Philly superintendent moves to fire teacher for speaking against school closing
Read full coverage at The Notebook.
Hope Moffett was removed from her Philadelphia classroom two weeks ago, on what looks like a pretext. Most observers connected the disciplinary action to Hope having spoken eloquently against closing Audenried High School.
The School District plans to terminate Hope Moffett, because she gave tokens to students that they used to leave class and attend a protest against the policies of Superintendent Arlene Ackerman, specifically, the planned conversion of their school to a charter under Universal Companies, Inc.
A letter sent to Moffett today by Assistant Superintendent for High Schools Linda Cliatt-Wayman recommends termination because she enabled students to leave school without parental permission, putting them in danger. Cliatt-Wayman said Moffett’s views opposing “the Renaissance initiative” had nothing to do with the recommendation and that she is “troubled” because Moffett still doesn’t acknowledge she put her students in danger.
Moffett reacted immediately.
“The idea that my personal beliefs regarding the takeover of Audenried High School are not relevant to the case against me is absurd. I stand by each and every choice I have made because I firmly believe that it is imperative that we as citizens stand up to corruption. Students, community members, and teachers cannot be denied a voice.”
“No matter how strong her beliefs, Ms. Moffett’s actions endangered the safety of the children she is charged with protecting. The incident was unsatisfactory.”
It is a stunning development in a school system in which it is a rare event indeed for a teacher to be dismissed for any reason. …
By all accounts, Moffett, 25, has been a top-quality English teacher, a Teach for America alumna who decided to stay with her students as they progressed from 9th to 11th grade. Her case has garnered national attention.
Text of Philadelphia Federation of Teachers (PFT) president Jerry Jordan’s statement:
“I am outraged that the district has given Hope Moffett notice of their intent to terminate her. The charges are ridiculous, and the PFT will fight to restore Hope to her teaching position and defend her for exercising her First Amendment rights.”
Petition in support of Providence teachers
Mayor Taveras of Providence fired (not laid off) all of them, every single teacher, effective the end of this year. Looks like an end run.
– – — — —– ——– ————- ——– —– — — – –
Update – for those of you in Providence, there is a vigil tomorrow, after school:
Join Students from across Providence on Monday, March 7th from 3-4pm
We will meet in front of Classical High at 3 then head over to in front of the Providence School Department (in front of Central High)
We as students should have a say in decisions that impact students, our teachers and our schools. The Mayor is announcing on Tuesday what schools he is going to try to close so come out now to demand that you have a say! Join students to stand up against attacks on our right to an education.
Students deserve stable schools where they are not punished for a fiscal crisis they didn’t create. Our schools are facing budget cuts and we must come together to make sure that they listen to our voices.
• Join us March 7 from 3-4! It is fine to come at 315 if you are coming from the Met, Hope High or other Providence Schools…
• Invite other students to our facebook event and encourage others to join our facebook page “Providence SLAP”
http://www.facebook.com/?sk=messages#!/event.php?eid=100855173330823¬if_t=event_wall#wall_posts
• Spread the word to your classmates about this important event! Encourage fellow students, family and friends to sign the online petition: http://tinyurl.com/SupportPVDSchools
For more information contact:
Providence Student Labor Action Project
Congratulations, Broad-freed Emerald City
Last week Seattle threw out their Broad-trained schools superintendent.
Goodloe Johnson’s tenure was rocky. I highlighted her trying to hire Teach for America (in a big bucks sweetheart deal, she succeeded) when Seattle faced NO teacher shortage. But apparently she lied to the board. She reorganized schools, firing teachers willy nilly (sound familiar New York? DC? NOLA? any other big city plagued by reform?) She instituted teacher evaluation with a test that should not be used in that way, according to its own manufacturers. And she generally pissed off the people of Seattle, parents, teachers, students.
When it was finally time to fire her, there was no debate, except whether to fire her with cause (deny her pension or severance) or without cause. They opted for the latter since that would deny her any right to appeal.
Congratulations Seattle. A small victory? Perhaps. But these days we should celebrate our wins!
Where’s the other list?
It was a good question. Monday morning the teachers’ room was buzzing with talk about “the layoff list.” Members and non-members approached me with questions, thoughts. But the most interesting was the open, teachers’ room discussion.
