math-pedagogy

[remote pumice]

Yee felt like I didnt explain that one well at all.. At the end of the question I show that you can do the whole factoring, but my guess is that it takes to much time to do that..

Feel like this question is made to just "see" the solution by looking at the numbers and answers..

@lament wraith Thanks for feedback appreciete it!

[lament wraith]

Nah, ACT questions would never require you to recognize a trick like that

It's faster sure if you see it, but I don't think a ton of students are worried about time

Moreso worried about how you would algorithmically do it given any 3 numbers

[remote pumice]

Great to know! In my country the admission test is all about time presure, do you have alot of time on the ACT? Never done it...

[lament wraith]

Well this server probably isn't the best place to ask that cause we're probably not the most representative sample, but I think generally it's not a ton of time, but it's enough

[remote pumice]

👌

[lethal leaf]

@lament wraith it's 60 questions in 60 minutes

Oh rip wrong ping my bad

@remote pumice it's 60 questions in 60 minutes for the ACT which is a real time crunch for most people

[turbid zenith]

Luckily though the first half is almost entirely very straightforward

[remote pumice]

@lethal leaf Thanks! Then I quess that question is made to just "see" the answer..

[lethal leaf]

I mean for that question I would just make a list of the factors of that number

Actually wait

I think calculators have a GCF function

And the ACT is an all calculator test

[stone tusk]

well gcf is pretty easy via Euclidean algorithm

[remote pumice]

New video! Any feedback is highly apprecieted! https://youtu.be/x0byubKfQsA Taking on question 6-9 in this one!

[round robin]

||>still not getting paid cuz underage||

[obtuse girder]

https://arstechnica.com/science/2019/09/college-students-think-they-learn-less-with-an-effective-teaching-method/?amp=1

[remote pumice]

Happy teachers day!

[round robin]

what ive observed is lecture style you don’t really have any open discussions so like you don’t really know what you dont know while if everyone is discussing there would be someone who poses some question that makes everyone rethink what they've learnt, so in a way to start to know what you donr

[lethal leaf]

I think for things like math having dedicated time to just doing problems in class and asking for help (from peers or the teacher) is really helpful

Note I'm only speaking in a high school experience, don't know how that would work in college

but for my calc BC class it was flipped classroom

we learned at home using guided notes sheets (fill in definitions, example problems)

and then in class we did the homework problems and got a daily 45 minute session of asking the teacher / peers for help

and then for my calc 3 class the class is structured where we do a few days of lecture

and then we get like 2 weeks of in class time to do the homework and ask questions

i found that in the math classes where it was the teacher teaching material every day

there was like 0 time to ask questions about last night's homework

and people were hella confused

[shadow basalt]

I think the issue with flipped classroom logic is that it presupposes that exact alternative

Like yes maybe 100% time to ask questions is better than 0%

But also having a professor/teacher explain a concept in a down to earth way

And being there for that experience

Is very valuable

[lethal leaf]

I mean what my teacher did was that if he found a number of people are having the same question

he'd explain it to the whole class lecture style

[shadow basalt]

Especially at the university level where advanced students tend to be comfortable asking questions in middle of lecture

[lament wraith]

I think the other thing is that most college courses have recitation where it's basically a flipped classroom, as well as normal lectures

most lower level college math courses*

[lethal leaf]

yea like I said, idk how college really works

never been there, ask me next year

[shadow basalt]

The ideal setup imo is class lectures with small classes and questions

And copious office hours

But that’s logistically difficult

But imo if class is “mandatory” then it should be reserved for lectures and relevant questions as you go

To be fair to the other students

Office hours are the ideal way to ask questions

Or just email

I send tons of emails to profs about stuff

[lament wraith]

There are things like piazza where students can ask public questions online too like a forum style

[shadow basalt]

Oh I love piazza

I had a prof that gave fake bonus points for answering questions

And that helped me learn a lot by rushing to get them

Every class should use piazza or some type of forum where students and teachers ask questions

It’s easier for profs than office hours bc you don’t have to dedicate time

And students can contribute

[brazen pendant]

the thing with office hours is… how do you do office hours sensibly with 500 students?

[scarlet perch]

an absurd amount of TAs is usually how i see profs deal with it lol

although, i've also had cases where

the profs and TAs made it so you had to sign up to go to office hours ahead of time

a queue system

which failed spectacularly as people got queued into the next quarter

[brazen pendant]

oh I assumed office hours meant you go to talk to the professor

not to your TA

here most profs don’t do official office hours but will respond to emails and might offer a meeting in person, and you can always go to the TAs

[proper geyser]

Happy teachers day, even i'm just a student.

[turbid zenith]

Oh hey haven't been here in a while

Thank you @proper geyser 🙂

[toxic spire]

There's a teacher's day?

What about a students day?

[wise vine]

Students' week is the last week of April

We celebrate it with many exams

[scarlet perch]

teacher's day used to be student's day, but it got confiscated

[brazen pendant]

We celebrate it with many exams
speak for yourself I don’t think I ever had many exams in april specifically

I had many throughout the year before uni, and in february and august now that I am in uni

and my highschool finals were in june I think

or maybe may, idr

but that was a one time thing

[wise vine]

all my finals in Uni are usually end of April

or before Christmas break

[tawdry venture]

all my finals are in june

[tidal whale]

Same

June gang unite

[round robin]

do some ppl find it fun to mark? imo its pretty boring the most interesting would be like giving comments

[wise vine]

@round robin Agree

[brazen pendant]

it’s boring af

[turbid zenith]

I agree comments are almost always better

Problem is they're time consuming

[lethal leaf]

How do people here feel about a math class based in software rather than normal pen and paper based classes

Like my calc 3 class, all the class work is done in mathmatica

Very little pen and paper

And I feel the focus is less on "ok do the problems correctly" and more on "focus on the concepts and how to apply them"

[stone tusk]

I think about the proof-based questions and maybe software can help with getting examples to get a feel for the problem.

Of course, the result would probably be pen and paper, but the intermediate steps somehow might allow it to be easier. Like solving geometry questions with geogebra and finding some relation that you prove on paper afterwards

[round robin]

i feel like thats a good idea if everyone is fluent at writing code

mathematica is kinda like spoonfeeding code tbh if its used for learning

[lethal leaf]

The emphasis isn't on learning how to code

We're allowed to copy paste from other parts of the assignments and edit it

Rather than "code" from scratch

And yes mathmatica is more like scripting not coding

[round robin]

thats quite a cool idea nonetheless

Im wondering
Whenever there is a group thing like say some project is it possible to make sure like no one gets like all the work done for some arbitrary group and like others having done none

[brazen pendant]

I mean the easiest way would be to assign each group a different assignment

that still leaves the politics within the group

[brazen pendant]

we once had a group assignment where we got 3n grade points to distribute among ourselves as we wanted to, where n was the grade given to the assignment. the idea being if someone did most of the work, they should get a few extra points as a thanks.
what actually happened was that everyone calculated exactly how many grade points they needed to ensure passing the subject and then gamed the system that way

I think it was a pretty dumb system :P

[scarlet perch]

it was a nice try ahaha

[lethal leaf]

There are no group projects

[stone tusk]

might make sense if groups are formed by the students

if students want to game the system, they must be able to find students that are okay with them gaming the system

[round robin]

Surprisingly students can still form groups where one person does all the work

idk how but yea

[lethal leaf]

Basically what happens is that they form a group

And one student is better than the other ones and has higher standards

And rather than try to get the other students to work at their standards

They just do the work because it's easier

At least that's what happens to me when I'm in a group and do all the work

[round robin]

ah

hm that kinda suggests group work is always a not so good idea lol

[severe cedar]

hi there! does anyone know how to make a PDF that expires after a certain time with javascript?

i know it's hard to make something super foolproof, but I just want something basic that will prevent people from simply opening the file after some date

so that I can distribute homework solutions and try to prevent people from passing around for future semesters

[turbid zenith]

Your best bet might be to share it on Google Drive so that it's read-only

[lethal leaf]

what my teachers have done is they require us to show work

and the solution sheet only has final answers

tho that can suck if you're genuinely stuck

[brazen pendant]

you really can’t stop students from getting access to past solution sheets, no matter what you do

[lethal leaf]

yea

[brazen pendant]

so your best bet is to either:
• just make sure to not reuse all the same exercises every year (maybe every two or three years)
• don’t care and have it be the students’ problem

[lethal leaf]

you'll see the failure when they take the test and bomb it

[brazen pendant]

(the latter only works with ungraded assignments, which I favour anyway)

graded assigmnents imo have way too many issues

from students copying from one-another, to having to actually carefully grade everything, to it being too easy to pass your course without having learned anything

[severe cedar]

yeah i think it's just an unsolvable problem

[novel kraken]

if you want to get hardcore you could design the problems with variables and then randomly generate different numbers every semester for the same problems

[round robin]

The student could just download

at that point any attempt is kinda useless considering can like change system clock should there be some method with ps

[remote pumice]

I think this one might be familiar to a lot of you mathteachers / teachers in general!

