I’m ok. But I wasn’t sure this past Saturday.

I hadn’t eaten much, just snacked. Walked to a grocery store – long walk, 2 miles each way, for some exercise.  When I got there, I felt a twinge. Figured it was from not eating. Went away. I shopped. And going home the twinge was back, a bit more insistent.

Got home about 7:30. It was hurting. I ate, thinking it would clear itself up. But no. Badly upset stomach? But aside from the food I just had, my stomach was empty. I tried watching some tv to take my mind off. Couldn’t focus. Tried the bathroom – nothing was helping. Hospital? That’ll be $150, could be for nothing. I’ll wait an hour, I told myself, and if it doesn’t clear up – the hospital. Five minutes later I couldn’t wait, and walked up the street. As I walked I made a mental note of all the extra steps that were being counted. The pain surged and ebbed. But now, at the low end, it was still a “5” on the 0 – 10 scale. And the high end was getting worse. Had I waited another half hour, I don’t think I could have made the walk. The wait wasn’t too bad. There’s a process that kept engaging me with a new person every few minutes. Registration. Then a little wait. I couldn’t sit still. But my pacing was making people nervous. I stepped outside. Then I got called to triage (it had a different name). That was before going to the Emergency Room. Then another quick interview to put me in a category. I think mine was “abdominal pain.” Then a clerk with waivers. Four signatures. I had trouble signing. And then the Nurse Practitioner, who was patient and kind. In the exam area she asked questions. I asked something I’ve never asked before – can I have something for the pain? It was spiking near a 9. I was nauseated. I almost passed out. I was breaking cold sweats. She put an IV in my arm, without drugs, so that it would be ready when they decided which pain med to give me. She also pretty quickly determined that I probably had a kidney stone. The IV drip changed the night. It took only a few seconds to drop the pain, a few more to bring it to a 1, and then 0, and I was pain-free for the rest of my almost 14 hours in the ER. I waited patiently for a CAT scan. There was extra waiting, because they had scheduled “downtime” for their on-line system – somehow that makes sense to do, but I can’t see how. And then it was 1:30. And I sat in the Emergency Room, and waited for results. I tried to drift off. But ER. Beeping. Noise. And now the guy who was moaning and screaming before (I was in too much pain in the previous paragraph to make a note) was playing music, loud music. I asked, not trying to look sad, but succeeding all the same, if there were somewhere, anywhere… And someone took pity (maybe the NP) and sent me to the exam area, where a curtain provided a modicum of a barrier but not much. But the exam table leaned back, and I used my jacket as a hood and a pillow, and got almost coach class quality sleep – maybe an hour and a half over the course of the next 2 and a half. I came out. A nurse brought me two pills. I was confused. One was for prostate function, the other an anti-biotic. I took them, and was ready to look for the NP, when she found me first. The kidney stone was on the CAT, and small enough to pass, but was obstructing something, it looked like I had an infection. The “prostate” med was actually to flush the stone, and the antibiotic for the infection, but the stone might need to removed. That day. She took my weight, and asked about the last time I had eaten. This was for the anesthesiologist. They were serious. Urology had some concerns. They were not positive. And they ordered more blood work (one number was way off when I came in). A urologist came down. She said it might be surgery, it might be another one of two uncomfortable sounding procedures. She was waiting for blood work. And she noted that I had not had a fever, and asked me to go back through some details. She noted that my pain had not returned. And then she left. I alerted some friends and relatives and work about what might be in the cards. And I waited. The shift changed. I got on a stretcher, and got wheeled into a curtained bay. I saw a doctor. I told him what I was waiting for, but he already knew. And then he came back. The white blood cell count was better. He hadn’t seen the number. Urology was considering the non-surgical interventions. And maybe 45 minutes later he came back. The number was way down. Well within the normal range. I should take ibuprofen and lots of water and the two drugs I’d already started, and I could go. Home. So it’s not done. I have to get rid of this stone. But I was being set free. Wait – ibuprofen? Will that do it? Whatever was in the drip last night, that was great stuff, brought the pain from 9 to 0 in no time. Turns out, it was a close relative of ibuprofen. No more questions. I was ready to go. Last stop, Discharge. Turns out, I have a copay. I knew it. If they admit you, the copay is waived. If they don’t, the copay’s a buck fifty. Why should NOT having surgery cost over one hundred dollars? This is a “health care cost savings” agreed to by my union. The high ER copay supposedly is to discourage frivolous use. But you read my story. What was frivolous? Could TelMed have visualized the stone, or the build-up in the kidney? Where else could I have gone to get my abdomen examined? To rule out appendicitis? Should I have gone to Urgent Care (only$50, I think) to have my vitals taken? I almost passed out from pain. Saturday night. Could I have waited until Monday to call my regular doctor?