My colleague wanted to know where the other list was, the list that showed which school Bloomberg plans to lay off teachers from.
Layoffs are not necessary. I said, and everyone got it. And still she wanted to know about the other list.
What was Bloomberg’s point (sowing fear I said) she asked, if he doesn’t give us something to compare against?
How could I both stay on message, and also acknowledge the clever question?
“Layoff List” is more Bloomberg propaganda
The layoff list that the DoE issued today, linked in tomorrow’s Times, is a fraud. He is trying to line up political support and public opinion against seniority.
It is a fraud because layoffs are not necessary. The money is there. He wants this crisis.
It is a fraud because he acts as if they are terminations, firings. “Let me fire for cause! Let me fire my least favorites! There is a budget crisis and I am allowed to fire, er, layoff” He is intentionally conflating layoffs (from which teachers would be rehired) with terminations (which is what he is after).
It is a fraud because seniority is the one measure (length of service) we have that is NOT arbitrary. We all know how long we taught. And we would know, if we were laid off (which should not happen, layoffs are not necessary), but if this bastard lays some of us off, we would know that we would be rehired, by license in seniority order. Not arbitrary order, seniority order.
What are his non-arbitrary alternatives? U-rated teachers first? When Us are given out completely arbitrarily? Sorry, no. And that was Bloomberg’s DoE that disciplined this principal. Principals pets exempted? How you ‘respond’ to the principal is the deciding factor?
By the way, way to go DoE/TfA staff. I notice that you are projecting (and you will be wrong!) but you are projecting heavy cuts to art, music, and PE. Save that unnecessary stuff for the private school kids, eh? And who without money really needs libraries (which you have been shutting) or librarians? Neat.
Our precalculus
I asked what you though belonged in a precalc course (thank you for your thoughtful responses) and then I explained a bit about our strange course sequencing.
Our Fall term of precalc is for seniors who need to be “calc ready” next year, but will not be taking calc with us. Some may not take calc at all.
Our Spring term is for (1) those same seniors and (2) our advanced juniors who just finished a two-term Algebra II/Trig course in January, and (3) a special group of juniors who were not advanced, but had done very well in all their math courses to this point, and just completed Algebra II, and are concurrently taking trig.
Basic idea: Fall is to repeat, with depth, some of the harder algebra from previous courses. It also hits a few gaps. Spring focuses on topics necessary for calc that are either underemphasized in earlier courses, or necessary but absent.
Both terms weave graphing-algebra connections together freely. Neither term brings in additional topics that do not support calculus. No units belong to probability, statistics, or any area that might be part of a course in “discrete mathematics.”
Topic List Fall: Systems of equations; 3 equations, 3 unknowns; conci sections (not in the algebra II course); polynomials and polynomial functions and their behavior; exponentials; and a chunk of trigonometry.
Topic List Spring: Repeat that chunk of trigonometry, and extend it into a major unit (for the seniors the extra bite let’s them improve. For the advanced juniors they just had some, easier, in the fall in their previous course, arranged for the regents. For the advancing juniors, this is tough. It is their first time, and it comes fast, furious, and at a moderate level of difficulty. Even if they miss some, they will, in their Regents class, get a not-as-hard, not-as-deep, not-as-fast rerun later in the Spring. Second topic will be exponentials and logs, much more detail, with application. Next will be rational functions, emphasizing graphing, asymptotes, endpoint behavior. Final unit will be series, sequences, and limits (about 5-6 weeks).
There is no new idea here. Nothing groundbreaking. The organizational piece of bringing the three groups together is challenging. But other than that, I’d say that this matches 80-90% of what you (readers who commented) thought should be there.
Thoughts? That trig transition needs work. Anything else?
Latex on WordPress, a small sample
Using the wordpress implementation of LaTeX allows me to get some math into posts, nicely formatted. I wrote about this at least once before.
This: latex \frac{1}{\frac{y}{x} + \frac{x}{y}} = \frac{xy}{x^2 + y^2} will become this:
when dollar signs are in front of latex and at the end of the type.
This: latex e^{ix} = \cos x + i \sin x becomes:
This: latex x = \sqrt{2 + \sqrt{2 +\sqrt{2 +\sqrt{2 +\sqrt{2 + …}}}}} becomes
This: latex A \cup B becomes
This: latex S \subset T \rightarrow n(S) < n(T) becomes
and so on. Ask me if you want to see anything else in particular. I’m no expert, but figuring them out is a good exercise for me.
