Except in Prose schools.

Now, some Prose schools got a pass on Danielson. They like Prose, some have told me. Honestly, we should all get the pass on Danielson. We should not have to sacrifice our union principals to get a good concession for all the teachers of NYC.

NYC Educator is writing more about Prose. He includes a shameful quote from a former UFT leader:

“PROSE … empowers teachers to make positive change”

It seems that some of our leaders forget that negotiating TOGETHER is a victory. Negotiating as isolated units would be, and is, a loss. But I guess it takes a real commitment to the idea of “union” to understand that.

Or maybe, reading our contract. I quote the contract negotiated between the New York City Department of Education and the United Federation of Teachers:

It is understood that all collective bargaining is to be conducted at Board headquarters level. There shall be no negotiation with the Union chapter or with any other employee group or organization at the school level. It is further understood that there shall not be established or continued in any school a Staff Relations Committee as described in the Staff Relations Plan issued by the Board on October 23, 1956.

No school by school negotiations. This is Article 1, seventh paragraph.

Photo Credit: Kheel Center for Labor-Management Documentation and Archives,Cornell University Library,Group Photo, Placards, Italian Americans, Jewish Americans, Rally

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Sort of. And now much of those decisions are out of their hands. So much so that I left it off my Mayor/Chancellor expectations list.

Bloomberg/Klein/Black/Walcott willfully closed dozens of high schools. I do not know the count, but 50 in all? Is that about right? More? They targeted bigger schools. These schools, whether incidentally, or intentionally, had larger concentrations of veteran teachers. And veteran teachers these days also means more Black and Hispanic teachers. They were mostly places where institutional memory and habit respected much of the language and spirit of the contract.

They also targeted elementary schools and middle schools for replacement by charters. That’s scores more.

Each closure dumped teachers into the ATR pool – dozens and dozens of veteran teachers who face systematic, mandated discrimination.

So new regime in, the annual PEP circus with large numbers of closures at once is over. Though the old regime already shut the biggest targets. And…

1. We are still watching the tail end of phase outs.

2. This year, under NYS pressure two Renewal schools dumped over half their staff (Boys and Girls HS and Automotive HS) – though with a promise of annual (non-permanent) placement for the next few years.

3. Now New York State (Cuomo/Tisch) is now going over the City’s head. They have targeted seven schools (five in the Bronx) for takeover next year. They have targeted an additional 55 schools (27 in the Bronx) for takeover the year after that.

Think of it this way: the Bloomberg closures also came with new schools opening. While many were charter schools, most were NYCDoE schools – so at least the number of teachers entering the ATR pool was near the number of new openings. These Cuomo closings are directly removing the schools from the DoE – those positions will be entirely lost.

This is nothing less than an attempt to break the job security provision of our contract. It is “disruptive innovation” – intentionally creating educational chaos for our schools, teachers, students, communities.

So, did de Blasio / Fariña do ok on school closures? They haven’t aggressively closed schools. But we barely got a break, between lagging phase-outs, the “Renewal” process, and Cuomo’s ill-intentions for next year, and the years after that.

I guess we could ask the mayor and chancellor to more aggressively oppose Cuomo. But what we really need is a real fightback against Cuomo and Tisch, to overturn the horrible changes to State Law, including these state-forced closures, but going back to basing teacher evaluations on test scores. We need our union, the UFT and NYSUT, to mobilize our members, both through demonstrations, and at the ballot box. But this requires some serious change of policy and practice.

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I think those who are defending them are wrong.

I’ll leave out the non-education stuff – that’s more complicated, and while de Blasio has chalked up some pretty big blunders, he’s miles better than the guy he replaced.

But on education, they’ve been in office for a year and a half. They only have two and a half left. I’m not so interested in what they’ve gotten right. Or in what they’ve gotten wrong. I am most concerned about how little they have actually done.

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.

And even with my low expectations, I’ve been disappointed. Here are a few issues that could have been addressed January 1, 2014, and what’s happened with them in the last year and a half.

