So considerate
I use variables in class. Algebra. It works that way.
I use funny scribbles that look like obscured numbers. Occasionally. Always when I teach factoring by grouping (what we did with one number we can do with a cluster in parantheses).
And for special problems, or for fun, I use special variables. I used to like smileys and unsmileys. But a few years back, I started with elephants. And sea monsters. Click for a sample.
And yesterday, see how considerate! a student sent me this link:
So perfect!
UFT Election Results?
I’ll be posting results of some sort (probably not finalized??) – I hope later today?
I am a candidate for high school executive board, the only seats anything close to “in play.”
I’ll be trying my hand at some initial analysis.
Some thoughts:
Michael Mulgrew’s total. Cross-endorsed by New Action, it should be relatively high. Will he get the benefit of the doubt for being new? Nah. If the total is strong, chalk it up to how tough he’s been over the first few months.
Middle Schools. Only head to head Unity vs New Action (don’t know why ICE has no candidates)
Overall turnout. We want the raw total to have gone up, or at least to have stayed steady. Especially important among active teachers.
Surprises. If turnout levels off or rises slightly, and the caucus by caucus percentages stay around close… then searching for deeper patterns means we’re looking for nothing. A few general remarks, and done. But if anything shows up quirky, there will be more to discuss. Don’t count on it.
Burnt Spaghetti
- Cook spaghetti (normal way)
- Toss with some onion (sauteed) and a little cooked tomato, or a small amount of tomato sauce.
- Place spaghetti mix in a brownie pan, lined with tin foil.
- Place under broiler. Take out when the spaghetti and onions on top are slightly crispy.
Small Schools by Mike Klonsky and Susan Klonsky
Here’s a review I didn’t mean to write. I read most of the book in the summer of 2008, while I was in New Orleans, helping (re)organize school teachers. What happened? I thought the book covered important background about what happened with small schools. It reviews their progressive origins. And it details how the corporations and foundations and government grabbed their banner and turned them into something very different. And I should have reviewed and recommended it. The background matters. The narrative matters. The dark fable matters.
But I didn’t write then. Why not? And why now?
Democratic Schools are good, and it is possible to create small schools that are democratic. YES….
became: Small schools are good. NO.
I didn’t write because I was not ready to share my critical evaluation of the (well-meaning, progressively-oriented) activists, who happened to be the authors. And now? One of their allies, Deborah Meier, recently wrote a column? blog post? in which she expressed ideas that resembled my unwritten criticism. That makes me feel less uneasy about sharing my own thoughts. So, onward.
The Book: Brief history of the small schools reform that progressive activists were involved in. And then the beginning of small schools as national policy – not as an outgrowth of the work of Meier and the education activists in Chicago, but as something new and different. (and corporate, and anti-empowering if there is such a word).
Four important chapters on this new small schools movement, this anti-democratic movement: Government Ideology (the Klonskys discuss this as “the ownership society”), Private management, corporate philanthropy (Gates, Broad, etc), and corporate ideological activism (think tanks). Each chapter carefully documents the growth of these four facets of this anti-democratic movement.
A final chapter, “Alternatives to Top-Down Reform,” is, for my money, short on ideas beyond recapturing “small schools” and involvement of parents, students, and teachers.
Thumbnail evaluation: The background is useful. It deserves a full book. (I’m guessing that one exists). But even the abbreviated form is useful. The meaty chapters (Ownership Society, Private Management, Philanthropy, Think Tanks) – all worth reading. All provide important detail. And the threads that connect the four really start to build the big picture.
Big negative: even though the book is brief (fewer than 200 pages, with notes, and small format pages: 8″ x 5″) it read as if it were much longer. Glass houses be damned, the prose is too dense. The style, idk, it’s almost academic, but not… in any event, it made for slow reading. I felt tired after each chapter. I accidentally reread passages. I intentionally reread passages because I hadn’t understood them the first time. This book is part of a series that claims to produce short, accessible books. My guess is that my difficulty reading represents a fault of the series editors, not of the authors.
Back to the authors. I’m sitting reading, and thinking: they were concerned with the democratic aspects of schools, but they focused so hard on “small” that they seem to have missed what was happening. Not retrospectively, but in the moment. This is, in part, Meier’s self-criticism: (I urge you to click through and read the whole piece. It’s excellent. And it really tells the history nicely, and briefly, and honestly)
It’s not the first time I’ve noted how even my good ideas can be “corrupted” for quite different purposes than intended. It’s the story of many of the political ideals I still hold to. Small schools were a tool, not an end….
Two of my favorite ideas: small schools and choice – have become bywords of reform, backed by millions and millions of dollars and the power of the city, state and federal government…
These two ideas became popular at a moment when the nation was moving to the right, not the left and when the idea that “the free market place” was the over-riding safeguard of our liberties held sway…
My slogan in the 80s and 90s was … self-governing small schools of choice, democratic schools where most decisions were made at the place that family, teachers and students met….We did not face a new educational crisis but just one more educational “opportunity” to rethink practices that have not served us well for a century and more….We could nudge, and we could set the odds in favor, but we cannot and should not override the opposition through mandates.
I believed, in hindsight maybe foolishly, that smallness was perhaps something however that could be mandated….
