Some reading to divert you
From what? From preparing for the first *full five-day week of school, of course!
- Jackie was already a scheduler and is now a math teacher with a very promising blog. Take a look, leave some encouragement… Oh, and clever names. You’ll find the 1618 in the e-mail, and the blog name is continuities.
- Syntactic Gymnastics, desperate to leave her awful mini-school, didn’t get out. She’s holding her head down and is committed to making it through this year without incident. It’s working so far. Oh, and she’s blogging again.
- Did you know that Google has a version in Leet (1337)? Boys and girls, stop this. L33t2 ^^@26!^/@||¥ |€55 ɮ¤¤1 than putting hearts instead of dots on “I”s, so just stop. And how do you pronounced “pw”?
- Irrational‘s having a good start to the year (me too, btw), though if you dig back a few posts, the summer wasn’t the hottest.
- And you probably already know about Leo Casey’s powerful teacher story, and about Dave Marain’s interview with a math reformer…
*In NYC, this is really the first 5 day week of the year.
Trinomial Factoring – Breaking the Middle I
(Here’s the older posts: 1 2 3)
3b(2b – 3k) + 5c(2b – 3k) Group the terms, pull a common factor from each.
(2b – 3k)[3b + 5c] Pull the binomial common factor forward.
(I use the square brackets for the visual effect, and clearly tell the kids that they are exactly the same as regular parentheses.)
3y(4y + 1) + 50(4y + 1)
(4y + 1)[3y + 50]
Mathematical Middle Ground
Just a quote from Math Mom. I’d say it differently, but not better:
I’m advocating for a middle ground — a position where math need not be only dull drill-and-kill mastery of basic skills. I believe in the direct teaching of basic skills, but I also believe in the value of using fun, interesting, and challenging problems as a tool to help spark more interest in mathematics, to help practice basic skills in a different context, and to give kids the thrill of the “aha!” moment that one gets when solving contest-style math problems, and the resultant confidence and self-esteem that comes from struggling with something difficult and succeeding.
This is part of the discussion at Math Notations on Part 1 of the Steen interview. It is from comment #20…
Category size
What do you think (that is, if you care at all)? I divided a “Math Teacher” category out of “Teachers” so that none of the lists on the side would be more than 10 – 15 long. More readable? or doesn’t really matter?
Also, was it fair to categorize blogs by what the author does, rather than what the blog focuses on? Hal likes books, but he’s a math teacher. ‘e‘ writes about teaching math, but she’s not a teacher. Sarai studies serious math, but blogs about nature and knitting and enjoying living simply. And I placed some people in the wrong slots. In the end, does it matter? Maybe one long, alphabetic list… And how many are hard to slot? Fred does unions, ed policy, and social justice. Homeslice is a teacher, but he does teacher unions exclusively. Is there a better way?
(Also, I need to list out lots of teacher-additions and bow my head for a few more deletions, but another day. )
Marain’s Math Maven Moment (Part 2 and last)
Dave Marain of MathNotations interviewd Lynn Arthur Steen, a math ed reform professor involved with the NCTM Standards back in 1989. Three links: I explain a tiny bit more, Dave published Part 1, and finally, just today, he publishes Part 2. That last one’s the link most of you want to click.
By far the more interesting set of questions and answers come from this last part. A puzzle. I chose 11 bits from the Q&A, and organized them. How?
- As AP courses go, AP calculus is one of the best.
- The linear model of mathematics learning is wrong in almost every respect.
- Use of technology is as important as use of fractions, and both need to be taught and tested.
- For life … factoring is a relatively useless skill. For higher mathematics, the conceptual role of factors is crucial…
- The new Algebra II may well be the last mathematics course ever taken by many of today’s high school students.
- The types of problems Singaporean children … are tackling seem more complex than their grade counterparts in the U.S.
- I read [the Standards] as clarion call for eliminating the tradition, most evident in mathematics, to select and educate only the most able students
- As mathematicians and educators … work together on common projects, each learns from the other and the frictions that led to the math wars begin to reduce.
- competent teachers need to be free to teach in whatever way is effective for them—which implies minimum constraints from state- or district-imposed curricula and tests.