- Remove Bloomberg/Klein/Walcott cronies. Most of this has happened at the highest levels, but it took a long time, too long. There would have been symbolism in cleaning house in the first weeks, or months. Instead they quietly left, Brodsky just this spring, and there are a few hanging on.
- Get rid of the lawyers. Useless cash drain. Shameful.
- Control “empowered” incompetent principals. Get rid of true problem principals. I see two high profile removals, a handful of sex removals, and minor stuff. I’m looking at this from a teacher’s point of view – these are abusive administrators. But what about from a child’s point of view? These are largely incompetents. And there are literally hundreds in the system – perhaps 200-300 out of 1800 principals. Most are poorly trained, left-overs from Klein. And as far as I can tell, no one has ever looked to see if they are competent to run our schools, to educate children. Where is the hard look at them? Where is the retraining? Where are the removals?
- Progress Reports. Get rid of the stupid letter grades (done immediately when they took office). End the fake preparation for dog and pony Quality Reviews. Not done. End the reviews by strangers. Not done.
- Funding. End the system of “charging” salary against school budgets. This system distorts the transfer process by rewarding principals for appointing less experienced teachers, and rewards them most for making a new hire (which adds a new cost of $60k or so to the system) instead of taking a transfer, which adds no new costs. It hurts schools, and students, depriving them of seasoned educators, and adding instability to many schools in poorer neighborhoods. This system has been kept in place, with no hint (yet) that they are even looking.
- Return to districts, with superintendents responsible for their schools and their principals. Disband the networks. These borough support centers or whatever they are called are a half step. And they retain some of the “networky” feel. As far as superintendencies, high schools got screwed. The high school superintendencies when I started, in the 90s, provided some real support (including in content areas), and had a real sense of cohesion. Under the new structures, none of this is recreated.

Coming in, de Blasio was more sympathetic than Bloomberg, and Fariña was a real educator, unlike Klein or Black or Walcott. But being a real educator and being a good educator are different things. Fariña’s tenure as a principal was not one that recommended her to us – she pushed good teachers out of her school and brought in more pliant teachers. I do not expect that she will carry out the work that teachers believe needs to be done. But I think it is reasonable for us to expect some progress, more than we’ve seen.

The poster children for lack of progress are the scores of incompetent, abusive principals. And we should press to have more reviewed, retrained, removed. But the reality of the moment informs two other priorities:

- We should be pressing the unit costing issue. The technical piece (this wastes money) and the affective piece (this makes principals bring in less experienced teachers for their kids, and plays out most harshly with the schools with the neediest kids), stand in sharp contrast to the argument for keeping the current system (there is none). A lot of bang for the buck is available – teachers and the DoE working together to save money and bring the best possible teachers to the kids who need them most.
- We should work on cleaning house – particularly the middle level, now that Klein’s tops are gone. I think the swarm of Klein-folk collectively keep his policies in place, sometimes informally, sometimes through foot-dragging, sometimes just through attitude. This is not as easy a sell as unit costing, and one removal hardly would make a difference, but the cumulative effect of replacing dozens, scores, hundreds would be real. And the sell “new chancellor needs to have her own people at the level where policy is implemented” is not a bad one. It would be helpful if some idiot TFAer got caught, publicly, acting under expired Klein/Walcott directives that contradict what Fariña has asked for.

In any case, the lack of progress is frustrating. But it should not move us into denouncing the chancellor. Rather, we should continue to push for progress on issues that matter.

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But they give it headlines that say something else

Concerns mount over tougher Algebra Regents test, and officials promise a review

Responses reflect ongoing uneasiness with the pace of New York’s adoption of the Common Core standards

– that we are concerned about implementation (nope – don’t like CC at all) and that says we are worried about tougher tests (nope, we are concerned that the scoring scale was rigged to make strong students score not so well).

This is advocacy-based journalism. When the facts don’t match the preferred story-line, use the headline to tell a story that differs from the facts.

There have been many people concerned, not just me.

But here’s what I wrote. Here’s what Patrick Honner wrote. You decide.

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Denver to Salt Lake City. Via all or most of: Wounded Knee, Mount Rushmore, Crazy Horse Memorial, Glacier National Park, the Salmon River, Lava Hot Springs, ID.