This week I'm going to put up 3 Praxis Core math questions every day! 😊

https://youtu.be/iJIFdUIK9O0

Any feedback is highly apprecieted from you guys. 🙏

[remote pumice]

Hmm... @wispy slate

Not sure how to answer you man 😪

😆

Because its fun, and helpful!

Absolutely true.. I agree that it would be optimal to make videos on stuff that hasent been done before..

But I also see nothing wrong to give the audience multiple choices to watch...

Thanks, now you actually give me some valuable critizism, really appreciete it buddy!

🙏

[lament wraith]

Stop

[remote pumice]

Absolutely

[lament wraith]

People learn things in different ways and people making more videos about it won't be harmful

People also learn things by looking at multiple sources coming from different points of view

[remote pumice]

@lament wraith I agree, wont make any "harm" for sure. The only "negative" thing is that the discoverbility gets really hard when so many other people has made videos about it..

[lament wraith]

If someone enjoys what they're doing, I really see no reason to tell them to do something else

[remote pumice]

@wispy slate But man, next time, instead of starting off your comment as you did now, and look like one useless hater, just say your critizism right away, you actually had some good points

No worries.. 🙂

@wispy slate Btw an example of something ive never really seen been made is this vid https://youtu.be/OJ6w-f6zpdk

thoughts about it?

36^2 = (30+6)^2 = 30^2+2x30x6+6^2

This one you can learn pretty damn fast in your head if you practice

Awesome, watching right now!

For sure!

Damn cool..

[round robin]

honestly mental math is not so useful nowadays with computers

[stone tusk]

Well, depends...if you can calculate something before you pull out your phone and type the password and open the calculator app and type the numbers..., that would make it useful.

[wispy slate]

is there any winter school for math students this year?

[brazen pendant]

what… does that question even mean

are you asking about whether a specific school is offering sth?

[edgy ether]

Yeah, but when is it most important to calculate things before your calculator? Usually, when you have a huge calculation, but then you would just program something to do it.

[surreal scaffold]

entrance exams are non calc? :p

[round robin]

algebra ♥

[turbid zenith]

Oh hey I see Arthur Benjamin

I love his stuff. Met him years ago when he came to our math conference.

[ionic dagger]

Mental Math rocks.

[turbid zenith]

Yes I did @wispy slate

I have an "Introduction to Higher Mathematics" course on YouTube 😛 It's really old now though

Thanks. 🙂 One day I'll get back into videomaking or something maybe

[brazen pendant]

did you mean: "I need someone to make me combinatorics videos"

I mean that's also more or less my experience about how it's taught in general

you do some intro level stuff

then you ignore it for a while, doing all sorts of other things and occasionally recalling some things from combinatorics when needed

and then if you go in that direction at uni, you'll eventually do the hardcore stuff

i'm not even sure what you'd teach in an intermediate combinatorics class

elaborate what you mean with counting? I'm not really into combinatorics ^^

(and have never had a dedicated course on it, just the stuff done in probability courses)

like what, 12345?

I'm not sure what you mean by counting

I’m not really sure how one coudl even make good courses about that

seems like a course on such a topic would necessarily just be a bag of tricks

which is neither satisfying to teach nor learn

no I mean how do you teach being clever

[tawdry venture]

that's nigh unteachable

you can't teach mathematical maturity directly

[grand laurel]

combinatorics overall feels a lot like a bag of tricks

there is little unifying theory

maybe that's why it's not taught extensively

I did some combinatorics in a discrete math class

and introduction to Ramsey theory

which is nice, but none of it appeared on the exam, bcs it's either way too easy or way too hard

[grand laurel]

that's exactly my opinion

by bag of tricks I mean that every problem requires a new trick never to be used again

and every solution seems disconnected from other problems

[crystal sapphire]

So basically what you're asking for is an olympiad combinatorics course.

[wild zealot]

I don't think combinatorics is a "bag of tricks" any more than integration or algebra is.

It's a newer subject that doesn't have the pedigree of being connected to physics or engineering like calculus/analysis is.

Like... a thousand years ago, x^2 + 4x = 7 was considered a completely separate problem from x^2 + 4x - 7 = 0. They just didn't have modern algebraic pedagogy.

[lament wraith]

I'm honestly not sure why you care so much about olympiads

Like sure olympiads can be fun if you enjoy doing the problems, but it really doesn't seem like you enjoy that

[viral pike]

Combinatorics is a newer subject?

[brazen pendant]

also re:geometry, I'm currently taking a course on axiomatic euclidean geometry and projective geometry, and I don't think it'll be very bag-of-tricks

more bag-of-theorems prolly

cause not everything in math is about problem solving

[tawdry venture]

gasp

what a shocking revelation! not everything in math is about problem solving!

what else could be the purpose of doing math, i wonder? it can't be math for the sake of math, that's for certain!

[round robin]

advancements in society are made by making problems small enough to fit in margins

[tawdry venture]

if anyone was not able to tell, my last three messages were soaked through with sarcasm

i tried to do this neurotypical thing where you don't mark anything explicitly and then act snarky and self-righteous when others misinterpret you

was i or sascha making any statement pertaining to that?

[round robin]

you can kind of replace the word 'mathematics' with a lot of other things

physics, chemistry, programming, pentesting

[wispy slate]

I feel that Math is the foundation for so many disciplines that it's the most important one to learn first and learn well.

[round robin]

usually you dont really quite need that much math

like itll be like say mid undergrad at most? like you would rarely need algebra in like chemistry or nt in basically anything (maybe except crypto, that is like algebra and nt) or top

exception is probably physics
physics and math are very related

i do art 👀
anyways like there is a lot more fields outside of the sciences, like history and suff

[wispy slate]

Medicine is virtually non-existent with out math. For instance, we can't properly take histrionics of the patients medication use and calculate the correct dosage from test results without it.

[round robin]

well i definately dont see myself doing math when writing code
like writing code is usually either graphics designing or like solving problems, which is a skill that doesnt strictly need math to get, you can easily obtain from other fields

yea web design is a lot of playing with css(graphics), usually the hardest part imo

[wispy slate]

The language you write in certainly wouldn't exist in the first place without the matheticians to develop it.

[round robin]

as in?

[wispy slate]

As in what? How do you think high level code gets executed on the machine?

[round robin]

like high level as in say js, python things like that?
like i dont quite see how 'math' gets involved in that

eh both depends on your goal

hmmaybe

hm so thats what you meant by problem solving
i was thinking more of like having to solve issues that appear like something doesnt look right or like you want this thing to be here and be compatible with different devices things like this

[knotty cargo]

well in respect to making a responvie design webpage you have to know what em does to px which comes from maths technically

or what viewport widths do to different devices based on the dimensions

but i agree with euler

oh wait this is the teacher lounge i'm outa here

[ionic dagger]

Hmm. Is there a site of "BEST OF" math. I'm thinking of creating a forum/discord for this: letting users add video links / math articles / books / mathematicians / problems / classroom math activities / home math activities. Fully searchable, categorized by type and subject, etc.

[austere lantern]

I'm sure you can find something akin to it if you searched around on the web

[full crystal]

Hey teachers!

Who might be well versed with multi variable calculus here 😶

I know it's not allowed to post here about that, but I got no response on the specific channel

[round robin]

huh

[brazen pendant]

I know it's not allowed to post here
does it anyway
dude

[lethal leaf]

Nice

@full crystal ask in #multivariable-calculus

[stone tusk]

or look at #❓how-to-get-help to see how to ask there

[full crystal]

🤦🤦🤦🤦🤦

If someone would have answered in multi var I wouldn't have come here

Anyways 😒

[stone tusk]

Channel description

This is not a channel to ask for math help.

[brazen pendant]

@full crystal go to the appropriate channel and actually ask your question

rather than just asking if you can ask sth

which you can always do

if your question gets buried you’ll just have to try again later

[wispy slate]

Sigh

Next time someone knowingly uses this channel despite knowing better, you are getting warned

This channel is for math teaching techniques, not to discuss math HW.

