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I beat my mother in Scrabble last night. Game was okay. She took an early lead (opened with JIBES for 46), but a few turns in I played UNAWARES for 61, and a little later FRAT for 34 put me in the lead for good.

When I visit my mom, we play. A quick stop is a game or two. A long weekend could be 4, 5, 7. I win more than I lose, but they are good games.

But we have not played. Not since my visit last September, over a year ago, my last visit before surgery. The surgery went well, but it was followed by a stroke.

Sometime last November I noticed a statin on her meds list. I spoke with the doctor – years ago she took herself off statins. She claimed they made her thinking fuzzy. I told the doctor about Scrabble. I am good for 3 out of 5 or even 3 out of 4 when I’m on a roll. But while she was on statins, I won better than 9 out of 10. And she played super-slowly and made mistakes. He removed them.

In December we were talking about recovery. I had questions about mobility, about memory, about the ability to socialize. And about Scrabble. He was hopeful that she will play scrabble with me, but may not be able to compete.  We will see evolution over the next 12-18 months.

But over the next few months, it was not at all clear that the doctor’s assessment would be correct. I cursed that conversation and its false hope.

But turns out, it wasn’t false. I’m sure I’ll win more than I lose. And the margins may be more than 17 points. But I’m thankful we have our Scrabble back.

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I don’t publish recipes because:

1. I don’t cook much and
2. I don’t use recipes

I mean, I have a sense of what foods / herbs / spices / flavors / textures might work together. It’s not nearly as tricky as picking a good math problem, or as incomprehensible as knowing whether or not clothes match.

Anyway, I don’t do sweetened yams, but Wednesday I planned a root vegetable mash that went sideways. So here goes:

Yams – 4 huge ones.
Carrots – or Other Things that go with yams. I chose carrots. Big old loose ones. 3 or 4 of them. Probably the equivalent of a full cello package. Is that a pound? I think parsnips (justalittle) might have worked, but not sure about the sharpness. Celery root would have been a waste. Squash would have been good. But too much work. Pumpkin would have been perfect.* Might have skipped the yams altogether. But Garden Gourmet’s not selling pumpkins this year. Bastards. So yams it is. Yams they are?

Sweeteners.
Bosc pears. Very ripe. Big ones. 4 of them.
Apples. I think these were Cortlandts. Big.
Honey. That was last minute. I was going to grab maple syrup, but the bottle was old and looked icky. And I have the bottom of a jar of honey that I got gifted a year ago (I use it slowly) by the Actual Beekeeper.

Some milk.

Spices?  I was going to skip them. But when the maple syrup didn’t look like a good idea, vanilla.
I guess you could do “pumpkin spices” – cloves, allspice, cinnamon, nutmeg.

Boil the yams for a while, until they are almost soft. Then throw in the carrots for a few minutes to soften them, but not as much. Pull out carrots and yams. Peel the yams. Throw them in the pot. Slice the carrots into slices or chunks (depending on diameter). In the pot.

Core the apples, and peel them. Slice them. Peel (carefully here) the pears, then cut out the bottom little pyramid with the core/seeds. In the pot.

Stir up the stuff in the pot. This was work. let them yams mush as you go. Keep mixing, mushing. Pour in some milk. Pour in some vanilla, if you are going that route. Keep mushing/mixing. I wasn’t sure about sweetness, so I grabbed a super ripe banana and mushed that in, too. Mush mush mush.

I put it in the oven. 350 seemed too high for this one. I tried 320.

After half an hour I looked. It had started to have a nice smell. I pulled it out. Tasted. Mushed mixed a little. The carrots were the firmest thing in there, plus some of the apples. But the apples would cook down. A carrot in yam matrix tasted good, and some of the fruit sweet was in the bite, but not much. I tried another spoon from a different corner of the pot. Same verdict. That’s when I went for the honey and vanilla. I poured a little vanilla. But the honey was my only measured quantity

2 tablespoons of honey

I know that because I poured in one tablespoon. Then I looked, and decided to add another.

