I got up. Had yogurt, coffee. Went to class. Professor was late. Got out. Found I got a ticket. (took photos, and felt “outraged” but not actually angry. I really wasn’t in the bus stop. And it did not spoil my good, mellow mood). Drove to my other college. Got a good spot, close. Couldn’t find my professor so taped an xkcd to his door (it’s a cryptography class, good comic just came out) went to the comfy chairs, sat down and read, and had an apple. Found professor, hung out in his office while he prepped for our class. Chatted. Went to class. It was mostly math that I knew. Left – got caught in some awful traffic near Sean’s (Chandradat’s) house, trying to avoid the awful traffic on the xBx. Munched pistachios. Rested. Jumped on the train to meet a friend with the same birthday (but only 45) for drinks in Carrol Gardens. Got some appetizers. A coworker was nearby, joined us. We took the train back north. I got home at 11, looked at the computer, and went to sleep.

So there were birthday calls and texts and facebook messages and e-mails. But otherwise, just a nice day.

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NYSUT’s opposition was to NYS implementation, not the Common Core as a whole. Progress, but less than we want.

Yet, they are still dangerous. They are still well-funded. They have access to media, to propaganda. They have influence from Arne Duncan through many state and local education departments. They have institutes and organizations and influential private donors. And they have already changed many of “the facts on the ground” – rewritten laws, broken contracts, attacked pensions, closed schools, opened doors for private charter school operators, test makers, etc etc.

We need to check them as they continue to aggressively assault public education. We must turn back new attacks.

We need to pursue the facts that they have changed, and changed them back. We need to undo their damage. (In NYC, the shorthand version is undoing Bloomberg’s failed legacy).

But importantly, we need to make certain our own allies are on board. Our national unions made awful compromises and concessions to the anti-public education reform movement. They can be brought back, but it will take pressure from below. And we need to take care that they don’t do as Nasser did in Moscow: signal left and turn right.

A month ago the AFT President tweeted opposition to Value Added (a way of judging teachers on test scores). Careful. My local, usually closely aligned to her, has opposed Value Added for quite some time . Instead they support a “Growth Model”. Honestly, the difference is miniscule. But a lawyer chooses words carefully. She didn’t oppose “Growth Models” – and that’s what we should have heard. We have a signal of progress, but no real progress, not yet. We need to keep up the pressure.

(Similarly, I oppose rating teachers on test scores. The AFT opposes rating teachers “primarily on test scores.” You think there’s no real difference?)

This weekend the New York State United Teachers (NYSUT) called for the removal of Commissioner of Education. (The NYSUT Board adopted the resolution, still needs to be adopted by the Representative Assembly this Spring). That’s progress.

The proposed resolution also brings NYSUT in open opposition to the Common Core “as implemented and interpreted in New York State.” That is progress as well. But it is not opposition to the Common Core. Really.

- Opposition to the Common Core would mean that NYSUT was looking to take New York State out of the Common Core.
- Opposition to the Common Core as implemented and interpreted in New York State means NYSUT is looking for NYS to implement Common Core better.

There’s a difference. We would want the former. If they polled members in NY, they’d know we want to dump the Common Core. But they chose, for now, the latter, a half step.

In a similar vein, the UFT called earlier this year for a moratorium on consequences for high stakes exams. We should have called for a moratorium on the tests themselves. Progress, but a half-step.

Let’s recognize what we have: The steps in the wrong direction have stopped. We have half-steps in the right direction. And we have need for much more progress.

It is crucial to our struggle that we get our organizations fully on board. Pressure from below has moved them. Let us state, but not overstate, our progress, as we continue to move forward.

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One area we should watch is “Accountability.” De Blasio’s campaign already promised

“in his first year in office, Bill de Blasio will eliminate letter grades of schools. Overall progress reports will remain available for parents, and educators, experts and parents will be convened to determine if the progress reports are the most effective long-term way to evaluate schools.”

Dropping the letter grades is a welcome change. It provides some immediate relief. But we should expect more relief than just that from “accountability”

The word, in today’s anti-public-education-reform parlance, does not mean what it sounds like. Their version of “accountability” creates scores for schools. (They also will be producing scores for teachers as part of the new teacher evaluation). The NYC Accountability systems involve two parts.

The first is a “Quality Review” where reviewers who may or may not be familiar with your school, and certainly do not work to support your school, conduct an on-site review in less than a week. The result is “Well Developed” “Proficient” “Developing” or “Underdeveloped”. There’s also “Proficient with Well Developed features” and that sort of thing. You know what else has well developed features? Anyway,

The second is a “Progress Report” where the results of the Quality Review are hocus pocus blended with a bunch of statistics, much based on standardized test scores, compared against other schools in a hard to comprehend formula, (and those schools may or may not look anything like your school), a little bit of standard deviations and averaging – and voilà! a number. And then the number is translated to A, B, C, D or F. By the way, the Progress Report formula changes each year. Also by the way, the borderline between A and B and B and C etc changes each year. Also, by the way, none of the versions of the formula ever made sense. Also, by the way, the DoE claimed to be making school closing decisions based on the letters (not true, but scared the hell out of school communities in targeted schools. The DoE had its own secret agenda in selecting schools to close)

So, you should also know, there is Federal and NY State accountability. This stuff, Progress Reports and Quality Reviews, that’s just extra that Bloomberg’s DoE glommed on to harass or terrify schools. But NYC DoE has something like 200 central staff, many of them pricy young lawyers with no knowledge of education, assigned to doing accountability to the schools.