We have 10 dedicated question channels and an additional channel for multivariate calculus.

[turbid zenith]

This is probably a little out of the blue but

Do any of y'all know where I might look to get more problems like this?

The sorts of things that require you to do estimation.

I'm not sure if there's a particular good resource for that sort of thing.

And coming up with the problems myself is ... kinda tough. XD

[stone tusk]

Well, there was this talk among people I knew about the question about the weight of commonly used objects (i.e. small denominations of money)

[ionic dagger]

that's a fun one. I think intermediate value theorem helps?

[stone tusk]

nah, the answers are far apart enough to estimate

[ionic dagger]

I'm confused. Is x measured in radians?

[stone tusk]

probably

[ionic dagger]

So all x > 1 cannot be solutions.

Let k = 97x. cos(k) = k/97. k/97 is a straight line from the origin to (97, 1). Cos(k) oscillates with period 2pi and one figures out how many times the line is crossed. (incomplete answer but I'm tired)

[vital shard]

that's a gre question

answer is 15

computed as @ionic dagger said.

@turbid zenith i want to say look at gre practice tests but i guess that's where u got this from lol

[ionic dagger]

Thanks!

[turbid zenith]

LOL yup @vital shard 😛

[brazen pendant]

today I have my first tutorial for my new class

hype

[turbid zenith]

Whee - I got to tutor somebody about topology today ❤

[round robin]

nice

[past fulcrum]

had 2 people give me correlation value |r|>1

please kill me

[round robin]

XD

[tawdry venture]

does anyone have any insight into this thing that's absolutely puzzling to me

so there's this problem i remember helping someone with on this server, it went something like this

Let f be a differentiable function with f(π/6) = 4 and f'(π/6) = 7.
Let g(x) = f(x)sin(x) and h(x) = cos(x)/f(x).
Find g'(π/6) and h'(π/6).

and apparently the student had trouble grasping what was even asked for

and i didn't even know how to like... combat that

like what do you even say

i feel like this might be due to a hard-rooted "function = formula" misconception but like how do i clear that up i guess

[novel kraken]

it's hard to say without personally seeing the context of how the student reacts, but it does seem like they might be a bit too deep in

I can't really think of any short solution past going back and working out what the derivative is and work through some explicit example of f,g, and h to look at their graphs in desmos maybe

I don't know, that's my 2 cents, maybe someone has some better ideas

[ionic dagger]

Er ... g'(x) = f(x) cos(x) + f'(x) sin(x). Evaluate at x = pi/6?

So g(x) = f(x) k(x) where k(x) = sin(x). k'(x) = cos(x).
g'(x) = f(x) k'(x) + f'(x) k(x) <-- product rule.
Then substitute k(x) and k'(x) and then substitute x = pi/6?

The visual / graphing concepts might be harder to understand than the algebra?

[tawdry venture]

i mean the thing is

i remember the student being borderline unable to grasp "g'(x) = f(x) cos(x) + f'(x) sin(x)" for whatever reason

[ionic dagger]

I see. Temporary substitution is nice.

[pine dock]

Ann is a teacher

Since when

[tawdry venture]

i'm a tutor, since about 2 weeks ago

[grand laurel]

why did y'all semesters already start, i still have to wait 2 weeks

[turbid zenith]

@tawdry venture I think the "function = formula" thing really is to blame

One thing that can really help is to completely remove things from formula-land and just have a table of values

Like say you have two functions f and g, and this is all you know:

You could ask, okay, if you define h(x) = f(x) + g(x), then what's h'(2)?

That can maybe get them in the right frame of mind -- that the function exists, but we don't know a "formula" for it, but just some isolated information.

Does that make sense?

[ionic dagger]

oooh nice one.

[tawdry venture]

@turbid zenith that is nice but i think i remember people getting confused at that one too tbh

[turbid zenith]

Right that's what I figured

I'm saying that's likely your best starting point for getting them to think about it differently

If you can get them to understand that, you'll have an easier time helping them with other problems

[ionic dagger]

Maybe if we made one or both functions simple parent functions or even simple polynomials?

f(x) = (x + 1)(x^2)
What is f'(x) using the product rule?

[placid mirage]

Maybe
we could start from what they already understand
I could ask for the derivative of $x^2 * sin(x)$
and after they mention what it is,
I could say " f(x) can be a shorthand way of talking about $x^2$, in this case it is not needed but sometimes we get things like $f(x) = 2x^3 + 4x^2 + 17$ or even more complicated and large looking ones."
then for the "$x^2 * sin(x)$ " problem we could abstract it with $f(x) = x^2$ and $g(x) = sin(x)$ to get them comfortable.
Once they have an idea of how the notation works we could say
"In math we often get interesting results by extending a simple idea or notion"
and then show that sometimes we don't have proper function we just get data,
and then show a table like Ashura mentioned about something like the population size of a bacteria colony and then show how sometimes we don't know what the formula is but we can still talk about it by the using name or notation we've given to it in order to approach some goal we have.
After this they'd probably have some intuition of how this system works and should attempt the problem on their own.
I'm not sure whether I have missed something or not, but this is kinda what I'd try but it'll be difficult on discord.

[burnt vessel]

Jack_The_Wizard:

[remote pumice]

Do you have the same solutions for this questions or would you approach them with other strategies? https://youtu.be/u0edkb-btgA

[lethal leaf]

I mean at some point you may have to go through back to the very basics @tawdry venture

Like I was tutoring my brother and he had just finished Algebra I

[tawdry venture]

no i'm just retarded end of story

[lethal leaf]

And I asked him to graph y = 2x

And he didn't know what I meant

Like sometimes people are completely missing a foundation

[tawdry venture]

no i'm just retarded end of story

[lethal leaf]

Wat

You didn't even do anything wrong tho

[tawdry venture]

yes i did

[lethal leaf]

I'm reading through what you just said and you did nothing wrong tho

You just ran into an issue about how to better teach a student and didn't know how to proceed

Nothing wrong with that

[tawdry venture]

it's not about teaching

I'M the stupid one

I'M the student here

I'M the student who doesn't understand yet all her classmates do

[brazen pendant]

is this really the place for self-depreciating venting

(and by that I mean: it’s not)

(please don’t)

[wooden agate]

Eyy 15/25 of my peeps from the first section got a perfect score on this quiz

(Which is esp nice after last week went... yeah)

[wooden agate]

Finally got around to grading my second section as well

14/20

Fuck yeah

[past fulcrum]

how long does it take u guys to grade usually

i have an intro to proofs class that takes me like 3-4 hours or so, im not really sure how many people

and a time series analysis class that i think takes around the same amount of time?

[obsidian temple]

i didn't do math grading in cooleg, but when i was doing computer science grading it was taking 1-5 minutes per person generally

(for assignments, i didn't grade exams)

[shut wing]

@wooden agate ur a teacher 😮

thats cooooool

[wooden agate]

I'm a teaching assistant

Also I only have to grade quizzes, these guys do homework on WebAssign

Which I don't like in a way, since it's a complete ripoff and at least in principle prefer problems crafted for a class

But then we'd be grading homework so

[shut wing]

oh wow

btw this is the teachers lounge am I allowed to write here

🤔

@wooden agate Teaching assistant wow hows that?

fun?

[wooden agate]

It's interesting for sure

[brazen pendant]

I have homework to correct, last week it took me about 4 hours (14 hand-ins)

[grand laurel]

it takes me 10-30 min per homework sheet and i correct like 10-20 per week

really good and really bad homework is corrected fast, but almost correct takes a lot of time. (this is for an algorithms class)

[ionic dagger]

Would anyone appreciate scan-tron graded homework? ... So some company is going to hate me for saying this, but a couple of years back I was bored and coded a scan-tron app for myself just to see if I could. Just print out an answer sheet, let the printouts be used for homework, and scan (preferably with a sheet feeding scanner) to see if the bubbled in answers are correct.

