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NY State backs down on inverse flub; no geometry gaffes until later today

June 23, 2011 am30 8:10 am

New York State asked high school students to find the inverse function of a non-invertible function. 32. If f(x) = x^2 - 6 find f^{-1}(x). Youch. Teachers across the state yelled and screamed, but most importantly called the testing hotline (I never got through, all busy). What was the response?

They backed down. But tried to weasel out and claim they had not made an error. Here is the language in their clarification memo:

“Because of variations in the use of f^{-1} notation throughout New York State, a revised rubric for Question 32 has been provided. Please rescore all students’ responses to Question 32….” And then they allow \pm\sqrt{x+6} or \sqrt{x+6} or -\sqrt{x+6} or “An explanation stating that the original function is not one-to-one and therefore there is no inverse”

Surrender? No. They ascribe their error to “variations in notation.” Actually, even if they were right, they have some explaining. How could the test-makers not be aware of “variations in notation”? Also, notice how there is an asymmetric justification burden on a kid claiming (correctly) that the inverse does not exist.

Before we got that memo, what response did they give teachers?

Tuesday late afternoon (report is by a math teacher from the Association of NY State Mathematics Teachers listserve): I called the state today about question #32.  I told the woman that by definition, for a function to be invertible it must be 1-1.  Her response was that every function has an inverse, it just that every inverse is not necessarily a function.  She said that the inverse could just be a relation.  I told her that she was wrong and then quoted her a definition that says that a function is invertible if and only if it for every input there is exactly one corresponding output value.  I then said that it was only invertible only if we restrict the domain to all value greater than or equal to zero, or all values less than or equal to zero.  It the domain is restricted in this way, the student shouldn’t write positive or negative.  She said that they can receive full credit if they only stated the positive solution, given that they explained that they restricted the domain to make it 1-1.  I asked her why did I have to expect so much from the kids when a bunch of adults who made the exam, didn’t make that distinction?  She told me that i wasn’t going to win the argument.  This error  is more apparent given that the question uses function notation.

Wednesday morning (report from another teacher on the list): I just got off the phone with a person from State Ed (who refused to give his name).  … After much discussion, I pretty much got him to agree that the inverse should be a function.  When I insisted that the answer should be correct with +sqrt, – sqrt as well as both, he finally said “use your professional judgement!”  I then said- why don’t they admit the question was flawed and issue a correction statement so we are all grading the question the same way?  His response was we will look into it.

Then Wednesday late morning they started telling teachers that they were working on a memo, which finally came at 1:48 PM.

June 2011 Algebra II Regents (multiple choice 1 – 27)

June 22, 2011 am30 6:18 am

1-3:

4-7:

8,9:

10-12:

13,14:

15-18:

19 (blurry, sorry):

20-22:

23-25:

26,27 (Last 2):

NYS Algebra 2 Regents June 2011 – bad inverse question

June 21, 2011 pm30 9:55 pm

32. If f(x) = x^2 - 6 find f^{-1}(x).

What do you think?  Horrible?  It was a two point question, and an answer of f^{-1}(x) = \sqrt{x+6} earned 1 point. What answer were they looking for?

I have no confidence in New York State’s ability to create a good test of mathematics, at any level.

How Bronx Aerospace earns its top rating

June 21, 2011 am30 6:42 am

I have described Bronx Aerospace High School as a place where you would not want to work. Several times. 1, 2. Yet it consistently earns one of the highest Progress Report grades from the Department of Education. Not only As, but very high As. One year, I seem to recall, it had the highest A in the City.

Elsewhere NYS reported on the massive number of papers scored exactly at 65. And as result, teachers are no longer allowed to “reread” papers that fall between 60 and 64.  But there are other ways to manipulate test scores.

Look at what the NY Post reports:

‘Top’ high schools’ shame

Among the most eye-opening cases is Bronx Health Sciences HS — which graduated 96.6 percent of its students in 2010 but managed to get only 3.4 percent of the class to the higher, college-ready standard.

Schools with the next largest gaps between their graduation rates and college-ready numbers were:

* Repertory Company HS for Theatre Arts in Midtown Manhattan, which graduated 85.7 percent of its kids but just 4.7 percent at the stricter standard.

* Bronx Aerospace HS, which graduated 88.6 percent of its students but only 8.6 percent at the college-ready level.

“I think what the state has to look at is where these kids started,” said Barbara Kirkweg, principal of Bronx Aerospace, where the majority of students arrive performing at low levels.

“If they’re going to use this measure in some way to paint schools, it can’t be with that broad brush without consideration of what was the preparation of these kids when they left middle school,” she added.

Read more: http://www.nypost.com/p/news/local/top_high_schools_shame_jO6to7cI91S44IWMg0KZcM#ixzz1PuBQuYXE

Losing January Regents – what the document says

May 22, 2011 am31 7:28 am

There’s been a little storm launched this week: the Board of Regents of New York State has just eliminated January Regents (we have June, and in all but Trig and Chemistry we have August). Also, Foreign Language Regents were completely eliminated.

Wonder what the document actually says? Here it is.

TO: P-12 Education Committee

College and Career Readiness Working Group

FROM: John B. King, Jr.

Valerie Grey

SUBJECT: Options for Funding the Regents Examination System
DATE: May 10, 2011
AUTHORIZATION(S):

SUMMARY

 

Issue for Action

 

How do we ensure the continued fiscal viability of the Regents Examination Program given the anticipated shortfall in funding?

Reason(s) for Consideration

Review of policy

Proposed Handling

The question will come before the P-12 Education Committee and the College and Career Readiness Working Group at its May 2011 meeting where it will be discussed and action taken.

Background Information

There has been a structural imbalance between our available resources and the costs of administering the Regents examination program for several years. Federal carryover funds have been used to fill the gap. These funds are now depleted. To address this imbalance in 2010-11, in June 2010, the Board approved a number of actions that are projected to reduce costs for the NYS assessment program by more than $6 million, including elimination of Grade 5 and 8 social studies exams, Grade 8 Second Language Proficiency exams, component retesting in Math and English Language Arts, High school foreign language Regents exams in German, Hebrew and Latin, and August Algebra2/Trigononmetry and Chemistry exams. The Department also continued cost saving strategies that were implemented in 2009-10 that reduced operation costs by over $4.0 million. In addition, the 2010-11 State Budget provided for a one-time revenue transfer of $2.5 million from a Special Revenue account into a newly created Education Assessment account. These revenues were used to restore the proposed cuts of the January administration of Regents exams, exam translations, and the high school foreign language exam in Italian.

For 2011-12, the Board of Regents requested $15 million in General Fund support for the Regents examinations. The enacted State Budget, includes funding of $7.0 million for Regents examinations.

