Bill Shillito

Do you have any vivid examples? Would love to talk about this with my proofs class!

You asked why it would help didactically. I just gave my own observations from when I’ve taught Monty Hall.

I would argue that convincing is a necessary but not sufficient component of effective explanation. The math seems to “stick” better if it aligns with experience.

I think one reason many struggle with Monty Hall is that they still feel like the probability “should be” 1/2 and so even a perfect explanation doesn’t convince them.

I think a simulation like this can create a visceral cognitive dissonance that allows that gap to be bridged. They can SEE it now.

I know this feeling well. 😂

WOOHOO! Our sandwiches paper has been published! 🥳

...in celebration, I'm going to claim that tonight's lasagna was a sandwich. 🥪

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

Teaching logic tomorrow ... with Clue!

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.

If we want to destigmatize “guess-check-revise”, we need to also revise our assessments so we’re not expecting students to factor non-monic trinomials on a time crunch with a bajillion other skills.

How can we accomplish that? Seriously, what would it take?

Unfortunately, “enjoying learning and understanding” isn’t part of the grade. 😭

The last step of subtracting from numbers with lots of zeros is done mentally.

You can easily justify it using the "Same Distance, Same Difference" strategy in @howiehua.bsky.social's video.

Although I first encountered it as a "Vedic Math" sutra — "All from nine and last from ten"!

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".

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

Deviled eggs for New Year's Eve!

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!

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. 😂

🙂‍↔️🫸 Calculus II exam
😎👉 Series finale

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.

Most underrated video game villain.

That means there are more questions like this? 👀

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

All great points! Full disclosure, this all came about because I wanted a quote for a calculus book I’m working on that isn’t just Ye Olde White Dude Newton or Leibniz again. Madhava and the Kerala school are some of my favorite examples of how much broader the history of calculus is. 🙂

Much appreciated! Are there any places where I could look at verified quotes from the work of the Kerala school in general that express a similar sentiment?

From Circle-ometry to Trigonometry: Select Videos from my website - YouTube See section 7.7 of https://gdaymath.com/courses/gmp/ for now!

I'm a fan of James Tanton's treatment! He motivates the sine and cosine from the question of "how high up is the sun?" and builds everything very intuitively based on that.

www.youtube.com/playlist?lis...

Honestly the best thing has been including the phonetic pronunciation wherever I can. 😂 Have not tried the anti-burrito method!

What do you do?

That part was never the problem with the honorific and last name approach. You need to pronounce names correctly either way.

(And I remember that lit teacher ALWAYS got my last name right. Which has always been pretty uncommon, even sometimes from people who've known me for years.)

My 9th grade literature teacher did this! At the time it made us feel very "grown up" and professional. That's why I also did so myself when I taught high school.

I don't follow this practice anymore nowadays, though — I'm not a fan of the constant gender reinforcement.

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

Correlation

xkcd.com/552/

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.”

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

"Logarithmic form" never made sense to me — I could never remember how it goes. If a^b = c, is it log_a b = c? Or log_b c = a? Which of the six permutations is the right one?

And I always found the phrase "a logarithm is an exponent" utterly unhelpful.

Inverses tell us WHY it's the order it is!

Here's how I always think of it:

e^(ln x) = x for the same reason that (x + 5) - 5 = x.

The whole point of logarithms is that they undo exponentiation, and vice versa.

If you do a thing, and then you undo that thing, you get back to where you started.

Inverses are the very heart of algebra!

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!"

Which of these is an "A"? Why? #Grading

Image source: www.mpusd.net/apps/pages/i...