Help me create a puzzle
I don’t have a good puzzle for you today, and it’s about time for a little math, so I’m making one up. Or working on it. Weird thing about puzzles – you can make up a puzzle that someone has already solved. I think that’s what we’re doing, but let’s try all the same.
Since this is from scratch, we need to develop the topic before the question.
Topic: How many ways can we express a particular number as a product?
How many ways can a number be written as a product? So, what does that mean? First of all, by number we mean “natural number.” Then, what’s a product? For 10, it can be written as 
Do we have material for a puzzle? Well, let’s list out the first few.
| Number | Ways it can be written as a product | Show us |
| 2 | 1 |  |
| 3 | 1 |  |
| 4 | 2 |   |
| 5 | 1 |  |
| 6 | 2 |   |
| 7 | 1 |  |
| 8 | 3 |    |
| 9 | 2 |   |
| 10 | 2 |  |
| 11 | 1 |  |
| 12 | 4 |    |
So what kind of questions might we ask?
We could ask to have the list extended. Make it up to 20. Or up to 50. Or even 100. And we could ask for observations about what we encounter.
We could ask for the number of ways some larger number could be expressed as a product. Might be fun to try to count for, say, 350.
We could ask for the number of ways some much much larger number could be expressed as a product. If we chose, for example, 792,000, that’s big enough that you might not be able to count by hand, and would have to do some generalizing.
We could ask for some observations. Which numbers can only be written one way? (and why should that make sense?) Is there a relationship between the number of factors and the number of ways? The number of distinct factors?
We could ask for a formula to figure out the number of ways for a number in general. But, as I sit here, I don’t know the answer. And, as I sit here, I expect that the answer might be “complicated” in a way that goes beyond what most kids and much of my audience can handle.
We could ask for formulas to deal with some specific cases…or at least the descriptions of a solution. As a teacher I might have asked for a formula (or description of solution) for powers of 2, or powers of a prime, p. My students frequently confounded me by starting by looking at powers of 10 – but maybe that’s better for grasping some of the complexity here. It might also be helpful to ask for solutions for the product of 2 distinct primes (such as 
But I’m leaning in a different direction. 2 is the first number with 1 way of being written as a product. 4 is the first number with 2 ways. 8 is the first number with 3 ways. See that pattern? Think it breaks down? 12 is the first number that can be written as a product in 4 ways. What is the first that can be written as a product exactly 5 ways? 6 ways? Do you want to jump ahead? 10 ways? 20 ways?
Some questions
- How many ways can each number from 13 to 25 be written as a product?
- How many ways can 350 be written as a product?
- How many ways can 792,000 be written as a product?
- Which numbers can be written as a product in exactly two ways? Can you show that all numbers with this property can be written as a product in exactly two ways? And that no other numbers can be written as a product in exactly two ways?
- Is there a general formula here? (Let’s leave this out, unless you actually know the answer. I have a guess “yes” but I’m not certain what that guess would be, and I’m aware that it might involve math that I have not studied very deeply.)
- If a number is a product of n distinct primes, how many ways will there be to write it as a product?
- Consider the first number that can be written 1 way, the first that can be written 2 ways, etc, ie 2, 4, 8, 12, 16,…. what are the next five numbers on this list?
- Do you have a question I haven’t thought of?
I’ll try answering these (those I can) during the course of the week.
What do you think?
Is there fun stuff for kids to play with here? For us to play with? Would this make a reasonable activity? (and if so, how?)
And has all the math here been done before? (I’d be shocked if it hadn’t been)
I’m curious what you make of this.
Happy break!
On not being a rubber stamp – Tom Sheppard, Episode 3 of State of the Union
This episode Arthur and I interview a Bronx ELA teacher, Rebecca Torres, and Bronx Panel for Educational Policy member Tom Sheppard.
Tom has been outspoken on PEP – and he doesn’t disappoint on the podcast – he discusses how he got involved, equity in terms of facilities, and then he starts on the PEP and governance and mayoral control…
By the way, there is a part II of Tom’s interview that will be in the next segment.
I’m really enjoying the teacher segments – love the fact that Rebecca had a strongly held idea, and modified it – because that made sense for her students. Were the people in charge half that reflective…
Comments, praise, criticism, praise, all are, as always, welcome and appreciated.
Здравствуйте, Ёжик!
Mystery, right?
In computer programming, when you are trying to get a new language to work, and want to check syntax, you try to get a program, usually just a line or two, that prints on command. If you are successful, you are greeted with “Hello World.” Serious. Go on. Google “Hello World.” See. I wasn’t making that up.
Hello, World!
In DuoLingo you learn lots of weird words, and useless phrases… For a few years I binge watched a bunch of “Nordic Noir” movies and series. The genre originally came from Sweden. Slow-moving. Sometimes plodding. Police procedural dramas. Hero has been traumatized, or is somehow psychologically off-kilter. Or just sad. Shows popped up across Scandinavia, and in Britain and Northern Ireland. There was a weak remake of one done in the US. Broadchurch was award-winning, or should have been. I’m too lazy to look it up. Shetland was alright. I loved Happy Valley – although for these depressing creations I’m not sure “love” fits. The Fall in Northern Ireland, with Dana Scully playing an actor playing a detective. A bunch in Finland, Norway, Iceland, etc. By my absolute favorite was Hinterland. It was set in Wales. One episode I was watching (this was all in English by the way) and a local doesn’t like our detective, and says something. From the tone of voice, it was mean. But the words? They were not English. I was curious, and started digging. Apparently I was watching one version. The other version, the hit version “over there” was filmed bilingual. It was complicated. Some characters were Welsh-dominant. Some code-shifted effortlessly. And some were less comfortable in Welsh. And there may have been some English characters who didn’t know a word (and no, that does not include the detective. He lived in England for a long time, but was in fact Welsh, so while his Welsh was uneven, he did speak, and he gets better through the show). And to make this happen, the actual cast was all bilingual, and each episode was filmed twice. Ok, so now I see a few episodes in the hit bilingual original. Called Hinterland in English, and Y Gwyll in Welsh. Too cool. I go to DuoLingo and say “teach me Welsh” and I spent a few weeks, and all I remember is “Bore da, Draig!”
Good morning, Dragon!
Which brings me to the title of this post. I am using WordPress. And not writing frequently, or at least not consistently. And if I ever had a fanbase, I’ve lost most of it. But someone named Eozhik is liking most of my posts. Funny looking name, right? Except I think I recognize it. Eo sound like “Yo!” and if it were in Cyrillic would be written as an e with two dots: Ё. Zh sounds like how a French speaker would say “jour” as in “Bonjour” – like a sh with the voicebox vibrating. There’s a Cyrillic letter for that, too: ж. And ik? Like Ick. In Cyrillic just an “ee”+”k” = ик. And put them together – we get Ёжик, which is apparently the name of my new fan. It’s also the Russian word for hedgehog.
Greetings, Hedgehog!
UFT High School Vice Presidents – with some narrative
George Altomare, who passed earlier this fall, was the first UFT HS Vice President. Of course I did not meet George until years after he had retired. He was on the UFT Executive Board – I think for the entire 11 years when I served. He used to promote the New York Association of Social Studies Teachers conferences. (New York Council of Social Studies Teachers? Not sure of the right name). He also used to play on his guitar to close out conferences – which songs did he play? Was it Solidarity Forever? Yup, he played at every AFT convention I went to. George lost the vice presidency to Michael Shulman in 1985.
Michael Shulman represented an opposition caucus – New Action. In 1985 he beat George Altomare head to head for HS VP, fair and square. But the union’s leadership grouping, called Unity, sued to overturn the election (that they had conducted!) A second election was held. Shulman won again. George retired the day the result was confirmed. Shulman is the only Vice President in the UFT’s history not to come from Unity Caucus. More on that below. Shulman served one term, and was narrowly defeated by John Soldini. Mike returned to the classroom, I believe at Fort Hamilton High School.
John Soldini (Unity), Shulman and Altomare were the only three HS VPs to be elected directly by the members in the high schools. Unity, desperate never again to lose the position, converted all the VPs to Vice Presidents at Large. Up to that point, high school teachers elected the high school vice president. After two amendments, all UFT members – teachers, paras, secretaries, retirees – from high school, from middle school, from elementary school, from everywhere else the UFT represents people – all of them voted for the “Vice President at Large for High Schools.”
Soldini was high school VP for over a decade. Sometimes he would have been the choice of high school teachers – but usually he lost among high school teachers, but remained in his position. The change in rules ensured that with solid backing of elementary teachers and retirees, John never again had to worry about high school teachers choosing someone else.
Soldini was VP when I came to my first high school level meetings. They were raucous affairs – high school chapter leaders challenged him on many items, and he pushed back hard. I definitely remember a few shouting matches. I also remember packed meetings, and sandwiches (I didn’t come for the sandwiches). There was real discussion about real issues directly facing schools. Of course that was before the massive break up of the high schools… What were there? 100 high schools in the city? And most of them sent their chapter leaders to listen to or yell at John.
When Soldini retired, Unity chose Frank Volpicella to be the next HS VP. An aside, my District Rep, David Shulman, thought he was in line for the post, and retired when he was not tapped for it. He didn’t speak about it, but I think he remained bitter.