I only thought for one second about the copay. How about a beginning teacher, with debt? Is the copay high enough to discourage someone at the bottom of our pay scale from making a medically necessary trip to the Emergency Room?

How about we stop calling health care concessions “cost saving changes” and start calling them “life threatening changes”? And then how about we stop making them.

At the New Cubed (NY, NJ, New England) math teachers summer conference that was held at Siena in July, a presenter posed a problem that required finding three numbers that multiplied to make 72. The list included 1, 8, 9 and 2, 2, 18 and 3, 4, 6 and several other triples (groups of three numbers).

So I wondered, could we look at 72 and see how many factor triples it has? In general, how many factor triples does a number have?

“How many factors” – I know that answer. Take the prime factorization, and increase each exponent by 1, and add them. I can explain.

• If the number is prime, there are two factors, the number and itself. If the number is the square of a prime (eg 49), there are three factors, 1, 7, and 49. But after some fussing, we realize that $49 = 7^2$, and that our 3 factors are $7^0, 7^1, and 7^2$ – and extending that, if we have a prime to a power, n, that we have from 0 to n possibilities… which comes out to 0, 1, 2,… , n so n+1 in total.
• If the number has several prime factors, such as 66, we get more factors. For 66, 1, 2, 3, 6, 11, 22, 33, 66, or a total of 8 factors. By examining the prime factorization – 2 x 3 x 11 – we might observe that there are 2 choices for how many 2s (0 or 1), 2 choices for how many 3s (0 or 1), and 2 choices for how many 11s (0 or 1). And 2x2x2 = 8. Makes sense.
• For numbers with more complicated prime factorizations, we combine these rules. $360 = 2^3 \times 3^2 \times 5^1$, so we can include 0, 1, 2, or 3 factors of 2 (4 choices), times 3 choices for how many 3s, and two choices for how many fives. 4x3x2 = 24. Are there 24? 1, 2, 4, 8, 3, 6, 12, 24, 9, 18, 36, 72, 5, 10, 20, 40, 15, 30, 60, 120, 45, 90, 180, 360. Yup.

But how many factor triples? That’s a new question for me. If I try a prime, such as 2, there is only one: 1 x 1 x 2. A square of a prime gives two: 1 x 1 x 49, 1x7x7. A cube gives three: 1 x 1 x 1331, 1 x 11 x 121, 11 x 11 x 11. Pattern? Maybe. A prime to the fourth gives four: 1 x 1 x 16, 1 x 2 x 8, 1 x 4 x 4, 2 x 2 x 4. A prime to the fifth: 1 x 1 x 243, 1 x 3 x 81, 1 x 9 x 27, 3 x 3 x 27, 3 x 9 x 9. And a prime to the 6th: 1 x 1 x 15,625, 1 x 5 x 3125, 1 x 25 x 625, 1 x 125 x 125, 5 x 5 x 625, 5 x 25 x 125, 25 x 25 x 25. Looks good! Let’s generalize. $p^3$ can only be written as $1\times 1\times p^3$ or $1\times p\times p^2$ or $p\times p\times p$ and wait just a minute – we could look at just the exponents – they have to add up to 3. And the answer for 7 will be… 0+0+7, 0+1+6, 0+2+5, 0+3+4, 1+1+5, 1+2+4, 1+3+3, 2+2+3. Eight. That pattern doesn’t work.

And there I leave you, with a bit of an exploration, and a false start.

If you were reading the newspapers this spring, you read a lot of horrible things about our chancellor, RIchard Carranza. It was a constant drumbeat. He hired friends. He demoted white women. He flip-flopped on math. He is responsible for schools doing poorly. He is anti-white. And there are teachers joining the chorus. Amazing, Joel Klein was never treated so harshly.

What’s going on? This is a reaction to Carranza’s proposals on diversity, and the introduction of implicit bias training. This is about race.

I didn’t love the implicit bias training, but it was ok. It certainly was not the horrible anti-white caricature portrayed on the blogs.