Cool, huh?

So what should we miss? What shouldn’t we miss? Towns? Museums? Parks?

What’s worth spending extra time in? What should be a quick stop?

Any recommendations on specific places to stay? to eat?

On types of places to stay, to eat?

This should be fun!

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It’s a bit of surprise that it happened today, six months before the first primary, sixteen months before the general election. The AFT Press Release claims that members were engaged in the decision process. That comes as news to me. Unions are organized in locals and chapters… certainly I did not see engagement at that level. But the AFT (and UFT’s) political action wings treat us not as a membership organization, but as a PAC. So I do not doubt that they did an in house poll and some sort of unscientific website survey.

In any case, the question is not about the eventual result – this union’s leadership is clearly pro-Hillary – and not even about the lack of process (though it would be nice to at least make a gesture towards asking members).

No, the question is about the timing. So early??? The answer probably has a lot to do with Bernie Sanders’ recent surge in the polls, especially in early Iowa and New Hampshire.

As pundits have pointed out, even if Sanders somehow slips ahead in those two states, they are outliers, he has only the slightest chance at the nomination. But cautious Clinton is taking no chances, especially after 2008.

From this seat, it was nice that Bernie was pushing the race to the left, raising issues of banking and foreign policy and economic policy. It would have been nice to let the campaign develop before an AFT endorsement. Anyone for an AFTers for Bernie?

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This year I had a number of students sit for Common Core, a number for the old Integrated Algebra regents, and a number for both. But I chose to teach as if they would all sit for Common Core. I made very few adjustments to what I usually do in algebra (mostly 1. changing a couple of “function” lessons into a full, rich, challenging unit – starting the discussions with graphs, then moving to applications, 2. tacking on a new stats unit at the end, and 3. leaving an extra few days for regents review.)

I have been doing this high school math teaching thing for a while. I have a pretty good idea of what my students know, and what they don’t. I can tell the difference between short-term memorization, and understanding. I see how they perform on a written test versus during classwork or question and answer sessions. And I had a fairly good idea of the content they would be looking at. And something weird happened. Two things, actually.

Kids who looked like high 80s kids, they got high 70s on the Common Core. I had heard similar reports from around the State, about high performers.

And kids who sat for both exams got virtually identical raw scores (points), but vastly different reported scores. And I heard anecdotally that something similar happened across all of New York City.

Anti-public education reformers (Cuomo, Gates, TFA, Rhee, Pearson, Coleman) claim that common core standards are higher, or that the content is more rigorous. But they are ignorant, lying, or both. Raw scores stayed the same, but reported scores showed large differences. The problem was in the conversion chart. Take a look.

It looks like someone has intentionally depressed scores between 70 and 90, most dramatically between 80 and 85! And it looks that way, because that is exactly what they did. That 5 to 10 point drop? Here it is. Not in the exam. Not in harder content. Not in higher standards. That drop can be found in a new conversion chart.

The exact mechanism is fairly uninteresting, but assuming that you have just read through four pages of this stuff, it would not be right to omit it.

All of New York State uses four performance levels. That’s the way scores on the Elementary School and Middle School tests are reported – 1, 2, 3, or 4. And for high school? We paid no attention to the levels, because we had actual scores, but Level 1 was failing, Level 2 was 55, Level 3 was 65 (passing) and Level 4 was 85 (mastery).

With the Common Core exams, the State amended these levels to cause a drop in scores. They added a Level 5. They set it at 85. And they took the old Level 4, and let the cubic regression set it. It seems to be sitting around a 73. This means a child who was ready to score an 85 on the old test, but who was well-taught for the new test instead, will score a 73. This is not this year’s child knowing less or being able to do less than last year’s child. This is instead New York State directly lowering scores.

Here is how they define the new performance levels:

- NYS Level 5 Students performing at this level exceed Common Core expectations.
- NYS Level 4 Students performing at this level meet Common Core expectations.
- NYS Level 3 Students performing at this level partially meet Common Core expectations (required for current Regents Diploma purposes).
- NYS Level 2 (Safety Net) Students performing at this level partially meet Common Core expectations (required for Local Diploma purposes).
- NYS Level 1 Students performing at this level do not demonstrate the knowledge and skills required for NYS Level 2.

