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Posts by Cal Armstrong

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chatOAME now has a *GeoBoard* visualization... Along with Desmos, GeoGebra, Polypad, and Graspable Math, we're really starting to fill in the visualization gaps that LLMs leave especially in a subject like math where noticing relationships is so important. What's still missing, #onted #mtbos?

3 weeks ago 3 0 0 0

I ran into a teacher who had never heard the phrase "productive struggle" before, and encouraged the presenter to copyright it immediately, so taken by it (law teacher).
It was coined by the awesomeJames Heibert in the late 2-noughts & forms a great argument against AI

3 weeks ago 1 1 0 0

There is a VAST difference between #AI access in independent schools & public schools which is only widening the equity gap! That doesn’t even factor in the fact that so many voices & cultures are missing from training data! via @heidisiwak.bsky.social @ecooorg.bsky.social #Edusky #dreamforward

3 weeks ago 8 5 0 0
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The inestimable @pbeens.bsky.social the maker of more custom GPTs than any #onted teacher I know.

" #AI can create the illusion of learning "

Cognitive offloading. Presenting to a full room at
#dreamforward on this snowy Saturday morning.

#education #aiineducation

3 weeks ago 8 6 1 0
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Setting up for the opening session at #DreamForward STEAM event today in Milton. Thanks @ICTC_CTIC and @HCDSB and @ecooorg for bringing teachers together.

3 weeks ago 5 3 0 0
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Setting up for the opening session at #DreamForward STEAM event today in Milton. Thanks @ICTC_CTIC and @HCDSB and @ecooorg for bringing teachers together.

3 weeks ago 3 1 0 1
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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

2 months ago 1 3 1 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

2 months ago 2 0 1 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

2 months ago 4 2 0 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...

3 months ago 0 0 0 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

4 months ago 2 0 0 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.

4 months ago 0 0 0 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>

4 months ago 1 0 0 0

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

4 months ago 2 0 0 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.

4 months ago 0 0 1 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

4 months ago 2 0 0 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

4 months ago 0 0 0 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

4 months ago 0 0 0 0

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

5 months ago 1 0 0 0

#mtbos gang, assemble!

5 months ago 3 3 0 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

5 months ago 3 2 0 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

5 months ago 2 1 0 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.

5 months ago 3 0 0 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

5 months ago 53 7 4 6

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

5 months ago 3 0 0 0

Thank you, that was a fun diversion!

5 months ago 0 0 0 0

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

5 months ago 1 0 1 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.

6 months ago 8 4 2 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

5 months ago 2 0 0 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...

6 months ago 4 1 2 0