[brazen pendant]

I have no idea what scan-tron graded homework is but I suspect it wouldn’t mesh well with actually useful homework questions (e.g. writing proofs)

[grand laurel]

it's basically multiple choice, so it's horrible homework

it's decent for in class use or maybe additional online questions for sanity checks

[brazen pendant]

is there anything reasonable you can do against shitty handwriting

[tawdry venture]

mark it down according to legibility or lack thereof

like, illegible solution \implies 0 points nmw

[brazen pendant]

there’s no marking

I’m just giving feedback

we don’t have graded homework

also it’s not illegible

just annoyingly ugly

it also contains the statement $v_i \in V \setminus {v_i}$

[burnt vessel]

Sascha Baer:

[brazen pendant]

so uh

[tawdry venture]

write "WTF" next to that

[ionic dagger]

Er lol. I was thinking more like ... answers 0-999 (like the AIME)

[brazen pendant]

what do you mean by that

the kind of homework we get mostly are “write a proof”

occasionally computations or applications of a theorem

but pretty much 100% free-form

[ionic dagger]

I understand, but with all the help channels I assumed there are some grade school teachers. AIME: So part of the road to getting on the US IMO team is a 15-question test where all answers are reduced to 0-999.

there are radical answers

[brazen pendant]

as in each answer is an integer in {0, …, 999}?

[ionic dagger]

but they say your answer will reduce to sqrt(A) + B/C where A, B, and C are whole numbers.

FInd A + B + C

it's a very crafty test

[brazen pendant]

that seems silly

[ionic dagger]

well ... there's thousands of kids who take that test in the US

[brazen pendant]

like that’s just an extra useless step

[ionic dagger]

Well it's required for grading efficiency

[brazen pendant]

I think the proper solution is to lose the standardized testing boner, not to concoct solutions to make grading them easier

[ionic dagger]

um ... yeah I disagree. BTW, they've done it this way for over 20 years so ... lol I don't think 1) they're likely to change and 2) they need to change really.

[lament wraith]

Just because they do it doesn't mean it's good

[ionic dagger]

Just cause there's another way doesn't make it better 🙂

[brazen pendant]

I mean I guess it makes sense in this particular context

[lament wraith]

They have to, because of the number of people taking the test and they have to get it back quickly

[brazen pendant]

cause the IMO is, well… the IMO

[lament wraith]

So that the next round can be done on time

[ionic dagger]

(please don't put me in generalizations that may or may not apply mode.)

[brazen pendant]

I don’t have very high opinions of olympiads in the first place

[lament wraith]

And the next round is all proofs that are handwritten and graded by graders so

[ionic dagger]

yes that is true.

[brazen pendant]

but that’s just me

and absolutely a subjective opinion

[lament wraith]

So arguing that because AIME does it then it's a good idea isn't really

[ionic dagger]

Er are you more into research Sascha?

[brazen pendant]

I mean I’m not there yet but yes

I find the setting of solving a problem under time pressure and without lookup tools very artificial

there’s also just that most problems really don’t interest me tho

[tawdry venture]

careful, you might upset the olympiad fetishists

[brazen pendant]

like just based on the topics

[lament wraith]

I enjoy olympiads

[brazen pendant]

I see the appeal

[ionic dagger]

I am honestly for both ... especially for high school students. People can bellyache about how most high school kids would do simple stuff, but (I say this a lot) Calculus is Newton so I definitely have faith in HS kids that want to do research.

[brazen pendant]

they’re just not for me

the linguistics olympiad is similar

for every interesting problem there’s 50 variations of the same boring ones

[lament wraith]

What the fuck does Calculus is Newton supposed to mean

I'd argue that as you get to a higher level the problems are nicer

[ionic dagger]

The process for research is ... follow and imitate then discover. And high school students are amazing at the first part (even copying Newton and material based off of Calculus since Newton).

I just think that the second part is accessible to a high-schooler's mind.

[past fulcrum]

so one of the hw problems i graded said to "guess" a value for correlation

and correlation is between -1 and 1 by definition

and some kid said 3 so i took points off and he complained to me during office hours today

he said it's just a guess so it could be anything, so i was like "if i asked u to guess someone's height and u said -7, that would be very bad"

am i wrong for this

[tawdry venture]

no

[brazen pendant]

yea no you did the right thing

[tawdry venture]

if your guess is guaranteed to be wrong then it's not an acceptable guess

[primal gull]

Hello fellow teachers! I am a senior at a university rn. Just wanted to say hi and keep up the good work! ( Please sign a petition to remove Theory of Ordinary Diffi Eq. class; hate that poopoo platter of a math class 🙂

[brazen pendant]

I'm sure there's good ways to teach it

I vaguely recall reading an essay about it once

[tidal whale]

Was it the one by Gian Carlo Rota?

[brazen pendant]

idk it's been a while

it gets posted to /r/math occasionally

[wispy slate]

@past fulcrum I may be in the minority, but if there's room for argument whatsoever over a question, then the question was too vague and should be corrected. Math shouldn't be pointless squabbles over bullshit.

There's a reason we invented formal logic, so that misinterpretation of a mathematical idea literally cannot happen

[past fulcrum]

well its an applied math class 🤔

like by definition correlation is |p|<=1 so if u are asked to "guess" it by looking at a plot and tell me a vaue outside that range there isn't really any way to justify it..

[tawdry venture]

a guess guaranteed to be incorrect shouldn't be a valid guess in the first place.

[past fulcrum]

thats what i said basicaly

[wispy slate]

You don't need to justify it, its a guess. Giving the points does no harm to you, and only helps out the other party. It also doesn't jeopardize the academic integrity of the class. The wording of the problem was vague, and should be taken exactly literally in a math class.

[lament wraith]

I think if you look at it from the angle of what the student understood about the question, it's pretty clear that the student doesn't understand what correlation even is and from that viewpoint, I think they don't deserve points

[past fulcrum]

im not trying to give them a lower grade, but if it wrong then it wrong

[wispy slate]

The main point I want to say is that it promotes question writers to write questions that cannot be misinterpreted. These types of questions should not be tolerated in a class that deals with argumentation using formal logic

[past fulcrum]

oh yea

this prof is using same exact hw as last year when i took it

but again it's an applied math class so all that shit is out the window anyway

i mean, at least in terms of the applied math classes offered where i am

[lament wraith]

I mean, I'm confused why you think the student misinterpreted the question here. Correlation really only has one, maybe two definitions, both of which require the value to be between -1 and 1 or 0 and 1

[wispy slate]

The misinterpretation is from the word 'guess'. Maybe he didn't know, but the question said guess, which implies that research into the topic isn't required.
Now imagine that other graders gave kids points that weren't correct but were within these bounds, you could easily keep tightening the constraints of what makes the question correct until only a guess of the correct answer remains as the only answer that gives points

That leaves the question up to the interpretation of the grader, and jeopardizes the academic integrity of the class

[past fulcrum]

well i am the only grader

and i gave points for any number between 1 and -1

i agree that it's a stupid question

[wispy slate]

How is a kid supposed to know that guess implies "correct answer for any number within the domain"

[lament wraith]

Because guess usually means that you should give your best guess?

[wispy slate]

no

[past fulcrum]

because saying that correlation can be 3 shows a misunderstanding of the math and not the question

ok

[wispy slate]

an incorrect answer also shows a misunderstanding of the math

[past fulcrum]

yes, that's what i am saying

[lament wraith]

I mean if it was just a correlation of a scatter plot with no exact numbers and the correct answer was 0.69 and I said 0.7, my answer is "wrong" but I probably understand what correlation is

[past fulcrum]

the plot was in fact so bad u couldnt even reasonably guess any value

[lament wraith]

At least a lot more than the person who said 3

[wispy slate]

@past fulcrum thats even worse

[past fulcrum]

also if i ask u to guess someone's height or weight or whatever and u tell me "negative 7" this is also bad, but after all it is just a guess, right?

[wispy slate]

You just told me the plot was so bad you couldn't guess any value

[past fulcrum]

which is why i gave points for any reasonable guess

[lament wraith]

I mean, if I told you I have a graph and didn't actually show you it, but asked you to guess the correlation

And you said 3, it'd be pretty clear to me that you don't know what correlation is

[wispy slate]

the question is bad. there should be no room for human judgement. The question didn't say "guess an answer within a valid domain" or "guess an answer that demonstrates your knowledge of correlation". Again this is a MATH class where formal language should be expected and encouraged. I don't care if its an "applied math" class or a "high school math" class or whatever math class. This question should not be tolerated.