Frank was stepping into a mess, with the break-up of the large high schools in full swing. Unity, which had signed onto the plan, was now backing away (though without much real opposition – dropping the responsibility on each individual school to put up its own individual fight, and we watched loss, after loss, after loss). In any case, there was a swarm of activity, but I don’t remember much about what Frank did. He was regarded as a nice guy – in fact once he said something really insulting about me – but I spoke to him, and he quickly and graciously retracted it – not everyone has that same sense of decency. In any case, now I was going to high school level meetings regularly. And among other things I noticed, attendance started to fall.
Frank retired in 2007. The high school division almost died when he left. Frank’s successor was a supporter of school reform. One time he explained that breaking up the big schools and their lazy chapters would inevitably give rise to a new cohort of active chapter leaders in the small high schools. It seemed unlikely then, and history has born out how completely full of shit he was. The fights against closing schools were hamstrung by having a VP who wasn’t really opposed. On big politics, his role at AFT conventions – introducing one pro-war resolution after another, was sickening. And there was not even something personable about him that mitigated the other stuff; I once sat with him, one-on-one, as he offered me a job (that I did not take) and during those ten minutes that seemed like an hour not once did he make eye contact. As an ideologue and a boring speaker who did not really listen to anyone else, the high school meetings became dreary. Attendance, already dwindling, plummeted. I recall once sitting in the room, in his High School VP’s meeting, and realizing that me, Zulma and Sam, 3 chapter leaders from the Bronx, all from small schools, were the only chapter leaders in the room. Everyone else were DRs and paid staff.
When Janella Hinds was appointed/elected (by the Exec Board), it was a breath of fresh air. Let me back up – the Exec Board election was actually an election – October 2012. I was nominated by New Action – and lost, 67 – 7 (never figured out where the 7th vote came from, there were only 6 New Action exec board members. I do know that Michael Mendel scolded me for asking for the count.) In any case, Janella was open to conversation, and committed to rebuilding the meetings in the HS Division. Lots of damage had been done, but slowly the meetings built back up. Now, with all the mini-schools, and the four hundred something high schools, attendance is not like in Soldini’s day… but in Janella’s first year or two there were times when we wondered if they would ever come back – and they did. Now there are high school events, high school awards, and some sense of a living division.
The electoral history since Janella’s election is interesting. She won in 2013 – both by Unity’s rules, and among the high schools – New Action and Unity combined to give her almost 60% of the votes against MORE. But in 2016, while she won (it’s a VP at Large), high schools actually preferred James Eterno roughly 51% – 46%. In 2019 she won both the total vote, and with high schools, over 68%. And in the latest election I won most of the high school votes (56%), but Janella prevailed in the other divisions, and since this is now an at-large – retained the position, 66% – 34%.
I wrote a High School Vice President electoral timeline earlier this fall.
Giving Season
I visited a friend this weekend – she had a present wrapped for me… I was embarrassed – I got us a nice lunch. I was caught flat-footed. I think of Christmas Season starting about 6 days before (like today, but I have final exams, so, for me, tomorrow). I know that’s old-fashioned. Christmas starts earlier and earlier. After Thanksgiving? After Halloween? The day before Labor Day?
But the personal presents aside, December does conjure up feelings of “giving season” to which I am not immune. With so many causes, how do you choose? I guess the decisions can be arbitrary. Here’s mine:
Rosenberg Fund for Children
I started donating three years ago. I was, more than anything else, recognizing the work of Abel Meeropol, who with his wife Anne adopted Ethel and Julius’ sons after the US government executed the parents. Abel had been a teacher - high school English, DeWitt Clinton, up the block from me – (Abel was never a UFT member). He was also a poet, and a songwriter – his most famous work was Strange Fruit. Anyway, donating to indirectly recognize Abel is a little convoluted – he DID help protect children of activists who were being abused by the system – but I think it’s perfectly okay – whatever the reason.
In the intervening years I learned a little more about RFC and its work. And just now I’ve been reading Robert Meeropol’s “An Execution in the Family” – and I was in the chapter on the founding of the Rosenberg Fund for Children when the appeal came in my mail and email. I think I understand better what the organization does, and feel even more motivated to help.
The Rosenberg Fund for Children was established to provide for the educational and emotional needs of children whose parents have suffered because of their progressive activities and who, therefore, are no longer able to provide fully for their children. The RFC also provides grants for the educational and emotional needs of targeted activist youth. Professionals and institutions will be awarded grants to provide services to beneficiaries.
– RFC website
I had been giving late January/early February, but the timing of the appeal worked – I gave. And I’ll donate again on my birthday. Here’s the link: Support the Rosenberg Fund for Children.
The International Dreamers Scholarship Fund
There are probably thousands of good causes to help high school students – I worked from the 1990s as a high school teacher – and this is one of them. It also caught my attention a few years ago, I got tagged on Facebook I think. The organizer is a daughter of a friend – the friend is Fred, daughter Jessica (who I feel like I know a bit, even though we’ve never met).
For over a decade this fund has been supporting students without documentation as they go to college. It supports vulnerable students. And it helps build community (not mine, but that doesn’t matter).
Dear Friends and Family, For the past 10 years, my school has supported a very special project: The International Dreamers Scholarship Fund, which helps undocumented graduates of the International High School at Prospect Heights (the school where I teach) go to college by helping to pay their college tuition. Since we began in the Spring of 2013, we have awarded over 30 scholarships. In January of 2019, the passage of the New York State DREAM Act made state financial aid available to undocumented students who arrived in the country before their 18th birthday. However, these students are still unable to access the federal loans and and grants that so many students need to cover the other costs of their education and are similarly blocked from employment opportunities that might enable them to cover some of those expenses out of pocket. As a result, the International Dreamers Scholarship is committed to continue supporting our most vulnerable students. Please donate below to help support this project that is very near and dear to my heart. Thank you.
– Jessica
And so I started giving a few years ago, and am happy to contribute each year.
Here’s a link to: Support the International Dreamers Scholarship Fund Facebook Page, and another directly to the International Dreamers Scholarship Fund donation page.
Ceasefire Now
Some giving is about a donation. But there is also giving your time, your energy, your voice. In the case of Gaza the need for an immediate and permanent ceasefire is clear.
And so I give my activism. Some are great organizers. There are many, but I am calling out one: I am amazed at the work that Jewish Voice for Peace has been doing. So important. So impressive. The slogan “Not in our Name” – the high visibility protests. The songs. I am not an organizer, but I can bring my support.
And so I give my voice. Others have bigger audiences, or speak with more clarity, or can share direct experience. But as each individual who opposes the bombing, the killing, the destruction, the hunger – as each one of us gives our voice – it makes it easier for others to join in. I’ve noticed that some don’t try to change my mind, they just ask me to remain silent. No. Remaining silent is not an option. I give my voice.
Children
I guess that’s my theme. This year. I think it’s a good one.
Honestly, in the past I was not moved by the season. Presents? Donations? Bah.
But now, older, in my very very early 60s (that’s what I call 59), it’s different.
So yeah. This is what I did and am doing. Makes me happy that I am making good choices.
COVID’s Lost Generation?
The New York Daily News just completed a three-part series, “COVID’s Lost Generation”, on the aftermath of the COVID pandemic – as it hit New York City school kids. (Behind a paywall, sorry, Part I: NYC school kids still face devastating fallout, Part II: Isolation, Anxiety present challenges to NYC school kids, and Part III: Money, time, running out for NYC school kids left behind.)
The stories are personal, and you feel for the kids. It’s well written. I happen to think that Bamberger is one of the better NYC ed journalists at this time. But the story is more complicated than compelling personal stories.
You probably can predict the narrative: Everything was good, even great. Then abrupt school closures. Disruption. Closures lasted too long. Students did not learn. Disconnected. Lost. When school finally came back, there was “learning loss.” Can’t catch up. Students were harmed emotionally. Some won’t come back to school, or are now chronically absent.
And while bits of that happened, let’s remember the big picture, the way it played out in New York City. Let’s look, or at least start to look, at the mistakes that teachers knew about, and the mistakes that leaders continue to make.
Timeline
Let’s remember some timeline – schools closed March 2020, and the closure was extended twice, until finally mid-April they announced schools would be closed until the end of June. During that time we were supposed to teach remotely. There was no actual guidance from the DoE on remote teaching. And there was precious little sharing of experience. Each school made it up as it went along, on its own. Mulgrew’s emails were infuriating “we got this” – well no, “you” are not “we” – and just no, why would you tell people who were struggling that they are doing fine? It was draining and stressful and just horrible to have the city turned upside down by the pandemic, and not to have support.
That spring and summer the DoE and UFT worked on the premise that some sort of “hybrid” schooling would be in place for at least the start of 2020-2021. Hybrid, I wrote about it at the time, was a very very bad idea. The idea that teachers would somehow teach remotely and live? Nah. It made no sense. I first learned about it when I was meeting with other UFT programmers, and one of Mulgrew’s reps showed up and told us to find a way – and then told us not to worry about details (we were programmers – so that was not going to work). Later I complained to DoE insiders I know – and I got the same reaction from all of them – “hybrid” did not come from the DoE – it was pitched, hard, by the UFT.
The planning over the summer got worse and worse. I am convinced that “Instructional Lunch” was also a UFT-inspired plan. The ventilation checks were comical. The space considerations had moving goalposts. And then the UFT made a big show of threatening strike action. Not over needing to go remote. Over testing.
