iiinova — where your digital self keeps evolving

No worries. And agreed that I am not sure what that item is assessing when graphing tech is in play.

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which 2025 exam? I'm not seeing an alg 2 exam with a graph for question 4.

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Progress is good! I wonder if they will ever switch over to something like TikZ for graphics.

Wild. I'm looking at a lot of Regents exams these days and now I won't be able to un-see this.

wat? am I going to be sad if I ask for more detail here, Dan?

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Oooo, whereas for the inverse I'm flipping the axes to reflect (pun intended) the change of input<-->output. And many perspectives does good math thinking make!

A fair point that I'll enjoy pondering. I was thinking last week about the exp & log relationship & getting annoyed when 'inverses' in a context are graphed on the same axes when, which I think is related to this. & thanks for chatting about this! I appreciate you taking the time to engage, Carl.

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similar in my mind, for celsius to fahrenheit I wouldn't swap the C and the F. one version takes C inputs to F outputs, the inverse takes F inputs to C outputs

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for abstract cases I'm with you. here t and v are defined in the context, so 'swapping' them doesn't make sense in my head. I can see doing something like t(v) = [expression with v], but not swapping. It's more v is now the independent, t the dependent.

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Coming back to this as I think it's where we diverge. I'm with you on 'an inverse reverses the inputs & outputs of a function'. And I see t = (60-v)/2.25 as the inverse of v = 60-2.25t. time-->volume vs volume-->time. does that match your thinking? or is this the split?

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I know a lot of the focus of that section is on the idea of inverses while trying to not get bogged down in notation. By the CCSS Progressions, "The point is to provide an informal sense of determining the input when the output is known." p245

$When it comes to inverse functions, the expectations are modest, requiring only that students solve equations of the form f (x)=c. The point is to provide an informal sense of determining the input when the output is known. Much of this work can be done with specific values of c. Eventually, some generality is warranted. For example, if f(x)=2*x^3, then solving f(x)= c leads to x = (c/2)^(1/3), which is the general formula for finding an input from a specific output, c, for this function, f. At this point, students need neither the notation nor the formal language of inverse functions, but only the idea of “going backwards” from output to input. This can be interpreted for a table and graph of the function under examination. Correspondences between equations giving specific values of the functions, table entries, and points on the graph can be noted (MP.1). And although not required in the standard, it is reasonable to include, for comparison, a few examples where the input cannot be uniquely determined from the output. For example, if g(x) = x^2, then g(x)= 5 has two solutions, x = +/- sqrt{5}.$

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Ashli @mythagon.bsky.social · 08/02/2026

Curious what you would change. Notation or something deeper?

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Sending you love, friend. Thank you for sharing some of his story. A generous and curious man passed those traits onto his kiddo.

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Ashli @mythagon.bsky.social · 02/02/2026

K8 reposted something of yours and I was delighted to see your name pop up!

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Ashli @mythagon.bsky.social · 18/12/2025

I used to always start on the last page that had no name for the same reason.

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Ashli @mythagon.bsky.social · 18/11/2025

Mine loves the Ranger's Apprentice series. I'll look into Method for Magic!

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Ashli @mythagon.bsky.social · 05/11/2025

*If A is true and B is true, what else could be true!?

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Ashli @mythagon.bsky.social · 14/10/2025

Great point. Aligned with "riding in the wagon."

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Ashli @mythagon.bsky.social · 14/10/2025

I'm wondering if the language is mimicking horse riding lingo more than car lingo. Horse, motorcycle, and bike passengers can't be totally passive the way car passengers can (well, a small child could be given proper buckles). Super curious about the other languages take!

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Ashli @mythagon.bsky.social · 19/08/2025

I also just got looped in. Listening to the sound track on repeat. Pondering how to get tiger/magpie merch. I love the language/culture breakdowns, like this one: youtu.be/qCmpU3ssip8

youtu.be

K-pop Demon Hunters explained by a Korean teacher 😈🧑‍🏫

YouTube video by Talk To Me In Korean

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Ashli @mythagon.bsky.social · 29/07/2025

That sounds sub-optimal. Mostly I'm just using light rail to go to/from the airport when I'm in Seattle, so I'd not noticed that quirk.

Ashli @mythagon.bsky.social · 29/07/2025

You can get an ORCA card and it works on all of these. I'm not sure on how the end-to-end fare works these days, though.

Ashli @mythagon.bsky.social · 10/07/2025

I love his work! magical.

