Puzzle: proving a quadrilateral is a parallelogram
Geometry teachers show their students several ways to prove that a quadrilateral is a parallelogram:
If _________________ then the quadrilateral is a parallelogram
- both pairs of opposite sides are congruent
- both pairs of opposite angles are congruent
- both pairs of opposite sides are parallel
- one pair of opposite sides is both parallel and congruent
- the diagonals bisect each other
Look at the following three proposed additions to the list. Some work, some don’t. For each, decide whether or not it is sufficient to prove that a quadrilateral is a parallelogram. If it is, explain why it works, if not, provide a description of a counterexample:
- one pair of sides is congruent, and the other pair of sides is parallel
- one pair of opposite angles is congruent, and one pair of sides is parallel
- one pair of opposite side is congruent, and one pair of opposite angles is congruent
Warning, one is very easy, one is mildly challenging, and one is fiercely hard.
Teacher pay scale – Teaneck NJ
As I find them, I will post teacher pay scales, concentrating on communities not so far from NYC. For the New York City Department of Education salary schedule, click current or future.
EEks! I put up wrong numbers. All corrected now – 1/9/07, 8:10PM
Teaneck’s Salary schedule is below the fold ———–> Read more…
UFT – Two (new) Chapter Meetings per Year
No, no, that’s not the number we want. But for schools where meetings do not occur, we could get them up to two without too much effort.
My district rep spends most of the middle of her days in schools. In fact, she gets to each school (lots, since we are in prime mini-school territory) at least once each term. For us, we like seeing her (except during contract negotiations, but even then I think we are fairly polite).
But in some newer schools, the DR’s arrival is a meeting. A meeting in a school where they may not otherwise be meeting. It does not solve our problems, but it is a beginning. We need to take those beginnings where they occur.
I understand, btw, that these meetings were supposed to be taking place in all the districts. Are they?
Teacher pay scale – Norwalk CT
As I find them, I will post teacher pay scales, concentrating on communities not so far from NYC. For the New York City Department of Education salary schedule, click current or future.
Norwalk’s Salary schedule is below the fold ———–> Read more…
jd3016
Yup, there’s a little bit more of me there than there should be. Ah, once this was a non-issue. Even well into my 30’s I walked 35 minutes each way to my old school. And I smoked. A lot. Then I quit the cigarets and moved to a job much closer to my house, and I grew. Eventually I got back to walking a bit, and back to a size not so much greater than before I quit smoking. But the last 2 years there has been unintended expansion, this fall particularly bad. People tell me it’s nothing horrible, but I know about the difference…. So now I am taking regular measurements. Back to daily walks. (Went ice skating in Wollman Rink with some seniors from my high school Thursday. WootWoot!) And you know, salad, fruit. Only one ban: no more chips.
I’ll take where I had stabilized as 2718 (and the charts say that that number is ok, though on the high edge of ok). Straight proportion: New Years, 3093 was the number. (Shouldn’t I really be using natural logs?). It would be nice to see 2718 again before the end of the school year. Better yet, 2558, that’s a pre-smoking number, just not realistic. And every once in a while I will post with the current number and a link back to this post.
Oh yeah, the category? “The Wide World”
UFT – Chapter Meetings
In the UFT Chapter Leader Handbook, there are two pages under the heading “Building a Strong Chapter.” (Definitely not nearly enough, not today). Anyhow, it says: “The secret of running a good chapter is plenty of participation. Your members need it. Many of them cannot go to meetings or become active otherwise, but they will want to help build our Union in the school.” And then it lists jobs people can do.
It’s not the same model I am looking for. We need to build strong chapters, (and we have far too few today). We need to involve every member in the life of the chapter. But today far too few are involved.
Chapter meetings are central to building strong chapters.
(More beneath the fold) ——-> Read more…
Retesting
When I started teaching, I had some of the weakest math classes in a high school full of weak math classes. I taught the material, tested, taught more material. Of course, depending on the course and the kids, three quarters might have been failing each test. Many attendance issues (you can’t come once or twice a week and really learn), placement issues (put the kid in a course that’s too hard, and what do you expect), classroom issues (combine a novice teacher with unruly classes with bad placements and attendance issues, and just imagine the chaos) and curricular issues (the NYS inspired math courses, then and now, are not logical, coherent courses of study).
Sometimes, when students fail, they should study more and take the test again
more beneath the fold —> Read more…
Teaching |ax + b| + |x| = |x – c|
Obviously, there are different variants as well. But how would you approach this with high school students? I realized that I was winging it, probably hybridizing what I learned in 1979 with some pedagogy I picked up over the last 10 years, and while my ‘method’ seemed to work perfectly well, maybe there is better out there.