By the way, performance levels are absolutely arbitrary.

I asked about this on the AMTNYS listserve, and received the following response from a professor who was involved in the process:

Jonathan,YES, the state has changed how it sets the scale. I can speak to this as I was a (small) part of the process.Level 4 now means “Proficient in CC”, and this was set by the Commissioner after a recommendation by a group of educators who argued loud and long about what a proficient student should and should not be able to do.Level 5 now means “Exceeding CC expectations”, and this was set in a similar way.The old Level 4 is gone, and it is replaced with these two new levels. The cubic is also gone, and I don’t know everything about the function that fits the rest of the scores. I do know, however, that educators took a hard look at the CC standards and at actual test items to determine which ones should be answered well by proficient students.The new exams are harder and the new standards are higher. We know that the State is closely monitoring the Algebra results because the Class of 2022 is coming soon, and they will need to pass at Level 4.Teachers should be looking at the number of points necessary to hit those cut scores and not at what percent corresponded to what score. The only four scores that really matter are the ones that set Level 2,3,4,5. The fact that a student got an 88 doesn’t mean he knew 88 percent of the material; it means he exceeded CC expectations. The fact that a student got a 62 means nothing except that he is eligible for the safety net.Best wishes to you as the school year winds down.

I had, of course, a snarky response:

Looking at performance levels instead of looking at scores is foreign to us. Just telling teachers to do so isn’t fair, not without looking more deeply.We distrust the state. Sounds like I’m being tough on the State, but it was the State, not the teachers, who changed the state exams, and renamed the state exams, and tweeked the state exams, and changed the state standards again and again and again over the last 15 years. It was the State that has produced at least one bad question out of every three exams published for a decade. The State has earned our distrust.Teachers face kids and parents, regular folks, who know 88, but who don’t know that 4 is the highest, (unless 5 is highest).Teachers also face parents and kids in some districts who score highly and want Regents Diplomas with Honors. http://www.p12.nysed.gov/part100/pages/1005.html#diplomaHonorsA district can “award a student a Regents diploma with honors or a Regents diploma with advanced designation with honors to a student who achieves an average of 90 percent in all Regents examinations required for the diploma.”Notice that, it’s not an average performance level of 4.5, it’s an average score of 90. And that just got tougher.

You can read the entire exchange, here.

And that, patient readers, is that. The State wanted to make Common Core look tough, so they took the old scores between 85 and 100, and stretched them so they are now between 73 and 100. Top kids have lower scores, by design.

Who’s responsible? Andrew Cuomo? Merryl Tisch? Candace Shyer? Steve Katz? Idk.

In Part I we saw how, when Common Core Algebra replaced Integrated Algebra, teachers tried to figure out how to adjust to the change. But even with adjustments, scores for top kids fell. I adjusted, as I had for exams in the past, but kids who seemed prepared for scores in the mid-80s saw scores in the mid- to high 70s instead. Similar reports came from across New York State.

In Part II we saw how kids no longer earn their scores directly. In the 1990s and before, score 85 points, and your score is 85. Since 1999 though, points and scores were untethered. The number of points was reduced to a number between 80 and 90. And for each exam administration a new “conversion chart” is created, that seemingly magically translates points into a score. Importantly, the conversion chart changes every time the exam is given. The number of points needed to passvaries each time the exam is given. The number of points needed to get an 85 varies each time the exam is given.

In Part III we looked at how the Conversion Charts are created.

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In Part I we saw how, when Common Core Algebra replaced Integrated Algebra, teachers tried to figure out how to adjust to the change. But even with adjustments, scores for top kids fell. I adjusted, as I had for exams in the past, but kids who seemed prepared for scores in the mid-80s saw scores in the mid- to high 70s instead. Similar reports came from across New York State.

