Math https://xitter.cf/t.co/4sxtN0nL4A Books https://xitter.cf/t.co/reA3xn4WJR Bridge Advanced Math Jan 2023, https://xitter.cf/t.co/dsbUYRNtgC lecture https://xitter.cf/t.co/MmD0BmJvKy
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Earlier this year, we finished writing up the solutions for the 700+ exercises in the book. If you adopt our textbook, @amermathsoc will send you the PDF of the solutions manual for free bookstore.ams.org/amstext-58…
Looking for a text to help students transition to advanced mathematics? This new book from Cioaba and Linde eases “the transition from primarily calculus-based mathematics courses to more conceptually advanced proof-based courses...”.
Request exam copy: ow.ly/ahoy50PMQen
ALT Sebastian M. Cioabă , co-author of A Bridge to Advanced Mathematics: From Natural to Complex Numbers
Sebastian Cioaba retweeted
Leo Messi has just scored these 2 goals in the span of 4 minutes at the age of 39.
I swear I'm genuinely out of words. I don't know what to say.
Sebastian Cioaba retweeted
Delaware’s northern border with Pennsylvania is one of the strangest state boundaries in America. Instead of following a river, mountain, or straight survey line, much of it is an arc of a circle.
The story of the circle's centre is wonderfully quirky...
1/n
Sebastian Cioaba retweeted
May I ask: what point is there to teaching and testing children in elementary school on the *names* of mathematical properties (“associate property of multiplication”, “identity property of addition”)? To me, these are so lame and boring and suck all the fun out. Is there any good reason to insist on learning the names? There are much better ways to test their understanding that a property is true, usually found in fun “contest” problems, like:
What is 10x9x8x…x(-8)x(-9)x(-10)?
(Vs “zero property of multiplication”)
What is 1/2 x 2/3 x 3/4 x 4/5 x … x 99/100?
Quick, what is 34x3 +34x7? (Vs “distributive”)
There’s a whole slew of such really fun problems, completely standard. I don’t care if you know what grownups call it. Do you understand how to use it as a “backdoor” to answer a problem immediately?
Sebastian Cioaba retweeted
Minimally guided instruction doesn't work with AI tutors either. One thing we are finding out is that Socratic questioning models are very frustrating for students when they withhold the explicit guidance novice learners actually need.
arxiv.org/abs/2609.29995
Sebastian Cioaba retweeted
Every New Yorker knows that Ellis Island is in New York, right? Actually, it isn’t. Just a small section is. More than half of it is in New Jersey, and it’s my favourite bit of mad US state trivia as to why.
Here’s how a tiny island became a Supreme Court tug-of-war.
1/n
Sebastian Cioaba retweeted
Fascinated by this TripAdvisor review of Machu Picchu. I'm not sure what Simone's expectations were.
'No ceiling.'
Sebastian Cioaba retweeted
Mathematicians are OUTRAGED that their high social status, with its accompaniment of wealth, women, and general extravagance, has been encroached upon by artificial intelligences of humble background.
Sebastian Cioaba retweeted
These experts say memorizing your times tables is important (Matthew Burns, federal Institute of Education Studies, National Mathematics Advisory Panel). But the 2023 California Math Curriculum Framework (CMF) says never mind!
The CMF - how to make poor math proficiency even worse!
thewellnews.com/opinions/cal…
Sebastian Cioaba retweeted
Gracias, Leo. 👏🇦🇷
#FIFAWorldCup
Sebastian Cioaba retweeted
France’s longest land border is not with Spain or Belgium. It’s actually Brazil.
French Guiana is a part of France, not an overseas dependency. Its official currency is the Euro.
Sebastian Cioaba retweeted
Especially in math. So many elementary teachers really struggle with math and don't know how the topics fit together. A good curriculum and good resources that spell out exactly what to do and what to teach would go a long way to improving primary math.
Sebastian Cioaba retweeted
What are the most effective methods of improving student achievement? An NYT investigation.
