda wants to have this vocation at 16 thing but classist snobbery kind of inflated every uni and polytechnic into a booming diploma mill

So now there's way to many graduates flipping burgers.

[scarlet perch]

ahaha

cries in usa

[wispy slate]

So they're now pumping up the prices of UG and paving the road to apprenticeships to go the same way as the Swiss and Germans really

But they also give everyone complete tuition loans (up to the doctoral level) that are basically interest free and then paid back as a tiny sliver of your wage when you're making bank. So its done nothing except give the government a future way to tax graduates into the future

[turbid zenith]

BTW, "I was sleeping with him" wins for today's line-that-made-me-double-take

[dusky shell]

[civic tree]

lol

[serene bloom]

[wispy slate]

lol

[lethal leaf]

What are y'alls thoughts on flipped classroom?

For teaching math

My math teachers started doing it for Honors Algebra 2 and Trig (a historically hard class in school) and for calc BC

And the grades have been way higher than they've ever been

But I want to hear your guy's thoughts

[true bone]

If the classroom is upside down I feel like I'd have trouble focusing

[lethal leaf]

Thankfully I'm not in Australia so it's still right side up

[brazen pendant]

is flipped classroom the one where you’re supposed to research the topic as homework and then do problems in school as opposed to the other way round?

[merry mulch]

sort of, in my experience you're given resources to learn about the topic outside of school

[brazen pendant]

(a friend of mine has a class that had such low attendance that now the prof just puts online video lectures and the lecture itself is for problem-solving and he’s there for question)

[lethal leaf]

So the teacher would give us a guided notes sheet (examples theorems and problems)

Then they'd make us a video walking through the sheet

And we'd go home and we're supposed to watch the video

And then in class we can do practice problems and ask questions

Because normally you don't have that much time to ask questions in class because they gotta get a lecture in to teach the material

I personally thought it was really really good because I could have a full conversation with my teacher about certain topics

[brazen pendant]

in high school, my physics teacher (in the advanced physics elective) liked to mix things up occasionally, so we had a few different ways topics were taught. some topics he’d just teach regularly. others we’d have time in class to read about them in a textbook and he’d be there for questions, and we got regular homework. finally, for some topics, we got some resources to read at home and then had time to solve exercises in groups during class, and in the beginning of each class we’d do a quick repetition of last week’s material.

of those, the in-class research was bad, the frontal lectures were alright and the last one was a blast

probably helped that those were the most interesting topics tho

(special relativity and an intro to the basics of QM)

[merry mulch]

for me i had flipped classroom in a chemistry class in high school and that worked quite well imo and i rly liked solving problems as a group in class

[brazen pendant]

there was one problem on one of the SR problem sheets that we discussed with the teacher over the course of like two weeks because we were sure there was some mistake - in the process we learned a lot

ultimately it turned out to be miscommunication

the question was ambiguous in a way neither us nor the teacher noticed, he was thinking of one interpretation and we of the other one, and both had answered the respective question correctly

[meager bronze]

I taught a flipped honors calculus class last year

I think it's a good thing to offer but I think this was a weird level to offer it at.

The students had never seen proofs before and so they never really learned how to write proper proofs. They were given theorems and stuff to prove on their own and present in class, and so they learned how to write proofs by watching other students write proofs on the board, but those students learned by watching other students...

And so nobody really knew what made a good proof until like 2/3 through the year

(for the record, I was told I was teaching it flipped, I didn't make the decision on my own)

[lethal leaf]

My teacher would go through proofs in the lecture videos (not rigorous proofs)

[meager bronze]

The way our class was set up, there were pre-made "scripts" that had all the lemmas/theorems on them

[lethal leaf]

The only thing the students had to do was take the notes and do the homework/quizzes/tests

[meager bronze]

students would figure it out on their own, and then in class they would volunteer to give the proofs on the board

there were no quizzes or tests

[lethal leaf]

and ask questions if they had any (which was the main reason for flipped classroom)

[meager bronze]

with the exception of a short final exam

[lethal leaf]

Oof my physics class was no quizzes or tests and that was hell

[round robin]

wait if you are supposed to do problems in school doesnt school become like a tutorial session with no lectures

[meager bronze]

what do you mean?