First, I think this stuff is worth doing. Not that the kiddies are going to have to solve this to be allowed on the boat across the river, or to answer the wizard’s question to allow entry to the secret castle or anything that exciting (though, please do remember Samuel L Jackson and Bruce Willis struggling with “As I was going to St Ives… in one of the Die Hard’s)… Nah, this is worth doing for cases and as a foreshadowing of piecewise functions.
Cases
We started by proving that 2|x| = |2x| (I did that) and then they proved a|x| = |ax| for a > 0
(For diehard – haha – math teacher-types, click) ——–> Read more…
$750 coming soon and only once
When NYC teachers ratified a new contract a year in advance, we got an unusual provision: some cash to be paid before the contract is effective. And it is coming.
The $750 arrives January
1612 as part of your regular check
We will see the money in the mid-January check. There will not be a separate check (I know, I know, we all eventually pay the tax anyhow, but it doesn’t seem nice that they will be taking out so much up front.) Without looking things up, some titles will get less.
So, I will enjoy the money. Not going to turn that down. Even the $450 I actually receive. But I’m not happy (not a big surprise, I guess.) (click to read on—-> Read more…
How many days in a year?
Ok, so two posts in one.
Puzzle
Today is New Years Day. This year, New Years Day falls on a Monday. Is that the most likely day for New Years, the least likely, or somewhere in between?
Before you jump up and down and say “of course Monday is just as likely as any other day” collect some empirical data, and see what it shows.
Conundrum
Not from me. I have linked Phil Plait’s Bad Astronomy site. Phil has a devilishly easy time making the question “What is a Year?” far more intricate than I would have imagined.
Happy New Year from jd2718
To those who occasionally wander over to this blog, I wish you a happy new year.
In the coming months I will be writing about:
- new teachers – how to support them, how to protect their rights, where their rights are being infringed upon or abused
- UFT chapters – what makes some work, what makes others not work, what should we really mean by a “healthy chapter,” what all of us can do to help
- New Action – I am supporting New Action in the upcoming UFT elections, and encourage other UFT members to do the same. I will be writing more about why supporting New Action is important for new teachers and for our union as a whole.
- Teaching Math – stuff from my lessons. I have been neglecting algebra. I’ll address this
- NYC Board of Ed – or whatever they call themselves these days. Bloomberg’s chancellor and his crew are capable of all sorts of intentional and unintentional idiocy. I’ll write about some of this.
- Puzzles – more. I may even add one tomorrow.
- Steps – I haven’t added any step streets in months. (Problem with photo uploads on wordpress – sort of my fault). I will move to Flickr and get going again.
- Other stuff – of course!
Let’s welcome 2007!
Link changes
On the plus side: + + + + + + + One new one, and I should add a few more. Rocking the School System in NYC is a monthly digest style blog of a 2nd year Global teacher in a small high school in the Bronx. Veteran, in her school. Anyway, she writes mostly about the teaching, the class stuff, and does it well.
Pissed-off teacher is a 30 year NYC math veteran. I don’t think I ever introduced him. I am pretty sure that I have added and subtracted a few without mention. Go ahead, click them all, especially the teacher links. I think they are all active.
On the minus side — – – – – – – – Canadian textbook math guy Tall Dark and Mysterious seems to have stopped posting, mysteriously. It’s no mystery then, what I decided to do with the link.
Mr. Babylon‘s irreverant, insulting, and raunchy accounts of teaching, not teaching, coping, and not coping in the ESL department of a rapidly shrinking large Bronx High School caused indignation from at least one idiot voucher advocate. Hey, moron, it is fiction. Or it was. Mr. B got excessed, and he’s either out of the system, or not at liberty to write creatively. Check out his old archives, they are a riot. But the link… Bye bye Babylon.
A good game for visualization
Today was the last day before break. I had four classes in the morning. We did little bits of math, but mostly we played. Today’s game was 3-D tic-tac-toe.
Now, I need to add, I introduced this in each class without naming the game. “In the simpler version of the game we are going to learn, there are two players who, each using a different marker, tries to create a row of maximum possible length while preventing his opponent from doing the same.” You could see the gears in the little brains spinning, hard. Of course each class eventually guessed at tic-tac-toe.
Then I played a game of regular tic-tac-toe in each class, and won each time. (Started on the edge, confused them). And then I drew a cube, we discussed why it was hard to play on the cube, how the 4-in-a-rows could be hidden, etc, and then “sliced” the cube to create 4 four by four squares, found a few four in a rows, and let them play.
In combinatorics, I offered a prize to the first one to count all the ways of winning. In Algebra II we did some real work first (20 minutes of extending compound inequalities to absolute value inequalities). In two classes I also showed them how to manage the four-in-a-rows without reference to the cube*.