1. Any review or evaluation of a school should be done by the administrators responsible for supporting the school. The evaluator must be responsible to the school (as the principal should be responsible to the staff, students, and parents, as the teacher must be responsible to students and parents, as the chapter leader must be responsible to the members, as the district rep must be responsible to the chapter leaders, etc)

The panic caused by Quality Reviews is quadrupled because it is being done by strangers. They don’t know the school, or the people. They look for oddball things that no one in the school knew they cared about (and often that no one in the school should care about). They have no interest in seeing the schools succeed.

2. All “scoring” of schools should be stopped. Boiling a school down to a number is wrong. (As is boiling down a student to a number). Release reports on graduation rates? Sure. But no cooking up a phony statistic or metric that pretends to rate a school. In other words, the Progress Reports should be ended.

3. The actual educators working in “Accountability” should be given productive work, supporting schools, in other DoE offices. The non-educators working in “Accountability” should be given the opportunity to find more appropriate work outside of education. And the Office of Accountability should be staffed by a couple of people to make sure the reports to the State and Feds are being filed.

So what do we look for?

1. The letter grades on progress reports, de Blasio’s campaign said they would go in his first year. We should make sure they are actually being dumped. This alone will make schools calmer (especially combined with a likely end to arbitrary school closings – which those in targeted schools were led to believe were linked to progress reports. Untrue, but made people crazy.)

2. The campaign promised “*educators, experts and parents will be convened to determine if the progress reports are the most effective long-term way to evaluate school.*” We care

2a. when this committee is convened. Best case, in a month or two, so its findings can be out before the 2014-15 quality review/progress report cycle. Later in the spring, or in the summer would mean that recommendations could be made for 2015-16. This would be disappointing, but perhaps more realistic. On the other hand, if September/October roll around with no committee, we may be in trouble. I do not suppose this is likely.

2b. who is on the committee. Educators, experts, and parents. I could stack that committee with great people, or with horrible people. Who gets named makes all the difference. Watch out that all the educators are actually experienced educators. If there are DoE people who never taught, or were briefly teachers, and not very good, that’s a problem. If “educators” excludes teachers, or only has a token teacher, that’s a problem. On the other hand, if the committee mixes teachers, principals, and superintendents… For experts, anyone from the testing companies would be a real issue, but I expect de Blasio and Fariña to shut them out. Real public education advocates would be great. Does Diane Ravitch have the level of detailed knowledge necessary? I’m expecting some balance here, but we should watch carefully.

2c. Finally, we should expect the blended single score (statistical nonsense) of the Progress Reports to be abolished. That would be best. Perhaps replacing the reports with unfiltered, unaggregated numbers would represent a middle ground.

3. Fariña will be making staff changes, bringing new people in, and getting rid of some of the old. The “getting rid of the old” should have as one of its foci the non-educators working in the Office of Accountability. This has three positive results – cost savings and a shift away from punitive data and increasing the weight of real educators in the DoE. This will be hard to watch, as we don’t usually notice mid-level lawyers slithering out the door. Perhaps we can keep an eye on the headcount. The best outcome here would be to disband the office. We would certainly notice that.

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They are asking for adverse consequences to be rescinded. Notice that this includes both dismissals, and teacher improvement plans. I believe in NYC we have not preserved the right to challenge a D rating that would lead to improvement plan type consequences for the following year.

Also note, the BTU is not waiting for statistical *proof*. They are moving on the first indications that there is discrimination. Also note, every anti-public school reform of the last dozen years, anywhere in the country, has hit Black kids and Black teachers the hardest. And many have hit older teachers disproportionately.

The Boston Teachers Union has filed a grievance with the School Department over its teacher evaluation system, asking school officials to rescind the “offending evaluations and improvement plans” and to stop discriminating against employees on the basis of race, gender, or age.

The union announced the grievance Tuesday morning in its weekly newsletter. The School Department fired back in the afternoon, issuing a press release and posting tweets that called the grievance an attempt to “block reform.”

The clash came months after the union first raised concerns that teachers who were African-American, Latino, male, or older were more likely to be rated “needs improvement” or “unsatisfactory.” Those ratings are the lowest of four possible marks under the evaluation system, which was implemented during the last school year.

The union was swayed in the last few weeks to take formal action after the School Department released an analysis of teacher evaluations that revealed patterns of potential bias based on race, gender, or age.