Although not followed through in New York, the ideas of small schools and choice was picked up by others. My joy that many a Big Business was also excited by our ideas gave me hope. My paranoiac antenna was overcome by the unlikely friendships the idea seemed to create. When charter schools began I saw them as an offshoot of our ideas…
I think in the focus on “small” they may have neglected to pay sufficient attention to “what kind of small” – this struck me at the start of the book, and even moreso in the the concluding chapter.
The Klonskys date the new movement to post-Columbine, but New York City was getting a small-scale small school invasion for several years immediately before. In the Bronx where I teach, breaking up big schools has a little more history. James Monroe. 1994. Replaced by little high schools that seem to be from the progressive mold: New School for Arts and Sciences (since closed), Monroe Academy of Visual Arts and Design (I figure the graffiti class can be a proxy for “progressive” no matter what anyone thinks of graffiti), Monroe Academy of Business and Law (saved by Justice Lobis for now), Bronx Little School (as progressive a small school name as you could imagine), High School of World Cultures, Bronx Coalition Community School (in the process of being closed). But just a few years later, the same New York State process began restructuring Theodore Roosevelt, and William H Taft (they were capped, I recall, in 1999 or 2000). The schools formed there were no longer of the same progressive type (though small). The names are themes, and fairly generic (arts, medicine, business, writing, “prep,” etc) and they feature fairly unprogressive reform (such as leaving the kids in one room all day, while the teachers rotate. Great for attendance.)
In any event, the flood of cookie-cutter mini-schools at the start of this decade, the book documents the process that got them going. But I don’t feel that they dug adequately for the roots.
Finally, a different sort of quibble: As a union person, I am especially interested in the roles of teachers and our unions. Their absence in chapter 1 reflects real history, but their relative absence from the concluding chapter bothers me. The Klonskys seem to prefer using “teachers, parents, students” and “educators” over “teachers” and “teachers’ unions” – I consider myself and my colleagues and our organization key “actors,” and would have preferred the language better reflect this potential.
– – — — —– ——– ————- ——– —– — — – –
“The Death and Life of the Great American School System,” by Diane Ravitch is all the rage today. And it should be. Important read. But you can also read history told by progressive activists (remember, Ravitch, while she supports public schools, is certainly not progressive).
The Klonskys are activists, and they have an important story to tell about how their movement was absorbed by its opposite, by its enemy. I’ve pointed to some faults, but I’m also telling you it is an important (and tiny and available on Kindle) book. Get it. Read it.
Vacation Pause
After a tough fall and winter, it’s been nice to slide into spring with a nice big break.
Did my taxes (or better yet, watched my accountant do them – gave up on doing my own a few years ago).
Visited family. Saw some (in the scheme of things) minor Connecticut flooding.
Saw two movies (Close Up is a twenty year old Iranian film by Abbas Kiarostami. He films some pretrial footage and the actual trial of a conman accused of impersonating another Iranian director, and then gets the conman and the family to reenact the scenes leading up to his arrest. The Secret of Kells was nominated for an academy award this year, feature-length animated. It was diverting, even riveting. Cool music. Beautiful artwork. Loved the forest. But the story, meh.) Will see at least one more, maybe a few.
Set up tutoring sessions for college students.
Walked a little.
Ate better.
And let go of blogging… but have a bunch of ideas percolating. Should be back soon, with a flurry.
For my teacher (and SRP) friends, enjoy the second half of break. And if you haven’t cast your ballot in the UFT elections…
RTTT-1: Duncan’s casino w/fixed winners & enough razzle dazzle to keep the suckers coming back
This is sick.
Race to the Top, offering states carrots ($$$ carrots) to wield sticks against teachers’ unions and needy districts (merit pay, breaking tenure, charter schools, etc…) turns out to be a 3-ring, 24-hour, 365-day affair. Educational gambling. The Arne Duncan casino. Minus the floorshow. Plus some racketeering?
First round. Lots of money. Well, nope. Only two states scored. Delaware and Tennessee. Delaware and Tennessee?
What good fortune Obama has!
Tennessee is home of Republican Senator Lamar Alexander. And, look at this, Tennessee is getting twice the money that the Feds said it should ask for. Can you believe Obama’s luck? Because not only is Senator Alexander a nice man. He’s also a key vote for ESEA. Chairs a crucial subcommittee.
Delaware Republican congressman Mike Castle also chairs a key subcommittee. Whoa, Obama is hot! And, get this, Delaware is also getting more than the feds suggested was the right amount.
Lucky is lucky. Just yesterday the Washington Post quoted Duncan saying how much he liked Castle and Alexander. Imagine that?
And do the other 46 states go home sad? No! No losers in Duncan’s casino! They get to keep beating their unions and poor neighborhoods as they prepare their applications for Round 2.
– – — — —– ——– ————- ——– —– — — – –
It’s time (past time) to say NO to Race to the Top. Let’s withdraw from the second round of this sick game.
Little latitude and longitude puzzles
So you think you know north from east?
Try this quizzies (no fair peeking!)
Put in order, south to north: Salt Lake City, Denver, Kansas City, Cincinnati, Baltimore, Philadelphia
Put in order, west to east: Detroit, Cincinnati, Knoxville, Atlanta, Tallahassee
NYC school closings blocked – decision summary – first coverage
A few hours ago the Joan Lobis of the NY State Supreme Court issued a ruling in the UFT/NAACP suit to stop the DoE from closing 19 schools, beginning in September. [edit: copy of decision, via Edwize]
Mostly she focused on the failure of the DoE to comply with provisions of the new governance law:
- The DoE did not prepare detailed Educational Impact Statements (the court described much of what was prepared as “boilerplate”)
- The DoE EISs did not specify where lost seats would be replaced (just that they would be absorbed throughout the City)
- The DoE EISs did not address special programs in schools being closed, and where those programs would become available.