And then schools opened, some. Not high schools. And there were delays. And opens and closes. And hybrid. It was weird. The whole year was like that. And then 2021-2022 we were back in person.
We lost a year and a half of schooling. We had some remote instruction. It went ok in some places (including my school), mixed in many places, and bad in a lot of schools. There WERE kids who never really signed on, who drifted away without the social interaction.
Remote Instruction
Little reality check. There was at no time a serious effort to improve remote instruction. Sure, some schools worked at it. Many individual teachers worked at it. But the UFT leadership offered little better than Mulgrew’s infuriating “we got this!” (Mission accomplished?) which wasn’t true. And the DoE always threw the responsibility onto principals, the majority of whom were poorly equipped to address remote instruction (and too many of whom are poorly equipped to address regular instruction).
Remote instruction sucked, but there was no attempt to improve it, to make it better. That seems to have been intentional. Carranza never initiated any joint work on studying or analyzing or improving remote instruction. And Mulgrew was so committed to telling the whole world that NYC schools were open (no matter what was happening on the ground) that he wasn’t going to risk that narrative by talking about remote – even though that’s exactly what teachers and kids needed.
So that’s a sore point, as I read the Daily News articles. Remote could have been better, if we’d try (and by we, I mean Carranza and Mulgrew), but we (RC and MM) apparently didn’t try, and didn’t want to consider trying.
My school, all instruction was remote, and we definitely got a better schedule than most schools, and we got better at teaching. It still sucked, but probably a lot less than at most other high schools. Hybrid would have been worse. Zoom in a room – that’s another post – was definitely worse.
Connecting
Hey, this was bad. There were kids who completely disconnected. There were kids who substantially disconnected.
And we’re back!
In some ways, the worst part of this narrative is the return.
Imagine you are in a movie theater. Technical issue. Movie stops playing. Twenty-five minutes. And then it starts again, not where it broke, but twenty-five minutes later. What do you do?
If you are me, you tell them to “rewind” or whatever they do today. Let’s pick up where we left off, right?
If you are the DoE, you keep playing, 25 minutes ahead. And then they moan when people walk out of the theater. This is a management problem, not an “attendance” problem.
That’s what the DoE did with schools. No attempt to adjust curriculum to meet students where they ended up, after a year of pandemic, of disconnection, of remote learning (not optimized, because Carranza and Mulgrew didn’t want to be seen as supporting remote learning). No, the DoE pushed schools to keep their regular curriculum, to get back to normal, and not to attempt to meet the needs of our students.
Of course they did suggest social and emotional learning – but as a non-tested suggestion – you can guess what happened in many schools, maybe most schools. Those who already attuned to their students’ emotional needs paid more attention. And those schools that were not, did not.
And then there is “Learning Loss.” Or actually, no there’s not. There’s no such thing. Learning Loss is a misleading label, a claim that kids know less now than before March 2020. Bunk. Kids learned less than they might have – but actually lose learning? Nope. When opponents of public education talk about learning loss, what they point to is that test scores of kids who came through the pandemic are lower than similar kids previously. Kids during the pandemic learned less than previous kids had during regular years. That’s not “lost learning” – it’s just “less learning” and was totally expected.
And this talk about “catching up” – they don’t mean catching up. They mean starting the movie 25 minutes ahead, and watching kids struggle. That’s not catching up. That’s bad pedagogy. That’s actually being mean to kids.
Summary
The pandemic was horrible. The effects on schools were horrible. But the DoE, and the UFT leadership, made it much worse than it had to be.
- They wanted to announce loudly that NYC schools were open, and so they refused to help improve remote instruction.
- Their decentralized approach guaranteed no Social Emotional support in the places that already had the least.
- There was no attempt to adjust curriculum to match what students now knew.
- Instead there was a demand to “catch up” – totally unreasonable, and kind of mean.
- The language of “learning loss” does not reflect reality – no one “lost” learning, (and consists largely of comparing kids to older kids who went to school without COVID)
And finally, I’ve been kind to the NYDN, but “a lost generation”? This is a tough story, what happened was not good. But a “generation?”
I’m Sticking with the Union
I got a slick-looking promo in the mail this week – a 6″ x 9″ folded, colorful piece – offering to save $850 a year – if I quit my union.
Hell, no!
Post-Janus, teachers no longer have to belong to their union, or to pay an agency fee. But most, the overwhelming majority, have stayed. But there is a lurking threat. And there are right-wing, anti-worker groups that have their sights set on destroying us.
The Freedom Foundation is who sent me the promo. The postcard (that I am not filling out!) looks like it is addressed to NYSUT, but actually goes to these rightwing frauds, authorizing them to disenroll you from your union. Don’t be fooled.
Our union, imperfect as it may be, is a vital part of our working selves. Any rights we have – were won through the union. And without the union the employer (the DoE) would be unconstrained from taking those rights back. When the union does not seem to fight hard enough, that’s a reason we should work to get it to fight harder. But make no mistake – our work would be far, far worse without our union. I’m sticking with the union. You should, too.
Right after Janus the Freedom Foundation and similar scum tried to undermine our unions. At least in NYC, with the UFT, they completely failed. Teachers knew not to quit. And new teachers still signed their union cards.
They will probably fail just as badly this time. Teachers should not be fooled by the dollar sign – this is anti-union crap.
But it is a hard fight. And it does not help that the union leadership has done some pretty lousy stuff. Exhibit A has to be the fight over medicare. Why would Michael Mulgrew want to force retirees, against their will, into Medicare Advantage? Why institute copays? Why remove popular Borough Rep Amy Arundell, and refuse to discuss the move? (sign here) And there’s more. It certainly feeds into a sense of cynicism – which could lead some teachers to misguidedly fall for the Freedom Foundation’s garbage. When Unity makes bad moves, it makes it harder with those of us, deeply loyal to the union, as we fight on behalf of the union.
Adding Fractions Wrong
Everyone knows… (that’s a bad way to start a post)
To add fractions:
- if they have common (same) denominators (bottoms), we add the numerators (tops) and keep the denominators:
and in general
- If they do not have common denominators (bottoms are different), we change the fractions to equivalent fractions (same value, different look, like and ) with common denominators, keep those denominators:
Or, instead of making two separate cases, multiply each numerator by the other denominator, and take the sum (that’s the numerator) and multiply the denominators: 
Adding wrong
I see kids add fractions wrong. Hell, in the US we can see adults add fractions wrong. Numerator plus numerator, denominator plus denominator. Tops with tops, bottoms with bottoms. If you haven’t seen it, you’re not looking.
If we want to add 1/2 a pizza and 1/8 of a pizza (a slice) we don’t get 2/10 of a pizza (less than half). The idea that this is adding is ridiculous.
But tops + tops over bottoms + bottoms DOES produce a result. Let’s name this process – I’ll call it MISADDING – and see what MISADDING actually does.
MISADDING
Being formal, define MISADDING as
A few days ago, Dave Marain published this:
It reminded me of MISADDING. On Saturday I played around with MISADDING with some kids, and talked about it a little bit with a mathematician. Here is some of what we decided:
- MISADDING
is commutative, since the underlying operation is regular addition.
- MISADDING
- Take a fraction, and MISADD
or
and in general
.
- MISADDING
and.
Those answers are equivalent.
But MISADDING? Uhn-uh.
but,
hardly the same thing. - MISADDING
then
. There’s a pretty straightforward proof, if you’d like to try it.
- MISADDING
. Nice, right?
- MISADDING
than if you MISADD with
.
- If we drop the notation, and write the fractions in parentheses with a comma, MISADDING
- MISADDITION
- Combining the vector idea with the in-betweenness idea, we could see the pairs (or the fractions) as an expression of slopes… Rewrite this
as (b,a) + (d,c) = (b+d,a+c), and now think of (b,a) as the line from (0,0) to (b,a) and its slope will be
. Vector addition will give us a point with an associated slopes between the two given slopes, UNLESS the points are on the same line, and then the result will be on the same line (equivalent to MISADDING two equivalent fractions, and getting an equivalent fraction as the result).
Too long, didn’t read version:
When you misadd fractions by adding the tops and adding the bottoms – the result will not be greater than the two originals (which is what you expect for adding positive numbers) but IN BETWEEN them.
And if you came here for a post about Mulgrew… (I’m stopping here)
How small an area?
I sometimes write about mathematics. This is not a post about mathematics. This is a post about Palestine. This is a post mostly written for New Yorkers.
I support an immediate ceasefire, and a permanent ceasefire. But this post is not about a ceasefire. It is about area. It is “geometry” in the sense of “geo” + “metry” or “Earth” + “measurement.” It makes distances and areas in Gaza more understandable by comparing them to distances and areas we (New Yorkers) are familiar with.
The Gaza Strip is small. Everyone knows that. But most people don’t have much of a sense of the size of things. I am writing to help you understand area and distance.
I read somewhere that Gaza is the size of Manhattan. I knew that was not true. Gaza is bigger. And I saw some detailed maps from the BBC. And they had scales of miles… and I knew I could make the numbers more meaningful for readers.
The Gaza Strip is 141 square miles. Brooklyn (70) + Queens (108) are 178 square miles combined. The Gaza Strip is about 80% the area of Brooklyn + Queens.