This additional funding of $7 million will ensure the following Regents examinations currently required for high school graduation and/or federal accountability purposes are maintained:

  • ·      Comprehensive English (ELA 11),
  • ·      Global History and Geography,
  • ·      U.S. History and Government,
  • ·      Integrated Algebra, and
  • ·      Living Environment

This additional funding will support the following Regents examinations to preserve policy options for the implementation of state law 3012(c), the state’s teacher and principal evaluation law:

  • ·      Physical Setting/Physics,
  • ·      Physical Setting/Chemistry,
  • ·      Physical Setting/Earth Science,
  • ·      Algebra2/Trigonometry, and
  • ·      Geometry

This additional funding will also ensure accessibility and support for English language learners continuing:

  • ·      Regents Competency Tests (RCTs)
  • ·      Translation of exams into Spanish, Chinese, Haitian-Creole, Korean, and Russian.

The $15 million funding request covered administration of Regents exams required for graduation, Regents exams that are not required for graduation, restoration of certain cost savings measures taken in 2010-11 and introduction of new Regents exams. Since the 2011-12 State Budget included $7 million, there is a funding gap of $8 million that must be addressed.  We recommend a combination of action steps noted below.

There are a number of cost containment actions that can be taken to reduce the costs of Regents exams by $3.9 million.

Chart A

Action Step Estimated Savings
Identify additional production cost reductions, leverage other funding streams, and make necessary changes in workforce. $2.3 million
Reduce the number of assessments printed and shipped (Regents and NCLB) to better align with the number of exams actually needed to administer. If a district chooses to order surplus exams for practice purposes they will be responsible for the additional cost. $.70 million
Review all vendor contracts to improve cost effectiveness and cancel contracts and in-source exam activities where possible and when it is less costly. $.60 million
Expand the distribution of related exam materials (i.e. teachers guides, scoring instructions) electronically $.30 million
Total $3.9 million

Based on prior discussions with the Board in March, June and October 2010, we recommend additional programmatic actions to reduce costs by $4.1 million.

Chart B

Examination Estimated Savings
Eliminate January Administration of Regents Exams $1.4 million
Postpone development of ELA 9 and ELA 10 $1.2 million
Continue the elimination of Grades 5 and 8 Social Studies Exams (eliminated in 2010-11) $.80 million
Eliminate Regents Italian, French, Spanish exams $.70 million
Total $4.1 million

New York is the only state to offer its end of course testing program three times per year; other states only offer one make-up opportunity. The January administration of Regents exams has had a history of being problematic due to school closings related to inclement weather, and rescheduling the exams or giving make-up exams is not possible at this juncture.

The development of ELA 9 and ELA 10 continues to be an important priority; however, given the funding shortfall, a temporary delay of this work is warranted. Traditional funding for Grades 5 and 8 Social Studies exams is not available; however, the Department is exploring other possible funding options.

When a Regents exam in a language other than English is not made available by the state, schools are allowed to use locally developed exams, aligned to Checkpoint B, to satisfy diploma requirements. There are also a number of commercially available exams that Districts may administer to students to ensure foreign language competence and attainment of the Learning Standards. (e.g., SAT II, AP, Cambridge IGCSE and International Baccalaureate).

The Department will explore longer term actions steps to address future funding shortfalls due to the uncertainty of the fiscal condition of the state and this program.

o      Revise the current practice of the public release of exams after administration.  Exams will be kept secure to allow items to be reused, thus producing savings on development costs.

o      Modify the current practice of the Department printing and shipping exams to explore other options if cost effective.

o      Pilot on-line testing to gauge the capacity of the Department and the field to administer exams electronically and to measure security risks.

Recommendation

It is recommended the Regents take the actions steps outlined in Chart A and Chart B and advise on long term actions steps.

Resisting Test Prep is Tricky

May 21, 2011 pm31 9:17 pm

I’ve been asked to do a math talk or a math teaching talk for a bunch of math teachers. (I like this).  The host suggested I consider tying into the common core standards, but even better would be a talk on organizing all math teachers for the revolution that is needed.

Clever me, I’m thinking about a talk on avoiding the common core, or teaching around it, or ignoring it.

But I don’t know if I can do that. First of all, I need to read the damned documents. Skimming is not enough. But second, if teachers are going to be rated on student test scores…

which offends me on so many levels I can hardly begin – the scores will not reflect teaching skill – the metrics to account for different circumstances are primitive and cannot advance appreciably, no matter how many tweaks – so much is not on the test – teaching encompasses habits and behavior, not just correct and incorrect responses – we already have a perfectly good way of telling if a teacher is ok (just watch) – the entire exercise invites gaming – the entire exercise hands the rating decisions to non-educator suits sitting in central offices…

but if teachers are going to be rated on student test scores, then job trumps honor. The quality of Pearson/Kaplan/state tests is so low that they can be successfully prepped, and I would be some sort of idiot if I told other teachers not to do so. And they would be stupid to listen to me.

Students being teachers

May 15, 2011 pm31 3:16 pm
tags:

Nah, not what you think. Not group work. Not seniors helping in freshmen classes (though I do that, and when it works it is wonderful).

I have a couple of former students, class of ’06 (my school’s first graduating class) with jobs in schools. One of them is a teacher, subbed last year, appointed this year, in a middle school near here, surviving quite ok. Another is a teacher’s aide in an elementary school in the South Bronx. And then there is TMW.

TM, for short, presented for high school with enthusiasm, but with the behavior of an excitable 4th grade boy. He wouldn’t stay in his seat! He called out. He made jokes, and was constantly laughing out of turn. He wasn’t bad, just exasperating. Middle school teachers, what do you do when a child literally rolls around on the floor?

But he grew. He got bigger. And emotionally he matured. I think he was almost behaving like a reasonable freshmen when he graduated.

A couple of years ago I needed some help from alumni, and a few showed up, including TMW. At the end I thanked him for coming. “But Mr. 2718” he said, “of course I came. You asked me.” I laughed. “In four years, TMW, how many times did you do something just because I asked?” He laughed too.

Revenge is sweet. TMW is now working as a dean in Brooklyn. Today he wrote me this:

“I often find myself disciplining students for the same shit I used to do. I’ve mastered the art of not cracking up at the ridiculousness of the youth…”

A disappointing math competition

May 14, 2011 pm31 11:53 pm
tags:

I accompanied a friend and his middle school mathletes today to a thousand-student middle school math competition at the Armory on 168th Street.

Turnout was huge. Over 1000 middle school kids, doing math for fun. That’s something. Plus coaches and spectators. There was a crowd.

The Armory looks better than I remember. I read this week that they will host the Millrose Games (after over a hundred years at Madison Square Garden).

The kids ran into the track, and did half a lap, by grade. Looked like it was fun for most, but awkward for a substantial minority.