If you put a constraint like this in a proof assistant, then it could easily spit out an answer like this one, and your proof would be useless

And who would argue with the computer? It spat out a valid answer according to the constraints given

[past fulcrum]

ok but what about "also if i ask u to guess someone's height or weight or whatever and u tell me "negative 7" this is also bad, but after all it is just a guess, right?"

valid domain is implied, that seems like a ridiculous point to make. of course any answer is wrong outside a valid domain

[lament wraith]

I'm honestly confused, like have you ever had a math class where the questions were actually written in formal logic

[wispy slate]

Yes. Its a guess. Its an answer an automatic proof assistant would provide

[lament wraith]

Any english words have ambiguity, I'm not sure how you plan to remove all of that

[past fulcrum]

it is a completely unjustifiable guess, and for this i take off points. to me that is wrong

[wispy slate]

"Any english words have ambiguity, I'm not sure how you plan to remove all of that" wtf are you smoking

math terms have definitions, and all definitions are in terms of the axioms written in formal language.

[past fulcrum]

like, correlation between 1 and -1 is what u learn the first day u learn what correlation is. and to take this class u would need to have taken 3 others first, all of which use correlation constantly. if ur telling me it's 3, regardless of why, there is something fundamenetally wrong

[lament wraith]

Another analogy would be if I were teaching you English and I asked you to give me your best guess on what my height was. If you replied with -7 pounds, then I would be pretty sure you don't know what height means

[wispy slate]

Again, if this is a constraint you put into an automated proof assistant, it could easily spit out 3, and you wouldn't know. The computer doesn't know or care about the idea of interpretation.
Questions like these encourage people to take mathematical ideas or constraints up to interpretation, instead of looking at purely the definitions.
A fundamental idea of math is to look at and think about only at the definitions. If you try to use intuition, you can easily come up with a wrong result because you had a fundamental misunderstanding of the definitions in your head

[lament wraith]

And yes, all English words have ambiguity, when a homework question asks you to prove something, it's pretty ambigious exactly what they want and what constitutes as a rigorous enough proof because most math classes won't prove things in formal logic

Isn't that exactly what we're saying too?

[past fulcrum]

u think math shouldn't use intuition? ????

[lament wraith]

The student had a fundamental misunderstanding about the definition of correlation

So we discourage that by taking away points

[wispy slate]

@past fulcrum not in a mathematical proof

[past fulcrum]

well this is not a question which requires proof

[wispy slate]

"when a homework question asks you to prove something, it's pretty ambigious exactly what they want and what constitutes as a rigorous enough proof because most math classes won't prove things in formal logic" That's the point. You have highlighted a fundamental issue of math culture that 21st century mathematicians are trying to fix.

This is what creates incorrect proofs and bad papers.

This practice is appalling and should definitely be discouraged.

[past fulcrum]

ok but this homework doesnt ask u to prove anything soooooo

i guess im done here, i have a quiz in 20 minutes

[wispy slate]

Just because it isn't a proof shouldn't mean that a culture of taking words to mean their exact definitions is discouraged.

The student constructed a valid argument that the answer was correct according to his own definitions of the words.

[lament wraith]

I'm confused why you think mathematicians think that this is an issue. Or at least, they understand it will always be an issue since it will always be a question of whether or not it is rigorous enough since it is unlikely that mathematics at the highest level will be done in formal logic

Would you have thought the homework was fine if the question asked "give your best guess at the correlation"

[wispy slate]

A valid question would be "guess the correlation. To receive points the answer must be within a valid bound of correlation"

[brazen pendant]

at that point, you have to write “your answer must be reasonable” for every single exercise

because if you ever don’t overspecify like that they can claim by example that a wrong answer should be accepted cause you didn’t say it won’t be

[turbid zenith]

Okay, I'm going to say, I think the word should have been "estimate" instead of "guess", but because you specifically asked for correlation, it should be reasonable to expect a reasonable answer that would be valid as a correlation.

[wispy slate]

I disagree. @brazen pendant specification to the point of not being able to leave anything up to interpretation is something that should be encouraged in a mathematics class.

[novel kraken]

how many points was this question actually worth

[brazen pendant]

Brad, I think mathematicians should be smart enough to not guess something inapplicable

otherwise you just prove that you either: didn’t read the question or didn’t understand the concept, in both cases you deserve negative points for handing sth in and arguing about it

[lament wraith]

I mean, if you're just the grader here, and don't have control over the question writing, would you give the students full points?

[wispy slate]

Sascha, I think mathematicians should be smart enough to have constraints that don't leave room for a valid yet non-intended answer.
otherwise people program theorems into proof assistants, or any math constraints into an auto problem solver, and produce unintended behavior.

[turbid zenith]

I don't see how the problem can be misinterpreted by a person who understands the material.

[wispy slate]

I would give students full points and toss the question

[lament wraith]

So you believe that this student may know what correlation is?

[brazen pendant]

then you’re being dishonest

[turbid zenith]

If you "guessed" a correlation of 3, you don't know what correlation is.

[lament wraith]

And just happened to guess 3?

I think I agree that the question isn't perfectly written but

[turbid zenith]

And your grade should reflect your understanding as judged by the grader, not however many magical pony points you managed to acquire.

[wispy slate]

@turbid zenith "not however many magical pony points you managed to acquire." I agree. Thats why questions should not be up to interpretation, because that's how you can arrive at situations like these.

[turbid zenith]

There's no "interpretation" to this question.

They asked for a guess to a correlation. That implies bounds.

[wispy slate]

It doesn't

[lament wraith]

So you think the student may know what correlation means, but misunderstood the question to the point they put something that couldn't be a correlation?

[turbid zenith]

Give me a situation in which "correlation" in a statistics class can mean something for which 3 could be a valid guess.

[stone tusk]

effect size?

[wispy slate]

@lament wraith @turbid zenith @brazen pendant
The question said "guess", @past fulcrum said that the plot was illegible. I could easily see a student not want to put up with an illegible plot and write some guess. The question didn't specify the bounds, nor did it say anything about "any answer within a valid domain will receive points".
I said earlier that "guess" can leave the constraints of what makes an answer valid completely up to interpretation. If there was multiple graders then one grader could have tighter constraints on what makes an answer valid according to his own interpretation of the question. This jeopardizes the academic integrity of the class.

[turbid zenith]

The fact that the plot was so bad you couldn't guess a reasonable value IS itself a problem, I agree with that.

Though I'd have to see it.

[wispy slate]

See? what constitutes a "reasonable value" is up to interpretation. You just said it

[turbid zenith]

Still, I think it shouldn't have to be specified on a test that of you're being asked to guess a value of some parameter, it should be a valid value of the parameter.

That's just common sense.

I think the guessing a height of -7 is another perfect example of this.

You "guessed" a number sure. But you didnt do a good job of guessing a correlation.

At some point at least a minimum amount of context based on the class you're taking can be expected.

[wispy slate]

"common sense" shouldn't be something encouraged in math. That's how you arrive at seemingly logical, yet incorrect, statements being formed and "proven" in papers

[turbid zenith]

Okay I'm gonna stop you right there. Common sense SHOULD be encouraged in mathematics. It needs to be honed into something more precise, but we dont need to completely destroy students' sense-making.

Intuition is NOT a dirty word in mathematics.

[wispy slate]

"It needs to be honed into something more precise", which is what this question failed to do

[turbid zenith]

I'm going to reserve judgment on the graph itself until I see it. But expecting a value within valid bounds isnt something the teacher has any obligation to re-specify. That was specified by asking for a "correlation".

[lament wraith]

If they didn't want to put up with a bad plot, and they knew what correlation was, they'd just write 0 or 1 or -1, but I really cannot see a situation in which a student who understands correlation writes 3

Not all questions need to hone into something precise, questions can be aimed towards checking a students intuitive understanding of the subject

[turbid zenith]

You know now that I'm thinking about it — if there was no clear pattern one way or another, wouldn't 0 or numbers close to it be the most reasonable answer?

[novel kraken]

I mostly consider learning math to be the act of improving my common sense, not replacing it

[turbid zenith]

It wouldn't make sense to give a plot with a correlation of 0.2 and take points off for somebody saying it was 0.3. But if you give them that plot and then they say the correlation is 0.95, then you're within your right to say "no that's not a very good guess because XXX and YYY"

But even then this is a different situation because the student gave an answer that was so wrong it could not possibly have ever been the correct value of a correlation.

Anyway, final verdict is that [A] the question could have been worded a bit better (I think simply substituting "estimate" for "guess" would do the trick), but [B] the grader is within their right to not award points for an answer that is so wrong it's completely unreasonable because it shows a complete lack of understanding of what "correlation" is.

