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I teach at a very academically rigorous school. But, there are a few things this school does that might surprise people:
1. Many teachers teach a wide range of grade levels. So you could have a teacher who *could* teach Linear Algebra teaching you in 4th grade math.
2. The school makes time for creative math and CS in addition to the regular class. So I get to work with students without pressure to get them past any particular test or goal posts.
In most other teaching contexts I've always been trapped teaching the most advanced topics since I was one of a few people who *could* ... having teachers with deep math experience from a young age makes a big difference.
And when I'm working with them outside of their regular class I can work on teaching something that doesn't fit well into a "standard" ... how to *play* at mathematics.
And the students really do need it.
@futurebird this is pretty fantastic.
When I was in 5th grade at a magnet school, I got tossed from the special math class for behavior. The teacher and I had a heated exchange. I could be a little snot.
After my mom got pulled in to hear about what happened she debriefed me at home.
"Yes, you were rude and out of line but, reading between the lines of what the vice principal said, the response was so severe because you asked questions she didn't know the answers to and you wouldn't let it go"
I don't know if avoiding that as a teacher is as much about knowing a lot about the subject as it is about being comfortable modeling what to do when you don't know something.
My students stump me all the time. Then we find the answer together, if one exists.
he/him @futurebird @PizzaDemon Beige bless you for this. Actually? All joking aside.
That's incredibly important, I wish I could have been your student. After high school, which solidified by belief that I inherently suck at math, I did online college.
I was kind of terrified of college algebra, but I eventually realized that this stuff is kind of amazing, beautiful, and occasionally fun. Thank you for preventing that sort of anxiety, it's just frigging miserable to walk up to that classroom door feeling like that. 
“Beige bless you for this”
not to derail from the topic, but so it’s true that beige.party is not a cult 
@futurebird @PizzaDemon That was my advice to teachers new to the Georgia Governor's Honors Program (summer experience for gifted high schoolers) who were freaking about content matter: You don't have to know it for them to learn it.
@Lichtenbergian @futurebird @PizzaDemon
My son went to GHP. Most of what he used afterward was the stuff he learned off-book.
@Mcdyer @futurebird @PizzaDemon Cool — what year?
@Lichtenbergian @futurebird @PizzaDemon
2012, I think. It was that year it rained so much in Valdosta (I make a joke).
@Mcdyer @futurebird @PizzaDemon No joke, the rain that summer was relentless.
@Lichtenbergian @futurebird @PizzaDemon
Now that you mention it, I think it was notable, and not just "
, Valdosta".
I understand y'all are in Rome now. That's an improvement!
@Mcdyer @futurebird @PizzaDemon They were at Berry College for a few years, but are now at Georgia Southern. (My last year as director was 2013.)
@Lichtenbergian @futurebird @PizzaDemon
Then a very heartfelt "thank you" to you! You and your team prepared the parents so well for the experience (including the day 3 phone call- I can't tell you how much I appreciated the heads-up, even though, like every other parent, I didn't believe my kid would succumb. Ha!)
@futurebird @PizzaDemon When my youngest was in 1st grade the teacher asked the kids to name parts of a plant. My kid said "Chloroplasts!" (thank you, Magic School Bus!) The teacher blinked, paused, and said "I don't know what that is, but I'll find out!" and she did. TEACHERS, PLEASE DO THIS! (Said kid now works for NASA as a planetary scientist & lab manager)
@epicdemiologist @futurebird @PizzaDemon I had a teacher who sent me to the library in middle school. "If you have so many questions, go write a report." I was confused but so was the librarian, who said "huh. Okay, well, what do you want to do while you're here?"
I still feel bad for that teacher. She was clearly exhausted. My question had something to do with an inconsistency in how she explained atomic weights. Her answer didn't make sense and I wanted to understand.
@futurebird I would love to hear more about where you teach. I’m a board member at a small private school that is similar in this way and am very curious about peer institutions. (I agree with you about the importance of having strong math teachers in the early grades, BTW.)
Of course, I'm one of those oddballs who believes that we should thinking about how to best prepare 4th graders for Linear Algebra...
Honestly I do think that an introduction to linear transformations, with an emphasis on their geometric interpretation, should be part of the elementary curriculum.
And my philosophy of math education reflects that: I cannot think of a simpler or more ideal situation for introducing, motivating, and understanding matrix multiplication than studying the Symmetry Group of the Square D_4, as it has a particularly simple action on the Cartesian coordinate plane.
So my idea is to start by emphasizing an intuitive understanding of D_4, via this manipulative and these worksheets:
https://github.com/constructive-symmetry/constructive-symmetry/tree/master/D002_Book_of_Algebra
Later, my idea is to revisit D_4 and learn how to compute its arithmetic without the help of the manipulative. The canonical representation of D_4 is the eight 2x2 matrixes with a single 0 and a single ±1 in every row and column. The determinant of these matrices is ±1, with the sign corresponding to the orientation.
Then almost by magic, the Stern-Brocot tree SL(2,N) is all those 2x2 matrices with natural-number entries and determinant 1, which also happens to hint at the result I mentioned before, that the modular group GL(2,Z) is equivalent to D_4 * SL(2,N) * D_4, where * is Minkowski multiplication.
So discussing any kind of algebraic module, let alone a module over a monoid, is usually reserved for second or third year Linear Algebra, but honestly I feel like a specific, concrete instantiation of this concept should be an Elementary/Middle School topic.
@leon_p_smith @futurebird I don't know any linear algebra or stats, but I use monoids every day for programming
@shapr @futurebird yeah I definitely appreciate monoids a lot more than I ever did as an undergraduate thanks to Haskell and functional programming. That certainly helped me see this particular big cosmic pun.
The ncatlab wiki's entry for "modules over a monoid" mentioned "modules over a monad".
I'm not even sure I know what that is. I mean, maybe I do? I mean, it is possible that particular construction corresponds decently well to something I have already built some intuition for, but I'm far from certain that's actually true.