The format of the exam was strange. Forty questions, worth 100, 200, 300, 400, or 500 points, according to degree of difficulty. Kid answers, shows judge, judge says yes or no, and the kid bring it to the scoring table, or tries again. The contest lasted 45 minutes.

There were a few problematic questions (I only saw one of the 6 exams). Units were required, but were unevenly used in the answer key. Many judges were outside volunteers (not math teachers). Good alternate answers were not to be accepted (and I heard of at least one \frac{1}{1} being rejected, when the correct answer was 1). I allowed a struggling team to cash in on “no remainder” when the required answer was “0” – I’m sure this was rejected in other corners. Some judges took quite long to examine a page, while other teams were waiting. In at least one case the question was very hard and functionally multiple choice; kids guessed each answer until I nodded yes.

Blaring music was played throughout the contest. not quite MSG, but you get the idea. The theme from Rocky, Let’s Get it Started, We are the Champions, with no break. On a roll? That sort of upbeat might keep you there. But when a kid gets stuck, how do they concentrate? I was horrified.

The scoreboard flashed math facts (for the spectators?) Unfortunately, some were not entirely correct, most were genuinely trivial.

And in 45 minutes it was over. There was no further math discussion. No exhibitions. No chance for teams to debrief. No second round. No time for spectators to listen to children try to answer questions.

The kids got turkey sandwiches, listened to the Emcee and the principal of the host school (Urban Assembly Math and Science, once advertised as the “Fun Math School.” I was none too impressed with the idea or the principal, who seems something of a showman, but the teachers don’t complain, so let’s leave it at that…)  There were performances from UAMS students which were far more suited for a school-wide talent show than a crowd of 1500, awards, and out. And Walcott spoke.

Math CAN BE fun. That’s not my objection. But the kids sat, 5 to a table, but isolated. No interaction at most tables. It was 45 minutes of doing problems, surrounded, but alone. They were praised for being there, but their accomplishments were secret. Ceremony replaced thought.

I’ve been to competitions. True, they can be boring. But “lightening rounds” can draw an audience. During break time kids play with puzzles and each other, and review problems. At the Armory, there was no break time. The city needs a better middle school competition.

ex-KIPP teachers, tell your stories

May 14, 2011 pm31 7:54 pm
tags:

Former KIPP Teachers: Share Your Story

from Schools Matter by Jim Horn
I am very much interested in talking with former KIPP teachers who may want to take part in an interview study on the KIPP teaching experience.  All participants are guaranteed complete anonymity, and no names, locations, or other information will be used that may jeopardize your privacy.  I have completed three interviews so far, and I am interested in talking with another dozen or so former KIPP teachers.  Email me if interested at james.horn@cambridgecollege.edu.

– – — — —– ——– ————- ——– —– — — – –

I think Schools Matters is the only blog I am actually banned from. And to make matters worse, I gave them a hard time for making fun of New Jersey Governor Christie for being a fat jerk. (Jerk, yes, but I do not think it is right to make fun of people’s weight). But it stays in my reader; it is well worth following. They select interesting articles to reprint, much of which I would not otherwise see. And Steve Krashen writes good stuff.

Frustration

May 14, 2011 pm31 7:05 pm

I’ve never posted negative stuff about my school, certainly not my students, and never will. But I’ve actually been frustrated enough these last two weeks that I prepared (but did not publish!) a brief post. Monday will tell.

Teacher – unfairly extended – fires back

May 13, 2011 pm31 10:09 pm
tags:

A middle school teacher was offered tenure by her principal – until the superintendent forced him to reverse the offer. The teacher absolutely refused to sign the extension of probation agreement (actually, I wish she would sign, as unfair as it is, so she could keep her job… but she feels strongly, and with some reason). This is part of something happening citywide – teachers are being denied tenure, having their probations extended, en masse.

The teacher wrote to her superintendent. Here is the letter:

(the teacher is ok with revealing school and name, but that will wait for the next post;  I’ve omitted identifying information – jd)

Dear [Superintendent],

We barely know each other. You visited my classroom last year and observed a lesson of mine. You actually wrote that visit up as one of the few positive things you said about our school in that year’s quality review. I saw you again this year for a brief moment as you walked into my classroom as I was rushing out for a meeting.

I really regretted that I wasn’t able to stay while you were visiting. If I had, I would have been able to show you the portfolio system that I created to track outcomes and re-cycle skills. I would have shown you how those outcomes translate into grades and informed you that students get as many chances as they need to try skills they are struggling with.  I would have encouraged you to stay for extended day and watch as striving readers and writers grab their portfolios and choose the outcome they want to work on that day. You would have watched as students chose a skill and after re-teaching the skill, we discussed how they might show evidence that they’ve learned it. You would have inferred that I will let kids show their learning in a variety of ways. I would have told you that it is my philosophy that the only grade that really matters is the grade that the student has at the end of the year.

You’ve given to [my DR]  an “attendance issue” as your reason for refusing to grant me tenure. The truth is, I do not have an “attendance issue” for several reasons. The first and most important reason is that any sick days I’ve missed are due to a serious medical condition that I have that was only diagnosed one year ago. Five of my six sick days were medically excused this year. All of the ones from the previous two years would have been except I wasn’t under a physician’s care. All of this can be confirmed by my doctors and clinicians. The second reason that I feel that the “attendance issue” excuse is misplaced is that, despite serious illness, I’ve managed to bank more than seven days in my CAR.

This is because I’m a fighter.

My doctors encouraged me to take a medical leave; that the stress of being at [my school] and working for [my principal] was too much, but the reason I chose not to was, first and foremost, I had a responsibility to my students, and secondly – tenure. I knew that if I took a medical leave of absence that that would be reason enough to deny me.

And so I soldiered on, it’s what I do.

You might be one of those people who are completely against tenure and think tenure is the problem with the school system – I can’t possibly know, but I do want you to understand why tenure is so important to me.

  1. The right to due process frees an innovative teacher like me up to try new and revolutionary things in the classroom without the fear of losing their job without just due process. That’s an important thing. People who work with children are the only people who work with a normal population of people where 4% lack a conscience and 100% have underdeveloped frontal lobes. These are a dangerous combination.
  2. Working on this tenure portfolio, in particular, has been life changing and solidified who I am as an educator and what I believe in for the future of education. It meant a lot to me and it went ignored.
  3. I’m an eight year teacher, and I have always excelled at my job, and to be told that the organization I work for isn’t sure that I’m the right fit for a lifetime career if I want it, feels like regression, not progress. And progress is important to me.
  4. As a non-tenured teacher there are certain important positions that I cannot hold. And since I cannot, I cannot influence change.
  5. This tenure decision comes at the end of one of the most difficult years of my life, but to say that I was the best teacher I have ever been is a complete understatement. I surprised myself again again with not only the progress of my students but with the confidence of my instruction.