- The DoE failed to provide printed copies of the EISs to parents and school communities.
- The SLT-CEC meetings had agendas and scripts provided by the DoE, and can not be considered to have been “joint meetings.”
- The DoE claimed that its failure to comply was not serious, and should be addressed going forward, but that the PEP decision should not be voided. The court found that “Respondents’ very arguments would appear to trivialize the whole notion of community involvement” and cited the reversal of the Smith closure as evidence.
- “if strict compliance were not mandated… agencies would be tempted to circumvent the legislative mandates”
- “where statutory language is clear regarding procedural steps… and those steps have not been taken, the administrative action must fail.”
The court further noted that if and when the DoE follows the law and obtains meaningful community input, they may make other decisions such as the Smith decision, to modify their initial proposals.
In so finding the court made the following four-part decision:
- The DoE, Klein, Board of Ed have “failed to comply with the requirements of Ed Law” 2590
- The votes of the PEP to close the 19 schools are “null and void.”
- Respondents must reissue EISs for the 19 schools to comply with 2590
- “As and until respondents have complied with Education Law 2590-h, they are permanently enjoined from prohibiting enrollment in the 19 schools affected by this decision.
More coverage
Daily News — Post — Times — Gotham Schools
Edit: more links (8 PM) — Inside Schools — Edwize — NYC Educator — New Action — .
We Win! NY State Supreme Court overturns school closures
Close our schools? Not today!
Bloomberg and his Chancellor tried to shut 19 New York City schools, to disrupt communities, displace teachers. And they violated letter and spirit of the new governance law in doing so.
Shortly after noon today the NY State Supreme Court blocked the closures.
UFT President Michael Mulgrew contacted the chapter leaders with the good news.
I will add information as I learn more. For now, there is a post at Gotham Schools.
For now, congratulations to Columbus, Jamaica, Maxwell, Norman Thomas and the 15 other schools, their teachers, and all of us.
Elections for UFT Exec Board – caucuses behave differently
In the UFT elections there are three slates running: Unity (the current leadership), New Action (partially in a bipartisan relationship with Unity, partially in opposition), and ICE/TJC (apparently two distinct organizations joining together to get more votes). The only part of the UFT elections likely to be anywhere near close (and I hope that they are not so close) is for the 6 high school seats. At the high school level, Unity and New Action cross endorsed three candidates each (including me). We are running against three ICE and three TJC candidates.
What would happen if ICE/TJC won? We sort of know. They won once before. From 2004 – 2007 they held those six seats. The official New Action leaflet says that they did nothing with those seats. It is true that they offered few resolutions (was it only three in three years?) But there’s worse. They were hostile and argumentative… not only about the issues where they disagreed, but personally. What were they trying to accomplish with the shouting? Now, all of them? No. But they run together, they have to share some of that responsibility.
What were they doing? I’m going to guess that very often they were just making the record. They were demonstrating to anyone who was listening that they were opposed, not only to specific policies, but also to the UFT leadership as a whole. The noise, to a certain degree, was the end in itself. How did this help the members? Hmm.
There’s a very different problem with Unity, and again I am painting with a broad brush. The Exec Board is a leadership body. It is drawn from across the union, the boroughs, the titles. It is a mix of people with and without union jobs. But it mostly sits silently and listens, and applauds when appropriate. Once or twice each meeting a member other than an officer makes a comment or asks a question, but there’s not a whole lot of that.
The union suffers for this. By keeping discussion private, and then by not having the private discussion, the leadership denies itself feedback. Unions are membership organizations, but here membership initiative is – I’m looking for a passive form of “discouraged” – perhaps “dis-encouraged.” Everything hunky-dory? Then it doesn’t do much harm to the leaders. Still not good. But today, where we are under attack from multiple directions? The feedback from the members, and even initiative from members is sorely needed. Having 80 silent Exec Board members doesn’t help.
On the high school level, all three Unity candidates do rise to speak: Alan Ettman, Greg Lundahl, and Patty Crespino. But there should be more. Unity is doing itself a disservice by not encouraging questions and discussion.
And New Action? We ask questions. We offer resolutions. We offer amendments. Sometimes we just throw out ideas. Sometimes they are accepted. Sometimes we compromise. Sometimes we are voted down. But when we get things passed, or improve a resolution, that benefits the members. And when we get a discussion going, 80 people learn something – if not from us, then in the back and forth.
Last Exec Board, perfect example, nothing exciting. We pointed out the representative from NYC who voted against the Health Care bill (Mulgrew later reported on him, and didn’t tip his hand, but made sure we knew we were looking) and in light of the UFT Charter School getting a 3 year reauthorization we asked for a report from the chapter leader later this spring (agreed).
Previous exec board – we offered amendments to the Central Falls resolution to include the Obama and Duncan remarks in the “Whereas” and to add as the first “resolved” to offer concrete support. Adopted.
Small things? Perhaps. But who else does them?
