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Cal Armstrong

@calarmstrong.bsky.social

I learn; I help others learn Mathematics Educator/Microsoft Education Fellow/PCMI - Institute for Advanced Study/Aux Police A/Sgt @cal_armstrong@mathstodon.xyz @sig225 on X/Twitter

409 Followers  |  462 Following  |  334 Posts  |  Joined: 17.08.2023
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"The Counter" February newsletter is out!
Highlights:
@ilanahorn.bsky.social "Mathematics Education at the End of the World", @davidpetro314.bsky.social OAMETalks on the OAME2026 conference & Michael Frankfort on Learning (Dis)abilities
sites.google.com/oame.on.ca/n...
#mtbos #mathed #onted

03.02.2026 18:39 β€” πŸ‘ 1    πŸ” 3    πŸ’¬ 1    πŸ“Œ 0
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WINTER PRESENTATION: CAL ARMSTRONG WINTER PRESENTATION: CAL ARMSTRONG

Chatting #AI in #mathed with the good folks in the Pacific North West on Monday, Feb. 9th!
app.smore.com/n/25hyx
#mtbos #ArtificialIntelligence #pcmi

02.02.2026 16:40 β€” πŸ‘ 1    πŸ” 0    πŸ’¬ 0    πŸ“Œ 0
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SEASON 5 HAS STARTED!
Check out our latest episode:

Is AI Helpful in Math Education?

Listen and subscribe on Apple Podcasts: podcasts.apple.com/us/podcast/d...

Or listen on Spotify:
open.spotify.com/show/3soGg9I...

Or check us out wherever you listen to podcasts!
#DebateMath

22.01.2026 12:41 β€” πŸ‘ 4    πŸ” 2    πŸ’¬ 0    πŸ“Œ 2
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Wondering about #AI in Education?
The AI experts come together again tonight online for Explor-AI-tion 2.0 : there's still time to register!
(there's a 50% off code for math folks!)
#onted #mtbos #iteachmath #AIInnovation
ecoo.org/exploraition...

13.01.2026 16:36 β€” πŸ‘ 0    πŸ” 0    πŸ’¬ 0    πŸ“Œ 0
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My favourite use for #AI this year?
I used the Santa emoji for an activity and needed the back of his head, so I asked ChatGPT to give me the image:
#mtbos #mathed #santa

17.12.2025 15:36 β€” πŸ‘ 2    πŸ” 0    πŸ’¬ 0    πŸ“Œ 0
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Love Christmas! My colleague made these Christmas Tree cupcakes to share. I'm enjoying it while I invigilate this end of term AP Calculus test.

15.12.2025 15:53 β€” πŸ‘ 0    πŸ” 0    πŸ’¬ 0    πŸ“Œ 0

Me (reading blogpost): Ugh, this is just AI slop.
Author: It's my work!
Me: No, I'd really like to read your work, but not AI's homogenization of it (It was formatted exactly like ChatGPT, em-dashes abound, "not this but this" structures, etc).
Author <blocks me>

14.12.2025 20:43 β€” πŸ‘ 1    πŸ” 0    πŸ’¬ 0    πŸ“Œ 0

Yeah, I remembered she was on on the battleship... I should have remembered she is Cher! :)

27.11.2025 13:10 β€” πŸ‘ 2    πŸ” 0    πŸ’¬ 0    πŸ“Œ 0

I was making a #OneNote Page for my Gr 10 class and we were turning back time to a previous topic to use in our new problem.
I tipped Cher's "If I Could Turn Back Time" in as a side-note.
Then I played the video.. and quickly deleted it.
youtube.com/watch?v=9n3A...
Little too racy.