Those scales are pretty close –
Gaza is 25 miles long (roughly). The distance from Seagate (past Coney Island) to Fort Totten (past Bayside) is a 23 mile walk (according to Google Maps). As the crow flies it’s probably closer to 20. And so on the map, measure the length of the Gaza coastline, and measure the distance from Sea Gate to Fort Totten. Should be close, with Gaza about 25% longer.
So Gaza stretches a little longer than Brooklyn and Queens combined, but only 4/5ths the area. “Narrow.”
Israel limits (before the current conflict) Gaza’s fisherman to 5 miles from shore. The same limit on Brooklyn/Queens boats might get them to the tip of Sandy Hook, but not the Jersey Shore, maybe Great Kills, but definitely not Tottenville, parts of New Rochelle, but not Mamaroneck. (Blue for yes, or maybe. Red for no.)
Brooklyn and Queens have combined about 4.8 million residents. Gaza has 2.3 million. That makes Brooklyn and Queens denser – at about 27,000/square mile – than Gaza – at about 16,000/square mile. On the other hand, Gaza had far less housing (before October 7). Overcrowding was already a real problem.
When the Israeli army ordered Palestinian civilians in Gaza to move south, this was the territory north of Wadi Gaza, about 60 square miles, a little smaller than Brooklyn. That’s about 40% of the area of the Gaza strip. Likewise, Brooklyn is about 40% of Brooklyn and Queens combined. So it’s something like ordering everyone living in Brooklyn to move to Queens in a few days or become a “legitimate target.”
But unlike Queens, the Israeli army has destroyed or made uninhabitable half of all buildings in Gaza. (the red bits on the map below.)
The Israeli army has now ordered most Palestinians in the south of Gaza to evacuate. Where? There is a “Masawi Humanitarian Zone” in the southwest – less than 4 square miles. (see the BBC map, above). This is a bit smaller than Canarsie. 2.3 million people, even with the worst crowding, could not possibly fit.
I can imagine people who have never left Brooklyn or Queens, their whole lives. It definitely happens. But it’s a choice. And even for most of them, there was probably a trip into Nassau, or an occasional foray into Manhattan.
For Palestinians in Gaza? Most have lived where you see, in the maps, and have never left. Never traveled. Never seen “the River.” Not their choice. And as tiny as that world is, imagine losing 40% of it overnight. 50% of the buildings. And now, really, 95% of the space? I can make the numbers real, but it is not just numbers, and what it is, that reality I cannot begin to imagine.
Finding School Survey Results (NYC)
Want to know what teachers think about a school? Best way to find out is to talk to those teachers… but that’s often not an option. And especially for teachers considering transferring, it’s important to get some idea of the mood and relationships – stuff that never appears on the school’s website.
One option is to check what teachers wrote on the school surveys. Now, this is not a perfect option. Many teachers do not fill out the surveys. Many do not trust that they are anonymous, and fill them out to please their administrators (I DO think they are anonymous. I encourage people to fill them out honestly). But this means that the surveys MIGHT reflect more positively than they should. The surveys can give a falsely upbeat view of a school. But a negative result on a survey – that’s a pretty good indication that there may be a problem – certainly I would recommend doing further research before accepting a position at such a school.
A positive result on the surveys might be meaningful, might not. I don’t put much stock in them.
A negative result on the survey is usually a clear warning that there is, or was, a problem. That’s a warning alarm. Do check to see if administration just changed – but otherwise – uhuh. Probably that’s a no.
In the past I published some results from these surveys. That’s years ago. I have time; I should get back to that. Gene Mann publishes abbreviated results for Queens (I think), which is a service.
But let’s say you want to find the results on your own. I am going to look at two neighboring middle schools in District 11 in the Bronx, 180 and 181. How do you we find them?
I generally do not navigate directly to the page, since I do not trust Panorama links to stay stable. I start at: https://www.schools.nyc.gov/about-us/reports/school-quality/nyc-school-survey and click the 2023 Survey Data and Analysis link.
That link brings me to this page: https://infohub.nyced.org/reports/students-and-schools/school-quality/nyc-school-survey and then I click on 2023 results:
Which brings me to the first Panorama page https://secure.panoramaed.com/nycdoe/understand:
Everyone wants to click on the red/orange “3151 Schools” first. I don’t. I start by clicking the blue buildings on the upper left “NYC Public Schools” – and I see a weird table (which I don’t care about):
In the upper left there are some options. “City” is highlighted. Change that. Click “School”
and we move to a massive table, with lots of colors. Adjust your window to fit as much as you can:
Those colors – the deeper greens are for good results, the rustiest red/oranges are the worst. The schools are listed by district, so I’m going to scroll down a bunch to reach District 11, where 180 and 181 are. I put the two schools on one screen:
Wow, that’s a lot of data. What to look at first? I suggest the three columns in the next to last group on the right: Teacher Influence, Teacher-Principal Trust, Teacher-Teacher Trust.
At this point we have our first order answer – teachers at one of the schools trust their principal. At the other, nope.
There’s more we might notice. At the second school, the principal trust box is one of the greenest – in other words – place may not be perfect, but teachers like the administration. At the first school, with lots of poor and mediocre ratings (from kids and parents too) I notice that safety is better than the other ratings (both teachers and kids say so). Probably doesn’t make up for the overall ratings, but something to think about.
Sometimes looking at which numbers do not fit the picture raises interesting questions. Kids love the school, adults don’t? What’s going on there. “Instructional Leadership” is much lower than “Teacher-Principal Trust”? Might be a “nice guy, can’t run a school” situation. And the reverse, instructional leadership is well-rate, but teachers don’t trust the principal? Things to think about.
Let’s go back and take a look at the individual schools. Find your way back to the first Panorama screen, but this time pick the red/orange building that says 3151 schools:
When you click on the building, you get a search list. Scroll down to your school, or type in the name:
And then click it. You will see a big set of blue bars.
That is the student results. Look at the top of the screen, and flip to teacher results:
Now, we have lots of options to choose from. This is 180, I’m going straight to Teacher-Principal trust, because that was what concerned me most. (Don’t worry about the blue bars, just find your question)
Turns out, there are a bunch of questions that go into Teacher-Principal trust (near the bottom of the list). Unfortunately, they don’t point to an alternative narrative.
I do notice that the numbers have all fallen a bit from what were already sub-mediocre scores the year before… but I don’t see anything that makes me curious to dig further.
Limitations
I want to be clear – the surveys don’t get everything “right” – they are what staff filled in. Maybe the staff was angry that day. Or maybe they filled in the survey with the principal standing over them. Lots of things could mess up the data.
But when a staff fills in negative information, I think that is at least a signal that you should look more closely.
And when the ratings for a school are consistent (high, medium, mediocre, low) but one or two scores buck those trends, I pay A LOT of attention to those exceptions, and you should too.
State of the Union w/ Arthur and Jonathan Episode 2
This episode is devoted largely to two teachers, chapter leaders, activists, who used to work for the United Federation of Teachers, but who got fired for thinking the wrong thoughts. We also talk about class size and To Kill a Mockingbird. And there’s an interview with a really dynamic math teacher (not me).
By the way, watch that teacher segment closely – it was fun to do – and we would like to do more of those.
Comments, praise, criticism, praise, all are welcome and appreciated.
City Tries to Reimpose Copays on Retirees – Who is Fighting Back?
What’s there to say about copays? I don’t like ’em.
I pay them. They went up and up while I was still working. And they are still here in retirement… because… I am not a Medicare retiree. I get stuck with the same copays as in-service members. Which sucks. There are a lot of them. And they all went up, and up, and up, in the last 2, 5, 10 years. Copays every time I go to any appointment, with very few exceptions. Of course I do pay them… my health care is still good, and mostly covered. But these copays add up to a hidden premium. Hundreds of dollars each year (yes, I know, premiums can be much more).
But if I were a Medicare retiree…
Medicare retirees have no copays. They didn’t used to. But in between something happened.
The City, New York City, the Office of Labor Relations… tried to impose copays on Medicare Retirees. They did. Retirees, Medicare retirees, had to pay copays. They were furious, but of course they paid every time they went to the doctor. And the New York Organization went to court – and the judge found what we thought – the City is not allowed to imposed copays on medicare retirees.
I keep typing “medicare retirees” or “Medicare Retirees” and what that really means is retirees who are 65 and over, who are on medicare. I am a “Non-Medicare Retiree” – a relative youth…
So the judge found that the City was wrong to impose copays, and retirees have struggled to stop paying them since some doctors did not get the message right away, and I know that retirees are due refunds, but honestly, since they are Medicare retirees (and I am not one) I don’t know if they have gotten the money back yet. Their money. Money they deserve. Money the City had them pay, in violation of the law.
So here we are, the ruling is clear, things are straightened out, or getting straightened out. And what happens next? The City appeals. In November 2023. Just a few days ago. The City wants to reimpose copays on our Medicare retirees. And I assume they want to stop copays from being refunded. And presumably they want to bill retirees for copays they have not paid, for service they already received.
OLR Commits Broad Daylight Robbery – How do we respond?
Horrible. The City going to court to rob its own retirees.
Me – I’m getting the word out that this is happening. I can’t do much, but this part I can do.
My union – the UFT….
It happens, the plate slips out of your fingers, you watch it spin and turn, and know what’s about to happen, but still imagine it somehow landing – somehow landing smoothly, intact, not spilling – and then a millisecond later it hits the floor, shatters, and the contents splatter everywhere.
