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A maximizing area question

April 6, 2018 pm30 12:30 pm

I gave this question to students as a challenge at the end of a trig unit.

A quadrilateral has perimeter = 60 and a 30º angle. What is the maximum possible area?

I think this is cute. The kids had to make some assumptions, test them, and use trigonometry along the way. It’s not “open-ended” but it does involve some investigation, and it is not just a direct application of what I’ve taught them.

What’s your answer?

Do you like the question?

And do you know why “What is the minimum possible area?” is not a good question?


Pity Arizona

April 4, 2018 am30 9:05 am

Arizona’s men’s basketball team lost in the first round to 13th seeded Buffalo, who lost in the second round to 5th seeded Kentucky, who lost in the sweet sixteen to 9th seeded Kansas State, who lost in the elite eight to 11th seeded Cinderella Loyola of Chicago, who lost the semi-final to Michigan, who lost in the final to Villanova.  That makes Arizona the biggest loser of the tournament.

Consider this, Michigan could claim to be the second best team in the tournament – having lost to the eventual winner. Kansas, who lost in the semi’s to ‘nova, can make the same claim. Radford, who got shellacked by Villanova in the first round, could make the same (though far-fetched) claim. Arizona, uniquely, can claim nothing better than 7th. This tournament’s biggest loser. And at a 4 seed, perhaps the biggest biggest loser since Iowa earned some pity in 2006.

Previous biggest losers:

2018 – Arizona (4)
2017 – Mount Saint Mary (16)
2016 – Purdue (5)
2015 – New Mexico State (15)
2014 – Oklahoma (5)
2013 – Colorado (10)
2012 – Harvard (12)
2011 – Akron (15)
2010 – Oklahoma State (7)
2009 – California (7)
2008 – Belmont (15)
2007 – New Mexico State (13)
2006 – Iowa (3)
2005 – Winthrop (14)
2004 – Florida (5)
2003 – Dayton (4)
2002 – Boston University (16)
2001 – Princeton (15)
2000 – Appalachian State (14)




Telling the Truth

April 3, 2018 am30 11:12 am

A liar is someone who tells lies. That’s not the same as someone who always tells lies.

Can you imagine that? Someone who always lies, every single thing they say? That would lead to amusing logic puzzles:

– but not be very practical in the real world. In my life I’ve known two horrible liars. They have altered, twisted, falsified, subtly reimagined, or created from whole cloth story after story. “She wouldn’t tell the truth if a lie would do” said the mother of one of them. But both actually told the truth the majority of the time. What’s the weather like, are you hungry, do you have time later today… there are many mundane everyday answers that even the inveterate liar doesn’t bother to confabulate.

Many politicians are practiced liars – not as prolific as my two friends, above, but for them it is an art. They often tell the truth. And sometimes they have to tell the truth, a defensive truth, when cornered by their instinct for self-preservation.

New York State’s budget was delayed for a day last week, when Brooklyn State Senator Simcha Felder tried to exempt yeshivas from state testing standards. Felder is a Democrat from Brooklyn. He caucuses with the Republicans. And in the cesspool of New York State politics, no one better represents some of their constituents to the exclusion of the others than Felder, who is a champion for ultra-orthodox and Hassidim throughout the state (and beyond New York’s borders) at the expense of the non-Orthodox and non-Jews he nominally represents.

Felder has voted for “standards” again and again. They don’t really measure much, but they selectively pressure urban districts. Urban districts are poor, and they have large populations of Black and Hispanic students. “Standards” are a key component of the system that uses standardized tests to intimidate students, threaten teachers, and destabilize schools. Some of these include Felder’s own constituents – the ones he doesn’t represent. Felder has happily acted as part of the machine targeting other people’s kids.

But this was different. The State Education Department was planning for superintendents to visit private schools, including yeshivas. And they weren’t going to enforce “test accountability” that terrorizes the rest of us. They were going to check that the kids were receiving instruction in English, Math, and Civics.

Bravo Mr. Felder, for announcing that even the most minimal rules are to be enforced against strangers, not against our friends. Such honesty.



February 5

February 5, 2018 am28 8:08 am

Yesterday was my birthday. I woke up in Boca Raton, and had coffee in the sun, by the pool.

I engaged, a bit, in a conversation:  If there should be consequences for administrators who bring false charges against teachers, what should those consequences be?  It’s obvious that there SHOULD be an answer, but not as obvious what that answer should be.

I know how many ways a polygon can be triangulated (Catalan). But a student proposed investigating dividing polygons into a mix of triangles and quadrilaterals, or only quadrilaterals. I played with her questions and related questions on the plane home. To make a larger n-gon I made a rough circle and then spaced out the right number of points. I didn’t bother connecting them (since I only want diagonals, anyway, and since my sketches are not very neat). So it looked like I was drawing lines in circles. Flight attendant asked – he likes circles and was hoping this was geometry.

Arrived in a cold rain, and before I reached the bus stop my foot found a huge puddle. 54, in the book.

Lack of knowledge, lack of experience

October 22, 2017 am31 11:20 am

Chalkbeat pays young journalism majors with school reform money, and uses school reform money and influence (directly or indirectly) to gain access to sources. But this just doesn’t add up to real journalism, not when there is a lack of knowledge about New York City an New York State, a lack of knowledge about education in general, a lack of knowledge about teaching, even, quite frankly, a lack of knowledge about school reform. We end up with school reform cheerleaders, (who may in the case of the ‘reporters’ not know they are cheerleading – the ‘editors’ probably know).

