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Notes from Tom Frieden – the Virus is Winning

January 10, 2021 pm31 12:04 pm

This Friday Tom Frieden, former head of the CDC, and former NYC health commissioner, published a sobering twitter thread about the US, NYC, and the virus. Without further comment:


Covid Epi Weekly: Humanity vs Virus – the Virus is Winning Perfect storm: 1. Uncontrolled spread in most of US, 2. Slow vaccine rollout, 3. Worrisome mutations increase transmissibility and could undermine diagnostic testing, antibody treatment and vaccine efficacy. 1/thread

A misleading narrative suggests that uncontrolled spread of Covid shows that public health measures don’t work. The plain truth: most places didn’t stick with the program long enough to get cases to a manageable level and now masking and distancing aren’t being done reliably. 2/

So yes, if you don’t use masks correctly and consistently, they don’t work. And vaccines don’t work if people don’t take them. CDC data getting ever more available and useful; Covid Tracking Project remains invaluable. 3/
Analysis & updates | Record Hospitalizations Point to Trouble in California and the South: This…
Record high cases, hospitalizations, deaths–with continued increases. There’s a 1-2 week lag between cases and hospitalizations and hospitalizations and deaths. Expect continued increases in deaths. Scaling up antibody treatment might help, but, like vaccines, rollout botched. 4/


How stressed are hospitals? New tool with HHS data shows % of beds with Covid patients, which is more reliable than % of ICU beds filled; ICU beds can be added more easily than hospital beds (convert surgical recovery suites, anesthesia rooms, etc). Anything >15-20% is bad. 5/


But it’s not limitation of beds that’s most dangerous, it’s limitation of staff. Health care workers are exhausted, at risk, relief months away, no reinforcements likely to arrive from other parts of the country. Great that vaccines getting rolled out. 6/
Why do some parts of country have much more Covid than others? Rates of hospitalization range 4-10-fold among states. Fundamentally: Opening too soon, leading to rapid resurgence Failure to distance and mask Failure to find and stop outbreaks Bad luck – superspreading events. 7/


In most places, public health measures didn’t fail, they weren’t applied. To a striking degree, this breaks down along partisan lines. Look at Staten Island. The northern part, which is poorer and more Black and Latinx, has worse health outcomes and shorter life expectancy. 8/

But southern Staten Island, which is richer, whiter, & regularly votes Republican, has higher rates of Covid, including higher test positivity (~15% vs.~10%). Similar differences, generally, between southern/northern California and US South and North. 9/
We take vacations but the virus doesn’t. Good thread from YYG; we are nowhere near herd immunity. As Josh Lederberg used to say, microbes outnumber us: it’s our brains against their numbers. Places like VT, Oregon doing much better than others. 10/
Reporter asked why Ca doing as badly as Texas despite more restrictions. Faulty premises. If Texas had California’s death rate, 8,120 dead Texans would be alive today. And places in California haven’t masked, distanced. Societal failure to implement public health measures. 11/
PCR test positivity rates are increasing steadily in 12-17-year olds and in 5-11-year-olds, these ages now highest of any age groups. Although imperfect, positivity rates are important to track. Not a good trend. Seeding of the virus throughout communities and the country. 12/


SECOND concerning trend: slow vaccine rollout. Some understandable–new vaccine, difficult storage. Some incompetence–run like grocery delivery not vaccination campaign, failure to support state/local microplans. Even for a competent government this would have been hard, and….13/


Grocery delivery: temperature, restocking cadence. Vaccination program: community engagement, detailed microplanning of who will vaccinate, where, when, how, and two-way communication, identification of trusted messengers and messaging in every community. 14/

Most important, least known documents re vaccination, buried. 1. Checklist 2. Action: 3. HCW We put together materials on how to plan for and communicate about Covid vaccination. 15/
Communication Strategy for COVID-19 Vaccines: The Essential Checklist | Prevent Epidemics
Some plain talk on vaccines. They’re stunningly effective and, so far, reassuringly safe. Allergic reactions to Pfizer vax: 11 per million, 70% among people with a history of anaphylaxis or allergy. Among people without such a history, about 1/500,000 16/
Allergic Reactions Including Anaphylaxis…
As of January 3, 2021, a total of 20,346,372 cases of coronavirus disease 2019 (COVID-19) and 349,246 associated deaths have been reported in the United States.



Operation Warp Speed: Stop hoarding vaccines!!! No need to hold back half. Get them out fast. Although it’s possible manufacturers will miss their production targets, that’s a lesser risk than not flooding the zone ASAP with vaccines. Jeez. 17/

We should move to Phase 1C1 ASAP (like, today)–all 65+, all health workers, all nursing home residents/staff, frontline essential workers. Good information on how to promote vaccination. Bottom line: focus on making it convenient and the movable middle 18/
Beyond Politics — Promoting Covid-19 Vaccination in the United States | NEJM
Medicine and Society from The New England Journal of Medicine — Beyond Politics — Promoting Covid-19 Vaccination in the United States
Hint: same folks not likely to wear masks not likely to get vaccines. Need to segment market and target messages to different groups. Focus on getting back to normal. Protecting jobs. Protecting our families. Despite rocky start, we’re making real progress – 7M vax given. 19/
Lots of unknowns re AZ/Oxford vaccine. Maybe less likely to give “sterilizing immunity”. Studies urgently needed on prime/boost approach to see if higher protective efficacy confirmed. Reassuring fewer serious infections and no serious adverse events. 20/
Oxford–AstraZeneca COVID-19 vaccine efficacy
2020 has been a difficult year for all, but has seen 58 vaccines against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) be developed and in clinical trials,1 with some vaccines report…
But…if it turns out that we have vaccines that are 70% effective vs 95% effective, it’s going to raise terrible questions. Scientific knowledge should be public domain, and walk-in rights for making the best vaccines for the most people are a moral imperative. 21/
Now, THIRD, if uncontrolled spread and slow rollout didn’t alarm you…new strains of virus. At first I thought maybe the UK was blaming mutations for sloppy public health work – but no. Strain is more transmissible. Not inevitable that it will spread in the US, but likely. 22/
I’ve never seen an epidemic curve like this. If strain becomes common in US, close to worst-case scenario, w/ baseline of full hospitals. (Not worst case: Covid CFR ~1/200. Worst case 1/10.) Potential for perfect storm especially with political turmoil and leadership vacuum. 23/
UK and Ireland deeply concerning. In just a few weeks, from less than 1 in 10 new strain to nearly 1 in 4 (Ireland) and half (London). Need more data, and relaxation of indoor restrictions undoubtedly helped the virus spread, but the trend is ominous. 24/
Sample shows one in four Covid-19 cases in Ireland last week were UK variant, Holohan told govern…
The CMO wrote to Health Minister Stephen Donnelly on Tuesday regarding the current Covid-19 situation.
Let’s be clear: new strains emerge. B.1.1.7 more transmissible so will cause more infections, hospitalizations, deaths. Strains may emerge that make testing less accurate, treatment less helpful and vaccines less effective. B117 is a shot across the bow. Covid here for years. 25/
We’ve failed at controlling Covid in US. If more infectious strain takes hold we’ll have to do much better. No avoidable indoor exposures. Maybe, better masks. We should definitely not change vaccine schedule now, but if we get a UK-like situation, this has to be considered. 26/
We have another 11+ days of absent leadership and active undermining of public health measures to save lives. These days are so very dangerous, for so many reasons, including the potential for exponential growth of the B.1.1.7 strain. 27/
Many years ago, Senator Moynihan said, “Everyone is entitled to his own opinion, but not his own facts.” That should not be too much to ask. We need to get back to that perspective, urgently, to protect ourselves and our families. 28/
Long but must-read article. As I think about 2020, I mourn the 400K+ (right number considering excess mortality) deaths in US, many/most preventable. But I can never forget–and do not want to forget–the horrific, lynching-like killing of George Floyd. 29/
How COVID-19 Hollowed Out a Generation of Young Black Men
They were pillars of their communities and families, and they are not replaceable. To understand why COVID-19 killed so many young Black men, you need to know the legend of John Henry.
“Concern for man and his fate must always form the chief interest of all technical endeavors. Never forget this in the midst of your diagrams and equations.” – Albert Einstein End/thread


Surge Since New Years

January 9, 2021 pm31 2:23 pm

Nationally there was a dip in new cases after Thanksgiving (New York State did not experience that dip; we have special leadership). But after Christmas the numbers have roared back. We are currently seeing a surge that is steeper than the spring (once the unreported cases are factored in.)

7 Day moving averages, for the US, NY, NJ, CT, MA:

Source: Worldometer

And we have not not yet felt the effects of B.1.1.7, the new COVID-19 variant that is now ripping through England, Scotland and Wales. The Kent Variant (need a better name) transmits much more quickly than what we currently have. And it has arrived on these shores. It is just a matter of time.

Yes, there are vaccines. There is light at the end of the tunnel. But there is a real danger that things will get worse, significantly worse, first.

An ugly point that should be made – new cases go up first – serious cases go up later – deaths go up later. This sequence is made worse when hospitals reach actual capacity – but the amplification can occur before, as the strain on the health care facility grows.

Cases per 100,000 population, daily, from December 31, up until January 8 (yesterday):

December 31:

January 1:

January 2:

January 3:

January 5:

January 7:

January 8:

Source: NPR Coronavirus by the Numbers (data originally from Johns Hopkins)

For a late November – late December time series (four maps) see this NY State is an Outlier post.

I think the mottled pattern in the final map reflects rapid, uneven spread, with uneven testing and reporting. With steady spread, the numbers move slowly, and regions appear to move together.


Cuomo’s Dishonest Math

January 7, 2021 pm31 3:12 pm

Pitcher is getting shelled. “When you going to take him out?!?!” scream the fans. The manager says “when they have more hits than at bats” Huh? He just said he’s never taking the pitcher out. Idiot. And dishonest. Hits are never more than at bats. Why not just say what he means?

Repression’s getting bad in a far off country. People ask an NGO when they are getting added to a watch list. “When the number arrested is greater than the population” They just said they’re never adding the country. The number arrested can’t be more than the total population.Idiots. And dishonest.