But mostly they played. And loved it.
more, and links to java gamelets –> Read more…
Winter soup
At least once a year, I make Winter Soup. I suppose it has a real name, but since I was a kid, that’s all we’ve ever called it. And we’ve always had it at least once a year.
Now that I’m grown up (sort of) I make my own Winter Soup, but I still make quantity suitable for a family of 4, with leftovers for a few days. For me it is going to be lunch and dinner, on and off, for over a week, unless I decide to freeze some.
I think I have changed the recipe over time. I am, in fact, certain of it. My mother did not use as much black pepper, and she didn’t boil the pulses long enough. She rarely threw in parsnips. I’ve changed to a Bronx seasoning brand. But those are changes of degree, not kind.
Ingredients:
- lentils
- split peas (I prefer mixed yellow and green)
- barley
- marrow bones
- neck bones
- carrots
- celery
- parsnips
- parsley
- onion
- black pepper, to taste
- Sazon seasoning (my mom used GW Gravy)
Quantities and Directions here —–> Read more…
Circle in the Square, in the Circle
There is a hard problems at the bottom of this post.
I like my students to be prepared to confront strange, hard, math problems. In combinatorics, each test is worth 90 points, with an extra 20 points at stake for attacking a previously unfamiliar problem. (Yes, I allow more than 100 points, but note, 20 points are on things they weren’t taught.) On the “new” problem I am not looking for a correct answer (though I wouldn’t mind them), but good process. The kids have to demonstrate Polya-style problem solving, with explicit reference to what they are trying, and why, and what happens. They should know to try diagrams, look for similar problems, break problems into chunks, or pieces, try simpler problems, or constrain a variable or try a particular case….
Click here for the problem —-> Read more…
The Good Concept
Imagine a film. An American writer comes to a post-WWII, four-power-occupied, smoldering capital, looking for an old friend. Soon, lots of smuggling. The writer gets punched a few times. There’s a girl. And a dead man, who might not really be dead. Sneaking between sectors. Sewers. Black and white. Music.
For any fans of Orson Welles or film noire, you must be wondering why I haven’t mentioned the Ferris Wheel. But this is not The Third Man, and the actor is not Joseph Cotten. The girl is not Valli. No Trevor Howard. And absolutely no Orson Welles.
The obvious tribute is called The Good German [official website]. It stars George Clooney, Cate Blanchette, and Tobey Maguire (with smaller roles for Beau Bridges and Leland Orser, among others).
It is not The Third Man. Not even close. But you’ll still want to catch it.
More underneath. There are no spoilers, don’t worry, read on boldly —–> Read more…
March for Justice
Yesterday I joined a march from Grand Army Plaza (by the Waldorf-Astoria) to Herald Square. The March for Justice was better covered on the news than anything I could put together, so I will just add a few observations and details.
(First, this march was in response to the killing of Sean Bell, an unarmed Black man who was killed 3 weeks ago in a hail of 50 bullets, in Queens)
The organizers advertised a silent march; the marchers didn’t buy this. There was chanting, beginning to end. The most common chant was “One! Two! Three! …. Forty-nine! Fifty!” a reference to the number of shots. People brought themselves out, and chose how to demonstrate.
My union, the United Federation of Teachers, discussed this rally a week and a half ago. Union President Randi Weingarten was involved with the organizers, announced she was attending, and initiated a discussion – but did not attempt to get the union to endorse the action. During the discussion several delegates who seemed to oppose the mission of the march spoke not to their opposition, but to minor complaints (one speaker even mentioned the first day of Hannukah). Far more positive: two of Sean Bell’s teachers were in the room, and spoke to the assembled delegates.
New UFT Contract Ratified
The American Arbitration Association completed its count, showing that the new United Federation of Teachers contract was approved by about 90%, though I can’t find the exact numbers, and there are separate counts for the separate contracts (Teachers, Paras, Secretaries, Counselors, etc)
Update: Teachers 89.6%, Paras 92.7%, School Secy’s 94.0%, Counselors 91.0%. (Courtesy of this post on EdWize) (Second update: if Edwize’s raw numbers are correct, then some of their percentages are a little off. Careful!)
The current contract expires October 2007, and the new one picks up there, and runs through October 2009 (25 months).
This contract was negotiated by a 300-member Negotiating Committee, made up of over 50% teachers (I believe). I was on it, and will write a little bit more about the experience in a couple of days. In short, I don’t think we got a better contract because of this mode of negotiating, but I don’t think we did any worse, and the involvement of teachers is a big positive.
