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Not summer reading. Summer books. Summer reading has been a little more than half of Mike and Sue Klonsky’s small schools book, and a few slow chapters of First Farmers, The Origins of Agricultural Society (which may be just a tad too technical for me, but it is fascinating when I force myself to struggle with it). I also snagged a copy of The Atlas of Changing South Africa (revised 2001, I once skimmed the original 1994 edition), but I have more dipped in to read maps than actually read text.
Ah, but summer books! I picked up a buttload of birthday presents last month (half a year late on the pickup):
- Bad Blood (Linda Fairstein). I have no idea what it is, but she was a District Attorney here in New York? I think I have to read this.
- Phillip’s Atlas of World History. For the collection. I have quite a few old maps and atlases, and current atlases, and historical atlases. And this one is new to me (not just the binding, the individual maps as well.
- A People’s History of American Empire (Howard Zinn). Nope, I didn’t already have this. I will dip into it here and there, but I don’t plan to read it straight through.
- cartographica extraordinaire. The Historical Map Transformed. (Rumsey and Punt) Wow. True coffee table book. The publisher, ESRI, is a major GIS vendor. This 13″ x 14″ hardcover blends historical maps with modern data via GIS and related computer mapping. The results are gorgeous. Stunning.
(other late-pickup presents were a set of wooden dominoes, hetian rose — it’s a tea, but what is it? who knows? — and two teas, one white, one green, labeled only in Chinese)
My reading to do list:
- Read Bad Blood
- Finish Collapse (I got done with the fun stuff, but bogged down in Jared Diamond’s conclusions)
- Finish Klonsky, and write a review.
- Finish First Farmers? Nah, I think I will restart next summer. Or over a vacation.
- I saw a review in The New Yorker for a new book called Traffic - Why We Drive the Way We Do (and What It Says About Us) by Tom Vanderbilt . I think I want to read it.
- Find and read a readable math book (read no math this summer. Boo. Hiss. Maybe H.A. Thurston’s The Number System?)
WordPress kindly includes all kinds of stats for us bloggers. I like the search engine stats. They show that most people come looking for salary info, and then by mistake (circus tents, dice, sea monsters), and finally for NYC public school info or for math problems and math ed related discussion.
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I finally got the sequel to The Lies of Locke Lamora yesterday; I was so excited about it finally being available in paperback, and so enamored of its prequel, that I picked it up without even reading the blurb. Then I got home, read the blurb, and steeled myself for a more typical novel about the ‘larcenous exploits of a band of daring thieves’:.
The Lies of Locke Lamora followed some momentuous events in the lives of a band of young priests, recruited from among the most talented and incorrigible of the orphans of the city of Camorr, whose rather unorthodox sacrament is thievery. The sequel follows the surviving priests, who have fled to another city, and according to the blurb, is about their attempt to swindle from the most reknown of the city’s gambling houses, a place where those caught cheating are guaranteed a swift, sure death.
The twist is that someone knows about their background and their plot, and is out to ‘make them pay for their sins’… Granted, his first book was off the hook, so Lynch could probably breathe new life into the old troupe of the gentlemen rogues, but if this was truly as deep as the book got, the result would definitely not be anywhere near as delicious as The Lies of Locke Lamora.
Luckily, it turns out that the sin being referred to is one from The Lies of Locke Lamora. Without giving too much away, before they fled the city, they avenged themselves on a bondsmage who killed some of their friends. They would have liked to kill him, but the Bondsmagi are a unique force in their world: they maintain a monopoly on magical ability by killing mages who attempt independent practice; their magic grants them some terrible abilities, like being able to voodoo puppet anyone whose name they know. Consequently, they can do what they will when they will without fear of retribution– the murder of a bondsmage led to the casual destruction of a city once– and will do pretty much anything for anyone who can afford their services.
Apparently, the Bondsmagi don’t like what was done to one of their own … So, an exciting premise. One as puzzling as that of the prequel: how can they possibly survive against the Bondsmagi?