27.11.2025 12:48 β€” πŸ‘ 0    πŸ” 0    πŸ’¬ 1    πŸ“Œ 0

Learning happens best when teachers look students in the eye, not look down on them.
Dialogue, not authority, engenders well-being.
Santiago Rincon-Gillargo at #otfcurriculumforum
#mtbos #onted #mathed

22.11.2025 15:19 β€” πŸ‘ 2    πŸ” 0    πŸ’¬ 0    πŸ“Œ 0
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"Learning to be taught" (the required compliance for reasonable management and safety, that becomes an overwhelming aspect of schools) is not equal to "Learning to learn" (Learning as a practice of freedom)
Santiago Rincon-Gillargo at #otfcurriculumforum
#mtbos #mathed

22.11.2025 15:19 β€” πŸ‘ 0    πŸ” 0    πŸ’¬ 0    πŸ“Œ 0

"We may not be able to replace the system, but we can create the friction that makes cracks in the system's concrete in which life can flourish"
Benjamin Freud via Dr. Santiago Rincon-Gillargo at @otffeo Curriculum Forum
@OAMEcounts #mathed #mtbos

22.11.2025 14:43 β€” πŸ‘ 0    πŸ” 0    πŸ’¬ 0    πŸ“Œ 0

"This is just axiomatically true... which is MathSpeak for 'Because I told you so!'"
@freya.bsky.social via www.youtube.com/@acegikmo

09.11.2025 02:57 β€” πŸ‘ 1    πŸ” 0    πŸ’¬ 0    πŸ“Œ 0

#mtbos gang, assemble!

05.11.2025 17:49 β€” πŸ‘ 3    πŸ” 3    πŸ’¬ 0    πŸ“Œ 0
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[New Podcast] This episode features Stacey Jacobs previewing their Nov 12th @oamecounts.bsky.social members only webinar "Empowering Math Learners: Executive Function Strategies to Support Math Learning". More info:

talks.oame.on.ca/season-8

#MathChat #MTBoS #iTeachMath

04.11.2025 04:01 β€” πŸ‘ 3    πŸ” 2    πŸ’¬ 0    πŸ“Œ 0
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OAME News - Nov 2025 Upcoming OAME Events At-a-Glance: Wednesday, November 5 - OAME Leadership Conference (virtual) - Link Wednesday, November 12 - OAMEtalks webinar on Empowering Math Learners (virtual) - Link Tuesday, N...

The @oamecounts.bsky.social November Newsletter is out!
What's going on in Ontario Mathematics?
(spoiler: Leadership Conference with Dr. Elham Kazemi tonight, Wed, at 7pm!)
sites.google.com/oame.on.ca/n...
#onted #mathed #mtbos

05.11.2025 13:06 β€” πŸ‘ 2    πŸ” 1    πŸ’¬ 0    πŸ“Œ 0
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Sorry, #AI ... the document is LONG because it's important, and the text has been chosen deliberately to convey meaning by the author. I don't need Reader's Digest abridged and condensed versions.

29.10.2025 14:44 β€” πŸ‘ 3    πŸ” 0    πŸ’¬ 0    πŸ“Œ 0
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LLMs are injective and invertible.

They show that different prompts always map to different embeddings, and this property can be used to recover input tokens from individual embeddings in latent space.

Paper: www.arxiv.org/abs/2510.15511

28.10.2025 02:05 β€” πŸ‘ 53    πŸ” 7    πŸ’¬ 4    πŸ“Œ 6

Me: And after you substitute into the equation, it's just arithmetic.
Student: What's arithmetic?

27.10.2025 22:01 β€” πŸ‘ 3    πŸ” 0    πŸ’¬ 0    πŸ“Œ 0

Thank you, that was a fun diversion!

24.10.2025 18:14 β€” πŸ‘ 0    πŸ” 0    πŸ’¬ 0    πŸ“Œ 0

Public embarrassment has always been a powerful motivator for me, too.

24.10.2025 17:54 β€” πŸ‘ 1    πŸ” 0    πŸ’¬ 1    πŸ“Œ 0
Slide shows: "Solve (x^2 -5x +5)^(x^2 -9x +20) = 1

Slide shows: "Solve (x^2 -5x +5)^(x^2 -9x +20) = 1

NIM: 4 pile game
- Draw 4 piles of dots, one has 8, one has 4, one has 2, and the last has 1 dot. 
- You can take as many as you want each turn, but only from 1 pile. 
- The winner takes the last dot. 