[lethal leaf]

Lectures are videos and you get a notes sheet with example problems that you try on your own and get walked through

that you do at home

and then you do the problem sets in class

for practice

and then you can ask the teacher for help if you have specific questions

you get more 1 on 1 time with the teacher

[civic tree]

sounds nice

i want to try inverted class

as student and as teacher one day

awa

[shadow basalt]

As a student

All of my friends who have had them

Hated inverted classrooms

They considered a waste of their money and found the reading/video learning format awful

Although the IBL style bunch was describing isn’t quite that

Due to the presentation portion (I took a class like that)

[wispy slate]

Inverted stuff is just not the same and having tried to self-study a portion of math doing this it just works so much better when you can bounce ideas off someone who knows what they're doing. There's a lot of false starts and it can cut a lot of the bs (even if it makes you look dumb)

[meager bronze]

don't you still get that opportunity to ask questions and bounce ideas off of the instructor during the class time? I thought the whole point of inverted classrooms was to maximize the amount of time where you could do that

as opposed to having to spend a lot of class time getting lectured on stuff that you could just read in a book

I'm just playing devil's advocate here, I do see some drawbacks with the inverted model that the standard lecture model does better

[shadow basalt]

From what I hear, as long as a professor isn't a jerk about office hours

you already can get the time you need with them

But not having an interactive lecture is brutal for learning

[meager bronze]

emphasis on interactive

just having someone spew words at you for an hour isn't good for learning haha

[shadow basalt]

most of my math lectures have been plenty interactive and people often ask questions

[grand laurel]

I had inverted classroom as a Student for my real analysis and abstract algebra classes

it was great

our teacher basically wrote a book that we had to read

we had simple online assignments

and class was asking questions about the reading of the week

and more simple exercises

there were additional homework and tutorial sessions

[lethal leaf]

I mean in high school you don't get office hours

so yea maximizing question time is the goal

if you're doing flipped classroom as a teacher

provide good video lectures that you made yourself preferably

and give a guided notes sheet

and go through example problems

basically do everything you can to avoid people asking "what is this topic" in class

you want people to ask specific questions if they ask questions at all

[round robin]

For those doing physics
Are landau books like still good for studying physics nowadays? haven’t rlly read them but have some people asking me about LL’s books
Personally I’ve read like the first 2 books
Imo his mechanics seem to assume knowledge of mechanics
Classical field theory had quite a pretty sr intro, otherwise it’s basically like griffiths but relativistic, while the GR is basically hilbert’s derivation from plugging lagrangians
Not too sure about his other books tbh, tho splitting qm into nonrel and rel seems quite uh unnatural imo

(dont really want to like recommend a book without actually reading through)

i should just isolate myself for like 2 month to binge read all of landau

[wispy slate]

I mean what level are we talking here, from times I've been bullied by physicists with LL, I'd probably imagine they're only appropriate for physics grad students. And even then to be taken as a supplement to a seminar or a second treatment of a subject.

Its the physics equivalent of "oh cool, you wanna learn AG, go read Hartshorne!"

[shadow basalt]

Wait that’s what I did to start AG lol

[wispy slate]

Rough intro imho

You need some good algebra background to take on Hartshorne on the first try

[shadow basalt]

Oh I mean I have a good algebra background

[wispy slate]

I think it would be fair to say that most undergrads should probably take a look at Eisenbud or something a bit more involved than D&F before attempting Hartshorne

But listen, I'm not exactly the one that should be measuring the average undergrad with my smol pp here

[round robin]

LOL BULLIED BY LL

[wispy slate]

@round robin Ayy, maybe read it, turd blossom

[round robin]

would prob take a few months to read through the books

[brazen pendant]

I can’t really give you a good answer, since you’ve read the only two I’ve got experience with already

I really didn’t like the style

[turbid zenith]

Awww

I missed the discussion on flipped classrooms :<

[signal smelt]

Hey guys I'm studying to be a math educator and I was hoping if there were some pointers in what to add into my resume if I want to get a tutoring gig. I have no history other than being a sophmore in university and being a part of 2 education programs geared toward being a prepared teacher and a good STEM educator.