I actually had this vision of you coming into my classroom to look over the portfolio with me. I really wanted you to read the letters that were written on my behalf because they were by no means your typical letters of recommendation. They were simply amazing.

I envisioned showing you the certificates for the almost 500 hours of professional development I’ve had since I started teaching (and let you read the things I had taken away from them), the best of my lesson plans, all of the observations and notes I’ve ever had from an administrator (including the descriptive rubrics from Texas).

I would have let you peruse the pages and pages of information that I sent to parents about the goings on in Language Arts. I would have wanted you to read my song parody (sung to the tune of “We Didn’t Start the Fire” by Billy Joel) – that I sang in my most awful voice to show kids that they can show the information they research in Social Studies in really fun ways.

You would have realized how vital I was to the school because you would have seen that I ran the newspaper (now it’s a literary magazine (I still help run it)). You would have seen that I run the Chess Club, a.k.a. the place where the kids come that don’t really have any other clubs, and that I was a HUGE part of the reason that [my school] won $5,000 in the America’s School Spirit Challenge.

If you have visited during 703, I would have pointed out — because you know his dad. — is an interesting kid. He stutters and is a little chubby (I think he’s about to have a huge spurt upward), but the girls DIG him. They think he is like McDreamy or something. But — is really starting to figure out that he’s ambitious, and he just might want to go to great school someday.

I also would have pointed out — because — and — used to go out. — lives with her grandparents, and her grandfather has Alzheimer’s and doesn’t remember her most of the time. I would have pointed out —, who’s also had it tough, but is working so hard to excel at school (and it’s paying off).

If you had come in during 702, we definitely would have talked about —. She has a severe reading disability, but this year she got her voice. She’s so meek mild usually, but you should have seen her as she translated my and [a colleague]’s English into Spanish in order to explain to her parents that she wanted to get tested to find out why she has such reading problems. This is a kid who’s finding a voice and advocating for herself. It’s one of the most beautiful things I’ve ever seen.

We also would have talked about —. I call him Prince — —. — transfered to [my school] from another school, and when he got here, I think he though he was on another planet. He had such trouble catching onto the workshop model, and he was so cynical of every word coming out of my mouth. It turns out, that — really thinks Michael Moore is the best thing ever, and he’ll talk all about corporate fat cats and how landlocked states effect the economy all day long. But the strangest thing happened just before the test, we gave the kids frequently tested vocabulary words to present to the class in a way to truly make them memorable. — mimed, and — rapped. And it was so cool.

If you had visited during 701, we would have had to talk about —. — makes us talk about him. He’s 18 feet tall, but he has the heart and mind of an 8 year old boy. Once I truly thought about it, and after he emptied his pockets to show me his dum-dum wrapper collection, I started buying him legos. Now he earns legos, and time to play with them. Things have generally really calmed down for this kid, and he has the worst ADHD I’ve ever seen in my life.

I also would have wanted to talk about —. When school started, I would estimate for the first two months of school, — was the social butterfly. She wouldn’t stop talking during independent reading.  So during a reading conference, I talked to her about a student that I had last year. I noticed that when she came to class with her glasses on, she was really serious and worked really hard, but when she forgot them, she was a lot like —. So — and I started to agree that she would wear invisible glasses to school. And now — is one of the most focused and hard-working students in the class. And when she’s not, I tell her, “Put on your glasses.” And she flies right.

I want you to know that I can write one of these paragraphs for every student that I teach, but I’m sure you’ve had enough.

I probably would have made time to ask if we could sit down and talk about technology someday. [My principal] had told me that you had been talking about the use of technology in the classroom, and so I would have wanted to share with you my vision of a digital reading and writing workshop with online portfolios for parents to look at that mimic the ones we kept in class this year. I would have told you about the grants I’ve already applied for, the fundraising project that I’ve got up and running, and the possibility that we could be selected to put the project up for voting for the Pepsi Refresh Grant (it’s $50,000, and we were selected in the preliminary round). I would have told you how Language Arts was going to be a game next year. The kids would have thrived.

I envisioned that this could be the start of something great.

But then Friday happened, and [my principal] put a piece of paper in my hand to sign even though, he said, he didn’t believe in it. He explained that you forced him to do it. I got the feeling that his job was on the line, so he didn’t have much choice.

I can’t sign a paper that says I haven’t proven myself worthy of tenure – that’s certainly not true. I have. Over and over again. I try to follow my conscience, and something is telling me that that is not what this is really about. If this is a blanket extension and no one in the district is getting tenure, then I’m fine with not signing it because this system is about to get really ugly, and I don’t want to be a part of it.

If some teachers in this district are getting tenure, then I really hope that you read this letter with an open-mind and you’ll reconsider your decision. I am a mission oriented teacher. I believe not only in education, but the power of education to change lives. I’m afraid that if you deny my tenure, there will be an important voice missing as whoever is in charge of [my school] next year tries to fix the school that Joe broke (understanding that that person could very well be [my principal]).

Signing away my right to complain or have access to courts over this process that has been so disastrous and torturous for me is to much to ask a person to do.  Agreeing that I need another year before I can be tenured is also against my conscience.

I sincerely hope you’ll look at the big picture, listen to the parents, listen to the kids, listen to [my principal], listen to this letter (my soul is in here if you look for it), but mostly, I hope you listen to you. Several of my biggest supporters say they have a good relationship with you, so I am giving you the benefit of the doubt. What does your gut tell you? If you truly believe that I am a wild card, then go ahead and deny me, at least you’d be following your conscience and doing what is right for kids.

But if any part of you is starting to think I might be the real deal (I am) or is concerned about who will replace me next year, please consider changing your mind. I am going to be really honest with you, at this point, this process/system has left me jaded, and I am going to need a while before I know for sure that I want to come back next year. But if your don’t approve my tenure, you’ll remove that possibility for [my school] and for the students. And, believe it or not, they need me. They really do.

Please reconsider.

Sincerely,

A Fordham Leadership Academy Xerox Tangent

May 13, 2011 pm31 9:43 pm

Betsy Combier writes about difficulties helping a Fordham Leadership teacher at a trumped up 3020a. A judge threatened to call security because she used the Xerox.

Regular readers may remember a thing or two about Fordham Leadership Academy for Business and Technology. We protested against Principal Bost for sexual harassment at the beginning of the school year. (Betsy focuses more on the financial misdeeds of the AP going after the teacher)

Rally Tomorrow – May 12 – City Hall to Wall Street

May 11, 2011 pm31 10:58 pm

on_may12_flier_uft – 4 PM – City Hall – and on to Wall Street

On May 12

Superintendent threatens principal for offering teacher tenure

May 9, 2011 pm31 10:31 pm

Absurd? Ridiculous? Yes. But true.

The story that follows is from a NYC teacher, third year, in a middle school in a NYC district. Her name and school are not available yet, but will be, soon.