Mix mix mush mush. Back in the oven. Maybe another hour. Or a little more.

It was good. The carrots (less sweet) were “floating” in a yam matrix with unidentifiable fruit flavors (apple/pear/banana) and while there was sweetness, it was dinner sweetness, less sweet than the cranberry sauce (but no acid), and far less sweet than the abominable yams with marshmallows on top that my sister asked for (what, no marshmallows?) before declaring mine perfectly good.

*Pumpkin is a good ingredient because the fresh stuff does not show up year round, and it has an interesting texture, and because, if you buy a small to medium sized one it’s pretty easy to get the guts ready for cooking. Take a small-medium pumpkin. It should fit on a plate. Saw it in half along the equator. Yank/scrape out the seeds. Fill the plate with water. put the pumpkin face down in the water. Microwave on high. 5 minutes. Probably not enough. Take it out of the microwave. Is the flesh ready to fall out? Nope? Try another 5 minutes. You might need a third 5 minutes, but that’s the longest it’s ever taken me. And then you can just cook with it.

I apologize in advance for asking such an obvious question; my union’s leaders seem to be getting it wrong.

Last Monday, the day before the midterms, they introduced a “Resolution to Unite with Organizations against the Toxic Political Atmosphere.” at the United Federation of Teachers Executive Board. (I’ve pasted it at the bottom of this post.)

Good and fine, except what they left out – nothing about the hate-mongering coming from the White House. You might think, “minor omission” – except they have a history. They have a history of being afraid of naming Trump.

Right after 2016 election (see the parallel?) they amended a resolution. See if you can guess where Trump’s name had been removed:

WHEREAS, the presidential election targeted communities on the basis of race, ethnicity, sexual orientation, gender identity and religion, and displayed abusive behavior toward women, has threatened the nation’s promise that all people are worthy of respect; and

WHEREAS, the presidential election has outlined an education agenda overtly hostile to public schools and teachers, promising to prioritize vouchers and charter schools at the expense of public schools ; and

They are afraid of naming Trump? Maybe not. Maybe November 2016 they were in a strange panic (many people were). So I raise my hand, and offered to insert the phrase “the provocative rhetoric of President Trump.” We all agree, vote, and go home, right? Not so fast.

The UFT leadership would ultimately vote, in unison, against naming Trump. But they needed to speak against. Normally one of them would rise to explain why they thought this language was a bad idea. But this time? No. They cued a speaker, not an officer, to go up. I was stunned by his words, and did not take notes. But someone did.

“Not the first time these things have happened” – 11 people killed in a synagogue in the United States? Yes, yes it is the first time.
“We don’t want to give him attention” – WTF? He’s got all the attention. He needs to stand accused of fomenting these attacks.
“Happened before and after Trump” – racist hate crimes are on the rise. Willfully ignoring this is offensive.
“People have spread this talk before” – but not from the White House? That makes a difference. A big difference.

And then they voted, and every officer, members of Unity Caucus all, voted not to mention Trump’s hateful rhetoric. This was a party-line vote, even if one or two broke ranks, and a few more party members remained silent in deep embarrassment

Trump’s incendiary attacks on rivals have created fertile ground for those inclined toward extremism. Why are United Federation of Teachers’ leaders afraid of stating this obvious truth? And they needed to use an intermediary? Why are they afraid of speaking themselves about Trump?

Resolution to Unite with Organizations against the Toxic Political Atmosphere

WHEREAS, three acts of hate-filled violence erupted in the United States in October 2018; and

WHEREAS, mail bombs were sent to more than a dozen public figures critical of President Trump; and

WHEREAS, a man with a history of violence murdered two African-Americans at a Kentucky supermarket following a failed attempt to forcibly enter a black church; and

WHEREAS, a man shouting anti-Semitic slurs killed 11 people in a Pittsburgh synagogue; therefore, be it

RESOLVED, the UFT stands with organizations from across the political, religious and social spectrum – from the AFT, the American Civil Liberties Union, the Southern Baptist Convention and the Archdiocese of New York, to the Council on American-Islamic Relations, the Southern Poverty Law Center and Black Lives Matter – in repudiating the rhetoric of hate. The UFT stands with organizations speaking against the toxic political atmosphere that helped give rise to these abhorrent acts.  We extend our deepest sympathy to the families who suffered catastrophic loss in these dire events.