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Reposted by Ashli

Rick Steves @ricksteves.bsky.social · 17/06/2025

In the spring of 2008, I feared America was on the verge of war with Iran — and, believing that it’s good style to get to know people before you bomb them, I made “Rick Steves’ Iran,” a one-hour special that could (and would) only debut on PBS. Sadly, this special has become pertinent again today.

ricksteves.com

Iran

Join Rick as he explores the most surprising and fascinating land he's ever visited: Iran. In a one-hour, ground-breaking travel special on public television, you'll discover the splendid monuments of...

197119983361

Ashli @mythagon.bsky.social · 12/06/2025

The majority of my taste in humor is thanks to Mel Brooks movies. Cannot wait.

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Ashli @mythagon.bsky.social · 14/05/2025

I think a 4. Slightly worse that "mid". Semi-related: In college I ran into one of my maths professor post final and he cheerily said that I did <Scottish accent>"Amazingly satisfactorily."</Scottish accent> I'd no idea what that meant until I got my grades (it was positive).

Ashli @mythagon.bsky.social · 03/04/2025

I avoided putting the final total anywhere on the paper to make it easier for students to dig in and discuss with one another with out the letter-status so front and center. (I also didn't post the grades till the end of the day so kiddos didn't come to class having already looked)

Ashli @mythagon.bsky.social · 12/03/2025

wontons (pork and vegetable filled, fried)

Ashli @mythagon.bsky.social · 27/02/2025

"Allowing other people who are not you to decide what matters to you." 37 minute video. Worth it.

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Ashli @mythagon.bsky.social · 27/02/2025

Oh yeah! Ground News is also fascinating since they'll show how different sources position the same story. Reading the headline differences is wild.

Ashli @mythagon.bsky.social · 26/02/2025

I've been following Jessica Yellin, who does News Not Noise, on substack and insta for national coverage. A friend of mine started getting the local paper and recommends it and I found a local indie news source on substack, but ymmv depending on locale.

Ashli @mythagon.bsky.social · 25/02/2025

That list and your last sentence are🔥

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Then for HS it has this:

Students also formalize the notion of a transformation as a function
from the plane to itself. When the transformation is a rigid motion (a translation, rotation, or reflection) it is useful to represent
it using transparencies because two copies of the plane are represented,
one by the piece of paper and one by the transparency.
These correspond to the domain and range of the transformation,
and emphasize that the transformation acts on the entire plane, taking
each point to another point. The fact that rigid motions preserve
distance and angle is clearly represented because the transparency
is not torn or distorted.

The CCSS progressions has this:

Initially, students view rigid motions as operations on figures
(“transformations in the plane”). Later, students come to understand
that it is not the figure that is translated, rotated, or reflected, it is the
plane that is moved, carrying the figure along with it. Students start
thinking, not of moving one figure onto another, but of moving the
plane so that the first figure lands on the second (“transformations
of the plane”) without moving the coordinate grid. This change in
perspective is makes it possible to describe the effect of a given
rigid motion on any point in the plane.

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I'd be interested for a take on this from topology or differential geometry. There is something odd with these nuances, but I don't know the right question to ask to get at the distinction. And I know some folks say the plane is just a reference and it's the object that moves.

new question: are those two sets of instructions actually different when both involve coordinates, which implies both are on a coordinate plane?

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I feel the same. "transforming figures" feels more "low floor" to me while a transformation of the plane is like a function F that takes each point P to a point F(P). I've yet to find a straightforward way to think about the delta between these ideas, though

I read the 2nd instructions as getting the same result as the 1st instructions were they for, say, a grade 8 student. Sounds like you are thinking about transformations as movements of figures vs transformations as functions from the plane to itself?

I say they are the same since the center of rotation is based on the figure and not the plane. I did not calculation, but played with objects on my desk to think it through. east-->north-->pivot = pivot-->east-->north

Hank Green @hankgreen.bsky.social · 14/02/2025

What's the center of rotation?

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Reposted by Ashli

The Project for Awesome is a very fun and silly but also important event that raises millions of dollars for global health and other charities voted on by YOU. It has just begun. Please join us at ProjectforAwesome.com/live

A goose, it says "I think I will cause problems on purpose."

907292762

Ashli @mythagon.bsky.social · 09/02/2025

And this is an underestimate by a wide margin. Indirect rate costs are not just in labs in schools of medicine.

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Ashli @mythagon.bsky.social · 08/02/2025

This is how you get research scientists to leave the US.

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Ashli @mythagon.bsky.social · 28/01/2025

Truth. I have a print on my wall titled "All I Ever Really Needed to Know I Learned in Kindergarten"