“The Boston Teachers Union expects and wants great teachers in each classroom,” Richard Stutman, the teachers union president, said. The union “also expects that the School Department will not punish teachers on the basis of race, sex, or age.”

“We are not arguing against good performance evaluation; in fact, we welcome healthy and constructive feedback,” Stutman added. “But the evaluation process must be done in a way that does not discriminate.”

In all, 272 teachers regardless of race, gender, or age received a “needs improvement” or “unsatisfactory” rating last school year, representing 7 percent of teachers. About 30 are no longer in the classroom.

Interim Superintendent John McDonough said it was too soon to determine whether bias or discrimination exists, given that there is only one year of data. He said the School Department, in response to the concerns raised, is devoting more attention to bias prevention.

But McDonough said the union has taken the issue too far, demanding jobs back for poorly performing teachers.

“That is totally unacceptable,” he said. “Under no circumstance are we going to rehire poor-performing teachers.”

Under the grievance, which is dated Dec. 2, the union in its request to rescind the offending evaluations and improvement plans demanded that “affected teachers be made whole.”

Stutman said in an interview that the union has not decided which members would be covered under the “class-action” grievance. But he emphasized that the union is not seeking return of poorly performing teachers, but trying to ensure fair treatment for all.

The disparity in ratings among teachers of different backgrounds was quite wide in many cases. For instance, 9.7 percent of all black teachers received a needs-improvement rating, compared with 4.1 percent of white teachers; male teachers were almost twice as likely to receive that rating as female teachers; and 11.3 percent of teachers 60 and over were deemed needs improvement, compared with 5.6 percent of those in their 20s.

Tension over teacher evaluation is one of two simmering issues between the School Department and the union. The two sides also have been clashing over a School Department proposal to give principals more autonomy in hiring teachers, prompting the union to file a separate grievance.

*James Vaznis can be reached at jvaznis@globe.com.*

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*Fariña’s selection alone sets a better tone. We can expect a different kind of conversation with, for the first time in ages, educators leading both the school system and the teachers union. And tone helps. But Bloomberg did a lot of damage. Where will Fariña start?*

Since before de Blasio’s election there has been speculation about who he might choose to lead the NYC school system. Names, ridiculous, serious, evil, laughable, all floated together. And now, two days away from inauguration, Bill de Blasio is naming Carmen Fariña Chancellor. There will be lots of excitement and speculation and what does she stand for and what does she stand against, etc. etc.

But for us teachers, the Chancellor is someone who makes decisions, who we sometimes agree with, and sometimes disagree with. Part of our work will be discussing with our new Chancellor, and part will be arguing against the Chancellor. And that would have been true whomever was chosen. The Chancellor is the schools’ Chancellor, the Mayor’s Chancellor, not the union’s or the teachers’ or the parents’. We want someone we can work through disagreements with…

In the current national context there will be outside pressure on NYC about testing and evaluation, and about curriculum. We are not an island (well… you know). And so, a month ago, I made a list of experiences and characteristics we would hope to see in a Chancellor (but not a list of political/pedagogical positions). I reasoned that we would work best with and argue most effectively with a Chancellor who spoke our language and shared at least some of our experiences.

There are a handful of people who would have checked all the boxes. Didn’t mean we would love them. We wouldn’t. Be we would be able to work with them. And Fariña checked all the boxes:

- My list: 10 years teacher. (Would be nice if the person had some time with extra responsibility before becoming a principal). 10 years principal. Public school. NYC. Not TfA. Not an anti-public-school-reformer. No one who has done grave harm to our schools.
- Fariña: 22 years teacher, (five years district curriculum coordinator), 10 years principal. Superintendent. Deputy Chancellor. All in NYC Public Schools. Not TfA. Not a testing/reformer. And while I would consider parts of her record mixed, there’s a lot of positive in it, and she certainly did not do grave harm to the system, even while she worked directly under Joel Klein.

I expect that teachers will not fall in love with the next Chancellor. I expect she will do a lot of things we don’t like. But I also expect she won’t be hated, and that she won’t pursue massively harmful reform strategies. And I hope that she will undo all of the Bloomberg destructive policies. And I expect that she will undo at least a few of them.

Fariña’s selection alone sets a better tone. We can expect a different kind of conversation with, for the first time in ages, educators leading both the school system and the teachers union. And tone helps. But Bloomberg did a lot of damage. Where will Fariña start?

Look at structure of the system. Look at curriculum. Look for some de-emphasis of testing. Look at hiring and how excessed teachers are treated. Look for school closings to stop. And look for new colocations to stop. Look for Progress Reports and Quality reviews to be ended or modified and reduced. Look for scores of lawyers and non-educators to be given the opportunity to find gainful employment somewhere else. Look for a housecleaning of high-ranking TfAers and other anti-public-school-reformers. Look for high school admissions, and kindergarten admissions to be remade. Look, over time, for some undoing of noxious changes to chancellors regs. Really, look for everything.

