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
Mathematics Educator/Microsoft Education Fellow/PCMI - Institute for Advanced Study/Aux Police A/Sgt
@cal_armstrong@mathstodon.xyz
@sig225 on X/Twitter
"This is just axiomatically true... which is MathSpeak for 'Because I told you so!'"
@freya.bsky.social via www.youtube.com/@acegikmo
@freya.bsky.social via www.youtube.com/@acegikmo
November 9, 2025 at 2:57 AM
"This is just axiomatically true... which is MathSpeak for 'Because I told you so!'"
@freya.bsky.social via www.youtube.com/@acegikmo
@freya.bsky.social via www.youtube.com/@acegikmo
Reposted by Cal Armstrong
#mtbos gang, assemble!
New project alert!
Which One Doesn't Belong? Second Edition.
I am deep in the middle of writing and would love input from folks who have used the routine in their classrooms.
Short Google form here—one page, eight questions, most of them optional: docs.google.com/forms/d/e/1F...
Which One Doesn't Belong? Second Edition.
I am deep in the middle of writing and would love input from folks who have used the routine in their classrooms.
Short Google form here—one page, eight questions, most of them optional: docs.google.com/forms/d/e/1F...
Which One Doesn't Belong, 2nd Edition
Hi! I'm Christopher, and I'm working on a second edition of the Teacher Guide for my Stenhouse/Routledge book Which One Doesn't Belong? This book celebrates its tenth anniversary in 2026. I have learn...
docs.google.com
November 5, 2025 at 5:49 PM
#mtbos gang, assemble!
Reposted by Cal Armstrong
[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
talks.oame.on.ca/season-8
#MathChat #MTBoS #iTeachMath
November 4, 2025 at 4:01 AM
[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
talks.oame.on.ca/season-8
#MathChat #MTBoS #iTeachMath
Reposted by Cal Armstrong
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
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
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...
sites.google.com
November 5, 2025 at 1:06 PM
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
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
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.
October 29, 2025 at 2:44 PM
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.
Reposted by Cal Armstrong
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
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
October 28, 2025 at 2:05 AM
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
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
Me: And after you substitute into the equation, it's just arithmetic.
Student: What's arithmetic?
Student: What's arithmetic?
October 27, 2025 at 10:01 PM
Me: And after you substitute into the equation, it's just arithmetic.
Student: What's arithmetic?
Student: What's arithmetic?
Reposted by Cal Armstrong
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.
Gail Burrill's algebra problem, and @gwaddell.bsky.social and Ed Keppelmann's 4 pile Nim.
October 18, 2025 at 11:18 PM
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.
Gail Burrill's algebra problem, and @gwaddell.bsky.social and Ed Keppelmann's 4 pile Nim.
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
There's still time to register (and *cough* there's a special OAME code for 50% off)
ecoo.org/exploraition...
#mtbos #mathed #onted
October 22, 2025 at 1:05 PM
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
There's still time to register (and *cough* there's a special OAME code for 50% off)
ecoo.org/exploraition...
#mtbos #mathed #onted
Reposted by Cal Armstrong
"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...
2004
DeBellis Valerie A. & Joseph G. Rosenstein
There are some fire quotes in this #MathEdPaperOfTheWeek
#mtbos #iteachmath
link.springer.com/article/10.1...
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...
link.springer.com
October 20, 2025 at 9:40 PM
"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...
2004
DeBellis Valerie A. & Joseph G. Rosenstein
There are some fire quotes in this #MathEdPaperOfTheWeek
#mtbos #iteachmath
link.springer.com/article/10.1...
Reposted by Cal Armstrong
This looks interesting! royalsocietypublishing.org/doi/10.1098/...
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 functions—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...
royalsocietypublishing.org
October 18, 2025 at 3:20 PM
This looks interesting! royalsocietypublishing.org/doi/10.1098/...
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
... mission accomplished! And a bonus visit with
Vicki Lyons
Forgot to take a pic with Peg & Vicki, but I got Gail!
#mtbos #mathed
October 18, 2025 at 3:09 PM
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
... mission accomplished! And a bonus visit with
Vicki Lyons
Forgot to take a pic with Peg & Vicki, but I got Gail!
#mtbos #mathed
October 18, 2025 at 2:28 PM
Each representation is correct, but which are helpful, at what stage, and for which purpose?
#nctmatl25 #mtbos #mathed
#nctmatl25 #mtbos #mathed
October 18, 2025 at 2:21 PM
Each representation is correct, but which are helpful, at what stage, and for which purpose?
#nctmatl25 #mtbos #mathed
#nctmatl25 #mtbos #mathed
So the previous session mentioned procedural fluency versus conceptual understanding.
The next session drove the point home.
#nctmatl25 #mtbos #mathed
The next session drove the point home.
#nctmatl25 #mtbos #mathed
October 18, 2025 at 2:08 PM
So the previous session mentioned procedural fluency versus conceptual understanding.
The next session drove the point home.
#nctmatl25 #mtbos #mathed
The next session drove the point home.
#nctmatl25 #mtbos #mathed
Reposted by Cal Armstrong
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
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....
pbbmath.weebly.com
October 18, 2025 at 2:06 PM
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
The only reason I would want to teach small children would be for the contexts - & sketches - they create!
#nctmatl25 #mtbos #mathed
#nctmatl25 #mtbos #mathed
October 18, 2025 at 2:03 PM
The only reason I would want to teach small children would be for the contexts - & sketches - they create!
#nctmatl25 #mtbos #mathed
#nctmatl25 #mtbos #mathed
Use "Create a mathematical sketch" rather than "draw a picture"
(it was referenced from another session so I don't have a reason why atm)
#nctmatl25 #mtbos #mathed
(it was referenced from another session so I don't have a reason why atm)
#nctmatl25 #mtbos #mathed
October 18, 2025 at 1:59 PM
Use "Create a mathematical sketch" rather than "draw a picture"
(it was referenced from another session so I don't have a reason why atm)
#nctmatl25 #mtbos #mathed
(it was referenced from another session so I don't have a reason why atm)
#nctmatl25 #mtbos #mathed
Reposted by Cal Armstrong
Note to self ... Look up research on gesturing in mathematics education.
If any of you out in the #mtbos have some ideas ...
#NCTMATL25 #mathed
If any of you out in the #mtbos have some ideas ...
#NCTMATL25 #mathed
October 18, 2025 at 1:39 PM
Note to self ... Look up research on gesturing in mathematics education.
If any of you out in the #mtbos have some ideas ...
#NCTMATL25 #mathed
If any of you out in the #mtbos have some ideas ...
#NCTMATL25 #mathed
"Because of the abstract nature of mathematics, people have access to mathematical ideas only through the representations of those ideas" from Adding It Up.
#nctmatl25 #mtbos #mathed
#nctmatl25 #mtbos #mathed
October 18, 2025 at 1:33 PM
"Because of the abstract nature of mathematics, people have access to mathematical ideas only through the representations of those ideas" from Adding It Up.
#nctmatl25 #mtbos #mathed
#nctmatl25 #mtbos #mathed
October 18, 2025 at 1:16 PM
October 18, 2025 at 12:23 PM
October 16, 2025 at 4:47 PM