iiinova — where your digital self keeps evolving

Bill Shillito @solidangles.bsky.social · 31/08/2026

Which of these is named "Kiki", and which of these is named "Bouba"?

A summation sign, the Greek capital letter sigma.

An integration sign, an elongated letter S.

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Bill Shillito @solidangles.bsky.social · 25/06/2026

I’m going to start calling non-commutative groups “abelian’t.”

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Matt Salomone @matthematics.com · 09/04/2026

#HoagieHomies : it's more than a hashtag, people

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Bill Shillito @solidangles.bsky.social · 25/03/2026

Giving students extra credit if they use \varepsilon instead of \epsilon on their LaTeX assignment

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Chanda Prescod-Weinstein 🌌 @chanda.blacksky.app · 25/02/2026

I think Harvard's plan to respond to the every-decade moral panic about grade inflation by capping A's is pedagogically obscene. Grades should be a measure of learning, not competition. Grade caps engender competition and anxiety where we should be teaching collaboration and a love of learning.

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Bill Shillito @solidangles.bsky.social · 24/02/2026

I feel this. I've had to return to handwritten exams, and I kind of hate it.

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Charlotte Lydia Riley @lottelydia.bsky.social · 23/02/2026

AI is going to trash every single way that we had modernised university teaching and send us back to handwritten exams and vivas for every assessment. Which will bring back every problem with those assessment models (and make us seem even more out-of-touch even as we just try to do meaningful work).

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Raj Raizada @rajraizada.bsky.social · 22/10/2025

Complex function domain-colouring of roots of unity, in @desmos.com Here's the graph: www.desmos.com/3d/hadt9rebbe They recently enabled colouring a surface using functions, so far only in 3D grapher. Side-effect: allows complex domain colouring, using 3D tool as a 2D one! #iTeachMath #MathSky

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Bill Shillito @solidangles.bsky.social · 13/02/2026

Question for anyone who's taught multivariable calculus (without line/surface integrals — just up through multiple integrals). If you were to choose a "capstone" topic that ties multiple topics together, what would you choose? Teaching the Calculus sequence again soon and trying to plan ahead.

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Bill Shillito @solidangles.bsky.social · 23/01/2026

WOOHOO! Our sandwiches paper has been published! 🥳 ...in celebration, I'm going to claim that tonight's lasagna was a sandwich. 🥪

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Bill Shillito @solidangles.bsky.social · 21/01/2026

Teaching logic tomorrow ... with Clue!

Suppose you've made the following deductions:

* The murderer must be Miss Scarlett or Colonel Mustard.
S ∨ M

* If Miss Scarlett did it, it was in the kitchen with the lead pipe.
S → (K ∧ L)

If your friend shows you the kitchen card, what can you conclude?
¬K

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Bill Shillito @solidangles.bsky.social · 15/01/2026

It’s ironic that the people who seem to be able to benefit the most from AI tools are the ones who don’t actually need them.

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Bill Shillito @solidangles.bsky.social · 02/01/2026

As my contribution to sharing subtraction strategies, here's how I do subtraction nowadays, using negative numbers! Made this up on the fly way back when I first started tutoring because I couldn't remember how to do multiple borrowing anymore and I never liked the lie of "you can't take 3 from 2".

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Bill Shillito @solidangles.bsky.social · 01/01/2026

Deviled eggs for New Year's Eve!

Left: Everything bagel deviled eggs, with smoked salmon and chives.
Right: Dua Belibis deviled eggs, with green onion, cilantro, and chopped peanuts.

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Manim Community @manim.community · 26/12/2025

We are aware of an ongoing situation concerning our GitHub organization and Discord server (both of which have been deleted) and are working on resolving this as soon as possible. In the meantime we have setup discord.gg/fGG4TFSdKh as a new home on Discord for our community, come join us there!

discord.gg

Join the Manim Discord Server!

Check out the Manim community on Discord – hang out with 95 other members and enjoy free voice and text chat.

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Bill Shillito @solidangles.bsky.social · 23/12/2025

Had a dream last night… except the main thing of the dream was that I stayed in bed until like 4 PM. There were other things going on too, but I think someone is trying to tell me to get more sleep. 😂

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Matt Salomone @matthematics.com · 22/12/2025

🙂‍↔️🫸 Calculus II exam 😎👉 Series finale

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Bill Shillito @solidangles.bsky.social · 22/12/2025

Most underrated video game villain.

A blue tornado with wide white eyes named Mr. Glitch, who was the villain of the Mathman segment from the children's educational show Square One TV.