She saw the story I wrote last week, about my friend up for tenure instead having his probation extended, about all the probationers in his school being extended, en masse, without even looking at them.

And she added her own story. Read it:

About Me:

  • -I have been teaching for more than eight years – all but the last three were in the State of Texas.
  • -I currently teach at a school that received an A.
  • -The TDI from my first year in the DOE called me a “Low Performing” teacher – I had 67 students, zero failed, one got a two, all the rest earned threes and fours. From my reading of that TDI report, the growth rate of my students was -.07 which seems to me to be just about a years worth of growth, on average, for my students.
  • -The new TDI report calls me “Average”, and it doesn’t mention the rate of student growth. I read this article: http://www.edwize.org/burying-the-bias-in-the-teacher-data-reports#_ftn2 and theorized that that could have something to do with the reason, but I will admit that all of these numbers and the analysis of them confuse me.
  • -As far as this year goes, with two CTT classes and one SETTS class, not one of my students failed the predictive assessment. I have every confidence that my students were amazing on the ELA that they took this past week.

———————–

(letter to UFT borough office follows)

Dear ______________,

Attached is the extension letter that I received from my principal this morning. I had previously been recommended, but due to pressure from the superintendent, my principal was forced to give me and the five other people up for tenure Letters of Extension (she told him that if he didn’t give us the extension letters that she would fire all of us). All of the other teachers were given extension letters weeks ago, and the principal decided at the last minute on Friday to recommend tenure for them, but I got my extension letter today.

I do not intend to sign the extension letter for several reasons. One, I am a teacher deserving of tenure (according to the rubric I was given in December) at a school in which I am a vital part of the community. Two, this process was time consuming and I will not go through it again. I spent months creating my tenure portfolio with the assurance from Alfred Gonzalez that the superintendent has promised that tenure would be handled on a case-by-case basis. I am an excellent educator, and my time needs to be spent innovating my classroom and not constantly worrying about how to present information about my classroom to a person that doesn’t seem interested in looking at it anyway.

This process has really made me question the effectiveness of the public school system. I teach at a school that I am completely in love with. I have a relationship with every single one of my 90+ students. My students’ test scores have shown more than a year’s worth of growth. I communicate with parents every week through email and provide and update a website with information. I have 51 glowing letter of recommendations in my tenure portfolio from parents, students, and colleagues. If the Department of Education is willing to communicate to me that they aren’t sure of me as a teacher, then I am prepared to find other ways to utilize my gifts as an educator.

Sincerely yours,

signed

——————-

When my principal gave me the extension letter on Friday he told me that he didn’t agree that I needed/deserved to have my tenure extended. He added that, “If you don’t come back, I’m notcoming back.”

I am officially “recommended” by the principal because he says he can’t change it, but…

Last Friday, at the last minute, he decided to recommend all of us for tenure because he felt it was the right thing to do.

The Superintendent basically told him that if he wanted to remain the principal, she would support him, but that if he wanted to leave, she’d understand. She also either told him or hinted to him that the staying and supporting wouldn’t happen unless he gave us all letters of extension (I was the only one that didn’t get one initially). She also told him that if he didn’t do it she would fire all of us. So this was a blanket extension – the superintendent hasn’t even looked at the beautiful portfolio that shows who I am as a teacher outside of faulty TDI reports (the reason I know this is that it has been in my possession except for the three days that the Assisstant Principal had it in her filing cabinet this week), and the principal told me that the superintendent has not been to the school and has not looked at it. It is now in my possession again because I want to make sure that I know if and when she looks at it.

All of this was told to me by the principal.

Yesterday, he gave me a Letter of Extension that I refused to sign. I have been assured by the UFT and the principal’s hunch is that I will be denied. Apparently, if that happens, I will be immediately removed from the classroom to await a hearing that will take “months.” I am prepared for this possibility.

I am also assured by the UFT that I will probably lose. They really, really pressured me to sign it. But I won’t do it.

It is nothing short of cruelty to give teachers a four-pronged rubric to satisfy and then not even look at if or how they satisfied it, and I don’t want to let them get away with it. But it does mean that I am probably going to lose my job because as a probationary teacher, I have no protections and they can fire me for any non-discriminatory reason they want. I spent hours and months putting together a true picture of the teacher they would be rewarding with tenure, and I am furious that it wasn’t even considered in the decision to extend.

I believe the main reason they are giving is that our principal has only been at the school for two years (even though the rubric says that two years is what is required). Ironically, both the principal and superintendent approved tenure for two teachers last year after he’d only been there for one year, but I’m guessing that was because the pressure to deny, deny, deny was less last year than this year.

When and if I am removed from the classroom, I have a feeling that there will be a lot noise from the parents based on the fact that with one request, I got thirty-four amazing letters of recommendation from them.

I think that my only hope is for the principal to convince the superintendent that it won’t be worth it to deny me because I won’t remain silent about any of this.

But it also means that I need to start planning for how I’m going to pay my rent and feed myself.

But I know this. The thing about which I am most confident in myself is my ability to teach and reach kids, and to learn and grow throughout my “tenure” as an educator. I did a pretty good job of showing that in my portfolio. And once I got started creating it, I didn’t even regret the process. It helped me know who I am. And if the DOE isn’t sure of me as a teacher, then I am certainly sure that I do not want to work for the DOE.

The irony is, I actually agree that tenure as it has been in the past is a problem and making the process more of a reward for excellence is a good idea, but I am so confident in my abilities as a teacher that I know that that is not what is happening here.

My questions are:

  • -Who are the teachers that are being granted tenure this year? What schools are the in? What kinds of schools are they in? What districts are they in? Who are they friends with?
  • -If my colleague who is also up for tenure is being honest (and I have no reason to think they’re not), why did the principal say “off the record” that the DOE is trying to get the tenure approval rate down to 50%? Isn’t that a quota and against any philosophy of tenure becoming a reward that you can earn?
  • -Why do the 2011 up-for-tenure teachers have to be the ones to suffer while the DOE tries to passively eliminate tenure by just not granting it to anybody? That seems patently unfair and downright shady.
  • -Why is bullying being used as a tactic in tenure decisions?
  • -Why is a person who has very little idea who I am as a teacher able to override the person who does?

I’m sure I have other questions about the injustice of this (for both teachers and students), but I can’t think of them right now.

I know that I can just sign the letter and keep my job, but my conscience tells me not to, and I don’t think I could make my hand sign it anyway.

Bloomberg escalates war against students, teachers, public education

May 6, 2011 pm31 5:20 pm

Today’s layoff notice was shocking? Not really. We knew. We all knew it was coming.

Many of us knew, all of us should have known, that he has been destroying public education for 10 years. One day he chips, another he chisels. Today he unveiled a wrecking ball.