Watch carefully: which Bloomberg damage is undone in the first month? Which Bloomberg damage is fixed by next September?

We should look for progress, and we will find it. We should push for undoing all of Bloomberg’s damage. There will be conversations.

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But was Walcott a bad chancellor? That question should be asked in context, and in comparison. Was he as bad as Joel Klein? How will he compare to whoever comes next?

There is no question that Joel Klein was reviled by parents and teachers across New York City. If the question was “who was more hated?” then Klein wins walking away. Walcott was not personally offensive the way Klein had been. He wasn’t provocative, mocking. He wasn’t hated. But that’s not the question here. Was Walcott a bad chancellor?

Klein really was bad. His disruptive reorganizations took a mediocre system and made it a disaster. He vilified teachers. He engineered the ATR crisis (through budgeting legerdemain, combined with hoodwinking the UFT’s leadership). He screwed up special education. He closed and reopened schools, improving nothing, but damaging communities. He appointed anti-public education reformers to high posts, including many who had barely taught. He helped make teaching a far less attractive job.

As Joel Klein’s damage peaked, he was replaced, first by Cathy Black (tell me again why the UFT did not oppose the waiver for this non-educator to become Chancellor), then by Dennis Walcott. Walcott walked in to the system in the worst shape it had ever been. And every day that passed, it stayed that way. And every day it stayed that way, the damage was deepened. The Board of Education and its schools are a worse place after Dennis Walcott then they were after Joel Klein. Walcott has been the worst Chancellor I have known.

I expect that teachers will not fall in love with the next Chancellor. I expect she will do a lot of things we don’t like. But I also expect she won’t be hated, and that she won’t pursue massively harmful reform strategies. And I hope that she will undo all of the Bloomberg destructive policies. And I expect that she will undo at least a few of them.

Dear Colleagues,

As you know, December 31 will be my last day as Chancellor. I am writing today to thank you for your unwavering commitment to our students and families. Over the past 12 years, first as Deputy Mayor and then as Chancellor, I have witnessed your outstanding efforts to prepare our students to lead this City and our nation. It has been a privilege to work with you.

You are engaged in an undertaking that is both noble and challenging, and not a single day has gone by without my reflecting on the magnitude of our shared pursuit. The phenomenal gains we have achieved are a testament to your expertise, creativity, passion, and dedication. You are the reason we are handing over a system of schools that is far better than when we started. What an accomplishment!

Under the next Chancellor, I am confident that you will remain focused on the critical work you are leading. While challenges clearly remain, I have no doubt that you can take our schools to even greater heights.

Thank you again for helping our students work toward graduating high school with the knowledge and skills they need to succeed in college and careers.

I wish you and your families a healthy, happy holiday and a wonderful new year.

Sincerely,

Dennis M. Walcott

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I know math best. In my 17 years in the system, we have had four sets of high school math state tests – Course I, Course II, Course III, then Math A, Math B, then Integrated Algebra, Integrated Geometry, Integrated Algebra II/Trigonometry, and now Common Core exams.

These changes were primarily political. Even the one that was almost pedagogical (I/II/III —> A/B) was primarily political.

We lurch from one to the next, never stopping to ask: “what should children learn?” “how much should children learn?” “what have children been learning?” We don’t examine the previous curriculum for strengths and weaknesses. (Isn’t Common Core an exception? Not for 9-12 math it’s not. It’s the worst kind of grab bag you could imagine, every topic + the kitchen sink thrown together without rhyme or reason)

We (meaning the people who set educational policy, not really me, and I hope not you) are bad repairmen, raking in $$$ as we perform repair after repair, sometimes we fix things, sometimes we break things, and we need to be stopped.

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One of the released PISA math questions sets up a similar problem – and then does not give even partial credit for a partial geek answer.

Before I share the question, I had every intention of fully ignoring PISA. The results are used to do things like justify attacks on teachers local unions in the US, or to set up charter schools whose kids would never learn to agonize over going with the Geek answer or the normal answer. The test is used to harm us, to create panic over a single data point (is there still a country between Sweden and Russia?)

But I was curious about what the questions looked like. Most of them seemed fine. But here’s the ceiling tile question:

PATIO

Nick wants to pave the rectangular patio of his new house. The patio has length 5.25 metres and width 3.00 metres. He needs 81 bricks per square metre.

Calculate how many bricks Nick needs for the whole patio.

Hmm. The 5 x3.25 patio, there are 5 x 3 = 15 nice squares that could be filled. 15 x 81 = 1215. But now we have a strip a quarter of a meter wide (hate when they have fractional remainders, 1/4, for a metric problem. feels like mixed units), and 3 meters long. We should think about the shape of the bricks.

(by the way, the geek analysis is about to cost me credit).

