Cool thing, if you like: you can make real-looking fractions and exponents on this blog.
The key is something called LaTeX, a special language for laying out text. WordPress blogs can handle a version of LaTeX.
you’ll need a dollar sign immediately followed by the word “latex” to start, and a dollar sign to end
type: \frac{num}{den}
You need the slash, no space, the letters f-r-a-c, and then two sets of curly brackets, no spaces, with the numerator in the first set, and the denominator in the second
type: base^{exp} or just y^x if the exponent is one digit or variable
I am using S instead of $, so you can see
Slatex \frac{5}{6a} S becomes
Slatex 3^{2x} + 3^x S becomes
Slatex e^{i\pi} – 1 = 0 S becomes
Scads of impatient munchkins out there. Instead of completing the whole thing, I’m putting up my quick version of the multiple choice answers, with a few choice comments. If you see a mistake, let me know! I’m not working with a state key.
Update: 31 - 39 (Parts II, III and IV) are now posted. Note: Feel free to try to answer other people’s questions. Note: before asking a question, read the previous comments to see if yours has already been answered
(the correct translation really is: 
, which the kids won’t know. So choose another problem instead?)
(vocab question. Boo, hiss. Do you want to know what empirical means? More, later)
(level of difficulty far exceeds what was expected. Bad question)
(you guys are supposed to restrict the denominator for the kids, even if they don’t like seeing the restriction)
(vocab question to hurt non-native speakers. Are we testing polynomials or grasp of English?)
(why was the first fraction not given in lowest terms?)
, where x is an integer} (this sort of non-standard choice drives me nuts)Update: More answers posted: (Parts II, III and IV)
I like the new Integrated Geometry regents. Despite it being a “standards-based” exam, the subject is so narrowly focused that it looks a lot more like a traditional test of content. However, they are still testing standards, and managed to over- and under-test some skills.
Overtested:
Undertested:
I am probably missing something.
There has been extensive discussion among NYS math teachers at the Association of Mathematics Teachers of NY State listserve
Next up: some questions about questions. There were problems….
I hold quite openly the position that the poorly designed tests that New York State administers in mathematics distort the teaching of math across the state. And I believe that high stakes tests in general have this effect. While I do not agree that we can at this point do away with all of them, we can and should get rid of most of them.
It is not just math. In this post NYC Educator provides evidence of how the high stakes high school test in English denies new immigrants proper instruction. (we don’t test grammar and spelling, so why should we teach them?)
There’s not much more you can do at this point, but we do have three exams with answers and one sample exam. I guess it couldn’t hurt to look back through them. New York State Education Department produces semi-repetitive exams. Relax (as much as you can). Do everything you know. And then go back and (multiple choice) take your best guess or (free response) make sure you have written something down, even if you can only start the problem. Leave no blanks!
The conversion chart will be available later today. Bear in mind as you work, 40 is guaranteed to pass. But maybe as low as 30 will pass? We don’t know. But as you are working it might not hurt to notice when you are certain of an answer, and how close you are coming to 30, then to 40…
New:
I posted multiple choice answers; short answers will come soon.
JMap will post the whole exam. (Monday?)
Commenter Hugh pointed it out
Update 6/25: The correct answers were 41 and 71. I was (happily) way off. Congratulations to all those students who did well, and good luck to those who need to give it another shot next year!
One pool for 65. One pool for 85.
Out of 86, how many points will you need for a 65? How many for an 85?
Last January, on Integrated Algebra, 31 and 68 (scales down to 67). On Math B 49 and 71 (scale down to 48 and 69).
Smart money says to roughly cut the difference, say 40 for a pass and 68 for the 85.
My money’s not smart… Algebra is a graduation requirement, Geometry’s not. So I think we can ignore the Algebra scale. Also, as this is the first (almost) content-based math exam in a decade, raw scores will be up. Not only do I think the scale will be more like Math B’s, I think the number of high scores will lead them to set a relatively high pass. My guess stays at 51 for the pass, 67 for the high pass.
Why would Geometry have a higher cut than Math B? Slightly more students take it, and do better than on B (B is an awful grabbag, Geometry looks like a fairly focused course). The big thinkers will see the high scores and assume that the test was easy (rather than understanding that the course is better organized), and set a higher cut score to compensate. That’s my guess: 51; 67.
What’s yours?
Yesterday the first exam in “Integrated Geometry” was administered throughout New York State. (see previous post)
My first reaction is that this is the best examination in mathematics New York State has administered in over a decade.
The exam was content-focused. There were a few algebra questions, two logic questions, but the vast majority of the points were directly related to the study of geometry.
The State did something good? Of course this is an accident. It is still a performance-based exam. Only, in the case of Integrated Geometry, when they wrote the standards, they didn’t integrate much with geometry. They were also so scared of the difficulty factor going off the scale that they avoided adding silly, confusing context to most problems.