I have not been actively following the “No” side of the contract ratification vote – I thought this one was worth a yes.

But there are over a dozen actual contracts – I often focus solely on the teachers’ contract – but there are contracts for counselors, paraprofessionals, secretaries, and a bunch more.

Voting down a contract is pretty serious business, especially when the therapists knew that the other units were likely to vote Yes.

It is our obligation, all of us, to stand in solidarity with the OTs and PTs. They will need our support.

It is our obligation to understand the issues that led to such a different result than the other units (teachers voted yes over 80% – lower than I anticipated, but still a large margin. All of the units taken together voted Yes by 87%).

Essentially, OTs and PTs are not paid in line with school workers with comparable professional training. By a lot. They are massively underpaid. And at negotiations de Blasio’s people essentially said “we don’t care; we won’t negotiate a correction to this inequity.” The DoE’s position is utterly unacceptable. The OTs and PTs perform critical work in our schools, often under horrible conditions, often without adequate space. They need to be treated fairly.

We must find a way to engage all of the UFT, including those who just approved a contract for their unit, in solidarity with the OTs and PTs so that they can get a swift and fair settlement.

There is an initiative called “AP for All” – it’s packaged as a “leveling the playing field” program. But there’s some issues.

Not every student is ready for an AP-level course. Or perhaps a student is ready, but not for the interesting selection of 2, or 3, or 4 courses offered in their school. Especially in the proliferation of mini-schools in Black and Brown neighborhoods in New York City, required AP with minimal selection can be a problem.

And then there’s the AP itself. Advanced Placement. A course that one day was billed as “college level” – but today is linked to a test. A test owned by The College Board, a kingpin in the US testing industry. The College Board distorts education, forces “teaching to the test,” lives and dies on manipulating students to take one, two, three, many high-stakes, high-cost tests, while picking up none of the cost for the educational and psychological damage they are doing. AP for All?  Meh. I’d rather support someone other than a corporate vulture.

I’d rather support, say, math teachers.

What about “Four Years of Math for All Who Want It”? In too many city high schools, kids run out of math. By, say, passing trig. There’s nothing else. What about requiring schools to offer four years to everyone? I don’t care if the “extra” course is calculus, statistics, solid geometry, personal finance, business math, or number theory. No one should “run out of math” in a city high school. (I was thinking about this while listening to a podcast called “Miseducation” put together by NYC high school students. Some of the voices they interview ran out of math, even though they wanted to take more.)

Four Years of Math for All Who Want It would be a better program. It would benefit all kids. And instead of lining the College Board’s silk pockets, we’d be helping a group that’s actually deserving.

The Tentative Contract Agreement (TCA) has some very important gains. This is a contract we need to vote yes on. And it deals with some issues, but incompletely. And it does not deal with some important issues. There are provisions that we should not care about. And it introduces a major problem. The way it was negotiated is an improvement on previous contracts, but there is still a long way to go.

Note: I am a co-ordinator of the New Action Caucus / UFT – but I am writing here for myself, not my caucus.

First, the very good.

Due process for paras. Before this contract, paraprofessionals could be suspended without pay based on a single allegation. This contract establishes elements of due process for paraprofessionals (pp 10 – 12 of the memorandum of agreement (moa)).