The City University of New York and the Professional Staff Congress (AFT Local 2334) reached a tentative contract settlement. The proposal gives back very little, makes some gains, but failed to make some key gains for adjuncts and part-timers.
The Delegate Assembly recommended the agreement by 92-13-7 (yes-no-abstentions), but in the immediate discussion afterwards the PSC leadership agreed to open a “contract bulletin” where views of some delegates could be shared.
Over thirty delegates responded with statements of up to 500 words. You can read them all here. You can read a summary of the contract proposal here.
Barbara Bowen is the president of the PSC. Sándor John is the most outspoken opponent of the agreement. Alex Vitale wrote a statement that captures the complexity of the issue.
Keith Devlin, mathematics commentator, wrote: that “Stopping teachers saying that multiplication is repeated addition” would be a good thing. He sharpened it (”I wished schoolteachers would stop telling pupils that multiplication is repeated addition“), and repeated it (”a plea to mathematics teachers to stop telling students that multiplication is repeated addition.”)
Now Josh has an interview with Devlin, and has opened up the comments section.
Denise at Let’s Play Math took it seriously, and wrote. The subsequent storm got covered by Denise, Mark, and many others, including me. Josh at TextSavvy wrote a bunch, but without allowing comments.
Now Josh has an interview with Devlin, and has opened up the comments section. I think the discussion there may become interesting.
For the record, I don’t question Devlin’s math (although there is wiggle room there), but his approach, once engaged with teachers, was irresponsibly inflammatory. And, for the record, the ‘error’ he picks on is certainly not universal.
Recall the Rademacher comparison theorem:
Let be an increasing, convex function, be a compact set, and be real contractions such that , then
where are independent Rademacher (Bernoulli ) variables.
Intuitively, replacing with the identity, this says that if we shrink the coordinates and then take random Bernoulli averages, the expected value of the maximum deviation is going to be less than that for the original coordinates. Therefore, it makes sense to expect that an appropriately modified version of this theorem holds for the case where and the are complex contractions.
In one version of a proof (see “Comparison Theorems, Random Geometry and Some Limit Theorems for Empirical Processes” by Ledoux and Talagrand), an intermediate step is to show that
and their main tool for doing this is a bijection which satisfies, for a given
They prove such a exists without explicitly specifying it, using the marriage theorem.
If I could somehow generalize this to the complex case, i.e. find a bijection which satisfies the above, I’d have at least this intermediate inequality. (As it turns out, this inequality is all I need for my applications, since we only use .) But the question is, is it even reasonable to expect this?
Blinkdagger and Wild About Math! are really stirring things up for Monday Math Madness (MMM) contests #13 and 14. And, Texas Instruments is giving away a VERY cool calculator (keep reading for more about the calculator), they’ll ship it internationally, plus we’ll allow anyone to win - even if you’ve won a prize in the MMM contest before. So, we expect submissions from everyone on the planet!
What’s different about the next two contests?
So, what are we doing differently? Well, we’re going to ask you guys and gals to submit your favorite MMM-caliber problems. That’s what you have to do be eligible to win MMM #13. We’ll pick the one we like best and then use it for MMM #14.
- If you submit the problem we pick for MMM #13 then you get one of the awesome calculators.
- If you solve the problem we announce in MMM #14 then you get an awesome calculator.
“Love is like pi - natural, irrational, and very important”
-Lisa Hoffman
I mean, everyone knows that irrationality is so not natural.
I’ve been silent for a long time, but after reading about Orson Scott Card’s ridiculous position on gay marriage, I feel compelled to say something. Like, wtf would Ender or Bean say? Did you think about that Mr. Card? WTF would Ender or Bean say? The article correctly points out the utter lack of reasoning in Card’s so-called arguments, and the comments have a nice supplementary discussion on judicial activism. Why is it that they only call it judicial activism when they disagree?