Only 4 problems that I have found so far had problems as written. (post later today)
Because they still test standards, not content, NY State repeated the same content (equation of a circle) in three questions, while missing quite a bit of content.
At the Association of Mathematics Teachers of New York State listserve, the main concerns seem to be how easy the exam appeared, and the repetition of material. (See the AMTNYS discussion)
Scoring:
The exam was 28 two-point multiple-choice questions, 6 two-point free response questions, 3 four-point free response questions, and 1 six-point free response question (the proof). This is a total of 86 points.
Today schools across the state will grade the exams, and mail them to a vendor. Next week New York State will convene a committee of teachers to look at each question closely, and make some recommendations about scoring. The following day a committee of supervisors, superintendants, teachers, and school board members will make a political decision recommendation based on what pass rate is acceptable. Until then, we will not know what the passing score will be.
Click here to enter the “Jd2718 First Geometry Cut Scores Pool“
Back to normal blogging…
The first edition of the New York State geometry regents will be administered at 9 this morning. The questions likely will fall close to those in the “test sampler” the State issued last fall.
This is the only math regents that actually stays (more or less) on topic, with the vast majority of the questions related to geometry. There is likely only one proof, but other opportunities to justify answers.
There are 28 two-point multiple choice, 6 two-point free response, 3 four-point free response, and 1 six-point free response (that last is likely a proof). The 86 total points will then be scaled (they claim psychometricians are involved, I would wager that it’s only a tad better than arbitrary).
Over under? I’m going for somewhere in the high 40s or low 50s equating to a minimum passing score (65). I call 51.
And we’ll be back in this space this evening reviewing the quality of the exam as a whole, and some of the individual questions.
Last summer I volunteered. The AFT’s summer organizing/solidarity campaign sent me to New Orleans.
Some of what we did was symbolic. Some was grunt work. Some was straight up solidarity.
It was good work, for a good cause. Plus they covered travel and all expenses. Would I do it again? I don’t know… but today the AFT called, and asked.
While I’m mulling it over, you could take a look. Go to the AFT Back-to-School Organizing web page. Or read the content, below the fold: Read more…
BRONX RALLY against ESPADA, sponsored by CASA (Community Action for Safe Apartments), the Mitchell-Lama P.I.E. Coalition and other groups:
FRIDAY, JUNE 12
11:30
Rally at Fordham Road and the Grand Concourse (D train stop), and march to Espada’s imaginary Bronx office in the Sears Tower across Fordham Road.
Can’t go, of course, it’s the middle of the school day. But nice turn of phrase.
Mamaroneck resident Pedro Espada pretends to live and work in the Bronx (so that he could run for State Senate from the Bronx). After his role in trying to flip the NY State Senate from the Democrats to Republicans, his fake office on Fordham and his fake residence off Bedford Park have enjoyed a little extra attention.
Will it? Won’t it?
Sounded too good to be true, and I was ready to disbelieve. Eximius College Prep middle school to close? Why get our hopes up? But more sources say yes. Could use some solid confirmation here.
Anyone?
A rumor has reached me that Eximius College Prep, one of the worst of the “Do Not Apply” schools in the Bronx, will be partially closed at the end of the school year.
It would be a good thing, if true. However it may be wishful thinking.
My source said letters went out saying to 6th and 7th graders, saying the middle school portion would close June 26. Maybe:
Folks, if you have information, especially verifiable information, please share.
(for more background, read “Insightful Reflection on Eximius” by someone who was scarred by the place.)
So how does swine flu affect your school? I don’t mean the sick kids – in today’s New York City Department of Education kids don’t matter – I mean your school’s Progress Report.
Did your attendance drop? Are you better off sending home any kid with a sniffle, to keep the damn pox from spreading, or refusing to send anyone home, to maximize attendance?
What about the Regents? Will the kid score better if you rush them home, bedrest them, and get them back fresh (hopefully) or keep them in school as long as you can, and do as much prep as you can stuff into his head?
Those schools you get compared to, any of them get shut? Because I don’t see how that doesn’t translate into a Progress Report windfall. Do you think one is close to being shut, but is playing with the numbers? Maybe an anonymous tip would close them?
But heaven help you if you are the only school in your peer group getting hammered with fevers. What’s going to happen to your regents scores? How many “points” will you lose for attendence?
</sarc>
When can we throw these damned Progress Reports overboard? They pervert education, turn good principals bad, and turn bad principals evil.
if you spend all your time with self-interested teenagers, isn’t it reasonable that that self-interedness will rub off a little?
Not a middle school thing. H at Coffee and Graph Paper talks about teaching math to inmates at San Quentin, talks about math as a right, as a human need.
H seems to be hoping that more volunteers will come forward. The state of California does not fund education past high school (is that right? the University of California?) Anyhow, they clearly don’t fund this fundamentals course at San Quentin.