- frustration among K-12 mathematics educators … [want] to do … the best for … students but … mandated to follow new curricula and programs that come and go …
- Mathematically able students [need] opportunities for horizontal exploration of optional topics … Far better to slow down, spread horizontally, and dig deeper into the hidden corners of the regular curriculum.
Two about kids and Allende
Twice in two-and-a-half years I’ve seen coming of age movies starring cute kids, set in the shadow of the US/Kissinger/CIA military coup against Chile’s Salvador Allende. And in both we hear Allende’s final words. September 11 was a tragic day in 1973, too. These are two good movies, but after the backdrop and the age of the characters, they have little else in common.
In Machuca we watch two boys in Santiago, Chile, a poor Indian and a privileged upper middle class private school student, become friends; then we watch the friendship disintegrate in the coup.
In Blame it on Fidel, we watch a young French girl’s reaction and adaptation to her parent’s involvement in the Chile Solidarity movement. Read more…
Marain’s Math Maven Moment (Part 1)
Ok, that was a stretch, going for 4 ‘M’s.
Anyway, Dave at MathNotations, serious time on hands due to recent retirement, writes Lynn Arthur Steen, requests an interview, and gets it. Steen is a mathematician associated (?) with the smarter half of the advocacy tail of the reform math monster. Get it? He didn’t write those curricula I fought so hard against, but he provided some of the more intelligent intellectual support. He’s a math professor at St Olaf College in Minnesota.
Anyhow, Steen’s a reasonably large name in the (not yet over!) math wars. So here we have Dave, who like me and many reasonable classroom teachers would like to defend the sane center against both extremes, our Dave gets to ask the questions. And Steen answers.
Go read the first part of the interview, here.
Puzzler puzzled
Today I ran a prize puzzle contest in combinatorics (I’ll explain that some other time). One of the puzzles, old but good, was:
Is there a positive integer,
, such that
and
taken together contain each of the digits 0, 1, 2,… , 9 exactly once?
Clear? To me, sure. To you? If English is your native language, yup. But one of my students, out of ESL but not a native speaker, took the phrase “taken together” to mean “added together.” Not the intent. But I will argue that there was at least some (haha) ambiguity. My problem asked for two powers of ten, with 10 digits altogether. The student’s problem was to
find a number of the form
such that
contains all ten digits exactly once.
- Can you solve the problem as originally intended?
- Can you solve the student’s (arguably more interesting) problem?
Puzzle twisted
Sometimes when I am teaching I throw out little puzzles. Can do it if I sense some restlessness – some extra intellectual stimulation to absorb that edgy energy (factoring bigger numbers is better than a binky for some 9th grade boys). Can do it if a nice puzzle is just staring at us. Today, the latter…
Naming angles is boring. But we’d just named three angles in a diagram with three rays with a common vertex. I drew the same thing but with four rays, announced this was for anyone who wanted to look at it, and asked how many angles. I also drew the diagram with five rays. (In each case the outer rays were spread about 60 or 70 degrees.)
We did other work, but got drawn back, and started discussing. I was of course expecting “six.” Someone got a higher count, but including the “external” angles (reflex is what our high school texts call angles greater than 180 degrees, but we were not there yet…) Nice twist. Do you want to try his puzzle:
Consider rays AB, AC, AD, and AE, none collinear. How many distinct angles can be formed using these rays as sides of the angles?
Pete Seeger in the Bathtub
![[At age 77, folk legend Pete Seeger still inspires]](https://i0.wp.com/www.salon.com/weekly/seeger960527.gif)
Nice stories about a good man.
Pete’s songwriting saved Ed’s rock and roll from being banned in Utah.
Ed’s intemperate comments got Pete knocked off a song list in the same state.
And three or four more engaging anecdotes.
Multiplication Principle
“In Jersey, from all that toxic waste, people have three hands with four fingers on each one. How many fingers does each Jerseyite have?”
“Twelve. Four times three.”
“Nah, ten. I made that mutant stuff up….”
Lesson Plans in NYC
There was a discussion at Happy Chyck Wonders (tell us about the potato chips again, please?) about lesson plans being collected. In the comments section, I quoted our UFT contract on lesson plans (teacher’s discretion, etc, etc, good stuff). But I couldn’t find the bit about routine collection not being allowed.