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Matt Enlow @unsolvedmre.bsky.social · 15/12/2025

For today’s Advanced Topics test I wrote my own @joeldavidhamkins.bsky.social -style question 😁 #iteachmath #MathSky

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Bill Shillito @solidangles.bsky.social · 09/12/2025

Anyone have any idea where I can find a direct reference to the following quote? Especially in its original script? I want to verify the translation. "Anantam api sankhyaatmakam iti budhyate. / Through numbers, even the infinite can be understood." — Madhava of Sangamagrama

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Bill Shillito @solidangles.bsky.social · 07/12/2025

Students who take AP Statistics are 3x more likely to be able to tell the difference between correlation and causation.

Screenshot of a College Board social media post promoting AP Precalculus. Large text reads “Students who take precalculus are 3x more likely to earn a college degree.” Below the text is an icon of a diploma with a ribbon. The bottom text says, “See why more schools are making AP Precalculus part of their math pathway.”

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Bill Shillito @solidangles.bsky.social · 18/11/2025

Which of these is an "A"? Why? #Grading Image source: www.mpusd.net/apps/pages/i...

A graphic titled “Student Goal: Ride the Bike Independently” shows four mastery levels with simple stick-figure illustrations of children on bicycles. From bottom to top, the levels are as follows:

* Level 1, “Emerging Mastery,” shows a child riding a bike with training wheels. The text reads, "The student is riding a bike, but only with the use of training wheels."

* Level 2, “Partial Mastery,” shows an adult steadying a child on a bike. The text reads "The student is pedaling well and staying upright, as long as someone is assisting."

* Level 3, “Sufficient Mastery,” shows a child riding a bike alone. The text reads, "The student is successful at riding the bike."

* Level 4, “Extensive Mastery,” shows a child doing a wheelie on a bike. The text reads, "The student can not only ride the bike independently, but also performs stunts!"

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Michael Kinyon @profkinyon.bsky.social · 07/11/2025

You kids and your six trig functions. Back in my day we had only one, and we used it for everything. sin(θ) sin(π/2 - θ) sin(θ)/sin(π/2 - θ) 1/sin(θ) 1/sin(π/2 - θ) sin(π/2 - θ)/sin(θ)

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Bill Shillito @solidangles.bsky.social · 07/11/2025

If you'd never seen the definitions for the dot product and the cross product, how might you have invented them for yourself? Who took two vectors, thought "I wonder how I multiply these", and came up with ... those? I've been toying with this since yesterday and would love to hear other thoughts.

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Bill Shillito @solidangles.bsky.social · 05/11/2025

Hey @desmos.com, any plans to have Desmos be able to choose between the math convention and the physics convention for θ and φ as a quick toggle? I've taught both math majors and physics majors, and it would be nice to allow them to choose the convention that their field uses. 🙂

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Bill Shillito @solidangles.bsky.social · 29/10/2025

How to graph y = cosh x: TI-84 CE: 1. Press [Y=]. 2. Press [2nd] [0] (CATALOG). 3. Press [PRGM] (C) to skip to the C functions. 4. Scroll down until you find cosh( and press [ENTER]. 5. Type the rest of the expression and press [GRAPH]. @desmos.com: 1. Type y = cosh x.

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Bill Shillito @solidangles.bsky.social · 25/10/2025

There's a part of math history that mystifies me. We used to have a whole bunch of interesting named curves — cissoid, tractrix, strophoid, involute, pedal curve, and so on. Now they've mostly been relegated to quaint examples in math textbooks. Why were these relevant? And what happened to them?

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Bill Shillito @solidangles.bsky.social · 24/10/2025

Question for anyone that teaches Calculus I. (Been asking this in a few chats.) What's the point of having students learn about the normal line? What's it good for specifically? (And "they'll see normals again in Calculus III" doesn't count.)

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Bill Shillito @solidangles.bsky.social · 21/10/2025

This was the exact moment I learned it's called "maths" across the pond.

A cropped screenshot of the ending credits to Puggsy on the Sega Genesis. The text reads:

AND REMEMBER THAT

11125 SQRD MINUS 181
13307 SQRD MINUS 712
21385X21386 SUB 1875

IS A SILLY MATHS
QUESTION

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Bill Shillito @solidangles.bsky.social · 11/10/2025

Ah yes, the four basic operations: addition, subtraction, checkmark, and multiplication.

A close-up of a parking meter with a digital display reading “SELECT SPACE LEFT / RIGHT.” Below the screen are colorful buttons: a blue plus, a blue minus, a green check mark, and a red X.

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Bill Shillito @solidangles.bsky.social · 10/10/2025

Cool thing I just realized about f-means! If deg(f) < deg(g), then the f-mean of a data set is less than the g-mean. So since f(x)=log x has "degree" 0 and g(x)=x has degree 1, the geometric mean is less than the arithmetic mean. (I always forget which way it goes — now I'll always remember!)