Feel a little bad for Gotham Schools?
Maybe just a little. They got hammered in their comments sections today. (I’ve cut and pasted some comments at the bottom of this post)
Their site has major short-comings. No one should be surprised hearing this from me. You’ve seen it on this blog, more than once, and in the last two weeks I’ve mentioned it no less than 3 times, at Pissed Off Teacher, at The Notebook, and indirectly, through corrections of their Rise and Shine summaries, which I corrected once, twice this week. (They ignored me). Would have done it a third time, but Tom Hoffman beat me to it. (and honestly, I looked for a summarizing or factual error this morning, just a four day week, and did not find one).
But I did not expect to find the flurry of attacks today. They focused on the website’s lean (pro-charter, pro-reform), on their habit of rehashing news from other outlets, and on their lack of independent reporting. Truthfully, I found them a little mean. But not wrong.
I will return to Gotham Schools, and some of its problems, in the near future. They go beyond what today’s commenters touched, to the core of how the construction of the organization reflects the purpose of the organization, and how the construction of the organization influences its daily work.
Why do you folks at GS failure to do any journalism of your own?
GS should report with accuracy on the unjust plight of the ATRs
I thought the folks who ran GS were reporters. There seems to be a lot of compelling questions to answer here instead of treating us to a daily stream of articles from the Post. I don’t understand why you don’t do your own reporting.
What you are asking of Gotham is to do something they are incapable of. Reporting news, finding news, uncovering news.
Hey, why do I have to lean to the right when I read these headlines?
This website spends too much time pushing the anti-public education “reform” agenda..
Gotham, stop shilling for the mayor and the New York Post.
A “structuring precalculus” tangle
A month ago I asked for comments on what might belong in a precalc course. I thank my readers for a nice group of responses, running through a thoughtful range of views. I will return to some of them, but later. First, I need to explain who this course is for. Think, for a second. It makes sense to design a course not just in the abstract, but to meet the needs of the students who will take it.
My school is just 9 years old. And we have tinkered several times with our math sequences. And we are in year 3 (the interesting year) of phasing in one which I believe we will keep.
Philosophy, first. We go slowly. Very bright kids, good at math (they all can add fractions), but we move more slowly, with more depth, than at similar schools. Choosing between acceleration (really just jumping to the next course) or moving from knowledge to mastery (staying in a course where the student already has some, but not complete, knowledge) we choose the latter.
We offer two placements for incoming freshmen – Algebra (honors), full year, or 2nd term Algebra (honors), starting Geometry in the Spring.
(Aside. Previously we started the “advanced” group in Geometry. We found that when the work was easy, we got immature 9th grade behavior that made the class hard to teach. When the work got hard – first definitions in a statement/reason system – we got immature frustrated 9th grade behavior. Our school gets kids from different middle schools with very different levels of preparation – and we could get kids acting out from the work being ‘too easy’ and others acting out in frustration, at the same point, in the same lesson.
Further, we found that kids who had “seen” everything in Algebra I in middle school usually raced through it. They might have excellent scores on the Regents, but the exam is only 50% Algebra, and that part is quite shallow. Our freshmen, we explain to them, have taken “tourist algebra” – seen all the sights, but not stayed long enough to appreciate them. So kids with good Regents Algebra benefit from 1 term of more challenging algebra where we might not need to dwell on the basics. They also get one term of hard high school under their belts, with some maturation that leads to more success as we start proof-based geometry).
And we added what I think is a wonderful twist: A student in our regular level who does very well for the first two-and-a-half years, can in the second term of junior year take the second term of Algebra II (this would be normal), and the second term of precalculus (this is the twist), in preparation for joining the more advanced students in AP Calculus AB the following year. We’ve made “moving up” easy.
The trick – what should that precalculus class look like?