Since there are 81 bricks to the square meter, the bricks could be little squares. One ninth (yeeks!) of a meter on a side. So two rows of them would be about .22 m, and we would have to get another row of partial bricks to fill our .25 strip (and lead to some wastage. or is it waste?) So it would take 3 x 9 = 27 bricks to complete each quarter square meter, or 27 x 3 = 81 of them to eat up the full remaining strip, so 1215 + 81 = 1296. My first answer. And I would not have gotten full credit. Because I forgot something.

What if the bricks were a different shape? We are tiling square meters, and the problem implies we can do that well. With 81 things – doesn’t that mean we are stuck with rectangles? 1 x 4 rectangles could work. That’s 1/18 of a meter by 4/18 of a meter. With one row long-ways and one row side-ways we could create a strip 5/18 m. wide. 5/18 ≈ .278, and now we are getting somewhere. Now, 54 long-ways bricks (stacked long side against long side) would create a strip 3 m x .22 m, and 14 side ways bricks would put a layer on top that was 3.11 m x 0.56 m, so there still is waste, but much less. 54 + 14 + 1215 = 1283.

And I still don’t have full credit. But now I have an approach to refine my answer.

Imagine bricks 3 m long and 1/81 of a meter wide. 81 of them cover a square meter. 20 of them would be just under a quarter of a square meter, so let’s go with 21 once, twice, three times. That’s a strip 3 m long and 21/81 ≈ .259 m wide, with minimal possible waste. Can’t get a better answer than this. That’s 3 x 21 = 63 + 1215 = 1278 bricks. Perfect answer.

So if the bricks are squares, we need 1296, but as the rectangles get further and further from square shape, we need fewer and fewer, with the minimum possible 1278.

And PISA would:

SCORING PATIO: QUESTION 13

Full Credit

Code 2: 1275, 1276 or 1275.75 (unit not required).

Partial Credit

Code 1: 15.75 (units not required)

OR

1215 bricks for 5m X 3m

(This score is used for students who are able to calculate the number of bricks for an integer number of square metres, but not for fractions of square metres.)

OR

Error in calculating the area, but multiplied by 81 correctly

OR

Rounded off the area and then multiplied by 81 correctly

No Credit

Code 0: Other responses

Code 9: Missing

PISA would give me partial credit, while a Finnish child who was 2 or 3 bricks short of a full load would get full credit.

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Today paired up with this year’s other Pythagoras Day. When does that happen? Nice discussion, gives kids a chance to engage their smarts.

When’s the next one?

How many have they already lived through?

What would make a good PythDay greeting?

How many might they live through? (Hint: is there a highest year in two-digit format that works?) (Query: can we use the four-digit year?)

How can we change the rules?

I’ve played this before. I’ll play it again (skipping a year…)

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I guess you should know that this is my 17th year. I have a Masters. And I’ve collected a bunch of additional credits, but no additional degrees. Probably if we added up the advanced credits, it would be around 30, but I padded that with some credit by examination a few years ago, so in NYC I am closer to 50. Not that those credits matter elsewhere. You should also know that I am on sabbatical this year, so I am not drawing full pay. But for this exercise, let’s pretend I am.

The list includes all the towns and cities in Westchester and Nassau that border NYC, and I’ve thrown in the NYC rates from September 1997, when I started, to boot.

District | Starting Teacher | jd2718 | Top Teacher | (deg, years) |

NYC 1997 | $28,749 | $28,749 | $60,000 | MA+30, 23 yrs |

NYC 2013 | $45,530 | $85,426 | $100,049 | MA+30, 23 yrs |

Yonkers 2010 | $57,772 | $118,709 | $131,016 | PhD, 30 yrs |

Mt Vernon 2009 | $51,540 | $109,616 | $122,275 | PhD, 20 yrs |

Pelham 2012 | $52,931 | $119,308 | $137,433 | PhD, 25 yrs |

New Rochelle 2013 | $54,969 | $119,593 | $131,839 | MA+90 or PhD, 20 yrs |

Great Neck 2013 | $56,829 | $119,270 | $136,856 | PhD, 25 yrs |

New Hyde Pk – Garden City 2012 | $53,620 | $109,140 | $119,702 | PhD, 26 yrs |

Floral Park- Bellerose 2011 | $56,088 | $105,768 | $123,616 | PhD, 25 yrs |

Elmont 2012 | $52,076 | $106,275 | $119,328 | PhD, 22 yrs |

Valley Stream 2010 | $55,574 | $112,362 | $123,510 | PhD, 26 yrs |

Lawrence 2011 | $51,432 | $113,989 | $130,072 | MA+90 or PhD, 30 yrs |

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We played who can get to 12 (by adding 1s or 2s). I wasn’t going for a rule, but my niece was close, so we (sister-in-law helped) got her to discover that 9 was a good number. And so was 3. And my nephew (younger) wasn’t going to discover it, but once his sister announced it, he kind of sort of followed.

We played puppies and kittens (game I learned from Sue Van Hattum. Adopt as many puppies as you like. Or as many kittens. Or an equal number of each. And – here’s a twist – whoever adopts the last furry animal loses). The two kids played with each other (I watched), and while the girl discovered some strategy, it was not a complete solution, and the two seemed to enjoy it.