Easy grievances to file. The TCA creates categories of complaints that can be brought to consultation, and if not resolved within five days, go to the district level. This creates five new classes of complaints (along with paperwork) that are functionally grievances, but do not require members to file an individual grievance. The categories are: Paperwork, Workspace, Workload, Basic Instructional Supplies, Professional Development, and Curriculum. (pp 4 – 6 moa)

More Arbitration Days. We get for our purposes more arbitration days by agreeing to use existing days better. 1. Class size grievances will be heard earlier, and resolved more quickly. In practical terms, arbitrators will handle 6 in a day (instead of 1). (moa pp 12 – 16). 2. Salary, LODI, and religious observance arbitrations will be scheduled 5 per day, instead of one per day. (moa p55) The Grievance Department estimates that we will get an additional 140 days that we can use to arbitrate matters that are critical to us.

Process for forcing the DoE to move on stalled arbitrations. Needs no explanation. (moa pp 53-54)

Next, the Incomplete:

Two observations: For most teachers (with an HE, or two consecutive Es) only two observations per year. (16 – 18). Our ability to challenge bad observations is blocked by the state law (which Mulgrew boasts he helped write). And students’ test scores still factor into our observations. We still have a long way to go

No Harassment. Language prohibiting retaliation, with a process that leads to arbitration. Hey, enforcing it will not be easy – but this is the first time we will have such language:

“The Board (“Department” or “DOE”) shall maintain an environment that promotes an open and respectful exchange of ideas and is free of harassment, intimidation, retaliation and discrimination. All employees are permitted to promptly raise any concerns about any situation that may violate the collective bargaining agreement, rule/law/regulation, or Department policy or that relates to their professional responsibilities or the best interests of their students. The harassment, intimidation, retaliation and discrimination of any kind because an employee in good faith raises a concern or reports a violation or suspected violation of any DOE policy, rule/law or regulation, or contractual provision or participates or cooperates with an investigation of such concerns is prohibited.” (p 19).

This does not come close to solving the problem of the abusive administrator, but it is a step in the right direction. We’ve got all these new arbitration days – we have to press Unity to use them to push back on abusive administrators.

ATRs – Placed in vacancies Day 1 (instead of several weeks in.) Salaries won’t count against the school. Mulgrew says we need to keep the pool under 500. I think that’s 500 too many, but these provisions are small positive steps. (38 – 40)

Next, Missed Issues

Abusive Administrator. This is touched on through the anti-harassment language, and implicitly by the increased number of arbitration days. But we need to keep pressing the union to respond to members in schools with abusive admins.

Class Size. Expedited procedures are one thing, but reducing class sizes should be the goal. We need to end the false dichotomy between raises and reducing class size. We need a campaign not based on contract, but on the common good, for reducing class sizes. We should target lower grades, and we should target higher needs districts.

I don’t care deeply about:

There’s a pilot for remote learning. Two classrooms in the Bronx will be videoconferenced with a third, so that AP Physics can be taught in three schools. There will be a pedagogue in each room, and class size is fixed below the normal level. And the experiment will probably fail and not be renewed. (33)

The Bronx Plan, which is for schools in other boroughs, too. This replaces the “renewal” program with one that requires UFT/principal cooperation before a school can join. There is shared decision making, and there may be extra money for some titles. (24 – 32)

Prose Plus is for existing Prose schools. They get to take an annual vote of no confidence in their principal. (32-33)

A+ credits will likely be Teacher Center credits for people trying to get their 30 above. At least 18, for new employees, will need to be these A+ credits. I don’t love the TC making money off our members, but it will be easier to get the 30 above. (19 – 22)

There will be join professional development (teachers + administrators) on how the observations should go. Unity seemed excited about this. For most of us, it’s another PD we don’t want or need. (18)

Chapter Leaders now get incident reports and the safety plan. I thought we already got that. (6-9)

The 13% appealable ratings now include people covered by the S/U system. (18)

There are now more “teacher leadership roles” – I don’t think many will get filled. (22 – 24)

Problems

The pattern was set by DC37, and the money is not great (2%, 2.5%, 3% over 3½ years). This is sub-inflationary – not by a lot, but it doesn’t keep up. For lower paid titles there was across the board money as well, so that some of them do keep up with inflation.

But the pattern is discussed in the Municipal Labor Coalition before the first union negotiates. The membership should have been involved in the discussion, BEFORE DC37’s contract. Agreements at the MLC that bind us later on, during negotiations, should be brought to the UFT membership first.