My union – the UFT… I could imagine publicly objecting to the City’s appeal, publicly standing up for retirees, insisting on “No Copays,” filing a friend of the court brief against the City, using those overpriced lawyers FOR the members instead of using those overpriced lawyers AGAINST us… I can imagine for a millisecond.
But sadly, I know. I expect nothing of the sort. I expect Mulgrew and Murphy and the Unity leadership to sit silently on the side, watching the OLR rob our Medicare Retirees, hoping our retirees lose, and are forced to cough up those copays. And when we question why they did nothing – they will claim it was all the City that did this – and try to hide their complicity.
Making Progress in Math in Retirement
I wasn’t positive when I retired (when I retired) what I would be doing. I had plans. They just weren’t firm. And math was going to be some of them, but exactly what and how?
My first chapter leader and my uncle – them, and others, but especially them – carefully explained way back when I was a new teacher that it was a mistake to “retire, full stop” – rather, it is important to retire – to something. And I took the advice to heart.
So I had plans related to hiking, and travel, and time with family. I had plans about reading more, or, really, returning to reading, as I’d lost my way. And I’m still working on all of those things.
But for math? Three ideas:
- Teach in a program that emphasizes reasoning for mostly students of color
- Read math with others. Math reading groups.
- Go to school. Take math classes.
And each one has been playing out.
Teaching in a Program
I stopped working in June 2022. And I wrote to the program I wanted to work for. One day a week, maybe two, would be perfect. I wrote. They answered. I wrote. They answered. I learned that they put their emphasis on their summer programs – a math day camp for rising 7th graders, and a math overnight camp for rising 8th graders. I learned that during the year there is a Saturday program. They asked me about summer work, but I had a big trip planned. Yay! And I thought they would hire me to teach in the fall in the Saturday program, but somehow a “yes” turned into “come in and sub” turned into nothing at all. I was disappointed – good program, good content. But an alum suggested another program that might like me… and I filled out an application. Now it was January, and I really wanted the program my heart was set on – I didn’t ask about the spring – I knew they emphasized the summer – I applied for one of the summer spots. And after a multi-step process that stretched for over two months, I had work for July and August at the math day camp for rising 7th graders.
My alumni will recognize this: I taught logic problems, and problem solving. Yes, yes, we did Ghost the Bunny. I had fun. The kids had fun. The program invited back for this fall – and I am working now – Saturdays. My “classes” are like the lunchtime seminars I ran at the HS of American Studies (¼ credit, lunch time, no tests, completely voluntary), and are actually topics I had done before: Intro to Set Theory, and Abnormal Arithmetic (base 4, instead of 0, 1, 2, 3 we use O, /, ∆, ◊).
Reading Math
I wanted to find math topics I didn’t know, and read a good intro with people at a similar level. Never worked out. Agreed with Sue to read a book that matched up with her third term of calculus. We met a half a dozen times, but some progress, but Sue had to travel, we kept getting interrupted, and it stalled out.
I’m going to give this another try, after the holidays. I’m thinking about an intro to graph theory, or to knots, or mayeb Jacqueline Stedahl’s History of Mathematics.
Studying
Fall 2022 – I took off. But I knew I missed it. And that winter I wrote to Queens College. Turns out, I had matriculated when I was there on sabbatical. That meant that I just needed to update my status, and no application was needed. In the Spring I took Point Set Topology, and enjoyed the level of challenge, and the study sessions with my classmates.
Currently I’m enrolled in two classes. I enjoy “Number Systems” far more than “Functions of a Real Variable” – but I’ll talk more about that another time.
I was surprised to learn that I am not so far from earning a masters. I mean, I have completely no use for an MA in Pure Mathematics – but another nice shiny certificate? Why not.
Surprise
Looks like I may be working with student teachers in the Spring… That was indeed a surprise!
Notes for November 15
I’m drinking ironwort tea from my Goodbye Columbus mug…
The tea is probably mixed with other herbs, and is popular in the Balkans. Or near the Balkans. The Balkans are badly defined, so let’s be careful. In any case, this one is from Croatia. They definitely have it in Greece, Albania, North Macedonia, and Bulgaria. I see it called mountain tea and shepherd’s tea and planinski čaj. It smells – herbal? a little anise-y? a little flowery? In any case, it tastes nice, and makes me think it should have medicinal properties. But the studies I found all seem to start from the conclusion that there should be those properties, so they don’t seem super convincing. They don’t seem super unconvincing either – anti-oxidants? Could be. Anti-inflammatory? Why not. Flavonoids? Sure. Phytochemicals? I’d be easy to convince.
There was a UFT Delegate Assembly tonight. I should figure out how to sign on and listen. But I did not. I went to them for almost 25 years. I’m taking a break. That’s what I’m claiming. In any case, I read several sets of notes. Highlight was a Gaza resolution – Ryan Bruckenthal tried to amend to add a call for a ceasefire. – Leroy Barr had already laid down the line – “no amendments” – every Unity person heard. And then some debate, and a vote, and the amendment failed. In the room it failed 111 to 153 (42% to 58%), and on the phone it failed 322 to 400 (45% to 55%). Altogether that’s 433 to 553, (44% – 56%) no call for a ceasefire.
It would have been a huge symbolic victory, to have the biggest teachers local in the entire United States call for a ceasefire. For those of you who support an immediate ceasefire (I do) this was a missed opportunity. On the other hand, those vote totals are MUCH higher than they would have been 20 years ago – something has clearly changed. Americans, or at least teachers in New York (but more than that) are far more sympathetic to Palestinians, despite Hamas, than a generation ago. Can you believe 44%? And on the other hand (I know, I already ran out of hands) there is no way we got that many yes votes without a bunch of Unity people voting our way, or as Unity leadership thinks, the wrong way. And that’s after Leroy gave an explicit speech about “no amendments.”
Something else at the DA, I story I am following. A delegate, well, Peter Lamphere, asked if Mulgrew would address the Queens Borough Rep being removed. That’s Amy Arundell. And Mulgrew said “no.” But it is important that the matter stays in front of delegates and chapter leaders. Amy was one of the most responsive UFT reps. Her removal hurts the members in Queens, and the chapters and chapter leaders especially. And, related to the previous point, she was removed after posting (actually retweeting someone else’s words) about war in Gaza on her social media, challenging narratives (that we later learned to be partially false).
Peter Lamphere: do you believe that members in Queens have the right to know why the boro rep was removed? (small applause) A: No. I don’t believe any member has any right to know personal information about any other. (similarly small applause)
This was my first post in November. My writing is inconsistent, and I do get busy, but mostly I have been overwhelmed by the world. And why, if I’m stuck, write today? I was stuck on something else, which is a good moment to try to blog. I was working on a podcast I could not manage to finish. Look for that one soon!
Four years later…
On June 3, 2019 I rose, for what I thought was the last time, to address the United Federation of Teachers (UFT) Executive Board.
I spoke about the use of test scores at LaGuardia to shoe-horn in extra white students and squeeze out students of color. I asked the returning leadership to address the recommendations of the Student Diversity Advisory Group, and to involve high school teachers in those discussions.
And then I quoted a movie line. There’s a line I like, from A Few Good Men (the truth? You can’t handle the truth!) <– not that one. It comes later, after Nicholson has been hauled off, and the two marines have just heard the verdict:
- Downey: [after the verdict was read] I don’t understand… Colonel Jessup said he ordered the Code Red.
- Galloway: I know but…
- Downey: [nervously] Colonel Jessup said he ordered the Code Red! What did we do wrong?
- Galloway: It’s not that simple…
- Downey: [anxiously] What did we do wrong? We did nothing wrong!
- Dawson: Yeah we did. We were supposed to fight for people who couldn’t fight for themselves. We were supposed to fight for Willy.
Look at Dawson’s words. “We were supposed to fight for people who couldn’t fight for themselves.” I turned this to the officers, all members of Unity, and the Executive Board. I did it once before, about standing up for probationers. And I did it again June 4, spoke directly to the officers – I would not be back – but they still had the obligation to stand up for members who could not stand up for themselves. Most of them, unsurprisingly, paid no attention.
One more word here. United Federation of Teachers representatives and staff have come roaring into schools where there is conflict – but this is usually when the chapter is well-organized, and already doing a good job fighting back. It has sadly been their pattern – when a chapter is weak, when a member is vulnerable, when there is a good chance that our side will lose – the officers look the other way. This is their pattern. I think people are basically good – this cowardice is learned, practiced behavior. And so when I challenged Mulgrew on standing up for those who could not stand up for themselves – I was really challenging how Mulgrew conducts himself as a union officer – and I was not at all surprised he did not listen.
As I left that day, before the pandemic, several Unity people stopped me to say goodbye. Two stopped me to ask why I was not going to be on the Executive Board. Unity swept the board in the recent election – and I’d lost my seat. At least one of the Unity reps was confused, valued the contributions I had made. It was sweet, but made no difference. I said goodbye. Thinking it was my last UFT Exec ever.
– – — — —– ——– ————- ——————— ————- ——– —– — — – –
I came back Monday, last week. It had been four years, and a few months. I came back after saying I wouldn’t – but I came back because these officers had removed Amy Arundell from her position as Queens Borough Rep – and Amy stood out as a representative who actually stood up for members and chapter leaders, including those who were having a hard time protecting themselves.