A kid seems to be in the wrong level of a class. He is doing poorly on every assignment, every test. “We should move him back a level” – but the AP answers “we can move him if he gets more questions wrong than there are questions on the test.” She just said that she’s never moving the kid. The number wrong can never exceed the total number of questions. Idiot. Dishonest.

COVID is going up in NYC. When will they close schools. Cuomo says “when the rate in school is higher than the rate in the community” Huh? He just said he’s never closing schools.

Think about it. Who has the highest rates?

  1. People with symptoms
  2. People who have been exposed to others who are positive
  3. People who have recently traveled
  4. Random people

In the community, all four groups get tests. In fact, categories 2 and 3 get a lot of tests.

In schools, category 1 does not get in the front door. Category 2 and 3 are not supposed to get in.

So when will a random sample of people without symptoms who have not recently been exposed have a higher positivity rate than a random group that includes people with symptoms and recent exposure? Never. Dishonest idiot.

“In a reversal, Governor Andrew Cuomo will now allow schools in all counties to remain open even if the seven-day positivity rate for COVID-19 within those counties exceeds 9%, long considered the state’s threshold to close schools.”



January 6, 2021 pm31 8:22 pm

A friend grew up in another country’s capital. There was political tension. One morning the tv was buzzing. There were tanks out the window. Good, he thought, no school.

He was right – there were some days off. The coup succeeded. Officials were fired. Leaders were executed. And life resumed.

By the way, the coup plotters were homegrown. Locals. But they were trained by a foreign power, a beacon of democracy. And they acted because the government had created a link to the other, evil, great power.

It seems, as I think about coups over the last 75 years, an awful lot of them were instigated, or even orchestrated, in Washington DC. But none of them took place there. And I thought none ever would. Until today.

Frankly, I was surprised by Trump’s video statement – because he told them to go home. This could have been much worse.

No credit, to him, of course. It is not clear to me what consequences he faces. But I’m guessing it’s a lot clearer to him. He’s a bully. And most bullies are cowards.

I watched too much tv today. TV news is addictive. I’m glad I usually skip it. But today…  I’m about to stand up and walk away. It’s been hours.

Side note: quite a few reporters use set “catch-phrases.” You should stop. Combine words with the meanings you want them to have. Oh, and “extraordinarily surreal”? Really? As opposed to “typically surreal”? And finally – the electoral college – sacred? Calling a government institution “sacred” is profane. And calling a racist, reactionary… I made my point.

Some Questions for 2021

January 6, 2021 am31 1:09 am

If you are reading this, you might know me. And if you know me, you know I can ask questions that are not really questions. That’s not these.

Real questions for the New Year (in the order in which I expect us to learn the answers)

November – January: How will the national elections turn out?

  • January 5 – what happens in the Georgia Senate runoffs? 2 Republicans, 2 Democrats, or split?

If the Democrats win both, I do not expect that Schumer plans to win any votes 51 – 50. They will more likely try to return to business as usual, and forge some agreements not to go full-on obstructionist in the future. If the Republicans win either one, they very well might defeat stuff 51-49 or 52-48… but I think they also may want to move away from full-on obstructionism. Certainly their distancing themselves from Trump make that seem possible. Anyhow, I started writing on Sunday, and I’m wrapping this up Tuesday evening. There’s definitely a slight edge for the democrats, but it is way too early to tell. Plus, in this instant, the actual lead is split.

(finally posting, almost three hours later, and the lead is still split, but it looks like both Democrats will win.)

  • Will the threatened Electoral College Certification Disruption Amount to Anything? January 6
  • Will there be disruption at the inauguration? I’m asking about scary violence, not peaceful pickets. January 20

When will New York City Schools close?

It’s a weird question, because all of our schools are open. Buildings are closed. And all of our high school buildings and middle school buildings are already closed. And many elementary school buildings are (temporarily) closed.

But yesterday Cuomo announced, for all practical purposes, that he would never shut our schools. And while Mulgrew challenged him (finally!), the line he drew in the sand was pretty distant.

Nonetheless, there is a new variant of the virus. It is in New York State. New York’s numbers continue to rise. The post-Thanksgiving surge never stopped (only state in the country where it never stopped), and now Christmas and New Years are starting to factor in.

I think it is 50/50 that the rest of NYC’s school buildings will be shut later this month.

By the way, safety is a real issue. But there is another, perhaps more compelling. Opening the buildings sucks up a large amount of our resources, of teachers days, of administrative time, of planning time – but only about 10% of teaching and learning are happening there – the vast majority is happening on line. Many schools chose to teach 100% remotely – and more would have, if the chancellor hadn’t prevented them.

The open buildings are a public relations ploy. It disrupts teaching, and endangers children and adults. We need to make sure that kids have devices – better than what was distributed in the spring. We need to guarantee them internet access, wifi. We need the DoE to find best practices that are occurring on line, to shar them, to promote them. 90% of our reality is remote. And we need real support in the remote world, as do our students. Instead the DoE wastes precious resources for what is essentially political propaganda.

What will happen with the vaccines?

  • How long will it take to get distribution going?
  • What kind of snafus will occur? (We are already seeing some of that in NYC).

When will most people be vaccinated? What about those who don’t want it? (forget the nutso anti-vaxxers – think about people who have a political agenda). And what about people like me, who think it is a good thing, but do not want to be at the head of the line?

  • And, right, do we think the vaccines will work? (Probably)
  • When will we know? (good question – in a month or two?)

When will progressives realize that Biden is absolutely not progressive?

Some of them already know. There will be frustration with health care, with spending, almost from the get go. But it may take the first foreign policy crisis for it to hit home. With Biden we have a return to an aggressive, interventionist foreign policy. No credit for Trump here. He was aggressive, and dangerous. But when it comes to sending in troops, he was no Bush, or Obama (or what Clinton would have been). With some luck it will take a year before we notice – but who knows if we will have any luck.

There is a another subgroup of progressives who will realize earlier – progressive educators. All of us are glad to be rid of DeVos and her privatization schemes. She was awful, although not particularly effective. And Biden did not go with a Democrat for Education Reform, and that is good. We did not want a return to Arne Duncan. But we get a Secretary and an administration that are not going to bring us away from standardized testing, that are not going to move away from test-score linked teacher evaluations. They will not promote charter schools the way the past three administrations did, but nor will they undo the damage already done. Our union’s leadership will be fine with Biden/Cardona, but they are wrong on testing, on evaluation, and on charters. We will find this frustrating. When will we know? If Biden/Cardona reject waivers from testing mandates this spring, there will be a bunch of quickly-disillusioned progressive teachers.

When will people realize that Biden is pretty liberal for a centrist?

The rabid right and Trump’s loyalest followers think he’s a socialist. Not true. But the New York Times and the Centrist Democrats think they got themselves one of theirs. They did, but not 100%. He’s pretty liberal for a centrist. He’s to the left of the last three Democratic nominees. He’s going to push the envelope on what they think is acceptable on spending, on infrastructure, on health care, maybe even on police reform and criminal justice reform.

With all the focus on COVID for now, it might take the Times a while to realize, but before the year is done, they will. With some luck, they’ll be forced to figure it out in the first 100 days. But given the year we just had, I’m not counting on having any good luck.

Will I retire?

That’s a June decision. I don’t want to. But this has been an exhausting year. Leaning? No. But if a buyout came, and the money was substantial, that might make up my mind for me.

Does COVID go out with a bang, with a whimper, or does it make a tactical retreat?

The number of COVID cases in the US is at its peak, and about to go up more. People are indoors, congregating for the holidays, and tired of isolation. But as poor as the prognosis looks for the next few weeks, there is progress. Treatment is far better than last spring, and the mortality rate is far lower. Vaccines have been approved, and are starting to be distributed. It is possible we go from 60 to 0 virtually overnight (not next week, but perhaps late in the Spring?). Biden could declare July 4 a national day of Thanksgiving…

  • Does the weather warm, the vaccines get distributed, and one day, even in March, April or May, all of a sudden, it’s like there are almost no more cases?
  • Or do the numbers go down, and go down, and but does COVID hang around, still a threat, albeit smaller, and then, gradually, over the summer, it gets really low, and it’s still infecting people in September, but there’s no new spike, or surge…
  • Or do the numbers go down quickly, and do we think we have won, only to face a new variant or strain in October?

I think we will keep reevaluating the situation, but we should have a first idea by April, and then real confirmation (or bad news) in the fall.

How will climate change manifest itself in 2021?

I wonder if it will be another crazy hurricane season. 2020 broke records. But who knows? We will see. I’m pretty sure we will see something.

Movie Theaters, Broadway Shows, Sporting Events?

  • When will they return? I’m guessing late spring, or summer.
  • How will they return? Limited capacity? plexiglass between seats?
  • Will I return?

Man, I miss the movies. And Yankees games. And hockey (after another spin around the sun). I miss my students’ PSAL events. And I would go to those – at least the outdoor ones. But the others? I really do miss the movies, but I don’t know.

Are masks and not shaking hands permanent changes?

I have no idea when we will know. I don’t hate the masks – outdoors, in winter, when they actually provide a bit of warmth. And our air is bad. Maybe getting one with a good filter…

But no, no idea. And no idea when we will know.

Will they close school buildings in NYC in January?

January 3, 2021 am31 4:14 am

There are so many issues with the QUESTION!

Schools are open – the question is about the buildings

Notice “school buildings”? That’s because our schools have remained open, and will remain open, for remote instruction.

High Schools and Middle Schools are open –
but those buildings are closed and will remain closed.

Also, high school and middle school buildings were closed before break, and will remain closed for the foreseeable future (probably not up for real reconsideration until February). So we are really only talking about half the schools in NYC. Oh, and also, even if that half are open, as we saw in December, many of them get closed because – well – COVID-19. So maybe we are asking “will they open 30 – 40% of the school buildings in NYC?”

New York State counts funny (their counts are low)

Then there is the New York State guideline – at 9% positive, schools close. The City’s numbers have just climbed past 9%. So will schools be closed on Monday???  Wait a second. New York State calculates the positive rate differently, nd the State’s numbers are still under 6% for NYC. So maybe schools will be open.