Enter District 11 District Rep Paul Egan and his horribly organized, but wonderfully inclusive UFT D11 website. He’s got the “Know your rights” pamphlet. And he’s linked the circular*. And here’s the key text:
If the development of a school instructional plan is a collaborative effort among supervisors and teachers, as part of that process teachers may be encouraged to share and coordinate lesson planning. Since the mechanical, ritualized collection of lesson plans does not further these goals, it is prohibited. – Spec Circ No 28, 1990-91
* Maybe the on-line version at the UFT website already had the link? Don’t care. I like Paul; found it on his site. He gets the credit.
( And the contract language, below the fold —->) Read more…
Leaning on the GCF… (Trinomial Factoring)
In the 1st post of this series I made a case for teaching factoring. In the 2nd I described multiplying polynomials by “double distribution” (no FOIL!) so that:
So we do Greatest Common Factor work and arrive at 3 examples like these:
| ax + 5x | a@# + 5@# | a?%?%? + 5?%?%? |
| x(a + 5) | @#(a + 5) | ?%?%?(a + 5) |
Then this:
a(y + z) + 5(y + z)
(y + z)(a + 5)
(I use squiggles for the intermediate steps. Ach, this is nice. We compare it to our double distribution. But we need one more step back, first.)
an – 5n + ax – 5x
n(a – 5) + x(a – 5)
(a – 5)(n + x)
Now we see the double distribution, moving from bottom to top. Note, the first step is to factor out the GCF “pairwise,” which I emphasize orally and by underlining the pairs within the expression.
One day for just this, nothing harder than:
And trinomials come the next day (and in my next post)
ATRs and Right of Return
A UFT alert (an e-mail to Chapter Leaders and others, usually under the name of an officer of the union) went out today. This one was under Jeff Zahler’s name. Here’s the central part of what it said:
All pedagogues who have been excessed, including those who are presently ATRs, have the right to return to their school within one year should a vacancy emerge in their license area in the school from which they were excessed. To exercise their contractual right to return to their former school, they must express their desire to return in writing to their former principal within one year.
I wrote Jeff, asking if an ATR could write a letter now, and he answered:
They can write the letter now if they wish. It then puts the obligation on the DOE and school to notify the writer of a vacancy.
Chapter Leaders, you should eventually get this info from your DRs and Special Reps, but even before then, let any ATR members know about Jeff’s advice.
Is the sum of the carnivalettes greater than? Hmm.
Kurt Van Etten at Learning Computation has a new carnival up. Carn-O-Math #XVI is divided into “The Good,” “The Bad,” and “The Ugly.”
The categories are for math educators, mathematicians, and computer scientists, respectively. More about that below. Kurt grabbed some good posts without waiting for submission. And so it should be. And so, I hope, it will be.
The quality is there. The size? Even though the academic year has just started, I hoped for a bit more. Next time.
Oh, and the semi-partition? There’s been discussion of dividing into two carnivals. I remain, strongly opposed. One of the nice things about a carnival is that there is a mix of topics that normally you wouldn’t find together. The reader chooses, and if you’re a computer geek but a post about long division catches your eye, more power to you. Can’t do that with separate carnivals.
Even in COM10000, my recreational puzzle is in the educator section (because of me, not the topic), while the sex partner post is in the mathematicians group (perhaps since it is such a major top of theoretical speculation for undergrad math majors…) On the basis of the math, though, think about “what is a random figure?” vs “what is the difference between mean and median?”
I don’t mean Kurt did bad. He didn’t. I mean that I would be concerned if any structure were made permanent.
Figs, Spider, Kitties, Olive, Salad
Meeyauw (guess what this blogger likes) asked for a spider picture. So I went through 2006 photos, and found some suitable vacation photos.
- That spider was on my balcony on Alonissos. It was the best of a rather poor crop of arachnophotos.
- Figs, yeah. Two years ago I was there in August – just plucked them off the trees…
- There were quite a few kitties in the Old Town on Alonissos. Up top is one of a pair, below are two ignoring each other.
- There were a bunch of gnarled ancient olives at the foot of the hill before the Temple of the Great Gods on Samothrace. This is one of them.