Do you see a winning strategy?

NIM: 4 pile game - Draw 4 piles of dots, one has 8, one has 4, one has 2, and the last has 1 dot. - You can take as many as you want each turn, but only from 1 pile. - The winner takes the last dot. Do you see a winning strategy?

Two things from #NCTMatl25 that I'm going to be using *this* week:

Gail Burrill's algebra problem, and @gwaddell.bsky.social and Ed Keppelmann's 4 pile Nim.

18.10.2025 23:18 β€” πŸ‘ 8    πŸ” 4    πŸ’¬ 2    πŸ“Œ 0
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I'm excited for my #AI schedule tonight at #ExplorAItion !
There's still time to register (and *cough* there's a special OAME code for 50% off)
ecoo.org/exploraition...
#mtbos #mathed #onted

22.10.2025 13:05 β€” πŸ‘ 2    πŸ” 0    πŸ’¬ 0    πŸ“Œ 0
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Discrete mathematics in primary and secondary schools in the United States - ZDM – Mathematics Education This article provides a status report on discrete mathematics in America's schools, including an overview of publications and programs that have had major impact. It discusses why discrete mathematics...

"Discrete mathematics in primary and secondary schools in the United States"
2004
DeBellis Valerie A. & Joseph G. Rosenstein

There are some fire quotes in this #MathEdPaperOfTheWeek
#mtbos #iteachmath

link.springer.com/article/10.1...

20.10.2025 21:40 β€” πŸ‘ 4    πŸ” 1    πŸ’¬ 2    πŸ“Œ 0
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Gestures can help children learn mathematics: how researchers can work with teachers to make gesture studies applicable to classrooms | Philosophical Transactions of the Royal Society B: Biological Sc... The gestures we produce serve a variety of functionsβ€”they affect our communication, guide our attention and help us think and change the way we think. Gestures can consequently also help us learn, gen...

This looks interesting! royalsocietypublishing.org/doi/10.1098/...

18.10.2025 15:20 β€” πŸ‘ 2    πŸ” 1    πŸ’¬ 0    πŸ“Œ 0
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So I had two tasks at #NCTMATL25 (besides presenting with Cynthia Shi) ... see @pegcagle.bsky.social and Gail Burrill
... mission accomplished! And a bonus visit with
Vicki Lyons
Forgot to take a pic with Peg & Vicki, but I got Gail!
#mtbos #mathed

18.10.2025 15:09 β€” πŸ‘ 5    πŸ” 0    πŸ’¬ 1    πŸ“Œ 0
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Okay, this is still an issue in high school
#nctmatl25 #mtbos #mathed

18.10.2025 14:28 β€” πŸ‘ 9    πŸ” 0    πŸ’¬ 3    πŸ“Œ 0
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Each representation is correct, but which are helpful, at what stage, and for which purpose?
#nctmatl25 #mtbos #mathed

18.10.2025 14:21 β€” πŸ‘ 5    πŸ” 0    πŸ’¬ 0    πŸ“Œ 0
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So the previous session mentioned procedural fluency versus conceptual understanding.
The next session drove the point home.
#nctmatl25 #mtbos #mathed

18.10.2025 14:08 β€” πŸ‘ 5    πŸ” 1    πŸ’¬ 0    πŸ“Œ 0
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Conference Proposals to Clarify Your Practice The 2025 NCTM conference kicks off in just a few days in Atlanta, Georgia. Social media is full of teachers preparing for the event and exhibitors inviting participants to visit their booths. While I....

Inspired by #NCTMATL25 to present at an upcoming conference? Both NCTM and OAME 2026 conference proposals close on Nov. 1st. Here are some thoughts on the benefits of writing a math conference proposal. pbbmath.weebly.com/blog/confere... #ITeachMath @oamelearns.bsky.social

18.10.2025 14:06 β€” πŸ‘ 7    πŸ” 3    πŸ’¬ 0    πŸ“Œ 0