Low counting or not, New York State is not doing well

New York State. The Gold Standard in combatting COVID. Well, no. New York was the global epicenter of COVID in April. And today New York is the only state to have new cases keep climbing without a dip since Thanksgiving. That doesn’t mean that Cuomo will admit his failure. He won’t. But it is food for thought.

By the way, the last few days have not made New York State look better:

Things are getting worse, not better.

Can we see how quickly the case rate is rising in NYC?

But that does raise the issue, if NYC says the positive rate is 9.4%, and New York State says 5.8%, but the numbers are going up, what is the trend? Let’s look.

Here are the zipcodes the City says have been over 9% for 14 days (as of last Tuesday)

Here are the zipcodes the City says have been over 9% for 7 days. Notice there’s a few more:

That’s some serious spread between two and three weeks ago.

Here is the map for “the last three days” (December 26 – 29):

That’s now a third of the City.

And finally, just looking at December 29:

That’s almost half the City. This sequence tells us what we already know – the COVID trend in NYC right now is up, and pretty fast.

The New York State numbers lag, but not too much

So if the NY State numbers are at 5.8%, that’s 5.8 and rising quickly. Getting to 9% for the State might be like getting to 13% for the City. Two weeks ago, one zipcode was there. One week ago, 6 zipcodes were over 13%. But now? 24 zipcodes in four boroughs – that’s one seventh of the city. And the Christmas “surge” has just started. Strictly using New York State numbers, the trigger will probably be reached in a week or two.

So that means schools will close? No. Not Necessarily

The trigger point may not be reached.

More worrying, de blasio indicated he might not bother following the rules. And a union spokesperson, hearing de blasio, did not complain.

How do de blasio and the UFT leadership ignore the numbers? They are so clear!

They claim that few cases are transmitted in school. They actually do not know that this is true.

Further, they ignore not the numbers, but a fact:  There are 1.1 million school children in NYC Public Schools – but on any given day fewer than 10% were in school buildings. Few kids? Very little transmission. But de blasio wants to increase five day a week in person schooling.

So, in a City where rates are soaring, the mayor wants to increase the concentration of children and adults, in spaces that mix individuals from multiple households? Yup.

The UFT leadership made the case from as early as June that with a low case rate we had an obligation to try to open school buildings. But with the rate no longer low, they still argue to open buildings. Something is seriously wrong here.

What should we do?

Please point out, gently, that this is insane. This pandemic has cost 26,000 lives in NYC, almost as high as the Spanish Flu a century ago (about 30,000). This pandemic has cost ten times as many lives as 9/11.

Talk to your colleagues. Information is our ally. Talk to your union reps – to your Chapter Leader, District Rep, Borough Rep, VP, and other officers. If they privately tell you you are right, insist that they talk to people up the chain. There needs to be more push back.

I’m not a fan of contacting elected officials – but honestly, today? any option. City Council, State Assembly, State Senate.

Get the word out, get the conversation going. The facts are on our side.


Decoding Puzzle: 1 + 1 + 1 + 1 = 3

January 2, 2021 am31 1:40 am

I found a new way to represent numbers, and multiplication with my new numbers is fine, but addition is a mess. Check it out:

0 + 0 = 1
1 + 0 = 10
2 + 0 = 100
3 + 0 = 20
1 + 1 = 2
1 + 2 = 11
1 + 3 = 101
1 + 4 = 21
10 + 0 = 2
10 + 1 = 100
10 + 2 = 1000
10 + 3 = 10000
10 + 10 = 11
10 + 11 = 20
10 + 12 + 110
1 + 1 + 1 = 11
1 + 1 + 1 + 1 = 3

Yes, these are natural numbers. Yes, addition is defined in the normal way (and is commutative). What’s going on?

Post-Thanksgiving surge is over, except in New York

December 31, 2020 pm31 2:50 pm

For the country as a whole, the surge peaked from December 8 through December 23, with the peak of the peak on December 18:

Notice the spring peak (NY, NJ, CT, MA, CA, WA, etc)  just looks like a little bump. The late-July/early-August peak happened mostly in places that did not see a spring surge (see Florida, below). And the post-Thanksgiving surge looks just like the epidemiologists told us it would.

– – — — —– ——– —– — — –

Except in New York State. In New York State, and only in New York State, the surge was there on December 8, but continues getting worse:

– – — — —– ——– —– — — –

What about New York’s neighbors? (you may want to disregard Vermont, where the rate is extremely low)

It is true that Massachusetts’ rate does not seem to be going down very much, but it is going down a little, and it is clearly not going up. The only one going up is New York.

– – — — —– ——– —– — — –

What about other states in the Mid-Atlantic?

– – — — —– ——– —– — — –

What about other states in New England? (Maine, with a relatively low rate, has plateaued, not gone down)


– – — — —– ——– —– — — –

What about other states with lots of cases?


And it’s not an Italian-American governor thing. Florida looks better than New York.

– – — — —– ——– —– — — –

And what about Wyoming?

Peaked at Thanksgiving.

The outlier is New York State.

Source: Worldometer Info


New York State is currently a rising COVID outlier in the United States

December 30, 2020 pm31 5:21 pm

COVID-19 case rates rose across the country this fall. And, in most cases, those rates peaked. In some states the peak was in mid-November. In others it was late November In others it was early December. In others it was mid-December.

But in New York State the case rate continues to rise.

Right before Thanksgiving Andrew Cuomo held a press conference. He went on and on about how well New York was doing. The big problems, he claimed, were in North Dakota and Wyoming. He said Wyoming three, four, five times. He dragged out the “O” to make it a four syllable word. To make it sound strange. He enjoyed making fun of other people.

At that moment Wyoming had a case rate of about 130 per 100,000, while New York’s was about 25 per 100,000. Now, 25 is not good. NPR has a Coronavirus by the numbers page, and draws data from Johns Hopkins and Harvard. I went to that page, and looked at the heatmap, where they indicate that 25+ indicates unchecked community spread.

It’s a good map, right? But there is a difference between 25 and 130. I made my own map, which I proceeded to update every few days. Look at how that bad rate in the upper plains dissipates, and watch as other regions’ rates rise, and then fall. That pale yellow? That’s still bad, that’s over 25.

November 22:

December 2:

December 12:

December 22:

December 29:

Does New York have the highest rate in the country? Absolutely not.

Is every state’s rate falling? Nope, 49 are falling. New York’s is still creeping upwards.

Oh, by the way. Today’s numbers? Wyoming 38, New York 54.



A counting problem, and a real problem with counting

December 28, 2020 pm31 2:10 pm

How many ways can we give eleven identical candies to four children? it is obviously possible (necessary) for some to get more than others, and there is not even a guarantee that each child gets something.

That’s equivalent to asking how many solutions there are to:

a + b + c + d = 11, a, b, c, d \in \mathbb{N} (including 0 in the natural numbers).

Now, you could give all eleven to the oldest, all eleven to the second oldest,… Or ten to the oldest and one to the second oldest, and ten to the oldest and one to the second youngest… This is going to be a long-ish list. In fact, I chose numbers just big enough that listing them would be an awkward exercise.

Solving the same problem, with smaller numbers, might help. Let’s give three candies to three kids: u + v + w = 3, u, v, w \in \mathbb{N}

Now we can make a list. I’m just writing numbers. 201 means two for the oldest, none of the middle, one for the youngest.

300, 210, 201, 120, 111, 102, 030, 021, 012, 003.

That’s ten ways.

But how do we scale this up?

One way, a common way, is to turn the numbers into a graphic. Lay the three candies out, and like the divider at the supermarket checkout, put in a physical barrier between the first kid’s loot and the second’s.  For 201 we can write ++//+. The pluses represent candies. So this is two candies for the first kid, then a divider, then another divider right away which means nothing for the middle kid, and one candy after the last divider for the littlest kid. If instead we were giving all three to the middle child, that would look like:  /+++/. Nothing for the oldest, all in the middle, nothing for the youngest.

Why are there three pluses? Three candies. Why are there only two dividers? There is one less divider than the number of kids.

So we can restate our problem as: How many arrangements are there of //+++?

Well, that’s a question with a well-known answer: \frac{5!}{3!2!} where 5! would be the arrangements of five things that are all different from each other, and 3! divides out the repetitions of +s and the 2! the repetition of /s.

A small, but important note: Any slash-plus pattern can be converted into kids and candies:  //++//++++++/+ would be 002061. And any candy-kid distribution can be converted into slashes and pluses: 222201 would be ++/++/++/++//+.

We might as well answer the original question. Eleven candies? four kids? That’s all the arrangements of eleven pluses and three slashes: +++++++++++/// which is \frac{14!}{11!3!} which is 364 ways.

– – — — —– ——– ————- ——————— ————- ——– —– — — – –

The April COVID-19 surge took John Horton Conway from us. Otherwise, he might have told us who created the Confederate monument that stands in combinatorics, that we need to take down.

Conway paid attention to credit. While on sabbatical in 2013 I took a Number Theory class with him. His historical tangents were fascinating. He not only knew who had come up with “if and only if” – but over a half century later, he was still a little jealous. And a little annoyed that his “unless and except unless” or some such, which he thought much more useful, never came into popular use. He kept track of politics, too. There was a story about a German mathematician with questionable choices of friends during the war… I often think that I should have ignored the number theory, and instead taken detailed notes on the mathematicians. The gossip-y stuff would have filled a paper, or maybe been the start of a book…

– – — — —– ——– ————- ——————— ————- ——– —– — — – –

My “pluses and slashes,” or “pluses and dividers,” I have been calling them that for a while. I privately chose not to use the more common name. John Horton Conway probably could have told me who came up with the common name – and whether they were being clever, or cute, or political.

In any case, *||**|*** for 1023 is conventionally referred to as “stars and bars” and if not an intentional Confederate monument is at least an unnecessary and unwelcome Confederate reference.

– – — — —– ——– ————- ——————— ————- ——– —– — — – –

I was talking to Sue Van Hattum yesterday, and she had not realized this, and was – rightly – horrified. She posted on Facebook. I told her I would blog about it. Which I am doing.