In Part II we saw how kids no longer earn their scores directly. In the 1990s and before, score 85 points, and your score is 85. Since 1999 though, points and scores were untethered. The number of points was reduced to a number between 80 and 90. And for each exam administration a new “conversion chart” is created, that seemingly magically translates points into a score. Importantly, the conversion chart changes every time the exam is given. The number of points needed to passvaries each time the exam is given. The number of points needed to get an 85 varies each time the exam is given.

But how are these conversion charts created? The crucial element is something that New York State calls “performance levels” – and we have already created mystery for what should be an open process – but let’s go on. New York State numbers students as 1, 2, 3, or 4, and those numbers have names that go with them. In high school we don’t pay too much attention – those are mostly elementary and middle school numbers (I got a 2 on the ELA, but a 4 on the Math!). We think 3 means grade level.

For the first administration of an exam only, the cowardly agents of the State gather educators from around New York, and sit them in a room. They look over the questions, and guess what a level 1 kid would get right, a level 2 kid, level 3, level 4. They assign difficulty levels to each question. The State (or a contractor) examines the results, looks over the real tests, and combines them into a range of possible points that could equate to a 65 (passing) and an 85 (mastery). Then they bring those results to another room, where the cowardly agents of the State have gathered a mix of educators and administrators from around New York, and in that room they look at the percentage of kids who would fail under each scenario, and choose one.

(Cowardly? The data, as presented, leave very few choices. The process is predetermined. The educators in the room do not produce a result different from what the State produces. They are involved only so that the State has someone else to blame. Cowards.)

In any case, they walk out of the room knowing that 0 points = 0 score, X points = 65, Y points = 85, and all the points = 100.

For each subsequent test administration, a single room of educators determines X and Y (passing and mastery), consistent with the cuts that were set on previous exams.

So how do all the in-between scores get converted?

One method would be to ignore the committee work, and just use percentages. That’s what our gut tells us to do. So 72/87 = 84% (after rounding).

Another method would be to take the committee’s points, and use linear interpolation to fill in the values between. For example, in June 2013 it took 30 points to get a 65, and 68 points to earn an 85. (Ignore that 30 is 34% of 87, and 68 is 78% of 87 – we are no longer looking at percents). So 72 raw points would 4/19 of the way from 68 to 87, and would earn a score of 88.

But the method the State uses is different. They take the committee’s points, and they find a curve that fits the points. This process of curve fitting (they probably use a cubic regression) has absolutely no science, no math, no research to support it. It creates a conversion chart, so they use it. Without reason.

My students have studied this, and are appalled. I use it to do some statistics, and later to talk about abuse of mathematics.

Anyway, here’s the June 2012 data. Notice the small differences between linear interpolation and cubic regression? They are completely meaningless and arbitrary – not really what you want to hear about when you are looking at grades going on kids’ transcripts.

Conclusion: Why did high scores drop when they shifted to Common Core? (posted here)

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Q: When is your score not your score?

There’s something that anyone working with New York State Regents Examinations knows, that no one outside of education would assume. There are not 100 points on the tests. Common Core Algebra has 86 possible points. A complicated “conversion chart” changes this “raw score” (actual score) into the “scaled score” (reported score).

It used to be different. When we had Course I, Course II and Course III Regents, and at all times before, you earned points, and those points made your score. There were 100 points available. Earn 65 points? Your score was 65. Earn 85 points? Your score was 85. People understood this.

The first of a series of disruptive innovations in mathematics in New York State freed the test from the content (they called this “standards based testing” but we no longer knew what questions they would be asking), and freed the score from the points. Really.

Here’s old Course I exams. See, no conversion scale. But each question has a point value. As a kid worked this exam, they had an idea of how they were doing.

And starting in 2002, there were Math A exams. 85 points. And the last page in the answer key included a conversion scale. Teachers were not happy. Some of the exam was impossibly wordy, and hard on weaker readers, but the scale made it up by making 51 points (60% of the points) equivalent to a score of 65. The State was using scaling to fuzz over the fact that they could no longer write an appropriate test. And a kid taking the exam? They had no idea how they were doing, even if they attempted to keep track of points.