[wispy slate]

@turbid zenith @lament wraith @past fulcrum
Vague terminology leads to incorrect interpretations.
In engineered systems, vague specifications/constraints/conditions lead to incorrect mathematical models, or incorrect module interaction, or bugs. Bugs that can lead to huge amounts of money lost or injuries/death to people.
I am sick and tired of hearing these people who write these specs who don't care about their interpretation being up to human judgement.
This is an issue with STEM at large, and is prevalent everywhere in engineering. The culture of people writing mathematical constraints being up to human interpretation is dangerous and kills people.
This is why strict formal specification in formal language and proof verification of mathematics ESPECIALLY in engineering is so important.

[brazen pendant]

I’ll consider this a sensible argument the moment someone gets injured due to vague intro to probability questions

and this one is far from anything I’d consider vague

[lament wraith]

Ashura, I think nilradical meant that the graph was impossible to actually read rather than having no correlation

[wispy slate]

@brazen pendant If you can't even promote strict constraints in classrooms, then how do you have any hope outside of the classroom?

[tidal whale]

A correlation is strictly between -1 and 1 though

That's by definition

[wispy slate]

yep

[tidal whale]

Again, going for 3 is a flaw on the student

No matter how weird, I must know that the correlation is bounded

[lament wraith]

I'm agreeing that the question may be poorly written. I'm just saying that you giving points to that student is incorrect

[turbid zenith]

I think that's where most of us stand.

[tidal whale]

Tell me this - what if I answered that the coefficient of friction was -0.9?

[turbid zenith]

Poorly written question, but still unreasonable student answer to that question.

[lament wraith]

You know what would harm more people working on things in the real world? Statistians that don't know what correlation is. That would probably kill many more people

[wispy slate]

I would toss the question. Its not valid.

[tidal whale]

Does that imply I know what a coefficient of friction is?

No Brad

[turbid zenith]

Wait wait wait

So if a student gives an unreasonable answer to a question

It's a bad question?

[tidal whale]

Riemann Hypotheses unreasonable

And no Brad all that does is encourage chopping concept and babifying students

[wispy slate]

If a student gives a valid answer to a question that the question writer didn't intend, its a bad question.

[turbid zenith]

@wispy slate I can't tell if you're talking about the stat question still, or the hypothetical thing that @tidal whale just said

OH

Okay, THAT I agree with

But, 3 is not a valid answer to a correlation question.

[lament wraith]

You've really been avoiding my question though, do you think this student might understand correlation?

[tidal whale]

Can energy be negative? Can height be negative? Can a coefficient of friction be negative? Can my velocity exceed the speed of light?

If one does not take into account past knowledge on estimation or guess problems, you lack fundamental understanding

[turbid zenith]

If it's something that's actually ambiguous and could be interpreted multiple ways then yes that's a problem.

[tidal whale]

But this kid overstepped bounds

Would you mark a kid giving you negative coefficient of friction on a Mechanics problem on guess work?

If 3 was within limits then sure, but the fact is that it isn't

Defending the student is now also a problematic idea

[novel kraken]

hehe

[tidal whale]

Alright, fixed my analogy

[brazen pendant]

a question is there to test the knowledge of the student
the student proved a lack of knowledge and therefore deserves a deduction in points
isn’t that all there is needed to be said

[tidal whale]

↑

[brazen pendant]

anyway, this is a kinda weird hill to die on and the discussion has become very repetitive

[novel kraken]

actually think there are some strange materials like gecko feet that have negative coefficient of friction

[brazen pendant]

I don’t think we’ll convince you, nor do I think you’ll convince us

so I think it’s time to stop

[wispy slate]

Again, I said earlier that "guess" can leave the constraints of what makes an answer valid completely up to interpretation. If there was multiple graders then one grader could have tighter constraints on what makes an answer valid according to his own interpretation of the question. This jeopardizes the academic integrity of the class. No one has argued against this point

[tidal whale]

Merosity pls

[wispy slate]

Fine I will stop

[tidal whale]

But you're guessing a particular quantity

[novel kraken]

the correlation between how much time the student cared about the problem vs this teachers lounge is 3

[lament wraith]

That applies to basically every question with multiple graders

[tidal whale]

The moment I constrain you to some quantity is when I apply some sense of rationality

[wispy slate]

@lament wraith I don't know how to explain to you how wrong you are

[lament wraith]

Having well defined grading scales is another, unrelated problem here really

[tidal whale]

A quantity is defined by it's definition

A student that knows their stats can't possibly do something as whack as give r = 3

[wispy slate]

Words used in a problem statement are also defined by their definition

[tidal whale]

It's impossible by definition

And you have a valid range to guess on

[wispy slate]

Again, that wasn't specified

[lament wraith]

I just find it ironic you talk about people injuring people with bad specifications when you want to give full points to someone who doesn't even know what correlation is

[tidal whale]

The kid already knew the bounds of r

Tell me this - what if I guessed the value of cos(x) was 2

[wispy slate]

@lament wraith the question should be tossed

[tidal whale]

What then

[lament wraith]

This is not something a grader can decide to do

[tidal whale]

cos(x) is strictly between -1 and 1

[wispy slate]

The grader should talk with the professor and atleast give a case to toss the question

[tidal whale]

If I guess 2 then I am conceptually flawed

[lament wraith]

cos(x) takes on 2 when x is imaginary, not the best example

What if the professor says no and you have to grade it

[tidal whale]

Dang it zoop you know what I mean

[lament wraith]

That ambiguity is exactly what he's arguing against

I don't know what you mean, students won't either

[tidal whale]

And if I restrict you to R?

[novel kraken]

it would be better to stomp the student by innocently asking them to explain why you should accept their answer

if they can't even begin to explain correlation, you just furrow your eyebrows

they walk out in shame

easy

[wispy slate]

@tidal whale @lament wraith if you made a program that guessed the value of the correlation, or whatever concept you came up with, and didn't tell it to throw an exception if you have an answer out of bounds, then you can have a broken system on your hands

[tidal whale]

But the kids were taught the definition well in advance

[crystal sapphire]

But people are not programs.

[tidal whale]

That corellation is between -1 and 1

Your analogy is flawed because knowledge of bounds is there

[lament wraith]

I'm confused what you're trying to argue here

I could see this student not putting a bounds on correlation in his program though, because he never learned correctly what correlation is

[wispy slate]

I'm simply saying that being vague on what exactly constitutes a valid answer is not appropriate for a math question.

The question should have specified that "any answer within a valid domain will be accepted" or something to that degree

[brazen pendant]

Fine I will stop

please actually do

[wispy slate]

K i really am done this time

don't respond to me to pretend like you had the last word though

[brazen pendant]

I’m saying we’ll have to agree to disagree

[wispy slate]

I'm fine with that

[brazen pendant]

you did not convince me, and we did not convince you

and that’s that

it’s just getting a bit boring, really

[turbid zenith]

Semi related... correlation is between -1 and 1 because it IS a cosine

When I learned that my mind was blown

The AP Stat prep material out there loves to ask stuff about correlation like "does a correlation of 0.6 mean the data is 3 times as linear as a correlation of 0.2?"

And a student I was tutoring kept falling for those, and i kept saying "no you can't interpret r like that". So eventually the student said "well how CAN you interpret it? It can't just be meaningless! "

And I realized I didn't know. So I looked it up and found the geometrical interpretation, and both of our minds were forever blown.

I dunno I just wanted to share that haha

[brazen pendant]

something something expectations and inner products are somehow similar?

I don’t know how to formalize that idea

but like… there’s some similarities between E[XY] and ⟨u,v⟩ it seems

[turbid zenith]

You take your data and normalize them

Then interpret the lists as vectors in n dimensions

The cosine of the angle between those vectors is r

Which is why the formula for r looks a lot like a dot product

[tidal whale]

Wait what

This whole time it was a disguised cosine?

Bless you Ashura

[turbid zenith]

https://www.johndcook.com/blog/2010/06/17/covariance-and-law-of-cosines/

[novel kraken]

you'd like the derivation of the Heisenberg uncertainty principle

[turbid zenith]

Question for y'all.

If I'm looking to do an adjunct position sometime, how long does that usually take? When do people apply?

I'm going to have my 18 hours worth of graduate mathematics in Fall 2020.

[ionic dagger]

it depends on where you live

(because I did it) Texas had (15 years ago) a rule that said you could teach the most basic math, pre-algebra classes, in Community College with just a Bachelor's. If you're into helping the most struggling in math ... there may be other states with this kind of opportunity. Usually you need a full Masters to teach Community College in most states which, logically, is a waste of time if you have a B.S. in math and don't mind adults who haven't mastered memorizing area formulas.

And I'm not sure if a BS is sufficient for a community college Pre-Algebra class in Texas these days.