Two out-of-curriculum graphing inequalities challenges
For Algebra II/Trig I decided that I would emphasize the relationships between graphs and equations throughout.
Even though there is no unit, today, as we are just starting some basic trig, the classes are taking a “graphing” quiz in which I ask them a few questions about fitting some curves to points, about graphing, and about transforming an arbitrary graph. (“Here’s the picture that goes with f(x). Sketch the picture that goes with f(2x).” That sort of thing)
Yesterday I did some prep for that. But I started them off with two problems that they found highly challenging. Great discussions. Good buzz. See what you think:
1. Sketch xy ≥ 0
2. Sketch
None of the kids had ever worked on a problem like either of these, and there were a ton of places to slip up. See if you can anticipate some. But the discussion was rich, and many seemed to have a sense of accomplishment afterwards.
Message from Mulgrew: contact Albany now, give kids a chance!
(Please circulate, print, post. And make the calls)
Dear colleague,
Right now, the New York State Senate proposed budget is a disaster in the making for the children in New York’s public schools.
If the cuts go through, we can expect class sizes of 28 in the first grade; the loss of most after-school programs; elimination of what’s left of music, art and other enrichment programs; no summer school; and a return to conditions after the fiscal crisis of the 1970s, as schools put off necessary maintenance and buildings get dirtier and more dilapidated.
We can’t ask kids to pay the price for the mistakes that adults have made with our economy. The kids deserve better than this.
We need you to call your state senator TODAY to voice your opposition to devastating cuts in this budget proposal.
Click here to send a fax to your senator and assembly member today.
Then call the state Senate at 518-455-2800 and ask to speak to your local senator.
Don’t know who your state senator is? Look it up here.
Tell Albany, “Don’t cut education — give a kid a chance!”
Sincerely,
![]()
Michael Mulgrew
(if you print this out
the link for faxing is: http://www.uft.org/r/61623/8871357
and the link for looking up your state senator is: http://www.uft.org/r/61624/8871357 )
Teachers – volunteer this summer to help other teachers
The American Federation of Teachers will again be running its “Back to School” program this summer. Teachers go South to help ongoing AFT organizing efforts.
I did it. Twice. Last summer I went to East Texas. We signed up brand new members. Many teachers did not belong to a union. Some were members of a “professional organization.” Some NEA. Some AFT. Many belonged to nothing. And we signed them up, and converted. But not so many. The year before, New Orleans. New Orleans was solid union once. But then Katrina came and did what they are trying to do all over now: they fired them all, made them reapply – but to a mix of turnaround schools and charters. And we went door to door, signing up members, former members, now working at a patchwork of schools controlled by different charter groups, and by different government agencies.
In both cases I met interesting people, met teachers, learned about teaching in a different part of the country. The AFT put me up, paid for the car rental and meals, took care of any training.
It was work, no mistake. But with a reward. Well worth it. Will I do it this summer? I don’t know. But you should. Two weeks, helping teachers, expenses paid… if you can’t, you can’t. But if you can… it’s not a lot to give, just two weeks, but it will be appreciated. Do it:
2010 Back-to-School Organizing Campaign
Change is coming. Are you part of the action?
When you volunteer to join the corps of organizers heading south this summer for the AFT’s back-to-school union-building campaigns:
You Give—
- Two weeks of work and dedication, with long and irregular hours.
- The benefit of your union experience, and your personal story of what motivates you to be an active union member.
- Empowerment to colleagues struggling against anti-employee and anti-union hostility.
You Get—
- A unique experience and relationships that last a lifetime. Valuable union-building skills.
- The satisfaction that comes from helping those in need.
- The knowledge that you are building union power for the benefit of us all.
What is the program?
When you join the 2010 AFT Back-to-School Organizing Campaign as a volunteer organizer, you are signing up for a two-week (at minimum) stint of hands-on new-member organizing in Southern states like Alabama, Louisiana, New Mexico and Texas.
What qualifications do I need?
The readiness and willingness to get involved. We provide the skills training, coaching and coordination—you bring the desire.
What will this cost me?
The AFT pays for your transportation and housing, provides a meal allowance, and covers incidental expenses.
General Info
- Please indicate on the application when you are not available in July and August. This will help us find a site that will work for you. The program is two weeks long, always leaving on a Saturday.
- You must have a valid driver’s license.
- The weather—most of the locations are in the southern summer heat & humidity. Dress appropriately and stay hydrated!
- Hours—the days are long, but interesting. A typical day can consist of early morning visits and evening meetings.
Travel/Car Rental/Airline
- You will receive your airline, hotel and car rental information from the AFT travel department.
- Your airline ticket (if you have e-mail) will be an electronic ticket sent to your e-mail.
- If you do not have e-mail, your airline ticket will be mailed to your home.
- Car Rental—You will pick up your car at the airport. Please do not purchase car rental insurance, refueling service, GPS navigation unit. Please do not provide frequent flyer to the car rental company.
Meals/Expenses
- Your meal expenses will be reimbursed up to $65.00 per day. You must provide an itemized receipt—not the credit card copy—for reimbursement.
- You must keep your receipts (including e-ticket & boarding pass) and document all expenses in the AFT Expense Booklet that will be provided.
- Expenses are forwarded to the AFT headquarters for processing. You will receive your reimbursement check at your home address within ten days or less upon receipt.