Details follow —————-> Read more…
Probability Paradox
In Combinatorics we are studying some combinatorial probability. Tomorrow the kiddies will have to deal with this annoying bit of coin flipology:
1. The more times a coin is flipped, the more likely the results are close to 50/50 heads/tails
2. The more times a coin is flipped, the less likely the results are exactly 50/50 heads/tails
So, how upset will my students be? (I am guessing: fairly)
And, do you have a neat way of explaining this seeming paradox?
Giving the science back to the kids
My previous entry was about the National Science Teachers Association distributing thousands of free copies of An Inconvenient Truth to science teachers.
Some New York City teachers want to do something about this.
At the last Delegate Assembly, (Wednesday, December 6) the following resolution was distributed:
Whereas Laurie David, co-producer of the AL Gore movie “An Inconvenient Truth,” tried to donate 50,000 DVD Copies of the movie to the National Science Teachers Association so science teachers could show their students, and
Whereas Linda Crosshauer, the NSTA president, refused the DVD donation of “An Inconvenient Turth” because the organization had already taken financial contributions from Exxon-Mobil and Shell, as well as accepted and distributed copies of the American Petroleum Institute’s own movie “Fuel-less: You Can’t Be Cool Without Fuel.”
Resolved, that the United Federation of Teachers request that Ms. David donate the copies to the UFT or the AFT so that all of our students and teachers can benefit from this vital award winning documentary.
I think I might like to strike out the second whereas, and limit the resolved to asking for some DVDs, and just for the UFT (the body that would be making the resolution). But I like the idea, and while it did not make the agenda last Wednesday, I think we should move it onto the agenda at our next DA.
(Thanks again to U Dream of Janie.)
Science not for kids
Al Gore’s “Inconvenient Truth” is causing a fuss, again. Apparently Paramount agreed to provide DVDs to lots of science teachers (I can’t see where the number 50,000 came from, but it sounds ballpark) through the National Science Teachers Association (NSTA) (which I frankly had never heard of, but that makes sense since I don’t teach science).
Anyhow, NSTA refuses, and my guess (government pressure) seems at least partially off: As U Dream of Janie documents here on her blog, cozy oil company relationships may be a larger, direct factor.
(You can view the trailer here.)
For what its worth, UFTers were distributing background on this to other UFTers at last week’s Delegate Assembly in Brooklyn (it was packed, but that’s another story).
Rapid turnover is a problem
Maybe this is too obvious to write, but here goes anyhow.
High teacher turnover hurts the schools, the kids, and (esp. imp from my POV) the UFT (my union).
Median years of service for New York City public school teachers has been asserted to be 5 years (for several years now). I suspect the real number has dipped closer to 4.
New teachers are generally less effective teachers. Sometimes they seem to bring more energy, but that does not guarantee the energy is usefully expended. It takes time, several years, for teachers to become very effective. When teachers leave our system quickly, they give their ineffective years to City kids, but not their effective years.
High turnover hurts the union.
1. Newer teachers are often afraid to assert their rights. They become targets for administrative abuse, especially in schools where the union is already weak.
2. Schools with only new teachers may effectively lack a union on the ground.
3. Newer teachers often come into the profession with the thought patterns of a young professional, or even a manager. It takes time these days for new teachers to understand the importance of teacher unionism.
Combatting high turnover would help build the UFT and improve education in NYC.
A Thanksgiving Puzzle
Sixteen people at our Thanksgiving table this year; my sister is hosting again. If all four kids got up at once, and then ran back to the table and sat down in any empty seat, how likely is it that none of them will be sitting in their original seats?
There are two notes, 1) where I adapted this from and 2) some hints about the topic, if you click —————> Read more…
Creative Grading
A Leadership Academy graduate and current Brooklyn principal can’t add. That’s what the Daily News and Channel 2 say. But that’s not the only worrying part of the story.
Lafayette High School Principal Jolanta Rohloff created a grading percentage scheme that was “interesting.”
| Percentage | |
| Regents score | 25% |
| Homework | 10 – 20% |
| Classwork | 10 – 20% |
| Exams | 60 – 75% |
Apparently the new policy went out in a memo mailed to parents, and was caught early enough that less than 200 went out. Channel 2 has it in a pie chart form (I don’t know if the pie is the original). ——->
Now, the percentages add up to 105 – 140%. This grading system does not work. So we can joke that this principal can’t add, have our chuckle, and move on. Not so fast.
(Skip down to #6 before you leave)
1. Anyone can make a mistake. But when a ‘leader’ does, it correctly draws an extra bit of attention. In this case, however, the DoE had to ask the principal to fix the chart. (I can’t tell from the coverage if she admits to error – if not, that is worrying)
click for the rest here ————————————-> Read more…
JD2718 