Testing, charters, evaluation, “Fair Student Funding,” the “Open Market,” “colocations,” overcrowding, restructuring I, restructuring II, restructuring III, school closings, “bonus” merit pay, gifted and talented – all he’s done is disorganize, delay, destroy.

But today’s layoff announcement stands out – there is no need for layoffs, money is there. Bloomberg rubs his audacity in our 8 million faces.

Our response is important. We must use the contract, to the extent we can. We must use the courts as is possible. We must mobilize public opinion as best we can.

Our greatest potential power, though, is not our lawyers or our media people. It is our ability to act collectively. This makes mobilizing next Thursday, May 12, important.

Far more important, however, is building the capacity to mobilize 100% of our membership, for whatever demonstrations or mobilizations we need. And today? We cannot do that. Building that foundation, that ability to act, is crucial.

Because the war was just escalated, and we have many battles ahead.

Open Market Transfers in NYC are open, but not open?

May 5, 2011 am31 7:41 am

Something is screwy with the open market transfers. I presume the DoE is at fault, and trying to harm us. That is, in recent experience, a fairly good assumption.

(I hate that phrase, open market. It is not an open market. It is a contrived system without rules and protections to make it difficult to transfer, at the same time the DoE forces, through closings and systematic disruption, many more teachers to need to transfer).

The expired (and still in force) contract says that the open market can open any time on or after April 15, and closes August 7. Past practice was to open it soon after April 15. And we did get a little note saying that it was open. The website says it is open. But this is three weeks after April 15, and…

Teachers can log on. And see no listings. Zero. None. Not “just a few” but actually zero. And I’ve learned that principals can log on, but cannot add listings.

What’s going on?

Maybe principals are delaying posting, until they know the budget. Um, no. Principals who want to post cannot.

Question 1:  Has the DoE said why it is screwing around?

Question 2: Are the postings for the newly formed schools, those “colocations” that are squeezing out closing schools, are they open? Sure enough a weird thing called The Teacher Hiring Support Center (it’s got DoE-ish lettering, but I am suspicious – someone should check if it is private) includes listings for all the new schools, with a May 13 application deadline.

Question 3: Are they delaying to force people to apply at start-up schools?

Question 4: Are they delaying to ease the crunch if layoffs happen? Friday Bloomberg will probably be announcing totally unnecessary layoffs. As a result, there may be some movement of teachers between schools.

Question 5: Are they delaying to disrupt the system? Hmm. Most people will transfer, if they have to, between April 15 and June 28 (last day of school). That’s 10½ weeks. Oops, May 13 – June 28 is 6½ weeks. Would Bloomberg tighten the schedule to make people nervous and jumpy? To make them more afraid?

The disruptive questions are 3 and 5. They match Bloomberg’s style, and his contempt for kids, for teachers, and for public education.

Those are my guesses, until and unless we get further information.

Not celebrating

May 5, 2011 am31 7:10 am

I could care less about the rich guy’s kid. Sure, he’s an egomaniac and self-promoter, but the way he gets his jollies by firing people on tv, or by ruining businesses, in either case, not entertaining, not funny. Were he to leave this place today, it would not be diminished, but I probably would not cheer.

It’s not so different about how I felt about another rich guy’s kid. Egomaniac and self-promoter. But instead of tv he found religion, and killed a lot of people. Osama did far more harm than Trump, but I will not / would not shed a tear. They disgust me.

Bin Laden was an excuse for war, torture, curtailing our own freedom. Now that he’s dead, will those evils be undone? No, they won’t.

Nor, however, will I celebrate.

I feel some sadness. Not for bin Laden, but for us.

The US Government used Osama bin Laden as an excuse. To launch two wars, leading to thousands of American deaths, and perhaps two hundred thousands Iraqis and Afghans, soldiers and civilians. To foment hatred. To make super-profits for Halliburton.  To demean Iraqi prisoners, and to demean their jailers, by tolerating and encouraging acts of humiliation, degradation, and torture.

The US government used him as an excuse to suspend the constitution, as if “but only for bad people” meant something. Rendition? As an excuse to make us uncomfortable and ridiculous at airports, and as an excuse to have screeeners’ hands probing our luggage, and then our selves and our families.

Wisconsin is an extension. Stealing our right to strike, our right to organize, is another. Stealing our pensions is more up Trump’s alley, but it’s all part of one ugly, growing assault.

I will not celebrate bin Laden’s death. I am saddened by our loss of freedom’s… but the culprit was not killed in Pakistan. The culprit is our own government.

Math and Solidarity

May 1, 2011 pm31 11:52 pm

I wish I had a big splashy piece for May Day. But no. Not here, not this year. This is just a little something I’ve been wanting to point out for weeks: math teachers played a nice role in EduSolidarity Day.

March 22nd NYC teachers wore red in solidarity with teachers in other states (Wisconsin led the headlines). And Steve Lazar (blogs at Outside the Cave, which despite coming from the Western Reserve, has nothing to do with Jacobs Field) thought: why not a blogger thing? a group answer to the question: Why do teachers like us support our unions?

So he gets me and Jose Vilson and Ken Bernstein (Teacher Ken) on board, and we launch, (facebook, too) and over a hundred bloggers write. Nice little splash. But math teachers? We were counted.