For me, the data point in the bottom left quadrant is absolutely critical to understanding why student achievement goes wrong so often: teachers making up their own curriculum.
nytimes.com/2026/09/28/upsho…
Sebastian Cioaba retweeted
🚨 Joel Huiqui on his conversation with Lionel Messi during Cruz Azul vs. Inter Miami:
🗣️ “It was just a casual conversation. I told him, ‘Leo, you really don’t slow down, do you? After all these years, you’re still finding ways to cause problems for every team you play against.’
I spent hours trying to figure out how we were going to limit him, but within 15 minutes of the game, I realized a lot of what we had planned wasn’t going to work. He just laughed.
I asked him how he continues to do it, and he said he honestly doesn’t know. He said it’s just something that comes naturally to him.
A few seconds later, he nutmegged one of our players and I just had to laugh. That’s Messi.
He’s a player I’ve admired for a long time and someone you always want to watch. It’s a privilege to have a player like that in front of you. Even when he scores against you, sometimes you can’t even be angry with your players. You just have to appreciate what you’ve witnessed.”
Sebastian Cioaba retweeted
An incredibly depressing article. A few points:
🔸If your kid can’t add fractions, they are not ready for algebra, even if the school is giving them A’s. It's an easy check. Make sure they can add, subtract, multiply, divide fractions.
🔸Lots of misinformed math education academics out there downplay the importance of foundational skills and tests. They are wrong. Note how her child developed test anxiety once she started doing poorly on tests b/c she had not acquired the knowledge to do well on the tests.
🔸Standardized test results probably do give a pretty accurate picture of how a school is performing in comparison to other schools. Testing matters, for so many reasons.
🔸High standards matter. Smart kids need to be challenged. Even her own daughter could see this.
I appreciate that the journalist shared her story and I hope other parents learn from the mistake she made. nytimes.com/2026/09/20/magaz…
Sebastian Cioaba retweeted
Your dog carries your stress in its body for months. A 2019 study in Scientific Reports measured cortisol in the hair of 58 dogs and their owners over a full year and found that the two rose and fell together. When you are stressed, your dog is stressed. When you calm down, so does it.
The synchrony was not driven by walks, weather, or the dog's own life events. It was driven by the owner. Dogs whose owners scored higher on personality measures of anxiety showed higher cortisol year-round. The dog's body was tracking the owner's emotional state over months, not moments.
The bond between a human and a dog is not a one-way relationship where the human provides and the dog receives. The dog is absorbing the household's emotional weather and carrying it in its endocrine system. Your bad month is its bad month.
This is what 15,000 years of co-evolution looks like. The dog did not just learn to read your face. It learned to sync its chemistry to yours, and the hair on its back is keeping a record of how you have been feeling since the last time it was groomed.
The next time someone says "it's just a dog," the cortisol data says otherwise. The dog is a mirror with a heartbeat, and the reflection goes deeper than behaviour. pubmed.ncbi.nlm.nih.gov/3117…
Sebastian Cioaba retweeted
We're hearing the same story from universities in both Canada and the US. Students are arriving unable to do basic math.
But the problem doesn't begin in university.
People tend to underestimate just how hierarchical math is. Learning new math concepts depends on what came before. When students don't develop a strong foundation early on, the gaps don't repair themselves. The gaps just get worse.
Then students are moved ahead when they didn't master the foundational material and later math is inaccessible. It's nearly impossible to learn more math when your foundation is made of sand.
University is not the best place to try to fix these issues. We need to look further back and address the core issue. And I believe in many cases kids are being done a disservice in especially K-8 math.
I think this is one of the most serious issues facing our society right now.
Sebastian Cioaba retweeted
Grade inflation doesn't help students. A high grade in math class should mean the student learned the math.
If a student gets a high grade but didn't earn it, it may feel good in the moment, but it shows up in the next course when the math gets harder. And that may not feel good at all.
Math is hierarchical & the gaps don't go away on their own. They just compound and make later math extremely difficult.