I broke out some wonderful dice that my games mentor gifted me. Blue dice have the numbers 5 – 10 on the sides. Red dice have 0 – 5. 2cm, wood. I gave my niece one red, and I rolled one blue, and we saw who got higher. I won two or three rounds before she called me on it. Then I gave her two red dice, and him one blue one, and they rolled against each other, sum of the red against the blue. And then I gave her five red dice, and him 2 blue dice, and they both had some quick adding to do. They played for almost fifteen minutes, and needed to be stopped. Completely engaged. (And no, not a fair game. I didn’t calculate the probability, but the expected value favored the younger child. Intentionally, to help maintain interest).

I pulled out some graph paper (1/2 inch) and some crayons. Here I didn’t involve my nephew (I asked him to draw me something), but I drew a rectangle for my niece, 4×3, horizontally oriented. I counted the boxes (12) and the lines on the outside (14). I asked her if she could make another 12 box rectangle. She copied mine. I asked her if she could make a different 12 box rectangle. She drew a 2 unit high rectangle, and counted, and closed it at 6 wide. I asked her to draw another 12 box rectangle. She drew a 6×2, but this one vertically oriented. I asked her to count lines for each rectangle – 14, 14, and 16.

My sister-in-law asked my niece if she could write a multiplication for each rectangle. Not where I was headed. But I understand that it is not obvious to non-teachers that not every encounter with mathematics needs to reach “fruition.” And it was fine, the girl knows a little bit about multiplication, so I sat back, and watched.

Next to the 4×3 she wrote 4 x 3 = 12. Next to the next 4×3 she wrote 4 x 3 = 12. Next to the 6×2 she wrote 6 x 2 = 12. Next to the vertical 6×2 she wrote 6 x 2 = 12, and started to cross it out. My sister-in-law started to speak, to interrupt the process, but I motioned to let my niece continue, and she did. And after crossing out 6 x 2 = 12, my niece wrote 2 x 6 = 12.

I was delighted. My sister-in-law was concerned. She wanted her daughter to see that 4 x 3 and 3 x 4 were the same thing. I did not. I thought the girl was in a good place, was developing a strong sense of multiplication, and would transition nicely, later. So I intervened to assuage her mother’s concerns while only denting, not exploding, her non-commutative model. I turned the paper, and let her conclude that a 4 x 3 could be a 3 x 4 if you looked at it differently. And I asked if 3×4 had the same number of boxes as 4×3. She answered without pausing. And 2×6 and 6×2? Ditto. Right, 4×3 and 3×4 in her mind were different things, with the same answer, and that’s ok.

I dragged out the rectangles challenges by asking if there was a different rectangle with 12 boxes with even more lines. She was stuck, so I drew a 1×12. She carefully counted. 26 boxes. I asked if that was the most, she was not sure, I began to draw 1/2 by something, counting half boxes with her along the way (she was good at counting by halves!), and she was certain that there were more lines. She counted anyhow. My brother, who had only watched part of this, asked if we would ever be done (with the most lines) and she articulated nicely a “keep cutting in half” approach.

Then I taught them Set (or rather, what makes a set. I turn teaching someone how to play Set into an enjoyable game itself. I’ve done this with high school and middle school students for years. The first day we never play). And then I sent them some turn-taking rules that I thought would be better for adults playing with little kids, and kids of different ages playing together. (I played these rules on Thanksgiving, 2 math teachers and a 2nd grader, fun for all).

I never wrote about going to the Math Circle 2013 summer conference a few months ago, at Notre Dame. But I believe my experiences there had some influence on this story.

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Instead, I think I can describe things that would be good, and things that would be problems. And where someone who wanted to look for a candidate might find one.

- Experienced educator. Some real time as a teacher. I’d like ten years, might settle for five without complaint, but five is pushing it. Would be nice if the person had some time with extra responsibility before becoming a principal, but that’s not necessary. Like being an AP, or playing some extra role(s) while still a teacher. Needs to have been a successful principal. I’d like ten years, might settle for five, but that’d be kind of weak. Might have gone on from there in any number of directions…
- Experienced public school educator. And “privately-managed public school” is not a public school.
- New Yorker. An out of towner is certainly not a huge problem, and there are plenty of icky New Yorkers, but all else being equal, a New Yorker is better.
- TfAer? Absolutely not. Absolutely unqualified on the basis of career path alone. Let them run their anti-education think tanks, their testing companies. (quick nod to the TfAers who have turned on TfA. Like this good one. Or that brave one. Good people, not for Chancellor.)
- No active “reformers.” The landscape is littered with anti-public education reformers, jumping from job to job, seeking new cities and communities to victimize. We don’t need one here.
- No one who has personally done grave damage to NYC’s schools.