The diversity initiatives? Man, there are guys who teach “separate but equal is inherently unequal” about the South, but are cool with segregated schools up here. Not cool. Don’t like the Chancellor’s plans (and some of them aren’t the Chancellor’s)? Where’s yours?

Instead of attacking Brown v Board, the critics attack the chancellor’s mistakes – and many of them are real mistakes. But it’s in the context of going after him on race.

Let me end this note with something I put on a listserve this spring:

I have no interest in defending this Chancellor in general. However, there are two specific exceptions:
1. when Bloomberg supporters criticize him, especially for problems that were caused or exacerbated by Bloomberg/Klein – in those cases the critics need to be called out for hypocrisy, and I do call them out
2. Criticism of implicit bias training. This is strange place for me – I’m not a big fan of this training, but I recognize that the current public critique, clearly from the Post and more politely from others, is hostile to public education and even more so to integration, and I feel a strong need to differentiate myself from those critiques, especially when I criticize the chancellor..
The loudest critics of the chancellor today are those attacking implicit bias training. I do not stand with them. When I criticize him (as I have done over the last year for Regent’s grading policies, class size, keeping too many lawyers, poor communication with schools, empowering lousy principals, etc, etc) I make clear that I am not adding my voice to those who criticized him on race.

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Thursday morning. Friday morning. Saturday morning. Scores of thousands of New York City teachers have enjoyed them, waking and opening their eyes, without being jolted awake by an alarm.

The only sour note? Knowing that, come September, sleep will again daily crash to a halt with the jarring ring, clang, chirp or loud nuisance song that we set for our alarms.

But does it have to?

(Worst alarm ever?  A very loud mosquito buzz.)

Five years ago, on sabbatical, my early class was 10 AM. There was no need for an alarm. Peace!

(you are generally eligible for a full-year sabbatical in the New York City Department of Education after 14 years of service. They are absolutely wonderful. If you are getting close, start looking into it.)

So I stopped setting an alarm. And something interesting happened. I liked getting up at 6:30. Solving the morning Kenkens. Making coffee. Reading a bit. And know what?  Every morning I got up between 6:10 and 6:40. No alarm. My body did just did it.

Sometimes I needed to wake earlier (for a meeting, or an event, or a morning meet-up for a hike). I experimented. My body got me up at the right time.

Did I make exceptions?  A couple of times, for flights. I might have set 5 alarms all year. And, by the way, I usually woke up before the alarm sounded, and successfully disarmed it.

All good things come to an end, as did my sabbatical. September came, but the alarm stayed off. I was fine.

Now, I can be late places, but that is because I dawdle. I don’t oversleep.

Would this work for you? Maybe, maybe not. I have some advantage (man, of a certain age, I do wake up more frequently than you do). But how can you know for sure, unless you try?

Set yourself a wake-up time. Remind yourself of it before you go to sleep. Don’t set an alarm. And see what happens. Repeat. And repeat. And repeat. Until you trust yourself.

I haven’t routinely set an alarm since June 2013. I can’t tell you how amazing that is.

Solution! – I requested a postponement to December 23.

I might follow this post with a little analysis.

I’ve delayed reporting the retiree numbers, because I have problems with the historic numbers. Retiree votes are constitutionally capped. The cap used to be 18,000. Now it’s more. My variety of sources include:

• Capped numbers (official and unofficial)
• Raw numbers (official and unofficial)
• Back-calculated numbers

The totals I am reporting are inconsistently calculated. I don’t know if there’s any sense using them to compare year to year, except as percentages between caucuses. If anyone can help me puzzle this out, I would work with you.

Anyway, imperfect as they are, here are my numbers.

“Functional” as a division requires some explanation. I’ll get some of it right, but I find it complicated. Functional Chapters are organized across schools, by members’ function – or job. Guidance Counselors, Paraprofessionals, Secretaries, Speech Therapists, Occupational Therapists, Nurses, etc.

Are non-DoE chapters “functional chapters”? I don’t know. I do know that when I say “our contract” I am excluding functional chapters – there are separate contracts for other titles.

In any case, since “functional” actually covers a range of titles and locations, lumped together, the votes there are more of a composite, giving guesswork a larger role in analysis.

These numbers look different from the teacher divisions. The total number of votes has not consistently declined. Unity’s totals have not consistently declined. There’s a significant unexplained blip from 2007 to 2010 in raw opposition vote.