[past fulcrum]

how do people even get adjunct teaching jobs? is it possible to just do it for a summer somewhere?

[ionic dagger]

From my experience you apply online at the specific CC or Uni you want to be an adjunct for. It's the usual job search experience. Submit resume / CV. Wait for a callback (I have never had someone not call me back so unless you killed a provost's favorite pet fish most math people with the right credentials should be fine). Go in for an interview and/or teach a bit in front of them as a sample.

After that the math department has your name. Also, almost everyone I know got at least one class the first semester/quarter that they wanted a class (it's math people ... math people don't "overbook" unnecessary adjuncts if we can help it).

[wispy slate]

"Guess a number for correlation"

Gives full points for any number from -1 to 1

Someone puts 3 and there's an actual argument for like an hour on the ambiguity on this

I didn't know the geometry behind @turbid zenith though! Thanks

(I feel like this is someone saying "guess a value for cos(π/8) given that we are in radians" and someone puts 6 and wonders why they got no credit.)

[tawdry venture]

[brazen pendant]

@wispy slate it was way more than an hour

[turbid zenith]

Are any of y'all familiar with the concept of "tracking" and "detracking" in (math) education?

[brazen pendant]

nope and I’m actually just writing this reply to get a timestamp cause I‘m too lazy to take out my phone and can’t see my pc’s clock

[wispy slate]

I'm more used to hearing about tracking as in tracking a students overall process or using tracking to see what their skill level is or using tracking to see what educational placement is appropriate @turbid zenith

[grand laurel]

reading the Wikipedia article on tracking (education) this sounds like the German school system

[brazen pendant]

okay yea just looked it up and our secondary schools are tracked

specifically, if you’re interested, here’s how it worked where I grew up (details differ throughout the country):

the first six years of school (eight if you count kindergarten/preschool/whatever you wanna call it) classes are of mixed ability. if a student is exceptionally {good/bad} at school, they may {skip/repeat} a year, but both are fairly rare cases (repeating is more common than skipping, which often only happens in first grade - though my sister was offered to skip sixth grade and go directly to secondary school)

after sixth grade, there are essentially two + one tracks

if no action is taken, the sixth grade teachers have a meeting with the child and its parents where it will be decided whether the student is placed in sek (the “upper” track) or real (the “lower” track). both of these tracks take three years to complete and prepare the student for taking an apprenticeship (in which they will learn a job alongside some extra classes over the course of 3-4 years). now, throughout those three years, students take “general education” classes together with other students from their track, but they may be put into the class of the other track for “important” subjects (which for us was language classes and math), and as a rule of thumb if you got changed into the other track for half of your classes you’d change track at the beginning of the next semester

alternatively, a student may take an entry exam to the gymnasium, either after 6th grade, or again after 8th grade. gymnasium is a six year track (four if you go after 8th grade, ofc) and intended for those who wish to go to a university. the level of education is imo significantly higher than in sek, it moves at a faster pace, with more contents and teachers who have at least a masters’ degree (often a phd) in their respective field.

completing gymnasium grants you access to any (with some asterisks) university course in the contry without further stipulations (such as having to get accepted). from my class of 20ish students, a total of five went to gymnasium; this was generally regarded as a relatively high number. I’d say about 15-20% go that path

[grand laurel]

sounds a lot less bad than what i experienced

we have 3 paths after 4th grade

for 5, 6 or 8/9 more years of school

the idea is to create blue collar workers, (lower) white collar workers and academics

but it's a total failure

by now over 50% take the highest track

which devalues everything else

so, that "normal" people can't even get an apprenticeship

and everyone thinks they should go to uni, because they feel otherwise their education is wasted

so there are way too many people in universities that shouldn't be there and manual labor jobs are looking for apprentices and can't find any

[uneven hemlock]

how does one get used to nerves when teaching

most of the times im fine and can communicate like a human being but sometimes i swear im gonna have a panic attack at the lectern

[brazen pendant]

prepare well, make sure you understand the things you’re trying to explain well-enough to be able to provide more detail if someone doesn’t understand it

I find that I get nervous iff I don’t 100% know what I’m talking about

[round robin]

tbh sometimes you’ll just get used to being nervous

[visual breach]

to what degree are teachers in the US allowed to set their own curriculum? I hear Pearson textbooks and tests are a national requirement

[past fulcrum]

what's it called when ur extremely caffeinated and grading hw at twice the usual speed

i think i might be giving points out inconsistently LOL

[trim violet]

caffeine lottery

[stone tusk]

hmm, maybe you can let students appeal for more points

[turbid zenith]

@visual breach It depends on whether you teach at a public school or a private school.

At a private school you can usually make the curriculum yourself because students don't have to deal with the mandated end-of-course exams.

[turbid zenith]

(I really enjoyed getting to create my own precalc curriculum ❤ )

[dusk sleet]

Hello fellow teachers. I, too, am a teacher. I teach. That is my job: to teach.

[grand laurel]

any tips on teaching induction to students that never heard of it before

should i focus on the concept or on presenting examples

i only have like 30 mins max, which is kind of ridiculous

probably a lot less

[wispy slate]

Induction is a concept that is not that easy to understand in 30 minutes. I liked the analogy of it being like a domino, but one has to do a lot of examples to truly understand the concept imo.

[grand laurel]

historically it's a lot of trouble for the students

this is a cs class

last year i did many examples

even some without any numbers

tilings of a chess board

which caused more confusion, i think

[wispy slate]

Yeah, I suppose examples on numbers like divisiblity or something that's 'obvious' would make it easier to understand.

[shadow basalt]

Tip

Deadass bring dominoes

And explain induction via dominoes

[lethal leaf]

For tutoring what I've mainly been doing is just homework help

Is that normal?

Should I be bringing in worksheets and stuff?

[shadow basalt]

It’s objectively better to help them with problems similar to their homework imo

Bc you’re just depriving them of practice otherwise

You could also help w their actual homework but make them do more problems based on how much help was needed

[solar nymph]

@lethal leaf it depends

if they are unable to do problems because they do not understand the mathematics

you need to help them understand the mathematics.

[lethal leaf]

yea I do that

if they don't understand the math I teach the math

I just don't know if I should be giving extra problems or not

[novel kraken]

I would charge extra for that, if the parents wanted it

for an hour long session I would try to strive towards half the time spent helping them with knowing enough to do their homework and the other half with working on fundamentals/gaps in their knowledge that I can see coming in their curriculum

but just depends, no strict limit, ultimately helping them to solve their homework on their own is kind of the main goal so whatever works, if writing up 5 or so practice problems for them to do at the end I have done that a few times

[wispy slate]

we loungin

[wispy slate]

Well hi raf

@wispy slate

We meet again.

As a math dumbass. I must say, more problems are really good if we know how to solve them (what steps) but if we are still figuring it out 1 problem may take us 30 minutes so hammering more on isn’t very helpful. so it really depends I think on the understanding.

@lethal leaf

@wispy slate bruh what

Ap

Weirdo

ik

but

that was a weird paragraph

We Loungin Tho ™

BRUH

@wispy slate i see how it is.

I’m bad at math.

And I was giving them a students perspective

Lol

Sorry

did the friend req not send

we loungin without melanie.

I’m bilingual if I formatted it weirdly lol

What

Yes

whats the other language

German

Yk I wanna go to college and stuff but being a food critic

Man

I could eat

For daysss

that IS the dream

Mhm

🤤

Prolly be a food critic in Italy learning Italian would be a piece of cake

oh?

Then I could eat pasta and pizza forever.

☺️

why u needa learn italian

u just need to know

"i'll get the whole menu"

😂😂

True true

I’d like to learn Italian though

So

id like to learn french

french>

I was gunna take French this year

But decided on Latin

i mean thats cool at least u get to understand more stuff easily

and its like u rappin almost

Because it’ll help me with French and Italian and honestly with how much course load I have (AP chem, apush honors lit, act math prep, ) I don’t feel like I’m learning anything 😂💀

Yea

AP chem

😭

ew

It’s so hard

i took honors chem and decided never to do chem again

I have a 97 tho idk how Bc it’s like a fucking different language and I’m close to failing apush but it’s getting back up

Yea

what u have in apush?

Next semester I’m switching into AP bio b

68

Lmao

ooo

😂💀

It was at

A 51

i have an 89, barely hanging

So I’ve come far.

Mhm

our phys teacher curves the grade

based on AP exam

for tests

so 66%+ = A

I have A’s and B’s a good gpa I normally don’t get c’s so.