Visit http://go.aft.org/B2Sapp to apply • Toll-free: 800/238-1133, ext. 4466 • E-mail: B2S2010@aft.org
Common Core Comment Period – awfully brief
Issue standards for K-12 for english-social studies and mathematics. For the whole country. With strings about to be attached. And the comment period is March 10 – April 2?
That’s 3 weeks, folks. For standards that could be with us for a very long time. And for standards that will be likely difficult to revise.
Maybe they are so good that they need little comment? No such luck.
I’ve been following Tom Hoffman (Tuttle SVC). His take? No such luck. (the link is to his first post. There are at least 15. He only does reading, er literacy, er English, er, I’m not sure. You know, that stuff that’s not math.)
I saw a teacher with a comment. Kate(t). What says Kate? Some pretty big problems. Ms. Flecha had something to say. Unh oh.
Maybe there should be enough time for lots of teachers, researchers, advocates, professional organizations to read closely, and to comment. I’d certainly like to read and comment, but I don’t know (working teacher and all) if I will have time in the next 10 days. And maybe there should be time for redrafting, and a second round of comments? Not likely.
Why do I think we are about to get steamrolled?
always liked parent teacher conferences…
I always did. But this edition (Thursday evening and yesterday afternoon) was one of my favorites.
Turnout: At my high school we get high turnout. Always have. And highest in 9th grade. But this is my first year (in the last eight) without ninth graders… And the Spring is always lighter, much lighter, than the Fall, but again, moreso for 9th graders. And I only teach three classes… But I lean on kids to drag their parents in. Bottom line: I have 75 students (but 4 have me for two courses), so 71, and I saw 20 parents on Thursday, 16 Friday.
Tone: I like kids. But in conversation after conversation, I realized I really like my students. There’s a weird bonus being in a stable small school (reread that, pause at the word “stable” so you don’t miss the meaning) – you get to know the kids. And in this case, 55 of my 71 are juniors, and 54 of them were my students freshman year, and 15 are seniors, of whom 4 had me previously, but I know all of them… (plus a sophomore). Anyway, especially among the juniors, being able to refer to their performance, attitude, behavior etc from 2 years ago was great.
A repeated fragment of conversation (maybe 5 times): “Honestly, freshman year Johnny was a bit (defiant/annoying/distracted/unfocused) but he’s really (select the appropriate area to mention academic/personal/behavorial/attitudinal growth).” And in several cases parents reported that their child appreciated my class far more this year…
Remember Kelly? (There was a great story about Kelly – not his real name – earlier this year – worth writing about a student, even though I try to avoid doing so). Kelly was one of those conversations…
Seniors: A couple of senior parents came by, just as a final visit (it’s hard to talk to everyone you’d like to at graduation), one was just a pure (and delightful) thank you. Another brought the older brother, alumnus, who became a math major in college, contrary to his original plans. And seniors in some degree of difficulty came by and got various forms of the “3 serious months” talk.
Tougher conversations: Any time a student is underperforming, I find the conversation tougher. In past years, when 95% of my conferences were positive, the few that did not go so well fell into this category. Underperforming, by the way, can mean failing. It can also mean a B+ student getting a C, or an A student getting a B+. Is getting a B+ really a problem? Absolutely, if it is clearly below where the student should be. But these conferences went well. Why?
- No big surprises. Students discussed problems with parents before the conferences. I discussed problems with some parents before the conferences.
- Previous intervention. For each kid, there’d been at least one attempt already to address the issue that we were looking at.
- A plan, with shared responsibility: For each kid, I suggested a very specific way of addressing what was going wrong. Most of these involved me doing something “extra’ – reaching out, accepting homework submitted in a non-standard way, maybe just being understanding/non-judgmental.
- No. I did not agree to things I was unable or unwilling to do. I avoided promises that I will have trouble keeping.
- Specific. I tried to identify one item that was the of greatest concern. In the past I may have (not my intention, but…) given the impression that I was making a general complaint about someone’s child.
In any event, I got the feeling that parents left the conferences on the same page as me, and with a shared hope/expectation that their child would soon be on the same page, as well.
More fun teaching Σ of geometric sequences
A reader wrote in with a great problem. This was months ago.
Wargle is an Irish blogger. Math and politics. Not the same as jd2718, but something like an Irish cousin… definitely worth a look.
The math tends to be more advanced than mine. Much of the politics is EU. Plus some random stuff. And language. And kids.
Anyhow, he wrote me privately, said he had this great problem, and I agreed. And I was going to use it to teach geometric sequences. Use it as my intro… But I forgot. Here’s how I introduced series, instead. That evening, I remembered Wargle/tax and kicked myself.
So the next day, now we’ve covered all of our 5 series and sequence topics, they kidlets have their desks lined up, ready to quiz, and I say to keep their notebooks out, and I dictate a(n Americanized version of) Wargle’s problem.
Man, they worked hard! And in both classes, the same result: some kids completed the list of numbers and summed them. Some kids guessed towards the sum, and weren’t sure why, some kids recognized the sequence, and used our formula, and one kid in each class suggested that the Total minus 40% of the Total should be $1000 (no euros, sorry).
What a great coming together, satisfying for all. I am glad I used the question on the second day rather than the first.