Our three sequences:
| regular | regular | regular (adv) | regular (adv) | advanced | advanced | |||
| Fall | Spring | Fall | Spring | Fall | Spring | |||
| 9th Grade | Algebra (1) | Algebra (2) | Algebra (1) | Algebra (2) | Algebra (2) | Geometry (1) | ||
| 10th Grade | Geometry (1) | Geometry (2) | Geometry (1) | Geometry (2) | Geometry (2) | Algebra II | ||
| 11th Grade | Algebra II | Trigonometry | Algebra II | Trig + Prec (2) | Trigonometry | Precalc (2) | ||
| 12th Grade | Precalc (1) | Precalc (2) | AP Calc AB (1) | AP Calc AB (2) | AP Calc AB (1) | AP Calc AB (2) |
So we’ve got an interesting structural precalc issue.
- The course serves as a full year course for students who will not take calculus in high school, but most of whom will take calculus in college.
- The second term alone provides a one-term bridge for advanced students from Algebra II/Trig (taught, as we are in New York State, with assorted regents content, ie, a little standard deviation and normal curve, a little calculator regression, just to add breadth and steal depth) to Calculus.
- And there will be a number of students who take the 2nd term of precalc simultaneous with the second term of Algebra II/Trigonometry, and that will lead them to AP Calculus.
Next post, I’ll discuss the issues relating to choosing which topics we chose to include, which we decided not to use, and how we are sequencing the course. And in a final post I will discuss my experience with giving only quizzes (no tests), an interesting, yet standard-free, experience.
Weingarten offers more concessions
In Wisconsin we see collective bargaining rights under direct attack. Furloughs, and other financial givebacks are becoming more common across the country. In New York City the mayor and the chancellor and the anti-seniority reformers (many carrying Gates-cash) are pushing to use layoffs as firings, and dismantle any sense of basic fairness.
And against this backdrop American Federation of Teachers President Randi Weingarten offers a new, ‘improved’ teacher evaluation system (using kids’ test scores) and a fast-track to firing teachers. It is very hard not to say something.
The Us won’t be fairer. The draft of the evaluation system for the transformation schools may well be the blueprint for our eventual agreement with the City, and it is nothing more than the current system + subscores + test scores. Principals who go after teachers will not find it more difficult to give arbitrary Us. Today, when Us are given unfairly, we still lose on appeal. The new evaluation will not change that. The new evaluation will not be fairer or more rational, it will just have subscores and test scores and arbitrary numbers attached.
The Us given to union activists, and especially to chapter leaders, are especially troublesome in this regard. No one wants to talk about Chapter Leaders with Us, or Chapter Leaders facing charges. Maybe we should make a list (and no, it would not be short).
There is more impact nationally. The ability of a local to say “No” is greatly diminished when the national union does not have their back. These ‘improved’ evaluation systems are already in place in some districts, often shepherded by the national AFT. Tenure is weaker in other states. This is the backdrop against which Weingarten offered up a quick-fire process. Locals should not adopt her proposals.
The New York Times article is below the fold (with my highlighting – jd) Read more…
Follow ups on Philly and Providence
I wrote about the Philly teacher who’d been reassigned for speaking out against a school closing? And a TfA no less? Hope Moffett. She got her letter calling her for a hearing for endangering children and for sharing her reassignment letter. This letter, however, did not require her not to share it, so they may not be piling on more charges. Read today’s update at The Notebook.
I wrote about every teacher being about to be fired in Providence? Look in the comments, where there is substantial back and forth with Tom Hoffman. Well, later yesterday, the letters started to come, and they are doozies. Tom blogged updates about them (his wife is a non-permanent teacher (?) in Providence).
But they are leaving anyhow…
Teach for America supplies teachers to the New York City Department of Education. They are high-achievers from fancy colleges. The NYCDoE pays a hefty per capita fee. The teachers promise to stay two years. Some stay three. Few stay more than that.
TfA cloaks their anti-union mission behind sympathetic personal stories. Peel away the hype – the narratives are fake.
Teach for America gets their feet wet, so they can become administrators, or charter school leaders, or so they can run districts, work for thinktanks, advocacy groups, or elsewhere in the education industry.
- Two TfAers started Educators for Excellence, a group devoted for advocating against seniority in layoffs. The two teachers are now former teachers, having left (maybe they still have part-time gigs?) to do their anti-union advocacy piece. With Gates $$$, I think.
- The Wall Street Journal ran a piece this week about a kid named Leblanc who is a great teacher (according to his principal) but is in danger of being laid off… he’s in his second year. Huge red flags, all over the place, and I’m ignoring all of them, except…. He’s TfA. If he is not laid off, isn’t leaving at the end of this year or next anyway?