@ me or DM me. I'm not frequent here. I'm just looking for work.

[turbid zenith]

@signal smelt Add those for sure, as well as a list of what subjects you would be comfortable in tutoring

For me I listed out a bunch of classes I was able to tutor in, especially AP's and such

[scarlet perch]

also, i know that some tutors will take an exam for the subject they wish to tutor in, such as if you're tutoring for the bio SAT for example, you would go in and take the bio SAT. If you were tutoring for AP Calc BC, you would try to find a way to take it and aim for a perfect. Since you're in uni, listing your GPA can't hurt either

[boreal yacht]

Is there a difference between doing math as an undergraduate and math as graduate versus <some other major> as an undergraduate and then math as a graduate?

Well, I'm sure there is a difference, but could anyone elaborate on it if there is anything to elaborate on?

[grand laurel]

i know some physics majors, who switched to (pure) math after their undergraduate. they were strong enough in math, that it wasn't much of a problem, but still had to work more their first year and (re)learn some things

[boreal yacht]

Hm okay. I am going to be a freshman engineering major this fall (engineers will declare their official major after their second semester at my school). I really like math and have considered majoring in math, but I figured if I majored in math, I would want to do more than a bachelors. So if its all the same, I figured why not major in electrical/computer engineering or comp sci, and then go to graduate school for math if I still care by then.

Is that something that people do?

[dusky shell]

why is this in this channel

[wispy slate]

@boreal yacht it is what my plan is if I decide to keep going to school after I graduate with my EE degree next year. I know another EE guy who is also considering getting a masters in math after getting his bachelors in EE. Given that so many engineers enjoy math quite a bit (I feel bad for anyone who is in engineering and doesn't like math) it is not uncommon for engineering students to either double major in math or go on to get a masters in math later

also, because of the massive overlap in bachelors engineering and math degrees, you would be taking most of the math classes you would need for a BS in math by getting a BS in engineering

[boreal yacht]

i see. thanks.

And I asked in this channel because im looking for more informed opinions

[wispy slate]

gasp you don't want random people screeching baseless advice at you? The nerve!

[scarlet perch]

if you don't want that, why are you on discord?

[boreal yacht]

eh, true. I guess I am also kinda directing the question to teachers. Is this a good idea, bad idea, or does it not really make a difference in their opinions?

Good point tho colorado

[grand laurel]

you are in the US right?

bcs in Europe, Germany specifically there is no overlap between engineering and mathematics bachelor's

and it would be very hard to make the switch

[boreal yacht]

im in the US. Tbh tho, im not really sure that there is that much overlap. calculus and ODEs overlap. Linear algebra seems like a grey area right now, not really sure. Then there is another 20 to 30 credit hours of math that engineers don't take. I intend to just take all of the math I can, and hopefully I will have time to continue studying math stuff on my own to make up the difference 🤷

[grand laurel]

also did you even take a proof based class yet

maybe you don't even like mathematics

[boreal yacht]

I've read about half of "Linear Algebra Done Wrong" (~ 1 semester worth) and done pretty much all of the exercises. I've been trying to learn group theory lately. I think I enjoy proof based mathematics, and I have definitely really enjoyed doing algebra so far. I agree its too early to take the plunge. I feel compelled to at least give engineering a try.

[grand laurel]

i did study 1 semester of engineering before i switched completely to mathematics

i had a very good "math for engineering" professor who got me hooked

so yeah, if you are unsure start with engineering

especially if calculus is compulsory for both majors anyway

but switching to math later will only get harder i think

because mathematics is purely proof-based and engineers don't really care about that

and mathematicians also care a lot about things engineers don't care about at all

[pine dock]

🤔

[lethal leaf]

Ok so I'm going to start tutoring once the school year starts

I have a question

What's a good way to get notes for classes I've already taken?

I have my AP Calc BC (calc 1 and 2) notes but nothing before that

[signal smelt]

@scarlet perch to be honest my GPA isn't the greatest. Lol I had a rough couple of semesters. I'd be proud of a 2.8 but I'm not even that.

[scarlet perch]

hm, do you have a major gpa? if so if that one's higher, i'd recommend including it

@signal smelt

if you're tutoring for specific courses, i'd recommend putting the grade you got from those courses

other than that you probably don't really need much

[brazen pendant]

wait what do you need your grades for?