Anyhow, here’s Wargle’s version:
Proof by taxation
A little story
One day your boss says, “Great job, we want to give you a bonus, were you planning a holiday this year?”. You say “well actually, I wanted to go here”, you show him a website, “but I can’t afford it”. “How much is it?”. “1000 euro”, you say. “Great, we’ll pay for that”. “Thanks boss!”. Happy days.
Later you realise that if they just give you 1000e you’ll have to pay tax on that. The tax rate is 40% so that’s a 400e tax bill, you still can’t afford the holiday.
You head up to your boss’s office and explain the problem. He’s still in a great mood and says, “Don’t worry, we’ll pay your tax bill too”. “Wow but there’s another bit of a problem, I’ll have to pay tax on that extra 400 too. 40% of 400e is 160e, I still can’t afford it”. You boss is looking less happy now and gets out a piece of paper. “Right, we’ll pay all your tax, no matter what” and starts writing down some figures
1000
400
160
64
25.60
10.24
4.096
1.6384
0.65536you hear him mumbling as he starts adding them all up. Suddenly Joan, his secretary, who’s been quiet all this time blurts out “1666e and 66c”. You both stare at her in amazement then after a lot more mumbling the boss says “my total is 1666e and .23c but I suppose if I added a few more lines to the sum it’d probably be 1666.66. How did you get it Joan?”
“Well, tax is 40% so he gets to keep 60% of anything you pay him. So the final amount in his pocket is the what you give him times .6 . So you’re looking for a number that when you multiply it by .6 gives you 1000. So 1000 ÷ .6 is the number you’re looking for because when you multiply that by .6 the two .6s cancel out and only the 1000 is left and 1000 ÷ .6 is 1666.666666666…”, says Joan.
So what we have proved is that 1000 + 1000 x .4 + 1000 x .4^2 + 1000 x .4^3 + … = 1000 ÷ .6 . There was nothing special about our choice of 40%, so replacing .4 with r (and .6 by 1-r) and dividing out the 1000 on both sides gives 1 + r + r^2 + r^3 + … = 1 ÷ (1 – r) Of course there are other ways to prove this but, I like my proof by taxation because it feels like it explains why they are equal.
On the UFT elections: my letter
I sent the following letter to some NYC teachers earlier this week:
Hi,
I’d like to ask for your support in the UFT elections. I am running for High School Executive Board, on the New Action slate.
I remain committed to improving math education. I also am committed to helping at the base – with new and newer teachers, and building (or rebuilding) chapters. And I am committed to helping our most vulnerable…
This commitment extends outside of my “regular” work. Last Summer I volunteered to help organize teachers in Texas. The Summer before, New Orleans. For years I have worked over the summer with Teaching Fellows, first getting UFTers in to give them tips, and for the last few years going myself and sharing survival strategies and tips.
I’ve touched some big issues, too. Last Spring I spoke (me alone) at the UFT Delegate Assembly against Weingarten’s proposal for a new, inferior pension tier for new hires. And this past October I rose to propose the UFT endorse Bill Thompson for mayor.
And I do what I’m supposed to. I’ve been a Chapter Leader for 8 years. I do what I can to keep us from having issues, or to deal with them quickly. I collect information, go to my DR, HS and DA meetings. I attend rallies, and bring others out. I was at most of the CECs and PEPs around school closings this winter, showing my support.
And I write. At https://jd2718.wordpress.com I talk about teaching math, about the UFT, but most importantly, about how to survive as a new teacher, and schools to avoid. The “Do Not Apply” list has generated substantial interest. (It needs to be updated).
And all of this activity is consistent with my slate: New Action. We are activists, committed to organizing chapters, taking a progressive stance, and advancing the interests of our members and our schools.
https://jd2718.wordpress.com/2010/03/15/uft-elections-vote-new-action-2/
Ballots are in the mail, and you either just received yours, or are about to. When you get yours, please vote. (for me and the New Action Slate please! but if not, than for the other guys. It strengthens our union, it sends a message to Bloomberg and Klein when more of us get involved, including by voting.)
Jonathan
ps:
to vote New Action, just check the Slate box. Do not make any other mark, or the ballot will not be counted.
If you choose, instead, to vote for individual candidates, do not mark the slate box.
Having fun teaching Σ of geometric series, and a π question for you.
I don’t know why I am teaching sums of geometric sequences in algebra 2. Actually, I know, but the reason makes no sense.
In any case, I’m teaching them. And having fun. Teaching is better (for them, for me) when I’m having fun. When they’re having fun. When the learning feels like play.
Anyway, they now know that if the ratio between successive terms is between -1 and 1, then we can find the sum. For example: 10 – 1 + .1 – .01 + … = . Cool.
Actually, I liked how I started. “Draw a square. Give it an area. Raise a rectangle on the side of the square, with half the area of the square. Note the total area. Raise a new rectangle, half the area of the previous. Note the total area. Keep going until your composite figure is double the area of your original square.” Immediately some kids started squealing that it wasn’t possible, but I would have none of it. “You started with 16, and you are already up to 31.5 – almost there. Keep going.” In another minute the squeaks turned into a chorus, and I confessed.
Then I drew a 2:1 rectangle, and filled in half its emptiness. Repeat, repeat, repeat, to general agreement that we could fill in as much as we like, but we’d never be done.