- I know a handful of TfA teachers who’ve lasted longer than three years. But they’ve all bounced school to school. Their school this year? Will lose them in a year or two.
Big picture – TfA and TfAers advocate against unions and rights of other teachers, for ideological reasons. They cloak their anti-union animus behind a claim of personal self-interest. They don’t tell us they are on a mission, instead they try to paint a sympathetic personal story. It is a fraud.
[this post is partially in response to Steve Lazar’s But Will They Stay? – written about new teachers in general.]
New Action website
We’ve been making some effort to keep the New Action website better updated.
- We’ll keep getting DA leaflets up
- We’ll link a bit more to current issues
- We’ll include some information on what we are doing
- We are including occasional signed pieces
- Comments are open (moderated)
For example, on the events in Wisconsin we’ve put up videos from the WEAC, the state AFL-CIO’s tv ad, the text of an Egyptian trade union leader’s solidarity statement (w/video link), a list of proposals New Action made to the UFT leadership, and an on-line petition to build support for the public employees, including teachers, in Wisconsin.
Providence: dismissal notices to all teachers
h/t Tom Hoffman.
From the Providence Journal:
PROVIDENCE — In an e-mail sent to all teachers and School Department staff, Brady said, “We are forced to take this precautionary action by the March 1 deadline given the dire budget outline for the 2011-2012 school year in which we are projecting a near $40 million deficit for the district,” Brady wrote. “Since the full extent of the potential cuts to the school budget have yet to be determined, issuing a dismissal letter to all teachers was necessary to give the mayor, the School Board and the district maximum flexibility to consider every cost savings option, including reductions in staff.” State law requires that teachers be notified about potential changes to their employment status by March 1.
“To be clear about what this means,” Brady wrote, “this action gives the School Board the right to dismiss teachers as necessary, but not all teachers will actually be dismissed at the end of the school year.”
“This is beyond insane,” Providence Teachers Union President Steve Smith said Tuesday night. “Let’s create the most chaos and the highest level of anxiety in a district where teachers are already under unbelievable stress.”
Meanwhile, Smith said he was caught completely off-guard by the planned dismissals…He said it makes no sense to send out dismissal notices to every teacher because the district has a legal obligation to educate all of its students, regardless of budget considerations…
Smith said the dismissals couldn’t come at a worse time. The union is getting close to resolving a lawsuit over seniority-based hiring. The teachers’ contract expires June 30. And both Smith and Brady have staked their careers on a first-ever partnership in which both sides have agreed to make deep reforms in four of the district’s lowest-performing schools.
There are about 2000 teachers in Providence. The Providence Teachers Union (ProTeUn, AFT Local 958) has no information on its website.
Need a Wisconsin song – Can you help?
It’s time to add some songs to the mix. We have chants. We have signs (man, are there some great signs out there!)
Today I got an e-mail from David Lippman, a satirical, lefty, anti-war, anti-corporate songwriter. I learned about his music from his mother. She was on staff at my first real job, decades ago, and she got me to see him at the Knitting Factory. He was performing as “George Shrub” from the CIA (Committee to Intervene Anywhere) and I don’t know what I liked the best, if it was the between-songs banter or the faux-spy sun glasses or the Ollie North- Bill Casey love song (You can call me Ollie, Ollie, I will call you Bill – rips off a Paul Simon song), or the indictment of middle class indifference (I got a new car, and troubles of my own, and I just don’t got the time. I won’t think about it, someone else will do it, maybe it will go away).
In any case, I google him up about five years ago, find he still performs, go see him at Arbeter Ring in the east 30s. Now, his mother was there, but she didn’t remember me. Not one bit. Not after I described what I did, where I sat, etc, etc. Maybe she had become forgetful. Maybe I was forgetable. Honestly, I was on good behavior at that time, and might not have stood out in any way.
So today I get an e-mail, he’s on tour again. And his newer topics include the Middle East and bail-out related nonsense. (By the way, Tom Paxton who did Rambling Boy, he’s got a great take down of the corporate handouts somewhere on youtube). But nothing on the events of this last week.
I write back: If you can’t sing about Wisconsin…
And he answers: I can. If you write it. I forget, are you on my staff? I just de-unionized them….