Nick Bacon took notes. Here’s how he recorded my words:
Retired 20 year CL and 11 year member of this committee. On my last day of this committee, I said two things – I won’t come back (long time, but back), but second reason – members of this committee need to be judged by how they help the people least able to help themselves. Not everyone here lives up to that. No one was the equal of Amy Arundell. Someone who serves members and members of other boroughs, replies, helps, that person is a model for what we should be like. Losing that model harms our members who need them most. I have things I might say about the politics – won’t say now. Obligation to our members. Properly and right away must return to the position.
Why don’t UFT staffers have due process. UFT Executive Board meeting 10-23-2023why-dont-uft-staffers-have-due-process-uft-executive-board-meeting10-23-2023/
Other people spoke about Amy. A bunch. One woman, a retired Unity chapter leader, struck a similar not, speaking about how helpful Amy is to individuals on the large facebook group. At least one of the speakers raised the issue of the war in Gaza (Mulgrew’s apparent immediate motivation for removing Amy was that she had advocated for a more balanced resolution on Gaza, and had social media posts that were supportive of Palestinians).
It is obvious to me that Amy Arundell was
- removed for her political beliefs, and for speaking to those beliefs, and
- was one of the most helpful representatives for our members and chapter leaders in Queens, and for members and chapter leaders in other boroughs who reached out to her.
This doesn’t change the things Amy got wrong – I’ve had screaming fights with her. Just in the last two years I have disagreed openly and strongly on health care, and on latest contract. But that’s not relevant here. The UFT’s Unity leadership is trying to purge one of their own – for politics (and she is right and they are wrong) – and without regard to the harm they are doing to members by removing her (real damage). That is why I came back.
There is a petition to reinstate Amy. Please sign, if you have not yet done so.
And me and Arthur discussed Amy on State of the Union with Arthur and Jonathan last week.
– – — — —– ——– ————- ——————— ————- ——– —– — — – –
It was weird coming back. The tables were different. The speaker’s mike is now on the right of the room – I ended sitting dead-facing Mulgrew. Some people came by to say hi. LeRoy came over, said hello. Shook mine and Arthur’s hands – Arthur and me came together. Janella invited us to eat – but we’d just eaten. I thought about walking across the room. Too weird. Something surreal about being there.
After the open mike came the questions (you can read more in Nick’s post, linked above) – questions about health care, and about Amy. And then Mulgrew spoke. He was in some sort of track suit – but nothing nice. Like he was dressing down. And his language – it was a rambly attack on people who disagreed with him. And on Amy, he refused to address the issue, hiding behind his excuse that it was a “personnel matter.” Arthur does quite a rundown here.
I have heard rumors that Mulgrew might not be ready to retire. Certainly he could not find an outside job as easily as, well, someone who might have some appeal to a prospective employer. And a soft landing with something cushy at the AFT? I guess it could happen. Maybe. Not sure. But what I’m getting at is – even though there’s probably consensus that his brand fell badly in value through the last UFT election and especially through the healthcare fiasco, and even though Unity probably wants to buy him a gold watch and push him out the door, he might realize that he’d be left with little.
In any case, that’s the impression I got, as he lashed out at opponents, rambled, repeated himself, talked in circles. I was reading a book, half-ignoring him, but close enough that when he was wild, I looked straight at him – it’s probably my conceit that it bothered him – who am I after all? – but he did seem to have trouble looking away from me. Maybe. Anyhow, we really seemed to be witnessing the raving and flailing of a boxer who’s been finished, refusing to admit that he’s been beat.
I’m going to come back to this Exec Board in a day or two. Leroy Barr said some things that demand closer examination. There’s other stuff, too. But I didn’t stay for the end. Me and Arthur had had enough.
– – — — —– ——– ————- ——————— ————- ——– —– — — – –
Actually, after the Open Mic, Arthur suggested leaving. I wanted to stay to hear the questions. Arthur agreed. I kind of wanted to stay for the resolutions, but after Mulgrew reported, he started to leave. Ibeth asked if he would stay for the Reports from Districts – he begged off – had a meeting. Me and Arthur did listen to the Reports from Ristricts, and that was enough.
Fifteen minutes or so after Mulgrew left for his “meeting” me and Arthur walked down the stairs, out the door, and turned uptown towards the IRT. We crossed the alley where Exchange Place should be, and some motion caught my eye, and I glance back. I saw Mulgrew – no entourage – no folder or bag or laptop – moving up the alley towards Broadway.
“Michael!” I caught his attention, he looked up and realized who was speaking. “You hurt the members in Queens! That was a bad move!” Mulgrew from five years ago, from ten years ago, would have yelled back. “Jonathan, you don’t know what you’re talking about!” or “Enough with your nonsense!” or some assertive, aggressive answer. But not today. Mike moved into traffic, crossing Broadway. He put his head down. He said not a word.
That’s a gross image. Can’t end there. Let’s close with our Marines:
The State of the Union with Arthur and Jonathan – Episode 1 – Amy
Arthur and me are doing a podcast. Here’s the first episode, in two pieces, on YouTube:
ps. Arthur blogs on substack. He used to blog at blogspot.
Arthur and me talk
I should write more about me and Arthur. We were chapter leaders at the same time. We blogged at the same time. We never belonged to or supported the same caucus. We served on the UFT Executive Board together. We’ve always been willing to talk.
And so we decided to talk some more. In front of cameras. A podcast. Or video podcast. We could talk about news. Interview guests. Including teachers. Actually talk to teachers about teaching – along with union news and education news and and and….
Great idea – we recorded a pilot (not yet published) but I was dragging my feet. I need to get good at the tech side – and right now I am not. But I’ll learn.
This week there was big news in the UFT. Queens Borough Rep Amy Arundell was removed from her post – and we both thought that Amy served her chapter leaders and members (and members and chapter leaders in other boroughs) well. Arthur said we needed to record. And so we did.
In the future (meaning really soon, I hope) I will add an image, a thumbnail, maybe closing credits, a soundtrack. We will get it uploaded to Apple or Spotify. We will have several shorter segments each episode.
But this first time? Two talking heads on YouTube. You still might like to watch. Oh, oh, the title? “The State of the Union with Arthur and Jonathan.” Enjoy.
ps. Arthur blogs on substack. He used to blog at blogspot.
Is my healthcare safe?
The easy answer might be “no” – New York City (Mayor Adams and the financial people who cut the budget), the Municipal Labor Committee (MLC) (really, representatives of the leadership of the major city unions, with greatest weight for the leaderships of District Council 37 (DC37) and the United Federation of Teachers) and the UFT leadership directly are aiming to cut health care for city employees and retirees.
Medicare
That is the easy answer. But it misses an important detail.
For over two years our retirees have been fighting to stop Mulgrew, the MLC and Adams from forcing Medicare-eligible retirees into “Medicare Advantage” – an inferior, private alternative to traditional Medicare. In the UFT many retirees against Medicare Advantage are organized in Retiree Advocate (RA), which I belong to. Some public action was built by the Cross Union Retirees Organizing Committee (CROC). And effective organizing by the NYC Organization of Public Service Retirees has led to multiple successful lawsuits, beating Mulgrew and Adams.
But I am not a Medicare-eligible retiree. I supported this struggle, but it does not affect me, not today, not yet.
In-service Health Care
Mulgrew has announced that he – or the UFT leadership – or the MLC – not sure the distinction is important here – are putting in-service health care out for bid – they’ve issued a “Request for Proposal” – an RFP. The winner gets to replace our in-service members’ health care with a new plan. It is easy to imagine NYC paying less for the new plan than for the current one. It is also easy to point out that chnage in our health care can be disruptive – new doctors, new offices, new rules – but we can also imagine how can changing care mid-treatment might cause issues.
But I am not in-service. I will assist in-service members – if possible – in avoiding this destructive disruption and benefit cut – but I am retired – this does not affect me today.
The Third Group
So what about me, and people like me? Retired from NYC Service. Not yet medicare-eligible. We get City benefits, including health care. I chose GHI (Emblem). That is a pretty popular option.
My health care is ok. Fine. Except the costs have been creeping up. And I resent needing prior authorization for things that should not need prior authorization. But it’s ok, Emblem, for the most part.
Is this what I had when I was working? Yup. But when I retired I changed things up, so that I could drugs through Emblem. I used to get drugs from the UFT Welfare Fund, but they cut teachers off when we retire. Also, Emblem sent me new insurance cards when I retired.
Maybe the In-Service thing, the RFP, will apply to people like me – non-Medicare-eligible retirees? Mulgrew hasn’t mentioned it. We don’t know.
Honestly, the UFT leadership should address us. Tell us what they are planning to do with us. To us.
By the way
There’s something else weird here. The UFT is not my bargaining agent. It was, when I was working, but not today. They don’t sign contracts on my behalf. I no longer vote on contracts. They don’t act to require my employer to honor the terms of my contract. I don’t have an employer. I don’t have a contract.
Look at it this way – if the retired teachers left the UFT, the rest of the UFT would look exactly like a union. But if the Retired Teachers Chapter (RTC) separated from the UFT, the RTC might look like a union support organization – an auxilliary. Or it might look like a benefits club. It would not look like a union.
Oh, something else. That MLC? Unelected. I have zero say over who negotiates on our behalf (Unity chooses). But worse – most NYC retirees – they don’t even have an auxiliary organization. They don’t have someone from their organization on the MLC. And even worse, NYC retirees include managers, who absolutely do not have representation – but who are bound by the agreements the MLC and City come up with.