Fast forward. I put up They agree its not geometric, and I ask them to look for the sum anyhow. “It’s slowing down, but maybe it doesn’t stop…” “Keep going. Notice anything special happening at π?” Of course they didn’t as they shot past it. But it kept them focused a bit longer. “No, it doesn’t look like it’s reaching a number” I egged them towards 2π, but gave them a break before they found that it runs right past that number as well. They have precalc to investigate this more fully.
But since they were playing along so nicely, I offered them this: . I made them rewrite it in sigma notation (always a cool exercise), and then asked them to play. We graphed their very partial results. They know it is point six something. But I don’t remember. Is the sum 2/π? Why? And how long does it take to become clear?
Regents Exams not really on the block
Despite this delightful cartoon, and despite the (overly hopeful) stuff I wrote last week, it turns out that there wasn’t a proposal to eliminate most NY State Regents Exams. Shame.
Turns out the Board of Regents requested that staff cost out the savings for a bunch of cuts, to have the numbers in front of them. There was never a proposal to make a single one of the cuts.
So, if the budget is tight next year, so tight that they need to actually cut, they will know in advance how much each item could save. None of this was going to happen now. None of this is likely to happen next year.
New Action, the Organizing Committee, and UFT jobs
Unity and New Action entered into a bipartisan relationship several years ago. One of the biggest products of that has been the Organizing Committee.
The OC works with District Reps, and sends teams into schools and helps newer or weaker chapters. The Organizing Committee teams are made up of two retirees, one Unity, the second independent or New Action. The Committee itself is co-chaired by two UFTers, again, one from Unity, and one from New Action.
The work of the OC dovetails with work that New Action believes is crucial: building and rebuilding the UFT from its roots, from its individual chapters. It’s work that many of our supporters have thrown themselves into with enthusiasm. And it is a committee that I think (and I am an outsider here, so grain of salt, please) could continue to be expanded.
As UFT jobs go, I don’t know where working on an OC team ranks, but I know that there are many who would prefer not to go into tough schools day after day. When I see the team members in my borough, Unity, New Action, and independent, I see a particularly hard-working, all-business group of former chapter leaders. They’ve chosen tougher work and direct member support.
– – — — —– ——– —– — — – –
New Action has been accused of trading our endorsement of Mulgrew for these jobs.
- it’s a bunch of folks who’ve sold their values for a few jobs in the UFT.
- a former opposition that has sold out to the leadership for a few Executive Board seats and some minor positions on the payroll of the UFT.
- the New Action leadership led by Michael Shulman and David Kaufman and some others have been given part-time jobs by Randi and if they were to allow New Action to run on a platform crticizing Unity, guess what happens to those jobs?
Really? Let’s look more closely.
OC jobs are, arguably, among the least desireable in the UFT.
OC jobs are not available to active members, and New Action supporters (like me) include people not even close.
Many (?) most (?) New Action supporters could have gotten better jobs – or additional jobs, by joining Unity, which we haven’t. Hm. Actually, that remains a problem as the lure of better jobs (or a job at all) occasionally gets to someone.
– – — — —– ——– —– — — – –
UFT jobs were traditionally given out on a patronage basis. This is still, unfortunately, the rule in many offices.
But the breakthrough, giving field jobs to independents and supporters of an opposition caucus, that rolled things around a bit. I was offered (didn’t take, bad fit) a PM spot. And there is even an ICE person now working as a PM staffer (Brooklyn Office? Staten Island Office? Somewhere out there).
The rules haven’t changed. But the rules are changing. And that comes directly from New Action showing willingness to work in a bipartisan way with Unity.
– – — — —– ——– —– — — – –
In many schools, chapters remain weak. Rights that have been codified on paper don’t have chapters to guarantee their enforcement. New teachers are hired, pushed around, not defended, and end up bitter, if they stay at all. The next generation of teachers reaches tenure without a sense of the importance of the Union, of collective action.
The efforts of the Organizing Committee are vitally necessary. Building, rebuilding chapters is a key step towards restrengthening our union and better defending all of our rights.
Why does ICE start with I?
I, they say, is for
Independent.
I means me. Stands for
Individual.
And is totally unsuitable to lead. Let’s look at the Mayoral elections.
I for
ICE.
I do what
I want. No endorsement.
Only New Action made an endorsement: Bill Thompson, last June. New Action moved the endorsement at the Delegate Assembly. And
ICE? No community, just lots of I’s. Some supported. Some opposed. Most sat on their hands.
Me? This blogger (New Action) rose to endorse Thompson.
ICE? One supporter repeatedly
Interrupted debate, to demand, among other things, alternating speakers. Then another speaker (Scott says he wasn’t an
I for
ICE supporter) took the floor on a pro-Thompson turn, and wasted the slot with a rambling diatribe about not voting.
I say what
I want because
I am
ICE. No leadership. All
Individualism and ego. (Mulgrew
Ignored the
ICE disruption and called on a genuinly
Independent delegate who supported Thompson)
—- —- —- —-
In all fairness, ICE finally took a position on the election. They wrote 8 days after the DA, less than two weeks before the election. You can read it: ice statement on nov 3 2009 vote for mayor (unless they delete the link).
Tell me, did they endorse the Green Party? I’m not sure. They certainly did not urge their supporters to support Thompson. “Throw your vote away!” Now that’s the sort of leadership we don’t need.
Individualistic.
Irresponsible.