So, dear readers, we are looking for some help composing biting anti-Walker, pro-union satire. Can you write a whole song? Or a chorus? Or find a few rhyming words to get him started? A couple of bars for a Mad City beat?
[clarification: Lippman would probably pretend to be Walker when singing. We are looking for something satirical, in Walker’s voice, or in the voice of one of his corporate sponsors – jd]
Truth to Power? –> From School to Exile
(Read The Audacity of Hope on The Notebook)
All eyes are on Wisconsin. And rightfully so. But we should not forget what is happening right here in New York, as the bully Mayor and his new Chancellor continue targeting teachers and schools.
But here’s a story from down the road a piece – head down the Jersey turnpike an hour and a half, take a bridge into Philly, and we see teachers and schools with problems that overlap with ours. But in many cases, the problems are worse. Remember, they had private contractors running schools? (Edison?) I think it turned out bad, even from the administrators’ points of view. And now they have strings of charter schools and “Promise Academies” called “Renaissance Schools” – with far greater penetration than we have in all but a few neighborhoods in NYC.
When a school goes “Renaissance” teachers find jobs elsewhere in the system, or reapply, but without union representation. Some will be laid off. There is of course no reason to believe that the education of the kids improves at all. This is a bald power play.
So here’s the story – yet another school announced to go Renaissance, Audenried High School. Parents, students and teachers were vocal in their opposition. Five teachers wrote a guest post in defense of Audenried at The Notebook (a Philly pro-public school news and commentary round-up site). At least two of them were disciplined with exile and an attendant gag order, and one of them went public!
The Philadelphia Federation of Teachers says that it will defend its members with every tool available.
Hope Moffet despite being TfA is now sitting in a basement office instead of teaching for the crime of speaking on behalf of her students, her school, and justice. Read more about her in The Audacity of Hope.


How would you solve this little trig eqn?
McRib asked me to solve: cos2x + cos4x + cos6x = 0
How would you solve that? Any guess on what I based my quick solution? Other methods?
(Let the domain be anything you like. [0,2π] is fine).
Wisconsin: Virtual Vigil for Labor
I received this from Anthony Cody. Please, read it, and sign up:
I feel we should stand in solidarity with the teachers and other
public employees in Wisconsin. Collective bargaining is a basic right
that all should have, and it is crucial that teachers be able to
protect their rights this way. Please join us in supporting the
Virtual Wisconsin State Employees Unions Solidarity Vigil here:
http://www.facebook.com/home.php?#!/event.php?eid=191312694226266
Math Teachers at Play #35
I have been sloppy about plugging math carnivals. But here I am, submitting. And visiting. And reading. So it would be nice if I mentioned that they exist.
MTaP #35 is back with Denise, at Let’s Play Math (love the name of that blog). It is well-organized, nicely annotated, and scrunched among some interesting mathematical poetry (if you count limericks as poetry).
Teaching off Topic (yet again) – addendum
I left something important out! Two weeks ago I did a rambling session with middle school mathletes, 7th graders, here in the Bronx (read about it here). But while I was rambling off-topic, I diverted. This was early. And it helped me win the group. And I forgot to report it.
My plan was to ask them if they are taking math (of course), if they took math the previous few years (decimals, per cents, adding fractions, multiplying fractions, dividing fractions, check on long division), if they did early elementary (long multiplication, long addition, all the little facts), stop, and throw in something about learning to count (before counting exercises 32 – 37 vs walking from 32nd to 37th Street). This is pretty standard “suck them in” get some choral answers going, get them to think all my questions will be easy… We don’t do work, I just bring them to the tricky question. (here is the script, roughly, in a comment to a post about a previous time I visited this school for math team).
When we no longer fear division, we should still respect it
But early on, I got a response I hadn’t anticipated. One or two little voices tsked when I said it was good that they did division of fractions (every time they said they knew something, I said something positive). They made clear that dividing fractions was non-interesting, non-engaging, and, perhaps I am overstating it, trivial.
Now, with an hour and a half, I intended us to have fun. But having division of fractions tsked at? How could not say something? So I said that it was good that they found it easy. That a lot of people didn’t. But perhaps it would be more interesting to look at again.
And I wrote on the board and immediately the squeals of “keep change change” and “keep change flip” began, and I did my best to look old and slow and confused (after having just been talking a mile a minute) – “Keep? Keep the change? What do we do?”