Getting back to business, I plan to post in a short while on using truncation to estimate expectations of random variables: this turns out to be a powerful and simple technique for answering several of the questions I’ve posted over the past few weeks, like finding the asymptotic behavior of without using the delta method, or showing that grows like where are Exp(1) random variables.
These last two weeks I have been in and out of elementary and middle schools. Great chance to peek at math texts. And you know what? I am not finding the books that say that multiplication is repeated addition.
Today I look at some (Scott Foresman?) whatevers, maybe 3rd, 4th and 5th grade. The book discussed “meanings” with an “s” of multiplication, and ran through several sections that covered repeated addition, skip counting, arrays, and cartesian product.
The arrays, by the way, were of relatively fat dots, meaning, I hope, that half rows or quarter rows could be introduced at some point in the future.
This whole brouhaha about “stop telling kids multiplication is repeated addition” — do we know that this happens everywhere and all the time? Are there textbooks that get it wrong?
Or was Devlin just jousting with imaginary opponents?
So here I am, almost two weeks in New Orleans, and I’ve written almost nothing. What have we (ten of us from NY, Chi, Philly, and SF, just today joined by a similar number from mostly the same places) been doing?
We knock on doors of teachers who are not members of the union. Patient, slow, we find a few who want to join now. We keep up visibility and know that more will join in time.
We helped publicize a Back to School event where school information, free school supplies, immunization, games, food, and an insectorium were all available. Road signs, flyers door to door. We assembled and sorted the book bags and supplies and books. And then we worked the tables at the event, helped with set up, clean up, etc. (The insectorium was cool)
We go into schools where teachers are overwhelned, and help set up a few classrooms, straighten, discard, rearrange, assemble, and just try to make ourselves available to teachers who could use help.
And then in the evenings we go for dinner. Lots of New Orleans food. Tonight was Voodoo barbeque. Emeril’s Delmonico on Sunday. The steakhouse in Harrah’s one night. Some Italian another. But mostly gumbo and more gumbo. Crawfish etouffe. Jambalaya. Po-boys for lunch. Or soul food. Food is important here. Food fills the gaps between work.
Although I have not done much concrete work for the upcoming school year, save the Spanish wiki I am building, I have done a lot of mental work with respect to my Spanish classes.
First, I am thinking more deliberately about mastery grading - assessing the students on what they know and are able to do - and plan to be more intentional in my practice. Marzano is guiding my thinking in this area. In addition to the traditional quizzes and tests, I plan to use more performance assessments and projects.
Second, I am also thinking my first week of school procedures: Responsibilities versus rules, impulse control, and actively teaching students what I expect, as opposed to hoping for the best, and then being disappointed when they don’t follow through. This thinking is based on the writings of Marvin Marshall.
Third, I have been tinkering with an online lesson planner. After one year of keeping lesson plans in a notebook, followed by two years of Word files, I decided back in June that I needed another strategy. This online planner allows me to plan, teach and assess using standards for foreign language. I did not get very far with this during the last school year. Again, I am hoping to be more deliberate and intentional.
Last, I am going to make the decor of my room more language-rich and student-centered by displaying posters of expressions around the room that the students can use for their basic communication needs.
So, there it is.
In relation to the last post, note that is the maximum 2-norm of the columns of . Since premultiplication by scales row by , if , then . A little more manipulation: let and , then determining becomes equivalent to the geometric programming problem:
minimize subject to and .
Surprisingly, it turns out that there is a closed form solution to this GP. To develop it, first assume that and note that for any , the optimal weights satisfy for all . A little algebra gives , which suggests (by letting ) that , that is, . I haven't really proven this is the optimal choice of weights, but this formula gives the same results that running some numerical examples in matlab/cvx does.
After plugging back through, you get that is the square of the 1-norm of the column with maximum 2-norm. Fascinating, huh?
At any rate, the question of whether becomes more tractable.
It seems that Monday Math Madness #12 over at Blinkdagger is tougher than other MMM’s have been. So, there haven’t been many responses to date. So, your chances are higher than in previous contests of winning — if you can solve the problem!