Oh, that 60% is passing? That went out the window quickly. In June 2003 the State gave a Math A exam that tons of suburban kids failed (it really was a poorly constructed test), and “fixed” the problem by jiggering the exam. They did not remove the inappropriate wordiness, the false contexts, or the over-penalization for rounding. They “fixed” the problem by dropping the passing score. By August 2004, 36 out of 84 (they changed the length) was now passing. 43%. They got kids to pass, but in the process convinced more teachers and administrators that they were incompetent.

Each new test had a slightly different chart. But the big changes were:

- Math A introduced (June 1999) (notice the 1999 – 2002 Math A’s are hidden in a “pre-1998″ link at the bottom of this page)
- Math A rejiggered after the June 2003 fiasco (that the state has never accepted responsibility for)
- Integrated Algebra, (June 2008) and now
- Common Core Algebra (from June 2014)

We now have a full generation that works with exams out of 82 or 87 or 84 points. Do they accept that using an odd-ball conversion chart makes sense? Most of us, no. Does the public get it? No. Is it fair to kids that they don’t know how they are being graded? No.

I’ll provide more details on how the conversion charts are created in the next post in this series, the third.

But that system of conversions is key to answering the question: “Why did the top scores decline during the shift from Integrated Algebra to Common Core Algebra?”

That’ll be in the fourth and final post.

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Why New York State has been changing exams so frequently over the last 15 years (disruptive innovation) should be the subject of another post.

But my bread and butter exam has been Course I. Then Math A. Then Math A (adjusted). Then Integrated Algebra. Now Common Core Algebra.

What you do with these exams depends on who you are, and where you are. At Columbus I taught a course that took kids who had already failed Course I multiple times. Me and Bill Gerold taught it. And we figured out ways to get a kid who tried hard to break that 65. It was kind of amazing. And given our success, and it was success keeping the school off the SINI list or whatever it was called then for a year, the administration refused to offer the course again. At my school today I teach a fairly old-fashioned algebra course, with fairly heavy emphasis on mathematical understanding, challenging problems, lots of fractions, rich discussion of process, but not much emphasis on real-world connections. And then I build in the supplements for the exam. Obviously this means different supplements every time they change the exam.

It works fine. Kids get scores in the 80s or 90s. Once I had a kid with 100, but that was not my fault. The kids, the school, the parents, they all care about the scores. More than they should. Since my kids already know some math (they can all add fractions) when they arrive, and they all can take a standardized test (they get into the school by passing a test), the pressure is not on passing, but on getting scores that look good. And on getting the average for all of their regents exams to be at least 90, which qualifies them for an “honors designation” on their diplomas. It’s a sticker, and I give out nicer stickers, some more colorful, some scratch and sniff, some glittery, but the kids want this sticker in particular.

So the new Algebra regents (common core) hits last June, 2014, and I was on sabbatical. But I heard from around the state, from the AMTNYS listserve, and from talking to people, and from my school, that scores for strong kids were down 5 – 10 points.

So we set about scrambling to see why the scores were down, and what we could do to bring them back up. I went to the AMTNYS conference in Syracuse in October. I talked to people. Teachers, professors. Consensus was that those who used the “modules” ran out of time, those who taught the old curriculum watched the grades fall a full 10 points, or 10+ even, and those who used a reduced sampling from the “modules” did best. The modules are NY State supplied materials that probably would require a 300 day school year to teach completely (we have 180. There are 260 weekdays in a year).

There was my answer – adopt portions of modules. Of course I did nothing of the sort. I took an already rich function unit, and expanded it. I added a couple of stats topics, taught differently than I had in the past, emphasizing equally what the stuff means, and how to calculate it. I ended the year with a week and a half of intensive test prep. And my students did well. But the scores were 5 – 10 points lower than I would have expected. Mid 70s through mid 80s. Something was wrong.

I’ll give you important background in the next post, some technical information in the 3rd post, and tell you what went wrong in the fourth and final post in this series.

Teaser: NY State lowered top scores intentionally.

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But were there other problems with UFT endorsements this year?

In the fall:

Charlie Rangel. They endorsed Adriano Espaillat against Rangel in the primary, and tried to sneak it through the exec board without mentioning who Espaillat’s opponent was. Espaillat lost.