During the discussions leading up to the adoption of the 2005 UFT contract (lots of money in return for horrendous givebacks), I asked the following question on EdWize:
Three off-topic questions that haven’t been answered elsewhere.
2. Under the new transfer system, what keeps a principal from rejecting all UFT applicants and hiring off the street? Imaging, if you will, that the principal’s neighbor’s kid just graduated from Teachers College…
Or remember Diana Lam’s husband? Will that sort of story become legal, and routine?
Just found it by accident, and noticed that no one ever tried to answer. Of course, reality was worse than my imagination.
I thought the lack of union control would lead to rampant nepotism. In fact, it led to widespread discrimination against senior teachers.
Oh yes, we all like free tickets. But that’s not (entirely) what this is about. I mean without watching kids.
When I was a little boy, my mother tried to regularly bring me to the theater – not dress up Broadway theater – local stuff, children’s workshop, young people theater. I loved it.
And forgot it once I got to the 4th or 5th grade. No plays for me. They were a bore, a drag. Even as a young adult, I rarely went.
And then as a teacher, I started going more often. Chaperoning. Big Broadway stuff. Especially when I moved to my new school. I’ve seen more plays in the last seven years than I had in my previous — than in all my previous years… And the habit comes back, a bit. And I go not just with school, occasionally, and more frequently.
This Spring I’ve been to two Broadway, one off Broadway, one off-off Broadway, and one college production. That’s five plays (really six, because one was actually two)
Three of the five, I brought students. Some were great plays but I was chaperoning. The fourth, I (world’s greatest uncle) took my niece for her birthday. Wicked. She’s 11, so I covered her eyes when they kissed. That counts as chaperoning, too.
The fifth was different. The Bronx UFT organized (and paid for) a night out for some Chapter Leaders and activists. We saw “Exit Cuckoo” off-Broadway, at the Working Theater (on 42nd, west of 9th).One, the play was good. And two, it was the only time this Spring I could sit back and not worry about the kids sitting around me. I was the guest, not the chaperone. Just so much more relaxing…
————— ———————— ————————- ———————– ——————- ————— ———– —– —————- —————— ————- ——– ——————— ———————— ————————- ———————– ——————- ————— ———– —– —————- —————— ————- ——– ——
Three ratings:
Wicked – good sets. Music, meh. “Clever” wordplay. Really for the kids. I liked the green makeup.
In the Heights – cliched story – generic uptown neighborhood (I heard this as a complaint a lot – it’s partially fair) – standard Bway music, except the opening and closing raps by Usnavi were original – Some wonderful choreography – liked the sets – liked the ‘action’ in the corners
Exit Cuckoo – closes today. One woman show. Lisa Ramirez plays an actress who becomes a nanny, and then she plays the agency head, and the other nanny’s she runs into, and the employers, and the group therapist, and a grandmother… Short (80 minutes), incredible lighting work (Ramirez takes on most of these personas with simple lighting and voice changes). You leave empathizing with the nannies. It’s really a play in class manners, and who raises whose kids, and how little the women on the two sides have in common. If it reappears, come on, it’s a cheap ticket.
Coming up:
West Side Story (definitely), Hair (maybe)
My resolutions this New Year were highly successful (mostly since they were already in the works when I made them): getting a new(er) car, and cutting my hair. I added to them, two weeks later: redoing my bathroom.
While not exactly cheating, they didn’t quite rise to the normally understood status of New Years resolutions. So, the borderlines successfully tucked away, I added 3 good ones in April: walk a mile each day, eat breakfast every day, no more chips.
And how have I done?
Walking: nice walks, 35 minutes at the short end to 3 hours at the long, about 4 times a week. Progress, but I haven’t met the resolution yet.
Breakfast: all but 2 days since mid-April. Success. Even if breakfast has just been a few raw vegetables + coffee.
Chips: not a single one, despite them being left in front of me on several occasions. More success.
A charter school operator in Illinois filed court papers, claiming not to be public.
When teachers at three of Civitas’ charters tried to organize, the operator went to court, claiming that these are not public schools, in order to fall under a different, more employee-hostile, set of labor laws.
So much for those who feigned outrage when I challenged the “charter = public” disinformation earlier this year.
Hat tip to Mike Klonsky.
I got my school to purchase a class set of mancala boards. Man, I am the king. Kids, freshmen through seniors, love it.
Today in my off-track geometry, we did one of Dave Marain‘s challenge problems*, I taught a quick lesson, (inequalities, including a theorem about a remote interior angle being less than an exterior angle of a triangle, argued about the proof, and Euler diagrams for conditionals, which was just a quick refresher), and then I taught mancala and they played for 10 intense minutes. They have concentrated construction time Friday, so they didn’t miss it today.
Tomorrow is games and puzzles day in logic anyhow (I do it once a week), and guess what I’m bringing?