And they giggled, and told me, and I reinterpreted as they led. And when we were done they knew, most of them, that they were telling me to multiply by the reciprocal. And truly, before we started, some of them already knew that.
[An aside here. Why “keep change change” with kids who are sophisticated enough to “multiply by the reciprocal”? My turn to tsk.]
And I mumbled something about filling a container. How many two cup containers can be poured into an 8 cup container? (but I can’t remember the actual example) and then I drew a square, divided across and down into 4 equal squares, and shaded one quarter, and then drew an L-shaped 3-quarter piece, and asked how much of the L-shaped piece would fit into the 1-quarter piece, and the answer came back one-third pretty quick and clear with a little chatter about this different way of looking at division.
And then I went back to the original, and asked why we didn’t just divide across… and were we allowed to do this or do we have to multiply by the reciprocal, and then I offered another example,
and they verified that they got the same answer each way, and then I offered a chance to prove the conjecture with
and I guided them to find that each way yields
. I drew the conclusion for them, that the algorithms are equivalent, I pointed out that the new algorithm could be more convenient, and I finished with one last example where they could use the new algorithm, but where it would be a silly choice:
.
Afterthoughts
I thought this was a pretty good 4 – 6 minute run. I stayed goofy, but I answered any of them who may have been unsure about the math being serious. I made a nice point about using correct terms, as appropriate. I explicitly pointed out (and demonstrated) that even basic arithmetic has things within it that is well-worth investigating. We examined multiple algorithms for one operation. I touched on multiple models of division.
This was unplanned. And not a topic that I run through “unplanned” frequently. For the future, I’d like to improve a bunch of things. I would like to explicitly name several (maybe not all…) models of division. My spiel was weakened because I was not clear, and partially conflated two. I should have a ready example that works nicely.
Actually, I should have a list of examples that work progressively to where I am going (some people call this scaffolding, but honestly, I’m not a carpenter). And I could pull from this list. For the area model I might consider and
as nice stepping-stones to perhaps
.
I should review Hung-Hsi Wu on fractions (hate me, progressive educators, but his stuff is hot). And – hate me more – on division.
In other words, if at some unspecified time(s) in the future I want to play, unplanned, with fractions, I would be better if I did some planning first. Where can I do some fun upper-elementary methods?
Puppies and Kittens?
Which one of my blogger-friends suggested this? I played for 10 – 20 minutes with two classes today (rather, I let them play), and it went well. All were engaged, and some made progress towards finding a winning strategy, and one pair I am fairly certain nailed it.
The two players go to an animal shelter, and take turns adopting kitties or puppies. The player who adopts the last animal wins.
On your turn, you must adopt at least one animal. You can adopt pups only, as many as you like. Or you can adopt kits only, as many as you like. Or you can adopt an equal number of each.
When you arrive there are 7 puppies and 10 kittens.
Play! Discover the winning strategy.
It’s time to stand up for seniority
The following article, about the Philadelphia public schools, is from The Notebook, “an independent voice for parents, educators, students and friends of Philadelphia Public Schools.” Consider bookmarking the Notebook, it publishes many voices, most of them pro-public school. I skim all their headlines, and sometimes click to read more.
With layoffs coming, it’s time to stand up for seniority
by Ron Whitehorne on Feb 14 2011 Posted in Social justice unionism
With many school districts facing budget shortfalls, teachers, including those in Philadelphia, will likely face layoffs.
The budget crunch coincides with a growing attack on teacher tenure and seniority as the governing principle for teacher assignment and layoffs. Even Antonio Villaraigosa, the mayor of Los Angeles, and long time teacher union organizer and staffer, has joined the chorus calling for “peformance” as the “driver” in decisions around these issues. And former Washington, D.C. Superintendent Michelle Rhee has made ending tenure and eliminating seniority central agenda points of her “Students First” campaign.
Much of the current debate over tenure ignores the many changes that unions have embraced to address some of the criticism of tenure and seniority based practices. Many unions, including the PFT, have agreed to changes in teacher assignment and transfers that give schools more flexibility and control over staffing. Unions, again including PFT, have also agreed to changes in teacher evaluation and made it easier to remove ineffective teachers. Thus, at its worst, the critics of tenure are attacking a straw man that bares little resemblance to current practice.