An experienced educator, taught ten years, principal ten, might have gone on to bigger and better. Worked/works in NYC. Not TfA. Not an anti-public education reformer.

Where should we look?

- Current, long-serving, sitting principals? Would a principal who had never served higher in the bureaucracy be able to handle such a huge system? Probably not, but, with a strong team…
- Someone at the top of the current bureaucracy? The higher we look, the more likely they’ve played the role of an active anti-public education reformer. Plus, at the top today, few have sufficient experience as educators. Suransky and those who have worked closely with him should not be considered. House needs to be cleaned.
- Someone who rose in the bureaucracy, but not all the way up? That gets interesting. How many real educators, with real experience, are there, mid-level. And how many are good people, and good educators? And how many are high enough up to have a handle on running a big system? Some. I think there are some there, and I think it is a good place to look. Just recently 7% of NYC principals signed a poorly considered letter in support of keeping the network structure in place (the networks need to go, the principals were wrong). Leave the letter aside, these principals were writing in support of network leaders who actually support their schools in ways that the schools appreciate. These network leaders, I’m sure there are others, may be a very good place to look.
- Someone who rose in NYC, but left for other educational pursuits? Depends on who, but this might also be a fruitful place to look. One of the names being bandied about is Kathleen Cashin, fits this profile (some people are fans – I’m not wild about her curricular choices – but I’m not naming names, so, enough). Betty Rosa does as well. And I’m sure there are more.
- Someone from outside NYC? Besides the obvious (I just indicated that this is a deficiency), where in the country are there people in education who are looking for jobs, not anti-public education reformers, not TfA? It is possible, but perhaps unlikely.

I’m not picking a name. But I’ll judge the choice against these criteria, as soon as De Blasio becomes mayor and makes it.

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I hear people talking about all the things De Blasio might not do. Sure. And it’s worth saying so… No illusions.

But tomorrow, you know that most important thing De Blasio won’t do? He won’t be Bloomberg. Vote as many times as they let you.

Also, Letitia James. Vote for her, too. Public Advocate. Sometimes they become Mayor.

And also, that casino thing? My union says to vote for it. The money will go for education. Just like the Lotto money… Hmmm. That didn’t happen, did it? And building casinos? To prey on those who are addicted to gambling? Look, if you want to fund education in NY State, tax the rich. They pay much less today than they did under Andrew’s father. Just bring the rates back to where they were. No on One.

As many times as they let you.

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In this post I review what the changes were, and summarize the results. I will follow up with more detail in the coming weeks.

In my school, the “advanced” math group, as freshmen, do one term of algebra (usually harder stuff) in the Fall, and take the first term of geometry in the Spring. 2012-2013 I had both of the off-track sections, and rewrote chunks of what I was doing. More significantly, I restructured the course in a way that seemed to me to be a little radical.

(I clearly miss the classroom. My mind instantly goes to little radicals: me, the square root of two…. puns are better with an audience)

1. Open with an extended logic unit, with proof. Much more than the old Regents Logic. Include extraneous statements. More rules of replacement and rules of inference, and prove the rules before using them. Venn Diagrams and Euler Diagrams and truth tables. Consistency. And indirect proofs. 4 weeks.

2. Have students create their own glossaries/reference sheets. Allow/insist on constant revisions and updates. Allow/insist that the students bring their reference sheets to each quiz and test.

3. Construction. Fully one quarter of the class periods (every Friday) devoted to construction. Some standard construction. A lot of more creative stuff. A set of Michael Serra’s geometry books – a good resource. Students required to have the tools with them at all time.

4. Oddball theorems.

a. Most high school geometry proof is 1. diagram + 2. some given information = 3. prove something that is already obviously true.

b. The other kind of proof is to prove a theorem. The book does this for the students. Or I do it in class. And then we use the theorem. Sometimes the proof of a second version of the same theorem is offered as an exercise. If this were the 1970s or earlier, the students would memorize theorem proofs, and recite them on a test.

But this is wrong! Proving theorems is at the core of what mathematicians do. The students need to be asked to prove theorems. And all the good ones are taken. So I ask students to prove less-known, less-useful theorems. We practice doing the real thing. We talk about the difference between proving a theorem, and doing a proof-exercise from the book. We approach them slightly differently. And we write them differently.

So how’d it go?

1 We covered all the material I intended to cover. Some of the time given over to construction embedded other topics. At other times the experience with construction allowed the students to move through material more quickly.

2 Most students experienced success writing proofs. Students recognized the difference between theorem proofs and ‘exercise’ proofs. Some students were taken with proof by contradiction. One asked if he could use it all the time. (Irony here, on homework in a graduate course earlier this month, the professor asked me to not to use indirect proof where direct proof was easily available)

3 The construction experience was overwhelmingly positive, and added to course, without causing us to skip material. Most students were pleased with what they were able to produce.

4 The logic unit did not detract from the course. However, not all students ‘felt’ the connection between the logic proofs and the geometry proofs.