*Find the sum of all solutions in terms of k:
Led to nice discussion of division by 0 (you know why), and how we could be certain we had all the solutions.
A 2nd year Bronx elementary school teacher is trying hard, but is concerned by what he sees, including test mania and a general cya attitude. The full post is here.
A few excerpts:
…learning becomes synonymous with direct instruction and rote bookwork. As much as I’ve worked to avoid that fate … the tone of my classroom has suffered from the pressures of the tests.
Another factor… behavioral issues. … So often the planning of seemingly simple activities must account for a dozen possible scenarios. Teachers, myself included, get to thinking that fun equals problems, so why risk that?…
What worries me the most though is that kids get turned off the whole idea of school at such a young age….most of our country’s poorest kids spend their days immersed in tedious and rigid environments that middle and upper class parents would never allow their kids to experience….
I’m behind on (lots of things including) updating my blogroll. If Is Our Children Learning (Ruben’s blog) is not there yet, it will be there shortly.
I don’t expect subs to do great things. Hand out a worksheet, put simple directions on the board, maybe collect some work… that’s enough.
Thursday and Friday our freshmen were on an overnight trip. My school’s been open 7 years, and this was the first freshman trip I’d missed. So, I get coverages, of course. Luck of the draw, my first coverage is for a geometry class. And the teacher did what I might have done – left very simple directions for the sub – have the kids read about transformations and symmetry, then fill in a glossary with a few words and a sketch corresponding to each term. There was a worksheet for homework.
Hmm.
Notebooks out!
I would have preferred a few days, and I haven’t done this in a year, but the topics were fun, and I decided to change it up, on the fly.
Now, I’ve got no graph paper. Kids, maybe they do, maybe they don’t (and I am barking at kids to borrow paper and pencils from each other, jeez, they thought with a sub they really wouldn’t work?).
Let’s go. Topic is transformations. Covers moving points around the plane, but for us to see, let’s move figures around the plane and see what happens to the points.
I decide to go for concepts, with some vocab discussion, but to get them to participate in developing as many of the algebraic rules as possible. The textbook (Jurgensen, Brown, Jurgensen) has one set of vocabulary, NY State uses another, let’s just throw it all out there.
I sketch (sketch only) axes, put up a triangle at (1,2), (1,6), (2,6) and put up another at (7, -3), (7,1), (8,1). “How far did I push the original?” Across 6, down 5. NY State calls that a translation. I’ve heard it called a slide. I like “push.” The Regents may write 
A transformation that does not change the size of a figure is called an isometry (detour into etymology). (I didn’t think about introducing “collineation” – but I had I, I wouldn’t have).
Rotations were next. I rotated something around an arbitrary point, told them that the algebra is simpler if we rotate around the origin. Put that same triangle up, and told them to rotate it 90° couterclockwise. Got E to give me the first point: 
I briefly began composing rotations…. but there wasn’t time, wasn’t nearly time. My class? I would have used rotations as a segue into a brief detour into modular arithmetic and a tiny bit about groups… but I was filling a period, not planning a week. Anyhow, they had a 20 second informal demonstration (through their own answers) to inverses…
Side board. Put up a triangle. What happens if we double each coordinate? (they wait for me. Honestly, this got the least participation.) New triangle is similar, but the sides are doubled. If we used 3, would have been tripled. A half? shrink. There is a center to these dilations, and it is the origin. Again, algebra is trickier if we have a different center. Isometry? No.
Back up front, they fairly quickly reflect across the x-axis, the y-axis, y = x, I do y = -x for them.
One minute on rotational and line symmetry.
Completely out of breath. I wouldn’t normally do this in a class period. But it was better than them reading it and taking notes. We had flubs along the way, kids who reversed coordinates, but by and large I got hands up straight threw, digressed all over the place, and got the kiddies to drive the lesson. We had a little time for worksheets, and some discussion.
(I asked for the same class the next day. I got it. Hooray! Except they had a “review quiz” and I watched instead of taught.)
Hand me CoM 52, and I’d be off doing card tricks. I’d divide the posts into clubs, hearts, diamonds, spades (no clovers, right, or are those clubs?)
Not Jason Dyer, at Number Warrior, who leads with a well-spun tale about Mersenne and perfect numbers and surprising lectures.
Then comes the actual carnival: almost 20 sharp links. I don’t know if Jason tilted it on purpose, but his carnival has a lot of things.
There are mathematical sculptures. Homemade mathematical calendars. Mathematical look at maypoles. Full color pictures of a Mayan mathematics text. And then this problem- click the Pat Bellew link for the answer – What is wrong with this photo:
(I was going to link to Pat’s post, had it not appeared in the carnival)
How could we show/prove that the diameter is the longest chord in a circle?
(What prior knowledge is necessary to support your answer?)
JD2718 