[scarlet perch]

@brazen pendant they're applying to be a tutor and looking for things to put on their resume

[turbid zenith]

For those teachers/TA's for whom classes are starting soon ... best of luck this semester! 😃

[brazen pendant]

can I pass this semester first?

no need to rush!

[turbid zenith]

D:

Best of luck finishing the semester!

[civic junco]

i need to get my techer to downlead discord and have him join this place lol

[brazen pendant]

I mean I’ll be fine DM; there’s only one subject that actively worries me

and the grade is averaged over five subjects

with my current guess of how the first exam went, even if that one goes as poorly as possible I still only have to barely pass the other two

and if today’s goes as well as I’m hoping it’ll fully compensate anything on that one critical exam

even a 0% grade

(of course it would still wreck my over-all average and make it impossible to get a distinction when graduating, but that’s basically impossible already because I only had “really good” grades last semester, which is not enough for that)

(graduation with distinction requires a grade average of ≥95% over all your major-related subjects from second year onward)

(it’s hard enough to get that in one subject)

[grand laurel]

≥95% compared to your peers or on test scores?

[brazen pendant]

peers are irrelevant

[scarlet perch]

that statement applies to life as a whole

[brazen pendant]

nah I like my peers

they’re lovely people

[lethal leaf]

Where do you guys get practice problems?

I'm tutoring a precalc student, algebra I student, and two elementary schoolers

So I need practice problems for them

Do I just make then up as I go?

[round robin]

yea

thats what i do most of the time

[civic tree]

thing is

you want to make them up in advance in some form because

the more advanced it gets the messier the numbers become

and sometimes the messiness of the numbers takes away from the ease of the problem, which will take away from the student's focus in understanding the goal of the problem

or method

whatever it is

doing it in advance isnt an easy way to do it tho

since ur gonna be meeting the day of and u probably dont know what they need to work on unless u are continuing from before meeting

idk

[shadow basalt]

i would just steal them

like find some competitor textbook

and use their practice problems

[civic tree]

mm yes

that's a good idea

wew

[shadow basalt]

(make sure the practice problems actually align w what the student knows)

[civic tree]

yeha

cross check in some form somehow idk

[shadow basalt]

Metal I'm the worlds foremost expert on avoiding doing any work myself

[civic tree]

ask for homework

lol

nice max

teach me the ways one day

[lethal leaf]

Hmmm I have the textbook my school used for honors Algebra 2

I can use that

And yea the plan is to focus on making sure they're doing homework and tests correctly

But if I want to brush up on a topic/make sure they're doing it correctly practice problems would be gucci

[strange bronze]

students are really bad at telling you what they dont know

or what theyre not sure on

you can ask "do you understand this?" and they'll say "yeah"

and then you ask them to do it

blank stare

practice problems keep them honest.

[round robin]

agreed^^^^^

[meager elk]

Also, just don't ask "who doesn't get it". One of my teachers (the best one I've ever had) always asked: "Raise your hand if you understand". He would try to explain everything again if atleast 25% students didnt raise the hand.

in high school pretty much noone understood physics cause noone was brave enough to say 'I dont understand, could you explain it again', thinking others get it.

[round robin]

ahhh

that sounds a lot better actually instead of like
so yall understand? great lets move on

[lethal leaf]

I find if I'm explaining something to someone that telling them to walk me through a problem or just explain a concept is a good thing

[turbid zenith]

One thing I've heard, in terms of how wording matters, is how instead of asking "Does anybody have any questions?" (expected that there are none), you can ask "What questions do you have?" (expected that there are some). But even then, I find a lot of students have trouble realizing they even have questions until they're kind of "released" to answer them, either as HW or classwork.

[civic tree]

ah

yeah

thats an interesting concept

to remember

[visual breach]

like when doing flashcards, it's better to ask yourself "do I want to remember that better?" instead of just "did I know that?" when deciding which flashcards to put in the "again" pile. Phrasing definitely helps with honesty

[round robin]

(actly how does flashcards work never used them b4 someone explain pls?)
for me i just write my own notes

[turbid zenith]

Ugh. What is the point of having eight graders multiplying three-digit-by-three-digit decimals by hand.