—- —- —- —- —- —- —- —- —-
The ICE blog covered me moving the Thompson endorsement. (although Eterno’s original correctly identified me as New Action – which they quickly deleted). And many individual ICE members came to me over the next day, and weeks, and even months, thanking me for standing up on that one, when their own leaders remained silent.
UFT Elections – Vote New Action
Vote
The ballots are in the mail, or in your mailbox. When you see yours, open it, and vote.
The number of members voting has gone down, and that’s not a good sign. Voting is a form of participation. When we cast a ballot (for any caucus) we show Bloomberg and his chancellor that we care. Do your part.
– – — — —– ——– —– — — – –
Vote New Action
When you mark your ballot for New Action you are voting for a progressive caucus. You are voting for a caucus that supports the leadership when they are right. You are voting for a caucus that opposes the leadership when they are wrong.
When you vote New Action, you are voting for the contention that discussion is good. You are voting for the contention that it is worth making proposals, passing or amending resolutions. You are voting for the contention that change is possible, progress is possible, on individual issues. You are voting against knee-jerk opposition (ICE). You are voting against silent acquiescence (Unity).
The New Action approach: will this help members? will this help organize chapters? It’s the best approach.
NY State considers dumping most “Regents” Exams
They claim they could save $13.7 million.
Closing a budget gap is the wrong reason to dump the Regents. But there are lots of right reasons.
It’s in a memo from, Dr. John B. King, Jr., Senior Deputy Commissioner for P-12 Education. I like that. I mean “P-12.” I haven’t seen that designation before. Anyhow, he’s new. Since September. And to do his part to close the budget gap, he’s proposing doing away with: (you can just read what I wrote, but click here to see the full memo) (it’s probably a doomsday scare tactic, but still…)
- January regents
- August regents
- Component Retesting in math
- Component Retesting in English
- translation into Chinese
- translation into Korean
- translation into Kriól
- translation into Russian
- 8th grade second language proficiency exams
- foreign language regents
- Geometry regents
- algebra 2/trig regents
- US history regents
- global history regents
- physics regents
- chemistry regents
- earth science (or living environment??) regents
- paper grading materials (pushes costs of printing onto the schools)
Well, that doesn’t leave much, does it?
- Algebra Regents
- ELA Regents (newer, slimmer, 3 hour version)
- 1 science regents (living environment most likely, but perhaps earth science?)
So?
They all should go. I would be glad if they did. But the memo is just a threat, a doomsday prediction. So I’m not holding my breath.
- Our New York State testing program, all high stakes, has wrongly been allowed to dominate the lives of students in all grades. It is regrettable that he did not include any of the 3-8 testing program… but he spared anything connected to NCLB
- The Regents suck. Apparently, they didn’t always. But from the first day I taught, 13 years ago, they were all a little iffy. And most have gotten worse. In my subject area, mathematics, they are regularly an embarrassment.
- No one knows why kids take regents, beyond that it is what kids in New York always did. Are they high school exit exams? Do they measure competency in a particular subject area? Do they measure competency with particular course material? Which course? All of these questions got dumb stares or evasive answers from the people at the top. No wonder the kids know that they are being tested, but don’t have a clue why.
- Most high school students are still faced with an inordinately high number of high stakes tests. Many take an AP. Some take multiple APs. Many take multiple SAT IIs. Almost all take PSATs or SATs or both.
Chaz says that we’re losing the gold standard in testing. But New York hasn’t held that distinction in at least a generation. If it ever did. I wonder, was it just a myth?
I find that born-and-bred New Yorkers often swear by the Regents. But they have never experienced life in a non-testing state. They might see things differently if they had.
If we really dump these, I’m looking forward to the following things going away:
- Time wasted on Regents marking.
- Class time lost to Regents testing.
- Class time lost to Regents prep.
- Getting measured by regents pass rates
- Covering inane topics, because they are on the regents.
- Not having time to linger on a topic and consider it in depth (because it is at most one multiple choice question?)
- Not being allowed to delve into an interesting related topic (because it is not on the test)
Alice and Mathematics
Tea party? T-party? With three elements, but time missing? She also hits continuity, logic, algebraic systems, even topology.
Here’s two paragraphs:
In the mid-19th century, mathematics was rapidly blossoming into what it is today: a finely honed language for describing the conceptual relations between things. Dodgson found the radical new math illogical and lacking in intellectual rigor. In “Alice,” he attacked some of the new ideas as nonsense — using a technique familiar from Euclid’s proofs, reductio ad absurdum, where the validity of an idea is tested by taking its premises to their logical extreme.
Early in the story, for instance, Alice’s exchange with the Caterpillar parodies the first purely symbolic system of algebra, proposed in the mid-19th century by Augustus De Morgan, a London math professor. De Morgan had proposed a more modern approach to algebra, which held that any procedure was valid as long as it followed an internal logic. This allowed for results like the square root of a negative number, which even De Morgan himself called “unintelligible” and “absurd” (because all numbers when squared give positive results).
Click the link above for the rest.
Why don’t I like these logarithm questions?
I feel obliged to run my kids through exercises like these two, but I don’t like them. Speculate: Why do they rub me the wrong way? Am I right not to like these?
1.
,
.
Express in terms of x and y.
2. Write as a single log: 1 + log v – 3log w
What do you think? I usually like what I teach. But I really didn’t like teaching these sorts of questions.
(This is the third of my mini-posts on teaching logarithms in Algebra II. Here are the first and the second)