But when it comes to layoffs, we can expect the unions to fight for the principle of last hired, first fired, and rightfully so. Without this principle, teachers have no job security. Older teachers at the top of the pay scale in a climate of budget austerity will be targeted for layoffs. New teachers at the bottom of the scale will be more likely to be retained. Teachers who are outspoken can expect to go, while those who are cronies of the principal will get to stay. Women, who have a nasty habit of getting pregnant, will be more likely to go than men. These are some of the historic reasons the trade union movement has always championed the seniority principle. It is no different in education.
Of course the District and the opponents of seniority will tell us that they are “for children” and want to keep the best teachers in the classroom. What they really want to do is render the unions impotent, pit teachers against each other, and save money at the expense of their workers.
Children will not benefit from a teaching staff that would be in all likelihood less experienced. Here in Philadelphia the highest proportion of inexperienced teachers is in the lowest performing schools, mostly in poor African American and Latino neighborhoods. While obviously not every experienced teacher is an effective teacher, research does show that experience is an important predictor of teaching success. We should be about retaining experienced teachers. The attacks on tenure and seniority will have just the opposite effect.
As teacher unionists, we should be about fighting the layoffs which will increase class size and undo some of the positive gains in student achievement over the last decade. But if they come, and it seems certain they will, we should defend the seniority principle and demand that no new hires, including Teach for America and Teaching Fellows, are made until every displaced teacher is recalled.
Teaching off topic (yet again)
The occasional lesson, free-coverage, or spot fill-in, allows a lot of freedom. Since there is not really an “on-topic” unless we count the ubiquitous test-prep, everything is off-topic, which is how I like it.
This week I was the guest at an after-school hour-and-a-half 7th grade math team session. I love this stuff. I could have done some model American Math Competition problems (we just gave the AMC this week), and thought about it, and maybe one day I will come and do some, but this week I did not.
We started with counting vs not-counting endpoints. Good buy-in, and tested if they could algebraically represent the result. They could. Good sign.
I ran some silly “guess the numbers” – in the first they added one to their number and told me the result. They did play, which was nice of them, although they laughed at how ridiculous it was. Then we did a “pick a number, multiply by 10, add your age” which they also, for the most part, considered lame, although not all of them immediately got the decoding. But then we did “A Little Math Magic” and after two rounds I gave them a chart to fill in, and I gave them enough time to play, and to look for patterns, and they did, magnificently.
In the wind-down from the Math Magic I introduced Fermat, although I only hinted at the content of Fermat’s Little Theorem. We instead just verified our base 10 modular arithmetic. But then we spoke about Fermat’s Last Theorem (ohsobriefly), and then Pythagorean triples, and they proposed some, and I checked some (on theme) by checking their last digits – nice point that we can reject if the last digits don’t add correctly, but we can’t accept on that basis only. And then I told them that there were no triples with all odd numbers, and asked why. OK, these are little kids, but bright. I was not sure what to expect. Two of them hit explanations based on parity. And one explained the approach nicely. I was quite pleased.
I wound up with a prisoners/hats problem, and a promise to return. This was FUN for me, (with capital letters, as you can see for yourself). It was also fun for them, with lots of questions about exactly when I would come back.
An hour and a half is a long time. An hour is a long time. In my regular classes I often digress or allow the kids to bring us off topic for a moment. Can make a nice break. With these little kids? I like digressions. And so I did wander off-topic. Two meanders were linguistic:
in the first i was discussing the difference between “problem” and “exercise” and used the word “algorithm” in my explanation, and went off to discuss “al-” words from Arabic in English, and then “al-” words into Spanish, then into English without “al-” (algodón/cotton, arroz/rice) but I think rice had a different path, and I lost them there anyway because despite being in an overwhelmingly Hispanic neighborhood, where much Spanish is spoken, not one of these kids (all Asian or African) knew “arroz” or “algodón.”
in the second I was introducing the prisoner/hat problem and I heard breaths when I used the word “warden” and sure enough, it was not a familiar word to most of them, and in explaining it I pointed out the correspondence between “gu+/v/” and “w+/v/” (warden/guardian, warrior/guerrilla, and so on) and this time a few got very excited, and one asked about “wily” and “guile.”