Something to ponder: Fix , is , where is a positive diagonal matrix satisfying ?
In the case where , the inequality is true, which is why it might be reasonable to expect it in the general case.
Woohoo! I think I’ve finished constructing examples that prove the optimality of two of our error bounds– that the various log and sqrt(log) factors are needed, etc.– tomorrow I’ll see what my advisor thinks of them.
Here’s an interesting question I came across during the process (I haven’t yet attempted to solve it, because it turns out I can avoid needing to know the answer for the general case by choosing a particular matrix for my example): Given a matrix , multiply all its entries by independent Rademacher (+/-1 Bernoulli) r.v.s — what does the expected norm of this random matrix look like? The answer depends on the norm (e.g. for the Frobenius norm, it’s trivially the norm of ); I’m interested in the spectral norm.
Just for aesthetic reasons, I’d like to say that it’s (maybe only, close to) the norm of .
The topic of charter schools has been coming up a lot. The majority of schools in New Orleans are charters, and that is where the United Teachers of New Orleans (UTNO) has had the least success to this point in organizing, where much of their effort is currently directed.
(As an aside, UTNO is the AFT affiliate here, and the “United” comes from their history - the teachers unions in New Orleans were segregated until UTNO joined Black teachers and white teachers into a single union, and I’ll double check the dates, but I seem to recall, less than 40 years ago.)
Anyhow, charters are a constant topic. Also, the volunteers, from New York, Philly, Chicago - all places where charters are issues.
But get this: the active people outside of New York think that charters are a problem, are used to break or weaken the union, etc, except, they keep saying, in New York, where you guys have good relations with charters, have organized the charters, etc.
Now, I know the UFT has two charter schools, and has organized several more. But aren’t the majority of charter schools in New York non-union? Didn’t the UFT’s (director? coordinator? I don’t know his title) of charter schools, Jonathan Gyurko, indicate support of the right rather than the need to organize charter schools in NYC?
Somehow AFT members out of New York have been given some awfully funny impressions. That should be fixed.
There are over 60 charter schools in NYC, including the UFT charter schools in Brooklyn, and the new Green Dot/Bronx charter school in the Bronx. Of those, about 50 are non-union.
No photos yet. Probably not until my return.
Most of our work (it seems) will be visiting charter school teachers and asking them to join the teachers union. Yesterday was our first day. It is long, slow work. People are afraid for their jobs, angry about how much they lost. Some are not sure if charter school teachers can be unionized. Some are concerned about dues. Plus, Louisiana is a “right to work” state.
And then there were teachers not home. Yesterday was the first day of school (no kids) for most charter school teachers in New Orleans. We spoke with husbands, wives, kids, parents, sisters, friends. Most people are willing to talk, happy to talk, even if it’s only about how long they’ve been back (since they storm. That’s what everyone seems to say, “the storm.”)
This morning another volunteer who’d been here before drove us through the lower 9th ward to see some of the recovery/non-recovery. It was mostly non-recovery. More about that later.
And it’s time for this blog to say some things about charter schools. Has to be done.
But now it’s time to meet my team for Day 2.
Just a list of posts:
What Kind of Recruitment for NYC Public School Teachers?
What to do about Teaching Fellows?
Teaching Fellows or the Teaching Fellows?
Teaching Fellows are new teachers
Using Fellows for what they weren’t intended
Organizing Teaching Fellows as teachers
Does signing a card make you a UFT member?
So, here’s the latest fun question. Suppose you know where all the are random variables. Now somehow choose a random subset of the sequence; what can you say about the expected maximum of this subset as a function of the expected max of the entire sequence?
It’s an interesting question in it’s own right, but it came up while I was trying to find a random matrix such that . A feasible choice is to take to be a digaonal matrix of i.i.d chi-squared r.v.s. Unfortunately, some restrictions on require that instead I take the diagonal entries to be chi-squared r.v.s times bernoulli 0-1 variables. I’m trying to determine if the norm of the matrix is still asymptotically .