I’m scared

Tbh

About the exams

its ok ull get through it

not even that far into the year

You will too

Yeah

I know

I’ve never taken AP

Just honors

It’s online too

Which is nice

what grade u in

But I can get behind fast

11th

o

My last school didn’t offer AP

So I had to switch to online

oh that sucks

For college I mean

i did AB calc online

Yea

Am I smart enough for AP 😂💀 no do I need it yes

Yeah I’m dumb

mood

I chose AP chem

Like

Tf

What kinda drugs was I on

Why did no one warn me

lmaoo

Or stop me

Like all these fakes

😒

i wouldve given u hell

Yea well

☹️

Now I’m stuck

In it

too late

I’m on week 6 out of 18

For the semester

I’ll get thru it

i mean do u ask for help on chem?

Yea

It’s mostly sociometry

I think that’s how you spell it

stoich?

But when I say I’m bad at math I’m low-key terrible. You need to be good at algebra

Yes ma’am

we surrounded by math geniuses here

Yes

youll do fine

But idek where to start half the time

Ik

I might not know what tf is going on

But I’ll get thru

Just the semester atleast I don’t have to take it the whole year

Praise everything that is good

i mean hold on

In this world

And not AP

u gonna do bio second semester only?

Yes

how tf thhat work

And I’ll get my credits like that

like for AP exam

I got dyscalculia

Oh

I take the bio

AP exam

I think

oh u have a whole disorder

Which is a breeze because I love biology

Yes

Dumb bitch

Mentality

😉

Math just isn’t my friend.

Okay😂

its aight we both got dyschemulia

I’m good at languages and I love learning languages.

Yesss

That’s tru

thats great

If I get through this semester

If I pull through.

i sit in spanish 3 barely knowing spanish

Yea

I took Arabic for two years and loved it but I moved to a place where no one speaks it and lost it

yooo

thats so cool

If I get through this semester with good grades ima be so happy.

wait lol

this kinda off topic for this channel

do mods care?

I’m on the brink of like being scared that I’m failing and a terrible person and that I’m gunna get behind and that I’m not putting enough effort into everything and I cry like once a week about school

So if I pass semester one

Ima do something nice for myself idk yet

imma dm i dont want ban yet

[brazen pendant]

do mods care?
not a mod but yea take prolonged off-topic discussions either to a discussions channel or DMs

[primal gull]

Hello teachers, how are you guys doing todai?

[wispy slate]

@wispy slate We mods care :P

For future reference, what @brazen pendant said was good.

@primal gull As a math tutor, I am doing well

In fact, I'm doing so well at my job that students are going from Cs to As and then no longer need me XD

And they keep those As

Somehow God tier tutor but below average math student LOL

[lethal leaf]

man I haven't been tutoring long at all

literally haven't had a repeat week yet, started last week

so idk if my students are seeing some improvement in class or not

I hope they are

[wanton cipher]

quick question - if you asked your students in an exam to find inflection points and they only gave the x value would you give them partial or full credit? I was gonna go with partial until I noticed all but one student answered the same way and now I'm wondering if it's the professor who is at fault here (I'm the TA)

[autumn fern]

What else should they give (other than a proof obv)? The f(x) value? That sounds unnecessary

[vestal quiver]

I guess it depends on what you mean by "point": it could be a point on the real line or a point in R² in which you draw the graph

[wanton cipher]

yeah... I'm TAing two sections I know the other section's professor would think half credit would be too much without the f(x) value but this professor is more of a well if it seems like they get the concept then it's whatever

it's hard grading when the two of them expect me to grade the same material so differently :p

[autumn fern]

It really doesnt matter, computing f(x)

If they proved x is the inflection point

[wanton cipher]

ok then full credit it is! thanks. I honestly think the other professor is absurdly picky and strict but I grade for him daily and for this other one it's my second time, he wants me doing tutorials and grading exams only, he grades the homework, so it's always hard for me to figure out how to grade, especially considering that there's only like 3-4 exams in his class and they're worth a ton

[autumn fern]

I would email both professors to give you peace of mind that full credit is the right call

[wanton cipher]

he's not going to get back to me before when he expects the graded exams and list of grades in his mailbox so best I can do is pick one and leave a note with the exams

[autumn fern]

Fair

It would surprise me if he was actually that stingy in this case

[weary veldt]

@wanton cipher
imo

1. they need to prove third derivative isnt zero or that theres an actual change in concavity
2. they give both x and f(x) because it specifically asks for POINTS, cartesian system is 2-d not 1-d

[tidal whale]

Isn't an R² point (x, f(x))

[brazen pendant]

without any further context, I would give the x coordinate (which is a point in ℝ) and prove that it really is an inflection point

[zealous dome]

what's the best way to learn about related rates

[lethal leaf]

My favorite online resources for calculus are Professor Leonard and Paul's Online Math Notes

Your textbook will be the best source for practice problems tho

[brazen pendant]

Exercise:
Here’s pseudocode for the Bellman–Ford Algorithm. Analyze its correctness and runtime and compare it to Dijkstra and Floyd-Warshall in terms of input, output and runtime.

One student’s answer:
“Analogous to Floyd-Warshall”

that was it

god I wish this got grades

it would be so satisfying giving 0 points for this

[wispy slate]

I will be tutoring talented kids that are preparing for math olympiads in 2 weeks! Kinda excited and anxious at the same time, the material is up to me to choose and Im just not sure what I should choose

Is induction too much for 14-15 year olds?

[storm arch]

I'm sure they can handle that xd

[tawdry venture]

they can

[round robin]

math olympiad i think you’ll expect them to have some level of like knowledge? unless its like gg be their first time but should b ok

[stone tusk]

@wispy slate Hmm, minimally I think we may need trigonometry (application to geometry problems), modular arithmetic especially for short answer questions, if proving is required, I'll go deeper with assorted combinatorics questions on invariants, synthetic geometry, functional equations, inequalities. Assuming they know their high school stuff.

[wispy slate]

Safe to assume they probably dont know much high school stuff

But thanks for your insights

[turbid zenith]

https://twitter.com/matthematician/status/1033030676721934336

Matt Salomone (@matthematician)

I think #mysterygrading describes how I used to assign points to student work before I adopted #masterygrading.

"Why did this get 7/10 instead of 8/10?"
"It's a myyyystery!" 👻👻 https://t.co/wb1OcAyRh5

Twitter

Happy Halloween.

[wispy slate]

Thanks

I have a student to tutor tomorrow. Let's see if he will show up. Gave him a reminder today.

Last time he tried to cancel 40m before the session started

Billed the department as a no show of course

[brazen pendant]

so what’s #masterygrading exactly?

[turbid zenith]

Mastery grading is a shift away from traditional grading where the grade is all about one-and-done tests and quizzes. It's based on the idea that if you don't get something, you keep at it until you do, with no penalty for doing so.

Instead of so-called "objective" point scores (which are pretty meaningless when you really think about it), scores are broken down based on actual learning objectives and are graded on a much smaller scale, for example "Pass/Revise"

There are two main variations I'm aware of:

Standards-Based Grading: Instead of meaningless entries such as "Quiz 7" and "Test 4", the gradebook contains entries such as "Chain Rule" and "Definite Integrals" based on learning objectives. When you see your grade book, you know exactly what you need to work on to improve your score.

Specifications-Based Grading: Rather than being graded on a series of specific content objectives, the grade is more based on criteria you have to meet. For example, perhaps for an A you need to complete this many of the proof homeworks with a passing grade, do this much of a project, etc.

Here's my standards-based grading rubric I made a couple years ago:

And here's a specs-based grading example from an Introduction to Proofs class I took:

[tawdry venture]

Instead of meaningless entries such as "Quiz 7" and "Test 4", the gradebook contains entries such as "Chain Rule" and "Definite Integrals" based on learning objectives.
sounds like what our practice classes do over here

[woeful folio]

what is this

[turbid zenith]

Well if a student wanted to go beyond in a particular topic they'd have to show they're already at a Proficient level

And then come to me so I can give them some further explorations

[tawdry venture]

btw, why is the scale 0, 0.5, 1 and 1.5 instead of 0, 1, 2 and 3?

is it some sort of psychological thing

[turbid zenith]

Because I wanted to set the idea that 1.0 is "complete", like "you've got it"

And 1.5 is "extra"

Because otherwise people would be like "what do I need to do to get the highest mark possible in everything"

Does that make sense?

[tawdry venture]

so it's a psychological thing

[turbid zenith]

Yeah