I checked my shelf. A dozen books on the topic, and only one reference I could find (they may be there, but unindexed). But on the web? All over the place. Lots of guides for secondary school mathematics. Texts in computer science and discrete mathematics. And some lecture notes by college professors.

bars and stars

– – — — —– ——– ————- ——————— ————- ——– —– — — – –

Where next?

  1. Get a new name
  2. Get rid of the old name

I admit that the old name “sounded” nice – it rhymed. And in comparison “pluses and slashes”? Meh. But I’ll take it. A better suggestion would be, well, better. Art of Problem Solving uses Balls and Urns (as well as the other), but that doesn’t really sound better. And it does not translate into this:  ++//++/+. I don’t see balls and urns. I see pluses and slashes. Sue suggested a relationship to 11001101, and there is a one to one correspondence, but the 0s aren’t really dividers, and I’d like to save them for something else.

And no need to wait for 1. before moving on 2. Do them both, simultaneously. Reach teachers, mathematicians, and eventually publishers? This should be easy.


Outsmarted by Michael Mulgrew

December 16, 2020 pm31 6:56 pm

I submitted a resolution to move away from blended learning last month. It was next on the agenda, 3 minutes left in the motions period, and they didn’t even tell me to get ready to speak. Mulgrew filibustered away the full 3 minutes.

So I was going to reintroduce the resolution this month.

Background – The UFT/DoE blended learning plan never made much sense pedagogically. It was going to disorganize teaching when we needed to be more organized than usual.

But until today, the UFT leadership had been strongly committed to blended learning. They adopted it as the union’s position – without ever putting it up for a vote.

So I was going to reintroduce it. But I got outsmarted.

I never got the email to submit a resolution, I thought, so I wrote to Leroy Barr and asked what was up. He told me it had been emailed on Sunday.

Sunday? What? I looked through my old emails. And found it.

The email came on Sunday. I opened it. I did not recognize it as the email to submit resolutions. Bad on me.

Here it is:

See. I got outsmarted.

Consolation prize – for the first time since May I heard Mulgrew raising some doubts about blended (it is at the root of all of our operational complaints. Well, he didn’t blame blended, he blamed the DoE for not being able to implement blended. But that’s just face-saving. This time the problem was blended, not the DoE.)

Sum of the Digits

December 14, 2020 pm31 1:03 pm

A little math puzzle.

I haven’t posted one of these in a while.

Consider the sum of the digits of three-digit numbers. For example, 311, sum is 5. 420, sum is 6. 911, sum is 11.

Try any or all of these:

  1. What is the average sum of the digits of a three-digit number?
  2. What is the most common sum of the digits of a three-digit number?
  3. How many three-digit numbers have the property that the sum of their digits is 12?

Solutions later this week (or in the comments – up to you!)

Representing the 814 - Erie Reader

Which COVID numbers do you check?

December 13, 2020 pm31 2:04 pm

Before Thanksgiving NYS Governor Andrew Cuomo held a press conference where he talked about how low New York State’s COVID numbers were, and how bad the numbers were in other places. North Dakota. Wyoming. He said Wyoming again and again, each time slowly, carefully forming each syllable like he was doing physical therapy for his jaw and tongue. “Wyoming.” He made it sound strange, foreign. I’ve learned that we do not make fun of names. Andrew needs that lesson.

Before Thanksgiving Wyoming had a case rate of about 130 out of every 100,000 residents. New York State had a rate of 25 out of every 100,000. As of yesterday those numbers were 73 and  51.

At Thanksgiving my neighborhood was middle of the pack in the Bronx as far as test positivity – around 3-4%. Today the middle of the pack in the Bronx is over 6%. My neighborhood is at 8.6%.  Brooklyn’s at 5.5% Manhattan’s at 3.0%. Queens at 6.0%. And Staten Island at 8.9%. (actually, these are moving averages from 4 – 10 days ago. To find out today’s rate, I’ll need to check in 4-5 days).

There were 4000 COVID positives in New York City yesterday. Before I go further, a joke:

The Lord Chancellor frantically alerts the English King (English so that I don’t have to translate the story) – “sire, the French are invading!” The King asks “How many knights do I have in my kingdom?” “Three thousand nine hundred and eighty-five sire” “Round them up!” “Four thousand, sire”

Yesterday there were 3985 COVID positives in New York City.

Where I am pulling numbers from?

Indirectly much of this comes from the COVID-19 Dashboard by the Center for Systems Science and Engineering at Johns Hopkins University which clearly is doing a great job. But I have trouble figuring out what I want from there. And for NYC, the source makes more sense. So here are the websites I consult daily:

NYC Health Department of Health COVID-19: Data page. I keep it set at the default (Latest), scroll down to the “Percent Positive and Test Rate of Molecular Testing by ZIP Code” and I look at the map (that comes up first, but also at the table, and at the “By Borough” which gives graphs of positivity rates over time.

I go each morning to a page NPR maintains – Coronavirus Is Surging: How Severe Is Your State’s Outbreak? – and scroll down to a big old honeycombed map of the US. I scroll over each state and see what the latest case rates are. These are those numbers “out of 100,000.” Apples to apples, and the numbers move slowly over time. The data comes from the Johns Hopkins site, but nicely packaged and easier to access.

Finally, I go to the good old World-o-Meter, go straight to the World-o-Meter New York State page, click “yesterday” (because that data is complete) and sort by “new cases.” That brings the five boroughs to the top, which is how I found 3985 for yesterday, which is like 10 times higher than not all that long ago.

I may follow up and explain how I read these sites (some of which is straight-forward, but some of which is not).



Going to UFT Meetings

December 11, 2020 pm31 8:24 pm

There are people with perfect attendance and that’s not me, but I do like going to union meetings, and my attendance is pretty good.

There are four different kinds of United Federation of Teachers meetings I attend. And all of them have changed during the pandemic.

DR Meetings

At my DR’s meetings we have a small group. It’s possible to have real discussion. And when I have very specific issues in my school, I can have a private conversation and get answers. Chapter Leaders meet each other, socialize. Eat. Sometimes we have similar problems. And when the DR makes a point, CLs can give specific examples, reinforce the point, clarify.

During the pandemic the DR meetings have become less rich. Losing the food hurts. Forget the line that food brings people to meetings – it’s true – but it’s the wrong people. Losing food hurts because the quality of conversation over food is generally higher. People focus better, listen better. Losing the social aspect hurts. I talk with who I sit with. And on a zoom? I am on my couch. Is it possible to get specific questions answered? Yes, but… not really in the flow of the meeting. I am better off sending an email or placing a phone call. And chapter leaders do not hear each other.

In August, when there was strike talk, large meetings were organized. They were on zoom. People talked. Communicated in the chat. I think the UFT leadership hated those meetings. Hated hearing voices that disagreed with them. This was not regular opposition people (who are actually fairly disciplined, and follow meeting rules) – but regular members who blurted stuff out. I think, as a result, many UFT meetings switched to no-chat options. My DR did. I don’t know if it was his decision, or if it was an instruction from the borough or 52 Broadway.

So at my DR meetings now, I see who else is there (unless they are on with a phone number). And we can chat via text during the meeting. And he does take questions from members.

Chapter Meetings

My meetings are different. I hold chapter meetings about once a month. The pandemic has, in a strange way, been good for Chapter Meetings. Attendance in normal times is 60-80%. During COVID it’s been more like 75-100%. Almost everyone talks. Everyone is heard. During key moments – for example when we were trying to agree on a reopening plan and trying to get the principal to agree to an exception – almost everyone has participated, actively, with an understanding that we would reach broad consensus before making major decisions – in other words, we heard all the voices, and those voices mattered. I miss the Entemann’s, but the chit chat still happens, the chat is active, and chapter meetings still feel quite social.

Delegate Assembly

The Delegate Assemblies are a different matter. In theory they are the highest decision making body of the United Federation of Teachers. In practice they are theater. Generally all decisions have been made in advance. The leadership hates discussion, and will minimize it. Times when delegates speak are tightly time-limited. The question period had been too short, and was made shorter by the leadership planting questions (items that could have gone in the main report) stealing time from actual questions. At several DA’s I have made motions to extend the question period. Resolutions the leadership wants to pass, pass. When they are not high enough on the agenda, they change the order. Opposition resolutions are prevented from being placed on the agenda by carefully controlled votes.

But the Delegate Assemblies are important. The president’s report might be the same report he gave somewhere else the day before, but for many delegates and chapter leaders, it is the first time they are hearing it. Many take diligent notes. In that theater that is the DA the leadership and opposition often gauge how strong the leadership support is, or how much opposition there is on a particular issue. It doesn’t stop Unity from getting exactly what it wants – but it can modify how much they try to get next time.

They also gather a lot of people. I often go to a DA with a list of stuff I’m going to take care of – check up on something that hasn’t been moving, make a request for a speaker, let someone know how something turned out. Other people reach out to me. When I blogged more, I was often approached by individuals from the leadership who were concerned about the accuracy of something I had written, or who wanted to make sure I knew that an issue I had raised was being addressed, or totally the DoE’s fault.

And socially, they are interesting. People meet. They chat. They talk. Some sit and make snarky comments.

The food’s nothing special – a piece of fruit. But it goes. It usually gets finished.

The pandemic has really changed the Delegate Assemblies. They are via phone. There is no one to chat with, there are no union officers or employees to conduct business with, you can’t sit with your Rep. But I am in touch with people via text and twitter and facebook, and it’s not like being 100% alone. The question period has been extended. That’s positive. And there are fewer planted questions. Also positive. But I wonder, and most of us wonder, if the questions are being screened. Losing the pear? That wasn’t a meal. But there is no opportunity to amend (they’ve revised the rules of order) – and amendments were where quite a bit of interesting stuff happened (not always from the opposition, which tends to put up entirely different motions. Discussion is still limited. Last DA I was victimized by Mulgrew’s filibuster. Weird. I had no idea he felt threatened by one chapter leader suggesting blended learning sucks. In June I spoke well and Unity put up a high ranking speaker to remind the delegates not to be swayed by strong rational arguments. And even with restricting how much they have to hear from delegates, they dare not stop it entirely. The claim that the Assembly is a democratic body is very important for the union leadership. And for the rest of us, there is a chance of speaking. With the electronic vote totals, you get the actual amount of support/opposition on a given question. And it still is, formally, the highest decision making body. I dare not skip it.

