I’ve got a couple lessons you might find useful as next steps w this group of students in the “Global Forecast” unit. See “Are They Related?” and “The Emissions Equation.” Maybe also “Degrees of Impact” docs.google.com/document/d/1...
Wow! Thats wild.
OpenAI ”acknowledged in its own research that LLMs will always produce hallucinations due to fundamental mathematical constraints that cannot be solved through better engineering, marking a significant admission from one of the AI industry’s leading companies.”
You can’t trust chatbots.
Hi @comapmath.bsky.social ! I’m looking for print Teacher’s Editions of your high school ‘Modeling our World’ series, but don’t see them available in your store (or anywhere). Know if/where I can find them?
A poster demonstrating how you can use a three-step plan of specialising, conjecturing and generalising to solve mathematical problems. The poster is split into four areas: 1) The classic problem "How many squares are on a chessboard?" 2) Solving the problem with much smaller boards. 3) Arriving at a conjecture involving square numbers. 4) Generalising the problem ofr all board sizes.
Specialise, Conjecture and Generalise.
A three-step plan to encourage and develop mathematical thinking.
I'm going to use this thread to share a few of my favourite tasks that lend itself nicely to this idea.
It would be amazing if everyone added their own in the replies.
In this editorial, I explore what it means to teach (mathematics) in a time of polycrisis. I use Anna Tsing's argument from "The Mushroom at the End of the World" to unearth the capitalist logics that underlie much of our educational enterprise to reimagine new possibilities. #iteachmath #EduSky
I figured you were busy wrapping up classes before break. I’m not doing much over break, so we can connect then if that works for you.
…Because the LSRL always goes through the point (mean(x),mean(y)), we can do this same thing for relationships that don’t start at (0,0). Was wishing I had your applet built for my data set! Thanks for the ideas you always share here!
Crazy that you did this today! I was thinking about this EXACT applet that I’d seen from you when I was building a lesson on bivariate data…
Unexpected email from Jonny Griffiths telling me there's a new 2026 update of his RISPS book, that's great investigations for impressionable A Level students. Download it now from www.risps.co.uk with links to Geogebra and Excel files
@jonny-griffiths.bsky.social
I guess 'relationship' probably means something like: "the degree to which changes in one variable predict the changes in the other"?
But...wait! If you give the data trend even the smallest 'slope' the r value all of a sudden jumps to perfect.
So, seems MAE is actually a very good predictor except in this 'anomaly' case where the data trend is horizontal?!
Someone help! cc: @triangleman.bsky.social @averypickford.bsky.social
Ah! This extreme case is interesting. Here is a situation where the MAE is basically zero (VERY little 'error of the model') but the r value indicates 'no relationship.'
So, measuring the 'error of the model' is not the same as measuring the 'strength of the relationship'
The internet says this: "In summary, while MAE and MSE relate to how spread out points are from a specific line of best fit not the overall variability of the raw bivariate data."
But I don't buy that. Both MAD and StdDev are also in reference to central 'structure' of prediction (the mean!).
Hey #statistics friends, I need help with a question:
With single variable data, we typically use MAD or StdDev as measures of variability. Why don't we just use MAE ('mean absolute error') or MSE ('mean squared error') as measures of variability for bivariate data?
A square table of 25 numbers 5 11 3 14 7 13 19 11 22 15 16 22 14 25 18 20 15 7 18 11 7 13 16 9
“When do our students really understand the algorithms we teach? When they can use them effectively, or when they understand how they work, and can reconstruct them if they forget crucial steps” dylanwiliam137385.substack.com/p/onions #iTeachMath
Thank you!
This video helped me see some good possibilities: youtu.be/Y7TesKMSE74
Thanks for this! Excited to learn.
I have a couple specific questions (if you have time):
- what is the value of being able to model sound waves w functions?
- is there a meaningful use of solving trig equations in this context?
Is the point of mathematical research to know *what* is true or to know *why* it's true? Emily Riehl lays out a strong argument - and what it has to do with AI - along great advice for the field in @science.org
www.science.org/doi/10.1126/...
"Big Tech and data center developers appear to be siting data centers in vulnerable communities...These locations show a troubling trend - they primarily impact working class and Black and Latine communities."
A couple things I’ve learned:
- know board/district policy and use it to force them to do what it says
- community needs to be educated on the issues and mobilized to show up
- ORGANIZE; find ways to coordinate communications, efforts, and actions so that everyone interested in working together
Anyone have ideas about connections between sound/music and trig functions? cc: @averypickford.bsky.social @maria-naturalmath.bsky.social #iteachmath
Why only K-8?
Elon Musk is set to make more than every U.S. elementary teacher combined See how your profession stacks up against Musk’s pay. By Alyssa Fowers and Leslie Shapiro
Every elementary school teacher On average, Musk will make $3 billion more per year than the 1.4 million elementary school teachers in the U.S. combined. Each figure represents 1,500 elementary school teachers. Together, they made $97 billion last year
Humans are bad at big numbers. Which makes it easier for billionaires (and trillionaires) to get away with hoarding wealth. Because most people just can't comprehend how much money that is.
So, I appreciate this WaPo effort to help people visualize what ridiculous amounts of wealth really mean.
Math education is complex. It can’t be reduced to single studies or one-size-fits-all claims.
NCSM’s new position paper offers a balanced, equity-centered, research-informed alternative—one that honors the real nuance of teaching + learning.
Read more → mathedleadership.org/position-papers
Hmmm. Were people purchasing the curriculum because it had the Desmos name on it? If so, that feels troublesome.
Oh…I see it! Nevermind.
Will you be posting your curriculum for the course at some point? (Or is it already there and I missed it?)
Could you see a way to do that with high school juniors or seniors?