Michael Zen retweeted
Feynman explaining physics from an armchair in 1983 and it's still clearer than most of what passes for science communication today. I'd take understanding over production value every time.
Michael Zen retweeted
"Not a copyist, someone who could follow him" is the whole story for me. Euler's blind years were productive because the knowledge had a second mind to live in. Fuss didn't just record the ideas, he carried them forward, and then turned them into a school course.
My reading: ideas survive less through being written down than through being passed to someone who can keep working them. Fuss's own name still sits on the Fuss-Catalan numbers, a nice trace of an apprentice who became a source.
Michael Zen retweeted
In 1772 an eye operation left Leonhard Euler almost completely blind.
He could still do the mathematics. He could not read it or write it.
So he needed someone. Not a copyist — someone who could follow him.
Euler turned to his old friend Daniel Bernoulli in Basel. Bernoulli knew exactly who to send.
Nicolas Fuss arrived in St Petersburg in May 1773. He was eighteen.
He stayed for the rest of his life.
At Euler’s side he helped push more than 250 papers into print. Not transcription — he developed the ideas, built the tables, worked the examples.
Then Euler died in 1783, and the assistant became the scientist. Academician that same year. Professor of mathematics. And from 1800 until his own death in 1826, permanent secretary of the Imperial Academy of Sciences.
There is a theorem named after him. A sequence of numbers too.
And late in life he did one more thing.
He took the algebra he had learned at Euler’s elbow and built it into a course for the schools of the Russian Empire. Three volumes. Algebra. Then geometry. Then the application of algebra to geometry — trigonometry, conic sections, and the foundations of the calculus.
That trilogy is where Russian school mathematics begins. Kiselev comes after it. The Soviet school comes after Kiselev.
Part I — Algebra, 1820. Four divisions, 59 chapters, 570 sections. From what it means for a letter to stand for a quantity, all the way to the irreducible case of the cubic.
Two hundred years. No English edition. Not once.
Until today.
amazon.com/dp/1809100054
youtube.com/watch?v=vlZfHBlP…
russianmathbooks.com
Michael Zen retweeted
From Amazon reviewer from Belgium:
"This book highlights that even fundamental subjects must be explained in a structured and more rigorous way."
Michael Zen retweeted
All is not lost one can ensure their kids on par with Russia and China or even above if one puts effort russianmathbooks.com/start-h…
Michael Zen retweeted
I had a music teacher who told stories about great composers as if he knew them and had performed in the orchestras that debuted their music. One of the characters in my novel, "The Faithful," is based on him.
Michael Zen retweeted
There's this modern idea that kids will learn all that they should on their own initiative. … False!
We cannot expect children to spontaneously want to learn new things. There's natural curiosity, but it's typically fleeting and undisciplined. Pushing and nudging is essential.
Michael Zen retweeted
The most mathematically gifted student I ever worked with initially resisted learning calculus.
He was already way ahead, and he liked doing puzzles with math that was already familiar.
But eventually he just wasn’t really progressing.
You see, there are levels of math that you have to climb in order to unlock the next thing. And kids don’t always see the long game, so adults have to see it for them.
So this kid… once his parents and I pushed him to learn calculus, he ended up LOVING it. And now he’s doing serious math using ideas from this area that he originally resisted!
That’s why sometimes a push is what opens the door.
Michael Zen retweeted
When I first started teaching I was told I was an 'energetic teacher' which, back then, I took as a compliment. Now, I treat it as an insult.
This was right next to my board. Tons of icons, classroom battleships that they got to have a go at if they answered a question well. We asked pupils to "get on the BUS" and enter the 'Green Zone' to use a green pen.
I taught evolution using bird masks and tweezers (every science teacher must have done this at least once). I taught specialised cells using speed dating and mitosis using a deerstalker and a magnifying glass.
I once had a lesson on questioning where pupils wrote their own questions on pieces of paper, put the tables on the side to resemble trenches and had to stop and answer the question on the scrunched up paper they threw at each other. I still have the video I had shared as, and I actually quote, as "good questioning practice"
I taught forces using a ton of water and bottles tied into a raft that students had to balance. I taught energy resources using a round the room activity whilst I sat there and did nothing.
If I'm being brutally honest. It was all shit.
The pupils during this time must have had an absolute blast. They were immensely fun but I was burning myself out trying to making the most 'engaging' lessons.
It didn't work. I had to switch it up.
I stood at the front, taught, asked questions, used MWBs, gave banging explanations and it worked infinitely better than whatever 'pedagogy' I had been told was good practice. I ignored a lot of what I was told. I was told off sometimes for it.
No icons. No gimmicks. No creative teaching. Just what actually works.
I powered through last time, hopefully I won't have to do it again.
Michael Zen retweeted
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Michael Zen retweeted
Learning advanced math ahead of time is the greatest educational/career life hack.
When a student learns a lot of advanced math ahead of time, they unlock the opportunity to dig into a wide variety of specialized fields that are usually reserved for graduates with strong mathematical foundations.
This fast-tracks them towards discovering their passions, developing valuable skills in those domains, and making professional contributions early in their career, which ultimately leads to higher levels of career accomplishment.
I’m not exaggerating here -- this is actually backed up by research. On average, the faster you accelerate your learning, the sooner you get your career started, and the more you accomplish over the course of your career.
For instance, in a 40-year longitudinal study of thousands of mathematically precocious students, researchers Park, Lubinski, & Benbow (2013) concluded the following:
"The relationship between age at career onset and adult productivity, particularly in science, technology, engineering, and mathematics (STEM) fields, has been the focus of several researchers throughout the last century (Dennis, 1956; Lehman, 1946, 1953; Simonton, 1988, 1997; Zuckerman, 1977), and a consistent finding is that earlier career onset is related to greater productivity and accomplishments over the course of a career. All other things being equal, an earlier career start from [academic] acceleration will allow an individual to devote more time in early adulthood to creative production, and this will result in an increased level of accomplishment over the course of one's career.
...
[In this study] Mathematically precocious students who grade skipped were more likely to pursue advanced degrees and secure STEM accomplishments, reached these outcomes earlier, and accrued more citations and highly cited publications in STEM fields than their matched and retained intellectual peers."
Michael Zen retweeted
this is basically why engineers can jump into bio or physics so fast
the math is already there, it's just the field's vocab that's new.
while studying math for national exams in India in high school, going from math to physics to bio in the same day really helped build my logical reasoning
Michael Zen retweeted
If you just:
– Explain things coherently
– Scaffold properly
– Check for understanding (not just nodding but actual demonstrated ability to solve problems)
– Refuse to put up with nonsense from lazy/adversarial students…
Then that automatically puts you in the top league of math teachers, even ahead of plenty of math professors.
Michael Zen retweeted
It's fascinating how a mathematical idea can transform not only calculations, but entire fields of science. Logarithms were more than a shortcut — they changed how astronomers worked.
Michael Zen retweeted
Before calculators, astronomers spent weeks multiplying long numbers. In 1614 John Napier turned that work into addition.
The trick: if bʸ = x, then y = log_b x. Exponents add when numbers multiply, so
log_b(xy) = log_b x + log_b y
log_b(x/y) = log_b x − log_b y
log_b(xᵖ) = p·log_b x
On log₂ x, every doubling of x adds exactly 1.
Slide rules, decibels, pH and the Richter scale all run on this idea.
One table of logarithms bought astronomers years of their lives.