High School Division Meeting

When I first started, John Soldini was HS VP, and there were maybe 100 high schools (and 100 high school chapter leaders) in the UFT. It seemed to me that most of them attended John’s meetings. The high school division concentrates opposition (the reasons for that are complicated, and deserve a separate post, maybe a few, and some serious discussion and input from others). In any case, John’s meetings were boisterous affairs, as he held his own among chapter leaders, half of whom had voted for him, half against him (roughly). Information got out, objections were heard, arguments were had, people ate something, and went home. Tell you what, everyone paid attention.

The high schools got broken up into mini schools, and we got to 200, 300, 400, and now 450 high schools. The break ups had a complex combination of causes, but one reason Unity signed on so hard at first had to do with breaking up concentrations of opposition. Later, as the DoE announced school closure after school closure, the UFT’s Unity leadership made schools fight as a school against closure, rather than fighting closure as policy, for the same reason.

Before this reached its peak Soldini retired and the next guy was a one term place holder, but after him, Unity put in the equivalent of BESE or PROMESA, an insufferable VP, hostile to high schools, who did his best to destroy the division. Meetings were worthless. Attendance plummeted. I recall Chapter Leaders being outnumbered by staff and paid reps at meeting after meeting. Yes, I was one of the few CLs who bothered to regularly show. I remember one, at 52 Broadway, with four Bronx HS chapter leaders, and NONE from any other borough, with maybe 17 people in total. If any of you are reading this, it was me, Alan, Sam, Zulma. Miss you guys.

So when Janella Hinds became VP, even without majority support in the high school division, things had to be better. And she was smart and engaging, and not afraid of conversations, even when people disagreed. It was worth doing work to build the high school meetings. And they did improve. But it was hard to maintain. Rotating half the meetings into the DR meetings in the boroughs was a smart idea. But even I travelled to them less often (I made one in Staten Island. Just once.) Those meetings brought together interesting people – in a large enough meeting for some back and forth, but small enough that people got a chance to talk. There was information. Questions really got answered. Food was ok. Conversations were good. In the last few years, however, I found myself attending fewer.

I went to a pandemic high school meeting yesterday. No food, of course. And chat was disabled, not a surprise. But we could not even see who else was attending. There were several presentations… and while there was an opportunity to ask a question IN WRITING there was none to speak, none to engage with each other. I tried texting people who I thought might be there. They hadn’t joined, or they left in boredom.

We listened as panelists spoke to each other. They spoke about virtual content and virtual content specialists. I did learn how central Blended Learning is to what the UFT is doing today. The Mayor announced he wants more kids 5 days in person, and keep others remote, and fewer blended. Even the writer for the Times wrote this week that shuffling between in person and remote was awkward. But at the UFT HS meeting no one who was allowed to speak was drawing back from blended; they were doubling down. Perhaps my suspicion is not correct, maybe the UFT leadership did not propose blended to the DoE back in May or June. But in any case, they are 100% on board today, more than Tweed is. More than City Hall is.

I should have signed off. But I was in the kitchen cooking, and did not want to miss if the webinar turned into a meeting. “We’ve heard what you said” “We would like to engage in conversation” and “We want to talk to all of you” were phrases, addressed without irony, at an entirely muted audience.

It felt like being a captive audience for an infomercial. I waited until the end. And then I felt dirty for having been there.




Stunningly Oblivious

December 7, 2020 am31 11:47 am

On Thursday, November 19, all school buildings (NYC public schools) were closed.

Today, December 7, New York City elementary schools buildings are reopening.

This is not because the situation has gotten better. It has gotten worse. Much worse. There is a huge wave of COVID moving across the United States. The case rate in NYC was 3% when buildings closed. The case rate today is over 5%. Hospitals across the country are reaching capacity. Cities, states, regions are bracing for shutdowns. Indoor gatherings are being restricted. Outdoor gatherings are being restricted. New Jersey yesterday imposed a 25-person maximum on outdoor gatherings.

Not everyone is reacting with proper concern. Many Trump supporters are refusing social distancing and masks. In NYC a bar owner was arrested yesterday, not for flouting public safety (which he had done) but for trying to run down a deputy who was enforcing COVID restrictions. And there are some restrictions in place. But more are needed in New York State. And Andrew Cuomo has dithered. As the surge begins he has avoided updating the state’s color zones. And in NYC Carranza, de Blasio, and Mulgrew are sending children and staff back into schools.

We know that the virus spreads in schools. Masks, conduct, ppe can mitigate that spread, but they cannot stop it. I know in my school, in March, one room where a significant number congregated, and several became infected. With more care we can slow the spread. We cannot stop it. Testing is a mitigation measure, not a prevention measure.

But why gather large groups in the first place? They are not bringing school back. Less than a third of students want to attend in person under current conditions (most choose remote learning), and of that 30%, only about a third came in each day before the 11/19 shutdown. That’s 100,000 out of 1,100,000 – Will they magically get the numbers to be better?

Perhaps they will get shorter rotations, with more schools on a daily or every other day schedule (rather than every other or every third). So 50% of the eligible kids. But half the system (6-12) stays remote. And only 30% are opting for this hash anyhow. Someone should get Tweed to release attendance, but today’s insanity probably brought 70,000 or so children into buildings.  We should get the real number. That is maybe 6% of NYC’s school children. Over 90% of our learning and teaching continues to occur on-line, where there is little planning resource being devoted, little media attention, and no COVID spread.

I watched Mulgrew’s press conference this morning.

You would have thought that they had a safe way to reopen all of NYC schools full time. They have a way to bring in one out of every 15 children.

You would have thought there was a cure. They have measures to mitigate the spread.

And you would have thought that we were about to, nationally, take control of the situation. That will come, but in this moment we are facing a rising wave, propelled forward by Thanksgiving gatherings, and about to be accelerated by Christmas gatherings.

Opening schools now? Stunningly oblivious.

Mulgrew Didn’t Do It

December 2, 2020 pm31 2:04 pm

Two weeks ago Bill de Blasio announced New York City schools would be moving to all-remote. A strange story has developed. It is not true

Here is the false narrative: The schools should not have been closed; the schools should reopen; 3% is too low a trigger to close schools; and Mulgrew and the United Federation of Teachers are to blame.

The most prominent proponents of this myth are Andrew Cuomo and The New York Times. And it is a myth. False.

When Mulgrew heard the news he was flummoxed. Astonished. Flabbergasted. Taken aback. The UFT, he said, had fought hard to OPEN the schools. The report that the UFT had set an artificially low trigger for closure, he said, was not true. That 3%? That was the Mayor’s. And, for good measure, Mulgrew added that he would be happier with the Governor’s zone approach (true) and that he himself had suggested that approach in the summer (possibly true. Sounds familiar. I can’t find it in writing.)

But Mulgrew’s short answer: what The New York Times were claiming – false. He didn’t say Cuomo was wrong, because he doesn’t say that, but we know. And I can confirm that Mulgrew was correct.

– – — — —– ——– ————- ——————— ————- ——– —– — — – –

The spring was miserable for students and teachers. The teaching was not even close to what we do in person. And it was really hard on everyone. We were exhausted. We were suffering from all the screen time. We wanted nothing more than to return to our classrooms.  And I was eager to help plan for the return.

When social distancing and space numbers came out, I wanted to help. And I worked on the numbers. And I talked to people. And I realized, nope. Not in NYC, not with these numbers of students, not with such limited space. And, importantly, not with the people we have at the top doing the planning without input from people who are capable of planning (who are not the people at the top).

By early summer I was advocating a remote opening. The City’s blended plans were nuts. (I was predicting they would lead to chaotic situations in the schools – that did not transpire, mostly because, and I did not foresee this, the huge majority of parents refused to send their kids into the buildings). But it wasn’t just the chaos. The blended plans were disorganized. They would disrupt instruction.

I called and organized. Discussed. Met. Blogged. I was fighting, every step of the way, against de Blasio and Carranza.

At first I didn’t get what was going on with the UFT leadership. Mulgrew began every meeting by saying “the numbers” “New York City” “safety” “we have an obligation to open”

With time it became apparent. I was fighting every step of the way against de Blasio and Carranza. And Mulgrew. There had been, formally or informally I do not know which, an agreement. Blended learning, I heard whispers, had been initially a UFT proposal to the DoE.

When we tried to get the union to release members’ opinions – some sort of feedback – some sort of survey – nothing. They didn’t want it. They had already made their minds up.

When the intractable problem of lunch arose we got a note – written in UFT Teachers Center language, explaining how “instructional lunch” was cool.

When the DoE flubbed ventilation checks (and allowed its inspectors to talk to principals) the UFT stepped in. The UFT sent in inspectors – not safety folks, but caucus members. They were instructed not to talk to folks in the schools, inclusing chapter leaders. And they filled in, often partially, some checklist, but they did not declare rooms fit or not fit to be used.

As July rolled into August members were getting edgier. There were more obvious problems in the “plans” and more obvious gaps in safety. The leadership preferred talking about safety, set some relatively low bars (eg. ppe must be delivered) and began some strike talk (which did not go well).

Mulgrew was doing what he could to handle member restiveness. And the focus on safety (where changes could happen) made a lot more sense for him than on school planning and organizing (which, constrained by “blended learning”, was irreparable.)

And during that focus on safety, de Blasio offered up the 3%. That’s a tighter trigger than anywhere else in the state. It was a gift to Mulgrew, to help him quell member unrest. And it helped a little.

– – — — —– ——– ————- ——————— ————- ——– —– — — – –

Michael Mulgrew has been working tirelessly since at least June to open New York City school buildings.

He has ignored contrary advice. He has avoided soliciting opinions from union members.

He has “explained” questionable City policies such as “instructional lunch” and “blended learning” – and may have even proposed them to the Department of Education.

When the DoE revealed its incompetence (ventilation checks) Mulgrew put his apparatus to work to give the appearance that schools were being inspected.