What do they honestly think the value of that is.

[normal aurora]

oh yeah I did do that

[turbid zenith]

It's just ... meaningless, no context, etc

"Can you memorize this algorithm and do it by hand"

Then you get stuff like "Maria can type 48 words in 6 minutes. What is her rate in words per minute?" Answer: "Terrible"

[slate turtle]

Because arithmetic is hard I guess lol

But moreso because number sense?

[turbid zenith]

I don't think three-by-three multiplication does much to build number sense. 😛 I think it kind of destroys it.

[grand laurel]

Maybe it's required in everyday life

I think it's important that people can do it, although one could argue it's bad to teach it at this point (or even in a math classroom at all)

[patent wadi]

hey i was wondering if anyone here is a hs math teacher in california?

[patent wadi]

does that also include asking for advice on becoming a math teacher? because im not tryng to ask about my math homework lol

just trying to confirm

[hoary pecan]

oh lol, thats fine sorry
but i cant help with that

[scarlet perch]

dm worked as one for a while iirc

[lament wraith]

Not in Cali

[scarlet perch]

o yeah didnt see that

[turbid zenith]

Um. Hmm.

Yeah I can't help with California yeah. :/

Best to look online for resources. Often states have their own requirements.

So you want to be familiar with those.

Licensure, etc.

[brazen pendant]

Maybe it's required in everyday life
yea no not really. knowing the multiplication table is extremely useful a lot. knowing in theory how multiplication algorithms work can come in handy in a pinch, but rarely. practicing to get fast at it is a waste of time

[brazen pendant]

in general, a lot of early math teaching is justified under it being useful, because it would’ve been 100 years ago if you wanted to become an accountant or vendor

[turbid zenith]

https://twitter.com/solidangles/status/1166497045961728000

Bill Shillito (@solidangles)

How many sides does a circle have?

Asking for a friend and her kindergartener daughter. If possible, please comment a reason for your answer.

This should be fun... Never too early to show students that definitions matter and math can be full of interesting discussions! ...

Twitter

[elfin plank]

what does it feel like when students confuse you with stupid answers

[brazen pendant]

two: inside and outside
proof: jordan curve theorem

sides in the sense that a square has four: doesn't make sense. That definition relies on straight lines connecting vertices. You could broaden it to define sides as the number of C1 segments in the curve, in which case a circle has one side

that's actually probably the most elegant way to go about it, what do you think? @turbid zenith

[turbid zenith]

LOL I love it

And yeah, C1 segments is what I was thinking about

Though would it be able to be called a segment if there are no endpoints?

[brazen pendant]

when I say segment here I suppose I mean an injective C¹ function from (0,1) to ℝ² which can be continuously extended to [0,1]

[wispy slate]

which channel should I ask about ergodic and dynamical systems?

[brazen pendant]

I… don’t think we have an appropriate channel for it. I guess whichever of #advanced-analysis and #point-set-topology feels less wrong to you

(I’m aware neither really fits)

we haven’t really had demand for a channel for that; at least I haven’t really seen and discussions about it

[wispy slate]

odds

odd

seems like it would be the how new thing

[brazen pendant]

I mean you also have to understand that the vast majority of the people on this server aren’t even at a level where they know what dynamical systems is. we only have a few active people who have finished their bachelor’s degree

I’m gonna miss out on the dynamial systems lecture next year (there isn’t a regularly occuring one and I have other priorities, but I’m sure it’d be very interesting)

[limpid mantle]

who here has experience with online homework platforms?

[round robin]

those that my sch tried are rather crip physical is still nicer tbh

(ok my sch tried like ms teams and one note both are ehhh not so nice)

[lament wraith]

What exactly are you asking

[remote pumice]

https://youtu.be/Z5T_onnzYS4 How would you guys explain question 4 in this video? I have a hard time giving a good solution for that one..

[lament wraith]

Yeah I feel like you should start off by talking about what greatest common factor even means

Some of your viewers and audience may have forgotten

The usual way to find greatest common divisor is to prime factorize all the numbers, and then just take the lowest power of each prime that you find