Health includes unspecified savings totaling \$1Billion over 3 years for all the municipal unions. (not sure what the UFT’s share is) (p3, moa). Again, this was bargained at the MLC, with UFT participation. It should have come to our members. One specific provision we know of is that the right to choose your own health plan will not start until your second year of employment (everyone will get HIP during their first year). We must guard against future incursions on our health care, and block proposals that push the second tier further.

The issue of Unity making deals with the City and the other unions, and presenting them to us done deals (and not taking responsibility) is very serious. We must work to expose this to the membership, and attempt to end this anti-democratic practice.

The Negotiating Committee actually did some of the negotiating this time – that’s a step ahead, although it falls far short of having meaningful engagement at the chapters. A sub-group of regular members did sit across the table from the DoE negotiators – but the real bargaining remained behind closed doors. The contract survey was better written, and Unity acceded to at least one member concern: Unity Bigwigs (including Amy Arundell) had wanted as many observations as possible – but the members wanted the numbers cut. And we did get the number of observations reduced.

People like the idea of an early contract. But if it is early, there should be no rush. The deal was done on Thursday, and delegates were summoned on Friday to a DA, without the MOA being published. The MOA was e-mailed during the meeting, where Mulgrew summarized the TCA. Delegates were asked to vote on a document they could not have possibly read. Unity distrusts the delegates, and some of the delegates, many of whom were at their first DA, felt it, and may have distrusted Mulgrew right back. The No vote at the DA was double on Friday what it would have been on Wednesday, had they given people time to read through the agreement and talk with their chapters first.

Conclusion

This tentative contract has good new provisions, especially due process for paras, reduced observations, and some repairs to our grievance machinery. It also has disappointing salaries, and a dangerous change in our health care. There are issues (class size, abusive administrators) that we need to continue to deal with outside of the contract. And we must challenge Unity’s practice of making deals at the MLC without membership oversight.

Overall, the good far outweighs these reservations. We should urge a yes vote.

This problem is not original, but pushing the solution in this way is fun. Watch, or play along. See if you can figure out what a nice ending might be.

Find a number that is 1 more than its reciprocal

Make sure the audience knows what a reciprocal is:  It’s what you multiply a number by to get 1 as the product, or colloquially, the “flip” of a number. For example the reciprocal of 9 is $\frac{1}{9}$. The reciprocal of $\frac{7}{8}$ is $\frac{8}{7}$.

I usually allow kids to explore in any direction, but for today’s purposes I don’t want that to happen. I’m going to control the investigation.

Get the kids to make some naïve guesses: 1 is too small since the reciprocal of 1 is 1. 2 is too big since the reciprocal of 2 is $\frac{1}{2}$ (and 2 – $\frac{1}{2}$ = $\frac{3}{2}$).

So let’s start more serious guessing. $\frac{3}{2}$$\frac{2}{3}$ = $\frac{5}{6}$, so that’s wrong. But it’s not such a terrible guess. $\frac{5}{6}$ is only a little less than one. We need a slightly bigger number. Add 1 to $\frac{2}{3}$. That will give us something a little bigger than $\frac{3}{2}$.

$\frac{2}{3}$ + 1 = $\frac{5}{3}$. Did that just give us the solution? No. $\frac{5}{3}$$\frac{3}{5}$ = $\frac{16}{15}$,  a little more than 1, but very little more than 1. But that helps us get the next guess. If we add 1 to $\frac{3}{5}$ we will get something very slightly less than $\frac{5}{3}$.

$\frac{3}{5}$ + 1 = can you imagine where I might be leading the students? What would you like the students to notice? What concepts would you like to share with them?

If you comment, mention the age of the children you imagine working with. I’ve been speaking with a few teachers, and we are trying versions of this with 10 year olds, 17 year olds, and everything in between….

I haven’t posted a mathematics puzzle or problem (for kids or adults) in quite some time. I hope there’s someone out there who still likes this.