And yes, when de Blasio proposed 3%, Mulgrew gladly accepted it – because it made it easier to sell a September reopening to a suspicious membership.

– – — — —– ——– ————- ——————— ————- ——– —– — — – –

But when The NY Times and the NY Governor accuse Mulgrew of sabotaging reopening by insisting on a 3% threshold? They are being willfully dishonest. Mulgrew has put reopening before all else – a fact which leaves many members concerned.

Life in Hell

In a twist, de Blasio’s latest screw-up is not his worst

November 30, 2020 am30 1:10 am

Over the last nine months Bill de Blasio has gotten a lot wrong. Almost every announcement has been late, off-base, and off kilter. He kept schools open when they should have been closed, he canceled break when students and teachers needed it, he announced policies without consulting teachers, families, principals, he came up with half-assed “models,” he insisted schools were opening on time, he announced without notice that opening was delayed a few weeks… His pattern – late, without consultation, lacking details, winging it, and – for the most part – wrong, without careful consideration, without real planning, without forethought.

That makes today’s announcement at least a little different. There were a couple of elements that were not completely wrong.

  • Elementary schools come back 12/7. D75 comes back 12/10.

So, those dates are arbitrary. And maybe 3% was a low trigger, maybe not, but all the precents are higher today, and rising. My neighborhood, middle of the pack, is at 4.5%. My school’s neighborhood is over 6%. Announcing return dates now is – I don’t know. Really dumb? But it’s political. He got scolded by the governor and the Times’ education writer, and he’s showing them – full stop. Instead of making the best decisions for our schools, families, teachers, students, he’s showing them. Really dumb.

  • High schools and middle schools are not coming back for now.

Ok, so that is more interesting. Treating different grades differently is something that needed to be considered. I am not taking credit, many people have talked about this, and it’s been done in other countries. But I mentioned it in these pages back in June and July. That’s when it should have been thrown out – not as a directive by fiat, but for discussion by schools and school communities, by families, by teachers, by the union.

There are tricky issues here – equity among families, equity among teachers. In July we could have thrashed them out, talked them through. Now? No discussion, just imposed.

Also, and this is obvious, we are looking in our rear view mirrors at wasted planning time, wasted scheduling time. Organizing schools for remote would have been far easier than what we were forced to do. And the best schedule for remote would NOT have been the same as the schedule we ended up using for blended in many cases. However, when I asked in the programmers group, most programmers (and this is a pretty with-it group) had at least built in a parallel remote schedule, so that when the switch came (and most of us thought it would) we were ready.

There is another kind of wasted planning time: pedagogical planning. Working to organize a solid remote class is different than working on blended. And it is not just methods and content. We need to tailor our teaching to appropriate amounts of screen time. We could have, we should have spent the summer preparing for all-remote, and the fall refining it.

  • In person school gets converted from blended to full-time, as possible.

For most classes, for most students, for most teachers, blended sucks. It is far worse than in-person. And it is worse than remote. So a proposal to drop blended, that’s good, right?

In fact, didn’t I just propose something similar? Less than two weeks ago I wrote a resolution, submitted it, waited my turn, and listened as Mulgrew wasted a few minutes to prevent it from being discussed. What was the key part?

Be it further resolved that the United Federation of Teachers will explore models other than “blended learning” for our schools, including fully in person for certain groups of students and fully remote for all others, and also including fully remote for everyone

Remote for all. Or remote for most, fully in-person for some. Isn’t that what the mayor just proposed?

I proposed “exploring” possibilities – implying that those involved would be part of the discussion. That’s, apparently, not the mayor’s way.

What happens when you act impulsively, make decisions without planning? In this case, two problems emerge:

  1. You confuse people. His message did not say “since so few kids opted for in person school, we think we can move some schools from two cohorts to one cohort and have that cohort in every day while maintaining social distancing” etc. Notice how poorly he explains himself (from 3:15 – 3:55 in this Youtube).
  2. You create gross unfairness and inequity. Five day a week instruction was not on the table this summer when parents chose whether to send kids in or not. Five day a week instruction was not on the table earlier this month when parents chose whether to opt back in. Parents said yes or no, mostly no, to the blended nonsense that de Blasio could not peddle. And now, out of spite, or out of carelessness, de Blasio is taking parents’ – and let’s be clear, mostly Black and Brown parents’ – sensible rejection of blended learning, and saying since you wouldn’t sign up for his blended mishmash, he won’t let you sign up for fully in-person school.

There should have been a process – not rushed – over the summer – where this was worked out. It would have been possible to think about giving families choices. It would have also been possible to think about which grades and which classes should be prioritized.

But fairness and equity go out the window when the mayor responds to political pressure instead of prioritizing the needs of students, teachers, and schools. His plans probably won’t be implemented, but that’s because of the COVID numbers. That’s not a silver lining.



Should we talk about blended learning? Some in the UFT do not think so

November 18, 2020 pm30 6:58 pm

I submitted a resolution to this month’s Delegate Assembly – to move away from Blended Learning. I am attaching the text at the bottom. I submitted as late as possible – five minutes before the deadline – assuming that I would be #14 on the list and it would not come up. I was a bit surprised – there were only two submissions. The Stop Blended Learning reso would come up.

However, with today’s closure, no one is teaching blended tomorrow. And the agenda included a dozen resolutions, and #1 and #12 I really want to vote on (#1, Black Lives Matter, has already passed).

So I was prepared to withdraw the resolution for today. I drafted what I would say:

Jonathan Halabi, Chapter Leader, High School of American Studies at Lehman College. – bear with me for a moment. We really do need to talk about blended learning. All of our members need to be part of that conversation. But we have a dozen important resolutions coming up; I want to get to them all. And, with today’s announcement, no one is teaching “blended” tomorrow. Michael, I’m not making a motion today. Let’s move the agenda.

But I didn’t get a chance to graciously withdraw the reso. The leadership of the United Federation of Teachers filibustered. Mulgrew dragged out the first motion, and added three minutes of commentary after, until the motion period had run out. I cannot recall another time when they killed so much time that only one motion came up during the ten minute motion period. Why is the UFT Leadership unwilling to discuss “blended learning”? We really do need to talk about it. There could have been honest disagreement in July. But today we have experience, and we should be discussing that experience (and probably concluding that “blended” is the worst option for most students, teachers, classes, and schools.

A Call to End Blended Learning

Whereas the pandemic has caused a crisis in our schools, and

Whereas it was incumbent upon New York City to examine ways to open schools, and

Whereas New York City attempted to implement “blended learning” and

Whereas “blended learning” has not proved to be a viable model for most of our students and schools;

Therefore be it resolved that the United Federation of Teachers recognizes that “Blended Learning” has not worked and will communicate this understanding to our partners in the New York City Department of Educaiton and

Be it further resolved that the United Federation of Teachers will explore models other than “blended learning” for our schools, including fully in person for certain groups of students and fully remote for all others, and also including fully remote for everyone, and

Be it further resolved that the United Federation of Teachers will negotiate with the Department of Education to implement models other than “blended learning” in our schools.


Black Lives Matter / United Federation of Teachers Resolution

November 17, 2020 am30 10:42 am

Thanks to Arthur Goldstein for sharing this in advance

Delegates and Chapter Leaders should always, where feasible, receive resolutions, memoranda, etc in advance of a vote. I’m not sure why this does not always happen. Perhaps our leaders are used to dealing with members of their political caucus, Unity, whose members always vote as they are told, and don’t need to see the documents. But perhaps the resolutions for tomorrow’s Delegate Assembly will be sent out early enough in advance (this afternoon or evening?) for us to have a chance to read them before being asked to vote.

In any case, this is a good resolution. I will support it. I am especially interested in the five points at the end:

  1. End Zero Tolerance discipline in schools
  2. Mandate Black and Ethnic Studies in schools
  3. Hire more Black educators
  4. Fund more counselors, social workers, and mental health specialists
  5. Fully integrate our schools with proper and equitable funding for librarians, PSAL sports, and access to technology.

Each of them addresses something that is really necessary today. I am glad to see #3 – not enough of us are aware how Bloomberg/Klein’s policies targeted Black educators, and shifted hiring away from Black educators. My school is working on #2 right now. And frankly, I would put #4 higher on the list. And am I reading 5 correctly, it calls, among other things, for integrating our schools? Wow, completely needed.

Black Lives Matter resolution

WHEREAS, the United Federation of Teachers reaffirms Black Lives Matter, and

WHEREAS, the statement Black Lives Matter means that until people of African descent are treated with dignity, humanity, and respect in all areas of our society and the barriers to their safety and health and full participation in the economy and wealth creation are dismantled, all lives do not matter, and

WHEREAS, our work is grounded in the fight for fairness so that every person we serve achieves their highest good, and

WHEREAS, throughout our history, our union has demonstrated that belief, time and time again, through our collaboration with and support for local and national organizations working toward the equity, access, and empowerment of every student and family we serve, and

WHEREAS, representation of and participation in heterogeneous communities allow each of us to grow in our understanding of the human condition and establish our role in the improvement of our society, and

WHEREAS, anti-Black police violence continues to take place in the United States without accountability; and

WHEREAS New York City represents nearly 60% of NY state’s total population of Black students, and

WHEREAS, we recognize that our students are harmed in our schools as the result of ongoing systemic problems, including segregation, funding disparities, and lack of equal access to academic, artistic, professional and cultural opportunities, and

WHEREAS, we know that these systemic barriers consistently, disproportionately impact Black students; and

WHEREAS, the UFT supports culturally responsive educational practices, including but not limited to, efforts to diversify New York City’s educational staff so that it more closely reflects its student population, and the expansion of Black studies as well as Asian, Latinx, Native American studies programs and LGBTQ history in our Pre-K-12 classrooms, and

WHEREAS, the UFT has supported recruitment, training and retention initiatives including, but not limited to, NYC Men Teach, the NYC Teaching Fellows, the Success via Apprenticeship Program, Today’s Students, Tomorrow’s Teachers, and the Young Men’s Initiative; and

WHEREAS, we are personally and professionally committed to the health and well-being of every student and staff member in our schools; therefore, be it