But the lack of knowledge, the lack of experience, the lack of historical context, they all slip through.  Here’s an example from last week – “Traditionally, students have had to pass five “Regents” exams in order to graduate. ” How do they write that? Don’t they know that traditionally there were two kinds of diplomas, and that one did not require Regents exams? That in the late 90s school reformers pushed for doing away with the “local” diploma, and that there have since been 15 years of battles over trying to reopen some non-Regents pathway?

And when they whine that these are just details, notice that a regular local newspaper easily doesn’t screw up the details.

School reformers don’t believe that experience and knowledge matters for teachers. Glass houses. They don’t seem to believe that experience or actual knowledge matter for ‘reporters’ or ‘editors’ either.

Teacher Evaluation

September 30, 2017 pm30 9:01 pm

At Wednesday’s Citywide Chapter Leader Meeting, UFT President Michael Mulgrew gave his version of the history of the current teacher evaluation system in New York City. Here’s his main points, and I think observers who like it and don’t like it will all agree that this is a fair summary:

  1. The old system, satisfactory/unsatisfactory, was not the “good old days” – you were at the principal’s whim
  2. The UFT was looking for a way to improve the system and improve teaching, and S/U was not going to do it
  3. Using straight up test scores made NYC look bad, when teachers here actually do a good job
  4. We got the state to use a “growth model” which measures what we really do
  5. The number of negative ratings is substantially down
  6. We are fighting for more options for the “growth” score, so that it can be based on performance, and not necessarily tests.

Omissions. Misinterpretations. And the deeper story.  In six points.

  1. Why is Mulgrew still arguing against S and U? It’s been 3 years since my last S rating.  But we all know why he’s arguing. Members in New York City still don’t buy it. At the Chapter Leader meeting, CLs sitting near me (not people I know) were saying NO and scowling when Mulgrew was trying to make the point. There is pushback, probably coming unevenly, but from all districts. Also, the UFT helped impose this on all of NY State, and there is likely more unhappiness out of the city than there is in the city (NYC has high turnover, newer teachers have nothing to compare Mulgrew’s system to)
  2. Being at the whim of the supervisor is not necessarily a bad thing, if s/he is a capable, trained, reasonable educator. This is the fight the UFT refused and refuses to take on. Where members were at the whim of an unqualified or malicious principal, we should have fought to have that principal’s judgment reversed, and to have that principal removed. Instead the UFT fought to have us judged on test scores. This is not a small mistake. And it continues. Because HEDI did not clear out the malicious and incompetent. Bloomberg/Klein’s small school policy created hundreds of admin vacancies when there was an admin shortage. Result? Literally hundreds of incompetents/abusives. And the incompetent? When things go badly? They take it out on subordinates. The categories overlap. There is still a need to weed them out, and it is still a fight the union is bizarrely reluctant to take on. They have even accepted an evaluation system where challenging the principal’s judgment is not allowed!
  3. Whoever thought of tying teacher training and teacher rating was either an enemy of public education, or an idiot. I can imagine this conversation:  “Members are resistant to PD, but they should love PD so we can say that teachers love PD and thereby ‘teachers are trying to improve the profession'” “I know, let’s make the PD high stakes and tie it to their ratings, that’ll make them love it”  If you can imagine the people having this conversation (and something like it likely took place), then you can begin to understand how the UFT leadership doesn’t get the resentment that much PD generates.
  4. And mixing rating and professional improvement? Bad idea. And by the way? I like learning about math pedagogy. I do it, willingly. But it has nothing to do with whether I am an ok teacher. Rating and Growth are naturally separate parts of teaching, and should have never been mixed.
  5. The “growth” model pretends to measure growth. In fact, it produces fairly random numbers. Good for you if you get a high number, not so good if you have a low one, and don’t believe for a second that your teaching really controls the outcome. There is no way to use test scores to rate teachers that actually makes sense.
  6. The number of negative ratings is down. I like that. But that’s not a system that makes sense; it’s a system that for 2016-17 didn’t do much harm. We got lucky. And for the teachers who got the bad ratings and didn’t deserve them?

Protest Charter High School for Law and Social Justice unfair labor practice

June 30, 2017 am30 9:16 am

There are things we know that apply to all schools.

  • Everyone must feel safe in their own school.
  • Curriculum must engage students and meet their academic and social needs.
  • And all voices – parents, students, staff and administration – must be heard.

The Charter High School for Law and Social Justice at 1960 University Avenue (by Burnside) denies voice. Worse than that – they fired three quarters of their teachers – precisely for trying to discuss conditions in the school.

The United Federation of Teachers moved to file a complaint with the National Labor Relations Board. This was the correct and necessary first step.

But we must do more. We must rededicate ourselves to helping all teachers and staff in New York City schools gain or maintain voice. We must organize the unorganized, and stand stronger in the face of injustice.

And we must bring pressure to bear on this charter school in particular. I am writing to the UFT leadership today, proposing we begin informational picketing at the school.

Richard Marsico, the president of the Charter High School for Law and Social Justice is director of the “Justice Action Center” at the New York Law School. Two more officers and several board members are associated with the Justice Action Center, or with the law school itself. I will also be proposing a UFT campaign directed to the “Justice Action Center” and its association with these damaging actions and unfair labor practices.

I am a strong supporter of public education. Public schools are a pillar of our republic. The current infatuation with charter schools will pass. But I recognize that we have a lot of work to do improving our public schools – what we teach, whether we test, and the environment inside many of our schools before we reach that point.

In the meantime we should continue to advocate for improvement in ALL schools. That includes making sure that all stakeholders have voice.