Robert Jackson. This guy has been a champion for public education, instrumental in winning the CFE case, our friend, our ally, John Dewey award winner. We endorsed Espaillat against him, and Espaillat won, 50% to 43%. But which one of these guys is still out there working for public education?

John Liu. Our friend. Damaged in a financial scandal that looks like it was intentionally dragged out to hurt him. Running for state senate against Tony Avella, one-time progressive who joined the semi-Republican IDC to keep the state senate in Republican hands. We have a clear side in this race, right? Wrong, the UFT sat it out. Avella won, 6,813 votes to Liu’s 6,245.

Jeff Klein, turncoat democrat who leads the IDC and keeps the Senate republican. He got primaried, about time. The UFT supported him anyway.

Tea Party backed, about-to-be-indicted congressman Michael Grimm from Staten Island was challenged in the general election. The UFT sat out the race.

In the spring:

When Karim Camara took a job with Cuomo, his assembly seat opened up. The UFT pushed an endorsement for Shirley Patterson, running democratic and independence parties (which should have been a sign). The endorsement pitch did not mention her Independence Party connection, her connections to landlord groups, or that her chief opponent, Diana Richardson was running with tenant organization support on the Working Families Party line. Richardson won, the first assemblyperson who won on the WFP but not Democratic Party line, and without UFT support at that.

Grimm’s seat opened up, due to Grimm being indicted, and once again the UFT sat out the race (they would not have even mentioned it had we not asked).

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Paul Egan had moved the contingency endorsement resolution (any endorsement questions that come up in the summer get referred to the Executive Board), MORE delegate Megan Moskop rose in opposition, saying that a special DA could be called, or that electronic voting could be used, and objecting to back room deals (the phrase “back room” drew hoots from the audience and a comment from Mulgrew).

We’ve had the contingency resolutions in the past, they are generally non-controversial. But we had the governor’s race sitting in front of us.

I rose to ask if a Cuomo endorsement could happen under the contingency resolution. And Mulgrew said no. For something that big, he said, we would not do it without the Delegate Assembly. Satisfied, I voted yes.

And then, over the summer, there was no official UFT or NYSUT Cuomo endorsement. Case closed?

Hardly. My question was two weeks too late. The UFT had already “watched” the Working Families Party deliver their line to Cuomo – ensuring that the best route for a strong challenge had been blocked off. One report said that the UFT (must mean an officer or top official) threatened to destroy the WFP if it didn’t endorse Cuomo.

Our role in the governor’s race did not improve. In September Regina Gori’s motion to endorse Zephyr Teachout over Cuomo in the primary was defeated by the UFT leadership’s caucus. And on the eve of the primary Randi Weingarten, AFT President, made phone calls, not as AFT President, to support Cuomo’s running mate. The UFT officially remained neutral in the general election. But not working against a powerful governor is not very different from working for him.

The rest is history. The WFP/Cuomo deal? Every promise Cuomo made, he broke. Cuomo and the teachers? We don’t need to ask.

If we had fought Cuomo, could we have stopped him? Wrong question. We didn’t get beaten. We lay down, and got kicked repeatedly in the teeth.

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This spring a student (her real name is not Nancy) posed a problem for herself: Starting with one newborn pair of bunnies, after one month the pair matures, after the next month the pair produces a new pair, and continues doing so every subsequent month, until after six months the pair dies. Describe the number of living bunnies after n months.

Problem

If you are not sure how this is going to work, the problem is for you. See if you can figure out how many bunnies will be around for the first few months, and then see if you can describe the relationship mathematically.

Challenge

If this set up is not a problem for you (if you can write the recurrence relation directly from the problem set-up), then I have a challenge for you: what interesting new problem can you create out of Nancy’s problem that would take someone who can already write the recurrence relation and make them think?

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Late in the fall of this past year (November 2014) I assigned freshmen the task of taking a problem that we had solved and discussed in class, and proposing a new problem as a modification or extension of the original. Some found it fun, and at least one remembered it later. (I’m sure it was more than this one.)

This February I started a special one-day-a-week class for freshmen (number theory and arithmetic, special topics of their choice, I did this once before).