RESOLVED, the UFT reaffirms our commitment to policies, initiatives and movements that promote respect for and inclusion of Black students and educators and move affirmatively to make it a reality, and, be it further

RESOLVED, that the UFT continues to urge its members to amplify our demand for justice, change and equity by supporting Black Lives Matter at School Week of Action scheduled for February 2021 and other activities in the schools throughout the year and, be it further

RESOLVED, that the UFT will bring the 13 Guiding Principles of the Black Lives Matter Movement* to the entire school year by participating in and sharing resources from the National Black Lives Matter at School Steering Committee’s new initiative, its Year of Purpose; and be it further

RESOLVED, that the UFT will join annually with the AFT, NEA and NYSUT and proactively encourage its members to invest in critical reflection and honest conversation in school communities, for people of all ages to engage with issues of racial justice; and be it further

RESOLVED, that the UFT will call for members to: participate in the planning of community forums and the creation and implementation of age-appropriate Pre-K-12 curricular resources; utilize the Culturally Responsive-Sustaining Education Framework (CRSE); and initiate school and community discussions around the actions needed to affirm racial justice; and be it further

RESOLVED, that the UFT continues to recruit, develop and retain a membership that reflects the demographics of the city in which we work and, be it further

RESOLVED, that the UFT will call for members to: use tools such as the AFT “Share My Lesson” website, including titles such as, Teaching About Bias, Diversity and Social Justice; exchange lesson ideas, instructional materials and resources about these socially relevant topics with one another; use the tools of the NYSUT Civil and Human Rights Committee and of the BLM at School Curriculum at (in the public domain); and share resources from Teaching Tolerance, NEA Ed Justice during Black History Month and beyond, and be it further

RESOLVED, that the UFT reaffirms its past, present and future commitment to providing inclusive educational opportunities including, but not limited to scholarships, community partnerships and events that support the advancement of students of color, and be it further

RESOLVED, that the UFT seeks reapportionment of city and state funds to bring resources into Black communities to foster self-determination and awareness through education, entrepreneurship, home ownership and the means to reverse generational economic disparities and, be it further

RESOLVED, that the UFT proactively engage in the necessary work to dismantle inequities in our systems through its coalition partners so that our students and families have access to employment, affordable housing and quality healthcare and, be it further

RESOLVED, that the UFT will continue to work with local, state and federal elected officials to secure permanent housing for our homeless students and students in temporary housing, and be it further

RESOLVED, the UFT stands in solidarity with Black students and educators as well as all communities of conscience, in the struggle for a more supportive, equitable and fair school system and society, and be it further

RESOLVED, that the UFT will commit to making demands along with student groups such as IntegrateNYC and Teens Take Charge and call on the NYC Department of Education and City Council to work towards undoing systemic racism and in so doing to:

  1. End Zero Tolerance discipline in schools
  2. Mandate Black and Ethnic Studies in schools
  3. Hire more Black educators
  4. Fund more counselors, social workers, and mental health specialists
  5. Fully integrate our schools with proper and equitable funding for librarians, PSAL sports, and access to technology.

When we return from remote…

November 15, 2020 pm30 4:48 pm

Will New York City public schools switch to all remote? Wrong question. First of all, it’s not “will we go remote?”, but “when will we go remote?”. But that’s not the right question either.

When we return from all-remote, how will we return? Because blended learning sucks. There’s the question. In the real universe, in person regular school is best. Remote is bad. But blended is the worst.

Already there are schools that have made their instruction remote, and do academic, emotional and social support in school. There are other schools where students come into the building, and sign onto zoom classes. There are other schools which are blended in name only, where instruction only happens when the kids come to the building. And then there are schools where the teachers are assigned to teach in person AND remote. Many of those teachers will burn out.

Blended, the way Carranza and de Blasio defined it, and the way Mulgrew pitched it, is not the reality in most NYC schools. Didn’t make sense. Couldn’t be.

The hand off between two teachers per class was unrealistic. The erratic in school / out of school schedule is problematic. Curricula were not redesigned for this strange modality. And the agreement to almost double class size for blended remote was ridiculous.

What other options do we have? My question is about what happens when the positive rate in NYC drops back down.

Short version:

  • Expand the RECs
  • Banish Blended. Bring some students in full time. Teach the rest fully remotely.
  • Real PD, practitioner-led, for remote teaching.
  • Lower class size
  • Adjust curricula. Adapt curricula.
  • Expand prep time.
  • Go easy on the kids.
  • Suspend standardized testing.


  1. Expand the Regional Education Centers. “Staffed by DOE employees and community-based organization partners, the centers provide children with three daily hot meals, remote learning time with their teachers, and activities like art, music, and physical education, as well as social and emotional support.” The RECs do not replace school. But the REC centers provide social and emotional support. They provide social interaction. And they free up schools, during this dangerous time, to focus on teaching.
  2. Banish Blended. Didn’t work. Instead of giving 100% of our students (actually more like 28%?) a bizarro part in-school part at-home experience, let’s create something that comes much closer to normal for  our students with greatest need (based on age, ability, or academics), and focus on doing the best we can with remote for the rest.
  3. Return to regular, in person, daily learning for select schools, grades, or groups of students. This will involve a lot of staff, because social distancing demands the groups stay small. Prioritize younger grades and groups of students who most need regular instruction.
  4. Keep entire grades and schools fully remote. The schools already doing this are reporting that fully remote works far better than blended.
  5. Develop real PD for remote teaching. That means teachers who are actually teaching sharing best practices. Some schools have done a good job with this. But Carranza is not chancellor of some schools, he is chancellor of NYC public schools, and he is responsible for ALL of them. That means a mandate for real remote PD, teacher led, across school lines (by District, Affinity Group, Borough, Content Area, Grade, etc). It’s so frustrating that we did not use our time in June for this, or at the start of September. But Carranza needs to create the time.
  6. Return remote class sizes to DoE limits. Better, lower them to 24 across the board, so that a full class (plus teacher) fits on a small zoom screen.
  7. Recognize how hard remote school is on students. Set reasonable screen time expectations and workload expectations.
  8. Recognize how hard remote school is on teachers. Expand preparation time. Minimize non-teaching responsibilities.
  9. Recognize that teachers cannot teach as much, students cannot learn as much, in a remote setting as in a regular setting (both of which, by the way, are better than blended).
  10. Clarify that this year we are not teaching to tests. If teachers are held responsible for standardized test scores this year, they will be forced to press too much work on their students.
  11. The DoE should suspend test-based components of teacher evaluation for this school year.
  12. The DoE should advocate for the Regents to announce that 3 – 8 testing is suspended for the year, now. The Regents are likely to get around to it, but by not making the announcement early, they put unfair curricular pressure on students and teachers.
  13. The DoE should advocate for the Regents to announce that June Regents are suspended for the year, now. The Regents are likely to get around to it, but by not making the announcement early, they put unfair curricular pressure on students and teachers.
  14. Get the College Board out of our schools, and let them take their AP exams, which they will once again make last minute changes to, and once again flub the administration of, with them. (Failing that, the NYC DoE should bill the College Board for administrative costs associated with registering students for the exams and supporting exam administration.)

There’s a question that’s bothering me. Where did blended come from in the first place? The DoE insiders I talk with have insisted that “blended” was not a DoE proposal, but that it came directly from the UFT leadership. They’ve certainly stubbornly defended it. I’d love to hear directly from the UFT leadership.

de Blasio’s Friday the 13th Problem

November 13, 2020 pm30 5:32 pm

Wind the clock back eight months. Friday the 13th. Of March. Bill de Blasio, bluster and fury but no conviction, insists that schools are staying open. It was the wrong decision (soon to be reversed). And, because it was last minute, with a last minute reversal, disruptive. The time for planning was harried and disorganized, and our schools suffered all spring as a result.

Today. Friday the 13th. He’s really still mayor? Parents and teachers and schools should “be prepared” to go remote for a short period of time.

We just finished, by the way parent-teacher conferences. Which came after “Fall Fest” activities (mostly remote) for our students. That was today. November 13. Friday.

Thinking back, our last parent-teacher conferences came after our last “Spring Fest” activities (in person). That was March 13. Friday.

I’m not complaining about moving to fully remote. I think it is necessary. I am complaining about last-minute decisions. I am complaining about the mayor’s lack of planning, and the negative effect that lack of planning has on schools, students, teachers.

I’m also repeating – none of this was necessary. Many of us, probably most of us, knew that the “blended learning” models were a mess. We knew that safety would be an issue. Some of us knew that the quarantining and spread around the Thanksgiving Holiday would be insurmountable.

Blended learning is disruptive. Shifting between in person and remote is disruptive. We need less disruption. We need careful planning. We need a mayor who plans.

And we need to move to remote – Monday sounds good. And we need to stay there until things are actually safe.

What a Lovely Day

November 8, 2020 pm30 5:07 pm

The sun is shining. People are in good moods, for obvious reason. The leaves are still on the trees, but in an array of greens, yellows, oranges, reds…

When we go to school tomorrow (many of us) the windows will be open, allowing the lovely New York City air to fill our rooms, replacing the air we exhale…

If someone is spreading the virus, it gets into the air, attached to droplets and aerosols and all those technical things that really just mean “floating bits of virus.” Now, just because it is present, that doesn’t mean you get sick. That depends, at least partly, on how much is present, and how long it hangs around.

That’s where the lovely weather comes in. Open your windows, and a small difference between pressure inside and outside will move the air. The more times each hour you get a fresh batch of outside air replacing the air you and your students have exhaled, the safer you are.

You are also on the safer side if the number of people in the room with you is low. I hear that only a quarter of NYC students are physically attending school – the majority are learning on-line. And even those quarter – they don’t come every day. They might come every other, or every third, or less. That puts our schools daily somewhere under 10% of capacity – which is pretty good for limiting the spread of the virus.

You can also filter the air. Not really “you” – the school can. But the filters would need to be HEPA or MERV-16, or at least MERV-13 to get the virus out. It sounds like most schools don’t have these. And the schools that do, most have them attached to their air-conditioning systems. But not the heating systems.