5 I got resistance from a small number of students to learning things that would not be on the Regents Exam, exacerbated by the difficulty of the material.

6 I polled both sections at the end of the term about what they liked best: Logic, Construction, or “Proof Geometry” – and was surprised to find that one section overwhelmingly preferred geometry, with logic second and construction last, and the other section was divided between geometry and proof, with construction last. This did not seem consistent with how engaged they were during the construction periods.

I will follow up, with much more detail, in the coming weeks.

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Both Yankee fans (one in pinstripes).

Both ended long careers

Both in New York.

And I was at both of their goodbyes. (In fact, I was at Mariano Rivera Day at the Stadium, and then at his last game. I was there when Jeter and Pettite took Mariano out for the last time, which is probably my #1 all time Yankee Stadium moment)

I did not get bobbleheads for either of the 2014 NYC Goodbye M & Ms (I chose to skip the Rivera bobblehead game, and Mendel apparently did not have a bobblehead day. I might have gone.)

I liked both of them from the first time I saw them – Mariano as a shaky starting pitcher. Do you remember – unhittable until the first hit, and then he would collapse? Mendel as a regular at UFT stuff.

I sat in the front rows at their goodbyes. With Fran Miller who got the guards to let her sit in the handicapped seating at the top rail (because her hip was painful), and with Michael Shulman who was friends with people at the friends of Mendel table.

Both got standing ovations, and I stood and applauded. A lot.

But I never met Rivera. I met Mendel. Spoke with him lots of times.

Rivera’s a baseball player. A star. He got paid a lot of money to play a game. He did play it well. But we cheered him on as he entertained us, and as he benefited. We are no longer talking about similarities.

If you don’t know who Michael Mendel is you’ll probably never know who he is. He was a teacher. And he worked for the members (paid by the union.) Now, I might say about lots of people at 52 Broadway that they work for the union, and that would be true. It’s not insulting. Could say it about Michael Mendel. But some people, you always know they are working for the members. Mendel was one of them.

At his retirement dinner, Amy Arundell and Adam Ross emceed. They were really good.

Larry Becker, DoE Human Resources, he killed. Made fun of Mendel for claiming knowledge of rules that were only written down on cocktail napkins or pages torn form desk calendars, and eventually pulled out an actual agreement, framed, written on a page torn from a calendar, with about five more stories and anecdotes in between. The audience howled. You listened to that, and you knew, this guy respected Mendel, he liked Mendel. Not only was delivery sharp, but he must have spent hours writing and revising that speech. You don’t that for just anybody. You prepare for something that matters. For Larry Becker, Mendel mattered.

Weingarten, Mulgrew, and Howie Solomon also spoke. And then Michael spoke.

There were times over the years that I loved what Mendel was saying. He was a lion with the DoE, when he had to be. He got indignant when members were wronged. It offended his sense of decency.

But we belong to different caucuses. There were times he agreed with what I said. And he told me so – and I appreciated that. It is such a nice thing when someone goes out of their way to say something nice. And there were times we disagreed. I remember one time I spoke quite clearly, and opposed to the direction our leadership was trying to take us. Many people were angry at me that day. But the next time he saw me, Mendel came up to me and said “Jonathan” and he may have been wagging his finger a little, “Jonathan, I disagree completely with the what you said, but I wanted you to know that you spoke very well.” Mensch.

And it wasn’t just me. He knew we are on the same side. He knew how to disagree, but also how to say a kind word. He even knew how to apologize, a rare enough skill these days. Remember his last DA? Megan (don’t know if she was TJC or MORE at the time) had presented a resolution a year or two earlier that Unity did not like, but also that was riddled with errors. Mendel took the floor to oppose it, and though there was no danger of losing the vote, he went entirely over the top in attacking and mocking it… And at the last DA he apologized, publicly. Not for opposing the resolution, but for expressing himself in an unfraternal sort of way. Mensch.

There were times he just got it wrong… but even then, he was doing what he thought was best for the members. Even when Mendel raised his voice at me (he thinks he didn’t, but he did), even then, he was “animated” because he thought what I was proposing was bad for the members. I never minded that. I wanted to change what he thought, of course. But how can you mind when a leader is passionate because he cares about the members? I’d rather get yelled at by Michael Mendel then be politely addressed by some of the snakes slithering around the system.

I liked Mendel’s speech.

He defended teaching – as a profession. “I don’t like it when people tell young people not to be teachers” I applauded nervously, because I myself have been waffling on my own advice-giving lately. The teaching part is wonderful, but I worry about how awful the system has become.

He wished for the day when teachers will again decide what to do and how to do it in their classrooms.

He told stories. Funny. Silly. He could have told about going head to head with some of the bozos at the DoE. But the story he chose to highlight is one about a member, a weak man who needed some help, and how Mendel yelled (yelled) at a Board of Ed guy, yelled at him to do the right thing by his employee, and how the Human Resources guy did just that.

Mendel standing up for someone too weak to defend himself.

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