  1. First, Vilson does a clever lead in (union=unity, not a job, a career) to his real post, over at Huff. Jose teaches math.
  2. I teach math, and posted. (It is my damned union. Can you imagine anything more foolish than fighting a lion with a folding chair? answer: yes, throwing away the folding chair). And then I posted again, more calmly, but not as well.
  3. Kate Nowak, at f(t). With a salary schedule she knows she’s getting paid like a teacher, not underpaid as a woman. Great math blog, by the way.
  4. Dan Anderson at A Recursive Process. Unions make teaching better. Another great math blog.
  5. David Coffey at Delta Scape. Letter to the editor (Michigan). Teaches math, and teaches math teachers.
  6. Suzanne Donahue at EduSolidarity Essays, reminisces about a strike she was on in the 70s, as a new teacher.
  7. Roseanne McCosh at EdWize. The union lets her speak without fear, including advocating against Every Day Math. (I am with you on that, Roseann)
  8. Zeno Ferox, at Halfway There (math teachers and philosophy majors, you can stop snickering now. Apologies to the rest, and no, no explanation is coming). Makes math teaching, public schools, and unions go together like milk and oreos and something else.
  9. Mimi at I Hope This Old Train Breaks Down. Wouldn’t have gone into teaching without a union. Writes about math and other things in her school in El Salvador
  10. Julia Tsygan at Learning (by) Teaching. In Sweden her union negotiates neither pay nor job security, but working conditions. And to do that, the union joins them… The day of the post she became union rep, and it’s still her most recent post… But I know her more as a math blog commenter than as a math blog writer…
  11. Brian Cohen at Making the Grade. The union helped Hope Moffett get back to class after the District tried to fire her for speaking out. Plus teachers need a support structure, and unions help kids. I found Brian’s blog, new Philly math teacher, into good teaching, but there was no e-mail, so I facebook stalked him to ask him to participate. Creepy, huh? But worth it.
  12. Nick Yates at Maryland Math Madness. Self interest. On Principle. In the Interest of Students.
  13. The official curmudgeon at Math Curmudgeon. Unions are the force that makes education work as smoothly as it does. High school math, from the right side of Vermont.
  14. Chris Hill at Math is a Shovel. Without a union, he’d be making more money with his math skills doing something else.
  15. Sue Van Hattum at Math Mama Writes. Unions push for smaller classes and better working conditions, which are better learning conditions. Sue writes about math for kids and college, alternately serious and playful.
  16. Owen Thomas at MathEdZineBlog. come over to our side/ treating people as ends-in-themselves/ is more *fun* than treating them as cannon fodder. (why do I think this was meant as poetry?) Vlorbik writes about little things. Like math, and guitars. And makes MathEdZines… foldables with symmetry groups hidden on them.
  17. John Golden at mathhombre. Never have I encountered a group more likely to be intent to seek the good of others – he only hope we have of gaining a voice is to stand together. Had no idea this math blogger (carnival host, even!) was pro-union. Should have known.
  18. Kristen Fouss at My Web 2.0 Journey. We need unions with all the stuff going on in those states. And she’s from Ohio. Lots of high school math, focused on course content.
  19. Courtney Ferrell at No Teacher Left Behind. Unions help us teach better. We drove together to a math conference, AMTNYS, in Saratoga Springs five or so years ago, but were not in touch. I was pleasantly surprised to see her name pop up.
  20. Christopher Sears at Omega Unlimited. Teachers need a collective voice to keep the public discourse fair. College guy. Policy and teaching.
  21. John McCrann, guest at Outside the Cave says kids are better served in a unionized classroom, and that the middle class deserves its fair share.
  22. Pat Ballew at Pat’s Blog. Go ahead, teachers, rattle the bars of your cage… use your voice while you still have one…. Great math teacher, blogs all math, all the time, hard high school stuff. Plus history.
  23. pissedoffteacher at Pissed Off Teacher. can’t imagine working without having a union watching her back. Blogs about teaching math, for a long time, the sweet kids, the crazy school, the off-balance administrators.

There could be a few here and there I missed. But 23 out of 105? Not too shabby for our slide rule and pocket protector brigade.

Two tiers in NYC? Not just schools. Parks too.

May 1, 2011 am31 9:41 am
Hat tip, David Quintana

Melissa Chairs Hearing on the Parks Enforcement Patrol (PEP) Program

April 29, 2011 by newsfrommelissa

New York City Parks Enforcement patchImage via Wikipedia

Melissa chaired a hearing on the City Council’s Parks & Recreation Committee on Wednesday regarding the Parks Enforcement Patrol (PEP) program.  The hearing focused on the disparities in the allocation of PEP officers among different parks and communities as well as workplace issues faced by the officers.

PEP officers are unarmed peace officers, who enforce the rules of our parks and are empowered to issue summonses for quality of life offenses, as well as disorderly conduct and unlawful possession of weapons.  They also review park facilities for health and safety issues.  There are currently 92 PEP officers to cover over 28,000 acres of parkland, with an additional 83 officers that are contracted by conservancies and other private entities to work in specific parks.  There are often just a few at-large officers on duty at any given time for the entire borough of the Bronx, whereas in a single park in communities of greater means, there might be a dozen.

Melissa and other members of the committee stressed the need for more resources for the PEP program so that these officers can cover more parks, particularly at a time when the City is seeing an increase in crimes committed on parkland.  Melissa also highlighted that the practice of contracting with private entities that are able to purchase increased security from the department while the majority of other parks go unsupervised sets up a two-tiered system in our public parks.

The hearing also focused on the issues that PEP officers face as a workforce. Several officers came to testify about the difficult and dangerous jobs they do, including doing car stops and removing homeless individuals from parks, without the help of the NYPD or the Department of Homeless Services. They asked for greater numbers of PEP officers and more support to help make our parks safer.

In the coming months, the Committee plans to hold another hearing jointly with the Public Safety Committee on crime in parks, which will continue to examine these issues.

Coverage of Wednesday’s hearing:

A probation extension incident

April 30, 2011 pm30 12:54 pm
tags:

A young friend, third year teacher, brought his portfolio in this week, so the administrators in his school could review it in making their tenure determination. He got the answer the same day – the same answer over a dozen colleagues, all who were up for tenure, got – extended. They did not review the portfolio. They did not come up with a real reason. “You will be better next year.” “There are just a few things you could work on.” “…classroom environment…” (peers consider that one of this teacher’s greatest strengths)  “TDR well above average, but inconsistent…”  (75th percentile with one group, 60th with another). More than a dozen teachers got the same. You see these people? They cheat. They lie.

How common has this become?

We suspect that principals are under orders to deny tenure more frequently. We believe that they have specific guidelines, not shared with us. These might include someone with a substantial number of absences, even though the sick days are provided by contract. These might include teachers who have transferred after two years. Principals might also have school-specific target numbers for denying or extending tenure.

New Action focuses on abusive administrators. And sure enough, these tenure denials and extensions are principals’ recommendations. And some of the principals are nasty and vindictive, and intentionally make teachers suffer. And some are just lousy principals – to be expected in these days, when Tweed promotes inexperienced administrators and rewards loyalty over competence.

But the villain in this story is not principals as a group (though some are, too many are, individually), but rather Tweed, which is promoting insecurity among the workforce, in order to cow us, in order to scare us into concessions, in order to intimidate us into not asserting our rights, in order to promote turnover, in order to make this a temporary job.

So again, how common has this become?  At how many schools is tenure being routinely extended, without cause?

Fewer Tests? My precalc experiment

April 27, 2011 pm30 9:31 pm

Actually, no tests. Just quizzes, and a final exam. Quizzes are 1 – 6 questions, most typically 3. And anything wrong? They can take the quiz again. Some topics, I want a one question quiz. Or even, in one case, a one question quiz that counted for 3 questions (Gave the kiddies 3 sides of a quadrilateral, and an included angle, and an unincluded angle, and asked for the area and perimeter of the quad).

Is this the vaunted standards based testing? No. No standards were consulted. This is part of playing with developing a new precalculus.

At the end of the year, I’ll need to summarize. For now, the kids love it (a few are neutral. One or two miss tests). Parents love it. Me, I’m okay. Motivation seems higher. There is less discouragement. I am concerned that there is less synthesis, but perhaps I am wrong. The paper work is annoying, both due to the frequency of the quizzes, and the tracking with requizzing individual questions.