- And look what I found! Another cucumber tomato salad. The port of Alexandroupolis. Followed by Sucukaki, which I think was beef/lamb ground with Turkish flavored herbs and spices. Excellent. (Also served on butcher paper. A gimmick…) This is July 2006. I ordered the same thing this July in Thessaloniki… nah. Just ordinary burger, without the wonderful flavor.
more photos below the fold —> Read more…
A problem with one carnival…
I have two. The Carnival of Education keeps messing with me. This week Educationwonk put up my post, but didn’t link it (fixed). Last week Mathew Taber put up my post, linked it, but got confused between multiplying an factoring. Not long before, Ed in Tex lost my submission, second time that happened with that host.
Second, you get carnivaled next to, um, people and ideas I am not necessarily very happy with. I just read on the current host’s site links to vile anti-union stuff. And he’s not the only one.
From here on, with the Carnival of Education, I will be more careful what I submit, and to which host.
Carnival of Mathematics? Of course! Math is good. And Whatsit’s Potluck. That’s the best.
The image is from an article about summer food poisoning. But that’s not the point I am making!
Link +s and -s
More housecleaning.
- – Baghdad Burning. Appreciated the blog, but in April she said she might be leaving Iraq, and hasn’t blogged since. I’ll take almost six months silence to mean she really isn’t going to blog. I hope she landed somewhere peaceful, and on her feet. [Update – Chris notes in the comments that she posted moments after this went up, with her story of leaving Baghdad. Best of luck to her in these difficult times]
- + Jose Vilson. NYC math teacher, teaching fellow. Thoughtful stuff.
- – I thought having a librarian on the list was neat, but Teaching Technology… seems to have given up the blog.
- + How long have I been reading Miss Profe (Hardknock teachers life)? Serious, meaningful, social stuff and education stuff. It’s about time to add her.
- – Chaz, supporter of a louder opposition in my union, stopped blogging almost a year ago. He left a note here saying he would explain. One day.
- + I am trying out Irrational: A Math Teacher’s Notebook
- – Mathematical Musings has become a tech specialist. She still has a nice blog, but it’s not for me.
- + I don’t know how Math Mom ever came off my blog roll, but she’s back. Not a homeschooler, but a parent involved in her (little) children’s math education
- – Understanding posted thoughtfully about teaching high school math at a California charter school, but he changed schools and abandoned his old blog
- + Math Trek at Science News is fun. Julie Rehnmeyer. Popular. Advanced. Applied. Well-written, often at the intersection of math and science for the educated layman.
- – Thought Learning Games was cool. Changed my mind.
- + Miss Frizzle returns with a new host. Welcome back.
- – Somehow the math education part of NJ (math involved, and math licensed parent) Linda Moran‘s blog disapparited. When I find it, I will relink it.
- + I came to A Mispelt Bog for a math carnival, and decided that it makes a nice read. John Kemeny does it. Some math and some higher education.
- – Did I mention dropping Jenny Kissed Me and Fields of Gold? If I had a tag, “Swedes who used to post math conundrums….”
Ice breaker – your teacher’s an idiot. No. Really.
As I really started to unwind on my first day speech I asked the freshmen to take out their programs and check and make certain they were in Algebra Section I (with the strange code ME21H-01) and one then another, then three more hands went up, and it should have been a sea, since I was speaking to a roomful of geometry students.
So I smiled and told them these stories, and the one about my first parent teacher conference day at my new school when a girl with the unfortunate habit of sticking up her hand to ask questions right in the middle (of what? didn’t matter, she found the middle) in my first period class stuck up her hand (right in the middle) and I let out an exasperated “What?” and she told me my shoes didn’t match, which was true, though they both were black, and that was really enough stories since I was almost out of breath and barely paused and didn’t stop until I reached a period.
Phew.
And now for some different fare…
A few posts about or by teachers elsewhere:
Browneyed Girl (name and school anonymous) got a comment warning her that her blogging my be violating some federal regulations. Read how thoughtfully she responds, and look how helpful her readers are.
Math Wars are raging in nearby Ridgewood, New Jersey. District wants to ask students probing questions such as “how do big numbers make you feel?” and parents want multiplication done only using Roman Numerals. Chiseled into granite. Too bad teachers aren’t speaking up for the sensible center. Widening gyre and all that.