Nancy (not her real name) worked in a team on Euclid’s algorithm. They did a very nice, very clear presentation, most of the students in the room were able to follow and perform the steps and work out a simple example. And then the team broke up.

Nancy decided to play with Fibonacci on her own. I was a little worried about real-world examples, but she stuck to the traditional “a pair of bunnies is born. In its first month it matures. In each month after that it produces a new pair. And she played it out and let the recursion and the problem statement match up fully. (My Ghost the Bunny is just word play)

And then she got bored, and played what-if. Nancy modified the problem – her bunnies would now have 6 month life spans. She carefully worked out what this would mean: 1, 1, 2, 3, 5, 8 all stay the same, but 13 – 1 = 12, and it gets interesting from there. Nancy identified the quantities that needed to be added (the two previous) and subtracted (six back) but had not written up a recursive formula when the class ended (we only met one lunch period per week, ate before we worked, and homework was not allowed).

But see why I’m excited? She played with a problem, then posed her own problem? Because she was curious. Ninth grader. Cool, huh?

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In the fall term of algebra classes I carve out a day here or there, or maybe a few half-periods, to work on extended problem solving. It is generally not on-topic. On-topic would allow the kids to know before they start HOW they should solve the problem, and that would spoil the joy. I usually choose problems with multiple paths to success. And I certainly do not choose problems that have an accessible formula – that would spoil the challenge.

This fall I did different problems with different classes – but all did the checkerboard, and some did Ghost the Bunny too.

I use an Understand / Plan / Carry out the Plan / Look Back approach with the kiddies, but too often “looking back” for them just means “check.” Over the years I have pushed “find another approach” or “find the relationship between two successful approaches” or “generalize a solution.” But this year I pushed in a new direction.

“Use your work and solution to think of a new, interesting problem.” The idea is not to simply make the problem bigger, or generalize it, but to come up with something related, but new, probably closely related and more complicated, but not necessarily so. And it was quite possible for the new problem posed to be easier than they realized or harder, to yield to a similar approach as the original problem did, or not to yield at all. After all, if they knew there would be a solution of appropriate difficulty, it would mean that there was not original problem posing going on. And after practicing generating ideas on earlier problems, we hit the checkerboard, and I assigned them to extend the problem, gave them time in class and at home, and required them to write up a problem solving “experience”:

- Understand the Checkerboard
- Devise a Plan
- Carry out the Plan
- Look Back (include posing a new problem)
- Devise a Plan
- Carry out the Plan
- Look Back (since many new problems were not solved, this included commentary on obstacles. Where problems were partially solved, we got suggestions for the next team to pick the problem up. Where problems were solved, we got ‘normal’ generalizations, but also suggestions for future work. From 9th graders. )

So, post-checkerboard, what problems got posed? Here’s a few that I recall:

- Solve for an abnormal 8 x 9 checkerboard. Generalize to squares on an m x n checkerboard.
- Solve for a checkerboard with the four corners missing. Try again with the four 2 x 2 corners missing. 3 x 3. Generalize to an n x n checkerboard with four m x m corners missing
- Variation (different group). Solve for a checkerboard with one corner missing. Then a 2 x 2 corner…. Generalize to an n x n checkerboard with a single m x m missing.
- Variation (there was a lot of removing squares going on). Solve for a checkerboard with a 2 x 2 hole in the center. 4 x 4. 6 x 6. Generalize to an n x n board with an m x m hole in the center.
- Solve for an 8 x 4 checkerboard. Account for the difference between two 8 x 4 boards and one 8 x 8 boards (the write up for this was beautiful)
- Solve for rectangles on a checkerboard.
- Leaving the board out of it, count trimonos, tetrominos, pentominos, hexominos. (I think this group got side-tracked into some fascinating but for the moment fruitless discussions of symmetry and handedness. Product? Nah. Discussion – excellent.

So, when you get an answer, are you at the end? For most of the kids the response is still “check, and that’s enough, unless the teacher makes you go on” – but for a substantial minority I think they got used to the idea that mucking around further is a good idea, and potentially fun or interesting.

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