But I think eliminating 6 tests a year, even if they are just itsy bitsy classroom tests, is a teensy blow for justice.

Teacher Data Reports in Texas?

April 26, 2011 pm30 10:15 pm

Not quite, but close.

Dallas history teacher and blogger Ed Darrell (of Millard Fillmore’s Bathtub) explained in a comment here:

Here in Dallas ISD it’s the CEI, or “computed efficiency index,” or some other bafflegab.

Bottom line, since I left Irving ISD I’ve picked up a couple of points on the state tests — just under 95% of my kids pass. Last year I picked up ten points on “commended” ratings. We’re five years ahead of plan in social studies on the scores on the state tests. We do well, and I do well, in all demographics. Some of my SpEd kids got commended ratings.

But according to the CEI, I’m bottom of the barrel.

NEA and AFT push constantly to get someone from the district to explain the ratings, but they can’t be explained to the satisfaction of any statistician who has looked at them.

It’s just one more weapon administrators and “policy makers” have for the War on Education, and especially for the Battle Against Classroom Teachers. These ratings are like neutron bombs — they take out the people, but leave the buildings standing.

These ratings are made by people who think a school is a building, and a child is a “raw score” on a test.

Folks, not only are teachers in trouble. America is in trouble.

A Spring Hike

April 25, 2011 pm30 10:00 pm

The weather was beautiful today. Well, it was nice. And compared to the forecast, it was beautiful. Instead of thunderstorms, we had just a bit of drizzle. And less sun than we would have liked, but more than we were promised.

I went with a school group, another high school, up the Hudson Line to Garrison and hiked Sugar Loaf. It was nice to be out. The hike was moderate. I hurt a foot a while ago, and thought it was better, but this was the first test. Foot?  Ouch, blisters. But the previous hurt is still previous. And the weather cooperated. Even the rain was just a nice interlude. The bugs were not too thick, and no mosquitos yet. (we did find two tics).

The kids were great. Seventeen, about half and half seniors and juniors, with two mature sophomores. They loved being outside, and appreciated the opportunity. Sometimes I just swept, sometimes I talked (remember, I didn’t know any of them, not from my school), and they were interesting and pleasant. Eventually I had some sort of conversation with each of them. All were ESL, all Spanish speakers, and all from DR except one from PR and one from Honduras. The boy from Honduras, when I spoke, there was something about his accent. I thought. And then asked “What is your first language?” Bingo. Garifuna. And then he told me about his family, and how the younger siblings just use Spanish and English, but how he continues to use Garifuna at home.

The cactus on Sugar Loaf looked healthy, there had been some sort of burn going up from the meadow near the start of the trail, with fallen and standing trees both scorched, and there were plenty of small animals to entertain the kids. Chipmunks. Frogs. Toads. And one pileated woodpecker.

They played a game in Spanish, actually two games, that I sort of figured out. They assigned each player a rank, eg Captain. Then one player would say “I took roll and everyone was here except the Major” the Major would object “The major is here!” and the first player would ask “then who is missing?” and the Major would reply “The Lieutenant” at which point the Lieutenant would object “The lieutenant is here!” and the major would ask “Then who is missing?” and the lieutenant would say…

The object was speed. It was not easy to listen for your name/rank, and to remember when to jump back in. Much laughter. Later, they played the same game, but with parts of a cow. The kids playing the eyes and ears had fun, but the <i>culo</i> and <i>teta</i> were just plain silly.

My school returns to Breakneck Ridge in a few weeks. I can’t wait. (2007. 2008. 2010.)

Rational Expressions and Functions: unit, worksheets, quizzes

April 24, 2011 am30 11:50 am

I created this year a unit on rational expressions and rational functions for some mixed precalc classes. We will end up with 10-11 days, some of them review.

I am proud of the idea. The execution? It will need much refinement. I liked the third worksheet especially (4 and 5, below) but it needs expansion, clarification, etc. The first two worksheets are probably fine as they are, but they are fairly standard stuff.

The first quiz is gimme. I taught most of these kids to factor 3 years ago, and did it again last year. The second was something new. Only about a quarter attempted the bonuses, but most of those were successful.

I think the third quiz is a wonderful idea, but it needs work. It was very open-ended, so the seniors who are ready to check out probably could come up with something, and the juniors who are scared of AP could write much more. But how to grade it?

1. Reducing, multiplying (worksheet:  PC2 Rational Expr Reduce demo  )

2. Adding and subtracting, review polynomial division, converting  mixed expressions to rational expressions and back (worksheet: PC2 Adding Fractions demo  )

3. Partial Fraction Decomposition (handout borrowed from a text the school uses for another course)

4. Graphing functions of the form f(x) = k + \frac{a}{x-h} – the effects of k, a, and h (worksheet PC2 graphing a over x demo ) This worksheet is for day 5 as well

5. More graphing functions of the form f(x) = k + \frac{a}{x-h} and slightly more complicated forms, eg  f(x) = mx + k + \frac{a}{x-h}. Emphasis on asymptotes. Linear behavior of rational functions. Worksheet from 4 and 5 probably needs to be stretched with more guided examples, and over more than 2 lessons. My kids tolerated it, but it was tough.

6. Handgraphing rational functions  Gelfand chapter 5 Functions and Graphs (there is a reason I had the school buy fifty of these suckers. I just didn’t really know the reason back four or so years ago when I pushed it through)

7. More handgraphing Gelfand chapter 7

8. Emphasis on end behavior – I borrowed someone else’s worksheet, didn’t work so well as it really wasn’t written for the purpose I tried to put it to.

9 and 10 will be for review and completion. Also for retaking quizzes that did not show knowledge of the subject. (this is not my general practice, but reflects the reality that these are days D minus 3, 2 and 1 before the AP exams.)

Quizzes:

Quiz 12: Adding or subtracting rational expressions (two challenging questions, factoring required) PC2 Quiz 12 demo Quiz 13: Decomposing a rational expression using the method of partial fractions (one question, plus bonuses) PC2 Quiz 13 demo Quiz 14: Graphing rational expressions. Two questions: read the graph, write the equation, and given the graph and the equation, explain the relationship between the algebra and the form. PC2 Quiz 14 demo

Where’d I get this geometry puzzle?

April 23, 2011 pm30 1:20 pm

Embarrassed. I shared a puzzle, thought it was massively cool. And I want to give credit, but don’t recall where I grabbed it from. Any helpers?

Consider a square. Consider four circles, centered one at each vertex, with radius equal to the length of the side of the square. What is the area of the intersection of the circles (in terms of the radius)?

The original only gave the quarter circles within the square. I think it gave sidelength = radius = 1. There was a diagram included, maybe?  And there was a word description of the region, something like a “bulging square”

You want to try solving this?

But more importantly, can you tell me who to credit?