So…
Is my healthcare safe? No – if they are not coming after today, they will.
They haven’t given up on Medicare Advantage. They are going after in-service health care. No chance they are going to leave us non-Medicare-eligible retirees alone.
But I wish they would tell us what’s going on.
No News Is No News: UFT Leadership announces plans are on hold; keeps all the plan details available on website, ready to roll (right over us)
Today’s Reading October 16, 2023
Fred has an excellent, well-researched piece on how Palestinians have had their water stolen for decades (and sold back to them at high prices), and how Palestinians in Gaza today face not only Israeli bombs, but the complete shut-off of water. I recommend it. Water as Weapon by Fred Klonsky.
UFT members, and especially chapter leaders, were stunned this weekend to learn that Mulgrew / Unity removed Queens Borough Rep Amy Arundell from her position supporting members, chapter leaders, and staff, and running the Queens Office. Rumors are swirling about secret reasons – but Amy stood up for the humanity and dignity of Palestinians in a deeply hostile, vicious environment. Which, by the way, has nothing to do with how well Amy serves her members, and frankly, members and Chapter Leaders from other boroughs. I first met her – maybe I’ll say more another day – as I was learning about SBO transfers, and she walked me through the process to help me make sure my (new) school got it right. Anyhow, I’m not writing today, but Arthur wrote all weekend. Good stuff. Take a look: Amy Arundell Is the Best Unity Has to Offer (October 13) and Michael Mulgrew Looks at Due Process (October 15).
The infuriating New York Times provides “liberals” cover for being racist or supporting war. I read “The Morning” by David Leonhardt (because it is free. I will not send them my money). And this morning, straight out of a deeply racist playbook, he denied the ethnicity of murder victim, killed for being Palestinian. Wadea Al-Fayoume was 6 years old, and Palestinian, born in the US, and murdered, for who he was. Which Leonhardt hides.
No link from me. Not to the Times.
Finally, I am trying to clear my schedule to join this – it feels important.
9/12
I did not want to write about 9/11 on 9/11.
I was in Christopher Columbus High School. Teaching Math. My AP showed me the news, but I assumed that it was a puff of smoke, and not much damage. I remembered the 1993 attack.
In the wake of 9/11 the United States launched two wars – leading to death and suffering – and leading to big profits for Lockheed and Blackwater and their ilk. And those wars? They were not waged against people who had attacked the Trade Towers.
This is MY city. I wasn’t born here, but I’ve lived here almost 40 years. The attacks on the Twin Towers were personal; they hurt.
Tourist on the E Train asks – “is this the right way to 9/11?” – A New Yorker responds “This train goes to the World Trade Center – that’s where you want to go” – “No,” says the tourist, ” I want to go to 9/11!” – and continues “You New Yorkers are so rude!”
Every time I have to take off my frigging shoes at the airport – I’m reminded of 9/11.
Everyone treats first responders like heroes when they are responding. And we sanctify the names of those who perished. But after? Firefighters and others – digging through that disaster zone – breathing that poison – developing serious illness down the road? Why don’t we think of them FIRST on the anniversary?
Not to make too much of it – but those towers were pretty ugly.
Our elections are not the fairest in the world. They are rigged against regular people. Corporations and the rich, and in NYC especially, big real estate, wield crazy influence. But at least we have elections, and count on them. Except that one time Rudy Giuliani almost got away with canceling ours – because of 9/11.
That stink, it crept over all of New York City. I was at the grad center, 34th Street, weeks later, and it hung in the air.
In this morning’s The Morning, the Times discusses separating the coup in Chile that overturned the elected government from the terror and torture that came after. The neutral statement of the possibility is disgusting. There’s no mention of CIA involvement, nor any of war criminal Henry Kissinger. Those of you who read the Times and call it “news” – you should really think about that a little more. Oh, and the Times doesn’t bother mentioning the date of the coup – It was in September 1973 – the 11th.
I didn’t know the little electronic shops that the WTC wiped out – but we had “redevelopment” in New Haven where I’m from – and no one I knew ever said anything good about wiping out small businesses. Why did city governments do that? Here’s “Radio Row”, left, and after it was razed, right.
“A noun, a verb, and 9/11” – I’m no Joe Biden fan. And he’s not much of a speaker. But gotta give it to him on that one. Summed up Giuliani pretty completely.
I’m not much for patriotism. It’s usually a screen for the government to build support for war, or corporate profits, or both. But in the fall of 2001, regular folks looking for survivors, helping us dig out, recover – I don’t know what to call it, but I felt pride in my city and in my fellow New Yorkers.
There used to be limits on government surveillance. We lost a lot of those limits in the aftermath of 9/11. The terrorists scared us, attacked us in our home. But it was our government, the US government, and Homeland Security, not the hijackers, that stole our liberty.
NYC Newcomers: Manufactured Crisis
Mayor Eric Adams is threatening budget cuts. That could have been a headline four months ago. Or a year before that.
This is what Adams tries to do – give more money to big real estate interests, give more money to the police force, give 6-figure jobs to friends/relatives/donors – and cut everywhere else.
“Migrant Crisis” is just a new opportunity for Mayor Adams. It’s just another chance to misdirect municipal dollars.
On one thing he’s almost right: there may be great harm done to New York City. But it’s his response to the arrival of migrants that will do the harm. There’s the cuts – his choice. But there’s also the nature of his response – all temporary, interim measures. No actual solutions. Short term stopgaps with long term costs. And can’t blame that entirely on Eric Adams – we need permanent dwellings – not “tent cities” – but where are the voices for real housing?
There’s nothing in the pipeline. Kathy Hochul (remember, New York State has a governor) botched an under-ambitious housing proposal this past winter/spring. And not all her fault either – suburbs went ballistic and stopped any housing from getting through the state budget. I guess you might say that some suburbanites are anti-housing – but we’d be closer to the mark by calling out their racism.
There’s another aspect of New York State response – distributing newcomers in a way that makes sense. New York City is the logical municipality to host most immigrants – but most is not the same as all. New York State has other major cities (Buffalo, Rochester, Syracuse, Albany). And the NYC metropolitan area extends beyond the five boroughs – Westchester, Rockland, Nassau and Suffolk should be involved. That does not mean even distribution across the state – a few migrants in every county – rural areas and small towns will not have social services that can be ramped up – and will have far too few opportunities for new New Yorkers.
Immigrants are coming to the United States – not specifically to New York. DeSantis sent migrants to NYC to make a point, and to increase pressure on NY. He demonstrated at Guantamo callous disregard for people’s lives, and he displays it again here.
The United States government should have responsibility for migrants to the United States – pushing problems, including funding problems, onto the states reveals fundamental issues with federalism. The lack of meaningful assistance from Biden… the media says he’s unpopular – I just think he’s useless.
Much has been made of immigrants not having the right to work. I think migrants should be able to work – but I don’t know if there is legislation, or what the other implications are. I do know that NYPD probably has better things to do then take away migrants’ property.
This manufactured crisis is an opportunity for those with a racist agenda in New York. We are just removed from Lee Zeldin’s racist campaign for governor – that over-performed on Long Island, parts of Queens, Brooklyn, and Staten Island. And perhaps more troubling, the New York Times hasn’t stopped it’s liberal hand-wringing over “crime.” And the Post. Jeez. Over the summer there was an incident involving a migrant (person unknown). The Post ran a story about the crime – with a photo of ordinary migrants – people – plain people. When a white person does something wrong – the Post does not run a photo of random white people.
Do we need to find $12billion? I don’t know the number. But there will be a cost of helping newly arrived people with food and shelter. Restrictions on work have to be thoughtfully removed. And solutions need to be permanent – not quick fixes. A fairer national funding system needs to be in place – including restoring taxes on the wealthy and large corporations – and we should not be considering cuts to schools or sanitation or transportation – or on a federal level to social security or Medicaid or Medicare.
New York City has ever been a city of immigrants. We have welcomed newcomers – or at least provided opportunity. Rather than being a burden or causing a crisis, migrants from other countries have built New York – both physically – and contributed to the rich diverse culture we have here.
New York City today must continue this tradition. People are coming here for a better life – and we should eagerly allow them to build that life here.
What is Math? (Questions, not answers)
It seems obvious, right? We all know what math is. But let me try to ask some tricky questions.
Numbers/Arithmetic
First, anything with numbers is math, right? Counting? I think so. Adding, subtracting, multiplying, dividing? Good. Exponents. Fractions! What about the theory that describes these numbers? Probably, right?
Geometry? Surveying? Construction? Drafting?
Then there’s geometry. The word comes from roots which mean “earth measuring”. That’s not really counting or adding. But not surveying – that’s something different? Seems like a fine line (haha) to be drawing. And construction of figures with pencil and straightedge counts – but drafting does not? That’s a little arbitrary. Really, why would any of it get grouped with arithmetic? And if some of it, why not all of it?
Algebra
Algebra seems an easier fit. It’s like arithmetic, but with a symbol taking the place of a number. And then there’s the stuff that flows out of and beyond algebra… functions, trigonometry, graphing, even calculus.
Other Stuff
What about logic? Some logic is math? And some is not? But none has numbers or anything like them? And Set Theory? And Graph Theory? And Knot Theory?