It is a lovely day today. Today we do not need to worry about what is about to happen to our classrooms. But we should. In the next two weeks we might have consistently nice weather. We might get lucky. But that luck will not hold for all of November and all of December. It will get cold. AC has already shut down, and heating systems will rev up, and circulate un-filtered air throughout our buildings, including your classroom.

What do we do when it is too cold to open the windows, but too dangerous not to?

Where is the plan?

For his part, de blasio is trying to increase in-person attendance, and increase the risk. Being mayor makes him in charge, it does not make him smart. And Carranza does what he’s told.

There has been a lot of time for the ventilation and filtration systems to be installed. If they have not, then the building is not safe to occupy when it gets too cold to open windows.

We need to rely on the UFT – even though the leadership seems heavily invested in keeping buildings open. If you will have a ventilation problem when the heat gets turned on – bring it to the Chapter Leader, have them escalate the issue within the union. Remind them they have an obligation to keep our students and their members safe. Remind them that even before Labor Day they knew:

“For most schools, maximizing outside air intake and eliminating recirculating air is a short term solution until winter, but with the mild outside weather now it is achievable and needed until the remainder of the MERV-13 filter shipment arrives.”




How Many Kids are Attending NYC Public Schools?

October 27, 2020 pm31 9:11 pm

Should be an easy question. How many kids are in school? Turns out, schools have been “open” for a month, and no one seemed to know how many kids were in them.

Open? Well, in this weird blended/staggered way, with most instruction taking place through Zoom. That includes kids who opted to stay home all the time. Kids who come in every other, every third, or every nth day, and receive half, two-thirds, or n-minus-one nths of their instruction remotely. And kids who come to school, go sit in a room, and log onto their classes.

But the mayor and the leaders of my union say schools are open… And certainly the buildings are open. And some staff are reporting.

So how many kids? On any given day? NYC public schools have 1.1 million students. But lots have opted for remote. Those who are coming into school are coming in every 2nd day, or every third day, or less frequently than that. And some who are scheduled to come in stay home on any given day.

Two weeks back I took a guess: 50 – 110k.

There’s about 1.1 million students in NYC. About half have moved to fully remote. That leaves 550,000. Some schools are on a 2-day rotation, more are on a 3-day rotation. There are others on 4 or more. Call the average 3. That brings us to about 180,000 students each day. 6% of schools have been shut (Red Zone). 170,000. The City has been hiding attendance numbers. I’ve heard that several large schools have gone de facto fully remote. Bronx Science? Stuyvesant? Dozens of kids each day. What’s the real number? 110,000? 80,000? 50,000?

But now the Mayor has filled in some blanks. In person attendance is 82.9%. And 280,000 students are attending school. We still don’t know how many are on a 2-day cycle, how many 3-day, and how many longer. But at least a third are on 2-day and a third are on 3-day.

That brings us to between 90,000 and 105,000 students in NYC school buildings each day. That’s between 8% and 9.5%. When people in charge note that the virus is not spreading in NYC public schools, they don’t mention that the buildings are under 10% of capacity.

Being elected Mayor, or anything else, gives someone an office. It doesn’t confer superior intelligence.

– – — — —– ——– ————- ——– —– — — – –

Apologies for the pause in posting. I’ve been exhausted by the world, by the country, by my city, and by my union.

Quarantined and Disrupted

October 14, 2020 am31 1:54 am

Glanced down at my phone to see who was texting. Today. Middle of the day. It was a former student. Now a teacher herself. Middle school. Why was she texting from work? She’s teaching in person. The text cleared things up.


She was unceremoniously sent home, to quarantine. One of her students is positive.


So she’s already been tested, and with some luck will be negative. But the teacher is home. Class moves to fully remote. They are disrupted. But is this a surprise? They were already doing some weird “in one day, out the next” kind of thing. Maybe every third day? I should ask. And there was weird recorded lessons, or live stream… I don’t know the details. But the class was already disrupted.

Every class in the city has already been disrupted. At best – at best – classes are 50% in person. Every third day is more common than every other day, and there are schools on less frequent rotations than that. Each school is different.

Little side note: this does not mean that each school chose what it thought was best. The DoE’s insistence on a full rotation with daily instruction outside of as well as inside of school, and the UFT’s insistence on “blended learning” straight-jacketed most schools. Some were able to go through the necessary hoops to get “exceptions” accepted – but remember how the first schools that decided they wanted to go remote were shot down? The schools chose, unless the Chancellor wanted them to choose something else.

As September passed, a new disruption developed: many schools offer in building instruction – via the internet. Students, mostly in some high schools, come to school, open a lap top, and zoom into their classes. At least they get a consistent daily experience. Bizarre, but consistent.

Who cares about educational disruption?

The Mayor, the Chancellor, and the UFT President have been focused on getting students and teachers into school buildings. There has not been any serious discussion of how education looks when a child gets to every third class, or has two teachers who may not be talking. I’ve yet to hear of any PD for teachers on how to keep the three parts of a class on the same page, when they are coming different days for the “in-person” lesson.

A fully remote program would be far less disruptive. But the Mayor, the Chancellor, and the UFT President have been focused on getting students and teachers into school buildings.

Maybe the Disruption is Not So Bad (math time)

There’s about 1.1 million students in NYC. About half have moved to fully remote. That leaves 550,000. Some schools are on a 2-day rotation, more are on a 3-day rotation. There are others on 4 or more. Call the average 3. That brings us to about 180,000 students each day. 6% of schools have been shut (Red Zone). 170,000. The City has been hiding attendance numbers. I’ve heard that several large schools have gone de facto fully remote. Bronx Science? Stuyvesant? Dozens of kids each day. What’s the real number? 110,000? 80,000? 50,000?

Disruption is disruption. But at 110, or 80, or 50 thousand – we are not talking about Gotham-scale disruption. We are talking about San Diego, Austin, or Wichita scale.


Normally I’d end with a barb. Another day that. Today I just want my student to be ok.

Commutative? Who Studies “Commutative”?

October 12, 2020 pm31 11:03 pm

It could come in any grade. It could come up in almost any mathematics course in the United States today. But why? What is “the Commutative Property” and why do we study it? Has everyone always studied it?

I may need some help from the mathematicians who read this blog. Which probably means Joel. Maybe Owen. Back in this blog’s  heyday I had literally hordes – maybe 8 or 9 – who peaked in. How far I’ve slipped.

A Little Math (skip ahead)

The real numbers (or, for most of us, “numbers”) are commutative under addition. That means that a + b and b + a have the same value, (assuming a and b are numbers, or, in more technical language, “real numbers”). When people say “The Commutative Property” – and by people I mean People who are not Mathematicians – they mean this fact, which educators label “The Commutative Property of Addition.” They label a similar fact “The Commutative Property of Multiplication,” ie ab = ba. Some teachers also teach students that division and subtraction are not commutative, which is usually fine, but sometimes puzzles children who are still wondering why “five minus seven” is different from “take five from seven.”

There are other properties, and they matter just as much. And they all have longer names, or descriptions, than we remember, or than we usually use. We use shorthand. There’s the Associative Property of Addition for Real Numbers, and the Associative Property of Multiplication for Real Numbers. There’s the Distributive Property of Multiplication over Addition or a(b+c) = ab + ac. There’s a special number called the Additive Identity (that’s just zero) and another called the Multiplicative Identity (that’s just one). And there’s a few more fancy sounding properties for pretty simple ideas like Closure and Zero Product.


Back to Reality

So here I am, last week, teaching kids a but about matrices. We are multiplying them, and I am stalling. This is a new operation, on a new object. They need more practice multiplying, more fluency, before I introduce what comes next. And instead of assigning all the odd exercises, I decide that I will find interesting things to do that will require some multiplying, and give them some practice. And so I decide that we will decide which properties hold for which operations for matrices.

Those would be two by two matrices with real valued entries, but I’m going to stop right there before I bore the both of you who already know this stuff and make the rest of you’s eyes glaze over. But I also stopped right there for the kids.

The Question

Commutative Property? I ask. Why do we study the Commutative Property?

And the clever answer “so that we know 7 + 3 is the same as 3 + 7” is just so wrong, because little kids who can’t pronounce Commutative (communative?) figure that out on their own. And I ask about the other properties, and the attempts to answer are noble, but universally wrong. They don’t know.

Would they be shocked to know that I have really old math books (1880s – 1930s) on my shelf, and that they do not contain the word “commutative”? No, not shocked, and not properly impressed by my old books. Barbarians. But I flip to the place where the properties should be, and I open the index for the books with them, and, not there.

Getting to the Answer

1960 I tell them. 1960 is roughly the dividing line. I type Спутник on the screen. Even the class without native Russian speakers gets it. Sputnik. Horrified to have been beaten into space by this beeping medicine ball, the United States vowed to close the Space Race by adding the words “Associative” and “Commutative” to every preteen’s vocabulary. And by teaching us basic set theory at a very young age. The New Math. Kids got some fancy vocabulary. I did. By second grade I knew what each one of these symbols {⊂, ⊊, ∩, ∪, ⊄, ∈, ∉} meant. I knew them well. I don’t understand why that didn’t get me a job at NASA. Most of my current students did not recognize any of those symbols. Those who’d seen any of them, it was the curly brackets. Or if they’d seen any of the others, it was one or two, and in 8th grade or later.

We do an etymology detour. Who can correct me?  I told them the “S-” in Sputnik is cognate with English “Co-,” that the “-put-” in Sputnik is related to “path” in English, and that the “-nik” means “doer” or “-er” or “person. Thus Sputnik roughly equals “with+path+person” or more naturally, “traveling companion.” If you are good with etymology, I feel shakiest with put~path. Help a fellow out.

One Last Detour

But before I get a chance to ask if Transposition Distributes over Matrix Multiplication, I have students in one class probing further. How could the US catch up in the space race? Wasn’t this “The New Math” thing worth trying? Nope. I don’t think so. The US does just fine going back to its bread and butter when it comes to science and technology – importing scientists. And the kids talked about Operation Paperclip and Werner Von Braun.

The New Math and Werner Von Braun in one discussion? Sounds like a Tom Lehrer playlist. Next week.