This is called Crazy Towers. A version of Towers of Hanoi with 15 pieces jumbled.

5 Reasons Why MINDFULNESS Is Good For 👩🎓Kids.

This is called Crazy Towers. A version of Towers of Hanoi with 15 pieces jumbled.

5 Reasons Why MINDFULNESS Is Good For 👩🎓Kids.

Pretty amazing #3dthinking here. #origami #geometry #mathchat This kid has mad skills.

Birth of a Theorem

In a prior post I mentioned that I had bought some books. I also mentioned that I don’t buy books that I don’t intend on reading. So I’m reading them now. I recently finished Cédric Villani’s *Birth of a Theorem*, a book dedicated to exploring the process of how he proved his Fields-Medal-winning theorem and gaining some insight into the life and work of a mathematician. In other words, pretty much what this blog is about, but by someone who’s a little older and a lot more accomplished than I am.

I am certainly not qualified to do anything resembling a “book review” but I want to give my idle thoughts on it. In general I enjoyed it.

——

I'm… interested to see what it would be like to read *BoaT* (I’m going to call it that because it makes me smile) without a strong immersion in the mathematical life. I am nowhere near what you would call competent in Villani’s broad discipline, which is PDE. However, I have taken functional analysis which means that although I was lost during the parts of the book that you weren’t really supposed to understand, but I sort of knew what certain words meant, I could often tell when things were important, and I didn’t understand a lot.

Oh, yes, I kind of snuck that in there: there is a (very significant) fraction of the book which is deliberately not meant to be understood: it is PDE in it’s full glory, with integrals, summations, indices. Sobolev and Fréchet and Jensen, Young, Minkowski. Long, tedious growth and analyticity conditions. Emails in plaintext with “estimates” and “regularity” and “perturbation”; many many patches of raw TeX.

I wonder what sort of effect this would have on a reader like my brother. Although the book feels like a pop math book, it reads like I am the intended audience. I read it as raw, real. But I don’t know if it is possible to understand it that way if it is one of your earlier visits into a mathematical world.

Lest you think the book is self-aggrandizing, arrogant pomp, I should mention that *BoaT* is rather clear about which sections you are not supposed to be understood, and the formatting is such that it is possible to skip them entirely, if you so choose. I feel that if you skip the typeset math you aren’t missing much, but if you skip the emails you really are missing something essential about the book. And moreover, so much of the book *is* intended to be understood, and it so earnestly tries (I can’t say if it succeeds) to explain so many basic technical ideas, and it works so hard to produce a colorful and recurring cast of characters that it I’m not convinced automatically that it would be inappropriate for my brother.

——

The writing of book was *incredibly* smart. If you think that mathematicians probably can’t write nontechnical stories well, I point to this book as a strong counterexample.

There was one point when I looked at this long list and said: “Fuck. He’s referencing *Ulysses*. I know he’s referencing *Ulysses* but I have no clue what he’s getting at.”

He describes his discovery that he won the Fields Medal in Chapter 40. I literally said “Gosh DAMMIT Villani” and my roommates looked at me funny.

He manages to get across the idea that mathematicians really don’t get to do as much math as they would like, without ever doing anything that sounds like ranting. Considering the extreme time pressure that he was under, and his appointment as director of the Institut Henri Poincaré toward the end, that’s rather impressive.

He also very clearly conveys what it’s like to live a life that is completely and totally doused in math, and yet is still well-adjusted and (mostly) “normal”. He talks about his wife and daughter, and reading manga, and his wide taste in music.

——

When the book came out, John Nash was still alive. Nash was Villani’s hero, and his recent death gave some parts of the book a tragic twinge. But Villani is no stranger to death and dramatic irony; don’t want to say more than that because it would ruin one of the more poignant moments of the book.

——

I want to conclude with one of the more remarkable one-paragraph stories of struggle:

Long afterword, [my partner] Clémont confessed to me that he had decided to bail earlier that weekend. On Saturday morning, February 28, he began to compose an ominous message: “All hope is lost… the technical hurdles are insurmountable… can’t see any way forward… I give up.” But just as he was about to send it, he hesitated. He wanted to find the right words to convince me, but also to console me. So he saved his message in the draft folder. Going back to it that evening, armed with pencil and paper in order to make a list of all the paths that we had explored and all the dead ends they had led to, he saw, to his amazement, the right way to proceed opening up before him. The next morning [he wrote out] the key idea that might save us […] All I sensed was the enthusiasm emenating from Clément’s message.

[page 110-111]

@mathheadinc : Lovely! RT @malynmawby: “@mathemaniac: Fibonacci Sequence Phi Spirals http://t.co/Kj7aYfdJ8Q” @lostinrecursion #mathart #mathchat

Lovely! RT @malynmawby: “@mathemaniac: Fibonacci Sequence Phi Spirals http://ift.tt/1mB19fx” @lostinrecursio

— mathheadinc (@mathheadinc) May 7, 2014

from Twitter http://ift.tt/171F9y2

May 07, 2014 at 02:02AM

via IFTTT

A selection of the pictures which produced this theorem.

youtube.com

Mathematics Teachers Learning Together

A talk I gave at #NWMC13. Aimed at math teacher leaders and coaches, I describe how different collaborative activities like planning or looking at student data can be deepened to support teachers’ professional learning.

Looking for educational chats to follow on Twitter?

*Try these!*

#ccss

#ccchat

#edchat

#edreform

#literacy

#literacychat

#engchat

#mathchat

#stem

#stemed

#edtech

#blackedu

#latinoed

#gaed

What I learned about teaching math in 2011

1. Timers are awesome.

Put a timer over the top of a problem (if you use PPT or Keynote) with an opacity of 50%, and give the students 1, 2, or 3 minutes to try the problem. I intially called this “Silent See What You Know”, but eventually dropped that headline and just used the timer, and they understood the rules. I get about 50% of students strongly engaged during the timer session, and the other 50% are at least silent.

When I am using the timer, I do not let them ask me a question, or any of their friends a question. I tell them if they are confused, then just spend the time being confused.

Students tend to believe there are only two states of learning: 1. Not knowing how to do the problem. 2. Knowing how to do the problem. They don’t realize there are a bunch of intermiate steps inbetween those two states. This timer section of the class is meant for them to discover those extra steps. When the timer is up, I call for all answers, and don’t care if they are right or wrong. I praise them all for getting to a solution, for getting pencil to paper.

2. Do things in small chunks.

Do a couple examples, then have the students do one problem. Then go over that problem. Then have them do one more problem as a pair/share. Then go over it in front of the class. Then give them three more problems. Have those problems are the board and ask students who are done fast to put their work on the board. Have the class set up in small time intervals, rather two long intervals ( I show you how to do it, then you do it).

My first year I would introduce the concept with a few examples, and then give them problems #1-10. The result would be that I would spend too much time talking at the start, and then they would too much time to work, which due to shorter attention spans, caused a lot more conversation than work.

… and some other stuff.