I’ve heard that Game Theory is more Economics than Math. I’m not sure.
Programming?
Programming and coding are often taught in math departments. I guess they have numbers in them, but is that enough to make them math? Sometimes math teachers teach them, right? But is that enough?
Physics
Clearly Physics is a science, and not math. But a lot of math and a lot of physics look a lot alike. Math is physics without things? And physics is math with things added? How close do circuits come to the line between them? How is there a field called Mathematical Physics?
Statistics?
Is statistics a branch of mathematics? Or a science that studies data (and makes use of a lot of math)?
I should end by giving credit to a book – Jacqueline Stedall’s The History of Mathematics – A Very Short Introduction which poses and answers some of these questions.
It turns out that there is some logic (no pun) to what we include and what we don’t include in mathematics today.
There’s also a lot of history, and tradition. Stedall discusses topics that USED to be part of mathematics – including artillery and astrology (not a typo). Her book is really worth a read (and just 100 pages)
Learning Loss
I’ve got no problem with you reading anti-public school propaganda – as long as you know that’s what you’re reading.
You want to say you read The NY Times for the crossword? Ok, I guess. Sports? Don’t pretend. News? Come on. It’s not news. It’s consistent hard centrist propaganda. Including when it comes to schools.
Best option? Stop reading it. There’s better news sources. But if you insist, at least identify the anti-progressive propaganda. and that includes the anti-public school slant. Like them pretending “learning loss” is a thing. Like that hack David Leonhardt did, again, this morning.
Learning loss, right? Most of you reading this are teachers, or were teachers. Think about it. A kid comes into your class in September, and they leave in June. And during the time they are with you, they “lose learning.” What’s that? They know less in June then they did in September. Seriously? They actually “lose learning”? I know that doesn’t happen. You know that doesn’t happen, except in some rare, pathological conditions. everyone knows that doesn’t happen.
A kid sits in your class for 10 months and knows less coming out than they did coming in. They “lost learning”. Has that happened to any of your students? Not mine.
And over the summer? The kids forget things over the summer? Sure. But those are generally not things that the kids really knew. I mean, they forget some stuff, but they are more likely to forget test prep material that they never really knew than things that they had actually learned. And when schools closed during the pandemic, did this happen? Sure. But not so much. And that’s not what the Times means by “learning loss.”
No, the New York Times writes “learning loss,” and they mean that a fourth grader in June during the 2020-21 pandemic year knew less than a fourth grader – not the same kid, they’re comparing him to some other kid – that he knew less than some other fourth grader from the previous year did at the end of the previous year.
The kid didn’t “lose learning” – he learned less than a kid who went to school when there was no COVID.
And actually, that’s not what the Times is saying. We – I assume you, dear reader, are a teacher – know that kids learned less during the shutdowns and remote instruction. But the Times did not ask us, would not trust us. The Times thinks that test scores (or their equivalent) fell. The Times thinks learning (at least for poor peoples kids) is equivalent to test scores.
This dialogue which would not make any sense to anyone with half a brain: “What did you learn in school today, dear little son of mine?” “Nothing – we didn’t have a test today” – this nonsense dialogue would make perfect sense to the Times editorial board.
They write “ there has been learning loss“ but they mean “the test scores in fourth grade this year are lower than the test scores were for the previous group of fourth graders.“
The ideas – the core of the Times propaganda in this instance – is not drawn from education. The “loss of potential or predicted learning” does not come from the vocabulary that includes “ level of cognitive development” or “reasoning ability”. Rather, it is economics imposed on education, profit and loss, expected earnings, Emily Oster, monetization of each child’s “value,” scores, units, commodities.
“Learning loss” isn’t a thing. Lower test scores might be. But the Times knows drama. They know propaganda. They lead with the lie that grabs attention.
UFT High School Vice Presidents
George Altomare, who just passed, was the first United Federation of Teachers HS Vice President. The list of those who came after is not too long…
Let’s start with the list. The high schools have ever been a rowdy division, and the heart of the non-Unity votes in the UFT. That’s worth some digging, some discussion, finding and recovering some of our own history. But for now, the list:
UFT HS VPs
| George Altomare | 1960-1985 | |
| Michael Shulman | 1985-1987 | Only New Action (non-Unity) top elected position in all UFT history |
| John Soldini | 1987-1989 | Last HS VP elected directly by members in the high schools |
Michael Shulman represented an opposition caucus – New Action. In 1985 he beat George Altomare head to head for HS VP, fair and square. But the union’s leadership grouping, called Unity, sued to overturn the election (that they had conducted!) A second election was held. Shulman won again. George retired the day the result was confirmed. Shulman is the only Vice President in the UFT’s history not to come from Unity Caucus. More on that below. Shulman served one term, and was narrowly defeated by John Soldini. Mike returned to the classroom, I believe at Fort Hamilton High School.
UFT VPs at large for High Schools
John Soldini (Unity), Shulman and Altomare were the only three HS VPs to be elected directly by the members in the high schools. Unity, desperate never again to lose the position, converted all the VPs to Vice Presidents at Large. Up to that point, high school teachers elected the high school vice president. After two amendments, all UFT members – teachers, paras, secretaries, retirees – from high school, from middle school, from elementary school, from everywhere else the UFT represents people – all of them voted for the “Vice President at Large for High Schools.”
| John Soldini | 1989-2003 | In most elections the majority of high school members voted for New Action – but as this was converted to an at-large (not just high school) election, Soldini retained the position. |
| Frank Volpicella | 2003-2007 | |
| Leo Casey | 2007-2012 | |
| Janella Hinds | 2012-2023 | Won the majority of high school votes in 2013 and 2019, but not in 2016 or 2022. In 2016 James Eterno (MORE/New Action) won high school votes 51-46%, and in 2022 I won high school votes 56-44%. See the note next to John Soldini, above. |
The Battle Over Medicare Advantage is Not Over
United Federation of Teachers retirees this week received an email from Retired Teachers Chapter Chapter Leader Tom Murphy. The email warned retirees that a City Council bill was actually an attack on collective bargaining rights.
The bill in question is Charles Barron’s intro 1099:
There has been a struggle going on for over two years in New York City – the City administration and the municipal unions want to move retirees off of traditional Medicare onto Medicare Advantage, and groups of retirees have been resisting. The Federal Government rewards municipalities (with cash) for making this move, but many do not want an Advantage plan – they cite doctors who won’t take it – and prior authorizations. The courts have stopped the latest iteration from being enacted. We are at a pause.
In this moment the City is preparing to appeal the court decision. The retirees are for their part pushing this City Council legislation, which would prevent the City from using the Medicare Advantage option in the future. The bill looked stalled, but just picked up a few new sponsors; they are up to 17 – but need 26.
In reaction to the letter signed by Tom Murphy, UFT retirees who generally oppose were furious: “Dreadful email from Tom Murphy,” “this is a betrayal,” etc.
Let’s step back for a second.
Not Personal
I don’t think the letter is personal. I doubt that Tom Murphy himself wrote it (he is certainly capable of writing an actual letter, but this has the tone of the anonymous hive that runs the 14th floor at 52 Broadway). This is a political battle between forces that are opposed. An individual’s name below an email does not change that.
Unity has not given up
There is a court decision. Medicare Advantage won’t be imposed September 1. We are done? Nope.
Unity, in sending this email, is reminding its troops that they are still fighting. They will struggle to defeat the Charles Barron bill. They will back the City appeal of Judge Frank’s ruling. They will continue to scheme up new ways to get our retirees into Medicare Advantage.
Unity’s message when Judge Frank’s decision came down was a neutral-tone “there will be no change as of September 1.” Seasoned Unity leaders probably realized that this was a pause, not a surrender. But other Unity members may not have. This message may be for them.
This fight is about Medicare Advantage
Opposition folks can write about “betrayal” and Unity can pretend this is about collective bargaining. In fact, we’ve been in a fight for over two years, and it really has not changed. Unity wants the City to collect the money the Feds will provide for moving retirees to Medicare Advantage. The City has made funding the Stabilization Fund partially dependent on the UFT (as part of the MLC) delivering a Medicare Advantage deal.
Every showdown in this fight has taken some odd form – Administrative Code 12-126, Intro 1099, the copays case, arguing about “rollout,” the City making it confusing to “opt out.” All of these details are important. But fundamentally all of this has actually been about whether or not our retirees were going to be moved into Medicare Advantage.
Unity Might be Concerned About 1099
There are now 17 sponsors, and other City Council Members may be thinking about signing on. Perhaps Unity is worried that its ability to get some Medicare Advantage plan adopted in the future – an MA plan that forces many retirees out of traditional Medicare – is being endangered by the bill.
I don’t know about that. 17 sponsors. 51 council members. Need 9 more. Not so easy. But maybe Unity knows more than me. Or maybe they know less – and not having a good handle on city politics, including the City Council – are getting nervous?
Unity not Confident Retirees Would Lobby Against 1099
I think this is clear. They got massively out mobilized last winter on 12-126. They were not going to embarrass themselves by going head to head with retirees on phone calls to city council. The letter does not include a call to action – that’s not an oversight.
Enough
I have written enough. The letter is unremarkable.
- It’s just about Medicare Advantage, no matter what it claims
- It’s from Unity – even if one guy’s name is at the bottom
- They might be worried about the Baron bill
- They might be reminding their folks that they have not given up
JD2718 