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Bill Shillito @solidangles.bsky.social · 09/10/2025

I've been thinking a lot about means recently! Probably some combination of (1) teaching our data analysis unit in our STEM 101 course at Oglethorpe and (2) all of @howiehua.bsky.social's great posts surrounding Mean Girls Day. I'd like to show how some of these various means are related. 🧵 [0]

A four-panel graphic showing formulas for four types of means. Each panel includes the formula and the name of the mean in bold text below.

Top left (red background): Arithmetic Mean, labeled “AM = (x₁ + ⋯ + xₙ) / n.”

Top right (dark blue): Geometric Mean, labeled “GM = ⁿ√(x₁ ⋅ … ⋅ xₙ).”

Bottom left (purple): Harmonic Mean, labeled “HM = n / (1/x₁ + ⋯ + 1/xₙ).”

Bottom right (dark green): Quadratic Mean, labeled “QM = √((x₁² + ⋯ + xₙ²) / n).”

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Bill Shillito @solidangles.bsky.social · 02/10/2025

Welp, looks like my Erdős number is still infinity. 🙃 (My journal submission based on my dissertation research got outright rejected.)

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Barbara Fantechi @barbarafantechi.bsky.social · 25/09/2025

What this thread doesn't mention: the English language contains the numerals lakh and crore for a significant percentage of its native speakers. en.wikipedia.org/wiki/Indian_...

en.wikipedia.org

Indian numbering system - Wikipedia

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Bill Shillito @solidangles.bsky.social · 25/09/2025

Hot take: The English language is not base ten. It's base thousand. Sure, we write numbers using the Hindu-Arabic digits 0 through 9, but the way our language is structured groups numbers in powers of a thousand. If anything, we're sub-base ten. (1/5)

Colorful text showing the number 573,961,284 broken into chunks of thousands.

First line: “573,961,284”.

Second line shows it as “573 × 1000² + 961 × 1000¹ + 284 × 1000⁰.”

Third line spells it out: “Five hundred seventy-three million, nine hundred sixty-one thousand, two hundred eighty-four,” with each chunk matching the colors from the first two lines.

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Bill Shillito @solidangles.bsky.social · 11/09/2025

Holding class discussions on readings is HARD. English teachers, how do y'all even do it? I'm honestly struggling. 😕

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Bill Shillito @solidangles.bsky.social · 05/09/2025

Student: “Babylonian numerals are kinda confusing… 60 is such a weird and unintuitive base.” Me: “Yeah I know right? Oh hey by the way, what time does this class end?” Student: “At 11:30.” Me: *waits* Multiple students: “…OHHHHHHHHHH” #MathSky

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Bill Shillito @solidangles.bsky.social · 03/09/2025

Today's lesson in COR 314! Students learned how to count in Iñupiaq and write numbers using the Kaktovik numerals (as well as convert between base ten and base twenty). 🧮 Lots of discussion about how the way we're used to thinking isn't the only way to do things! 🙂

A list of number words in Iñupiaq, counting in 1s up through 20 and then counting in 10s up through 120. At the bottom is text that asks "What do you notice? What do you wonder?"

A display of the Kaktovik Inupiaq numerals, along with a conversion of the number 17 : 5 : 13 : 4 (in base twenty) to 138,264 (in base ten).

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Bill Shillito @solidangles.bsky.social · 17/08/2025

Anyone else moving to more in-class assessments this semester due to AI concerns and not particularly thrilled about it, but not feeling like they have much of another choice? 😕

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Zach Weinersmith @zachweinersmith.bsky.social · 14/08/2025

Bonus panel here: www.smbc-comics.com/comic/dress #smbc

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Bill Shillito @solidangles.bsky.social · 14/08/2025

Me: After I graduate I’m gonna write my own textbook! And start a new video series! And program a game! And go to the gym! And cook more often! And… Also me: I dun wanna get up it’s not noon yet

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Bill Shillito @solidangles.bsky.social · 09/08/2025

Anyone have ideas for games (especially combinatorial ones) that inherently involve taxicab geometry? Not just games that happen to take place on a square lattice but where taxicab distance is actually an important part of playing the game?

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Bill Shillito @solidangles.bsky.social · 29/07/2025

Who’s going to be at #MAAthfest next week? Let’s meet up!

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Bill Shillito @solidangles.bsky.social · 25/07/2025

My dissertation is officially uploaded, so I finally feel like I can say I have my PhD! 🥳 scholarworks.gsu.edu/entities/pub... It's been exhausting going to school while working full time at Oglethorpe... But looking forward to doing my own projects again, like video-making and textbook-writing!

scholarworks.gsu.edu

Using Combinatorial Game Theory to Introduce the Concept of Mathematical Proof in a Mathematics for Liberal Arts Course

This dissertation investigates students' development of the notion of mathematical proof in a Mathematics for Liberal Arts course through the lens of Combinatorial Game Theory. There has been extensiv...

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