Yonkers teachers have a contract in front of them. The vote is now, and we are waiting for details. Let’s see if a major metro New York teachers union can get a raise without paying for it with givebacks. As a back story, a Yonkers teachers strike almost 10 years ago led to a large raise, setting the stage for NYC’s United Federation of Teachers to negotiate several time-for-money swaps, in an unsuccessful attempt to keep up.
Teacher on the Edge is all revved up and ready to do great union work in her school. So why is she stuck dealing with bossy teachers trying to control what she teaches?
Mocking me! I just deleted a bunch of porn link spam. The message in the body of each post: Order of Operations on Google.
That woman in my school…
not one of our teachers. Not a nurse. Not a parent. Not an administrator. Not a flunky from the Region or the District or the Supe’s Office, or Downtown, or the Learning Support Organization, or any of those other unimpressive dens of unimpressive bureaucrats.
She is a teacher with a pay check, but with no job. We have an ATR, an Attendance Teacher in Reserve assigned.
ATR? Excessed from a school, and hasn’t found a new assignment. Excessed teachers used to get placed when there were openings in their license area in their District, but could end up with nothing. Under the nasty new decentralized transfer system, ATRs have no rights to any job – emergency certified teachers off the street can get a job an ATR wants, but the ATR is guaranteed a salary.
Maybe she is happy doing nothing and collecting? Too insulting to answer. But I’ll answer anyway. Absolutely not. This is a teacher. She wants to teach.
Many ATRs are from large high schools that are being phased out (even one Chapter Leader is ATR) where dozens have been left without work.
Many others are D79 teachers. District 79 “reorganized” this Spring, closing centers such as GED and schools for pregnant teens. Several hundred teachers were left without work(?), (and not by seniority?) That’s how that woman got to my school, where we don’t need an ATR. She wants to work, she can work.
The UFT protected her pay. That’s a start. Now we need to protect her dignity.
Resisting the TI
At my first school a few years back, we received a buttload of TIs that most teachers were not using. The AP gave me one. I told her I didn’t want it. She insisted, said I could work with the kids (bright kids, math service aides) in the office using it. What should I show them?
I found two families of graphs that I taught the kids.
Plug cos(At) and sin(Bt) in for x and y in parametric mode. Let A and B be 3-digit, relatively prime or almost relatively prime numbers. Set the window from (-1,1) to (1,-1). And run t from 0 to maybe 20pi. (Lissajou figures)
Another is in polar mode, r = 1 + theta/10 + cos(5theta) Let theta run to 20pi, set the window to +/-6 in each direction. (a spiraling 5-petal flower. Looks like a “leaf.”
So the kids had fun, and got good, and the AP saw, and agreed to take the calculator away. Victory was sweet.
Fair Student Funding: Staten Island I
We’ll continue exploring the Fair Student Funding numbers. To repeat – the cuts are delayed 2 years by the “hold harmless” provision. The increases will be phased in (about 50% this year).
The major effects will likely be to disrupt programs where the cuts are a large percentage, and to move teachers from school to school, but without any guarantee that a $300,000 increase at one school will hire as many teachers as a $300,000 decrease at another school will lay off.
These are the previous posts, where there is more analysis:
- FSF: When does the excessing start?
- FSF: 111xx (numbers for LIC and Astoria)
- FSF – Rockaways
- FSF – 5 Bronx Campuses
And the remainder of this post, below the fold, details FSF numbers for those parts of Staten Island south of the Verrazano-Narrows Bridge. To see that chart, click —> Read more…
Prepuzzle puzzle: What is a random triangle?
Zac who commented here has a blog, squareCirclez, and I was reading it and found a question he found elsewhere. I would call it a puzzle:
He reprinted a story, and linked to the source, the Winter 2004 bulletin of the North Carolina Assoc of AP Math Teachers. The kid does the work based on the teacher’s definition of a random triangle:
- choosing angle A,
- choosing angle B,
- choosing angle C,
Whoa?!
- Step 1 includes the assumption that half of all triangles are obtuse. Part of the conclusion is buried in a shaky assumption.
- Even in obtuse triangles, two thirds of the angles are acute.
- Why should we randomly choose angle measures?
What is a random triangle? how can we generate them?
I have 3 ideas:
- Lengths. Randomly choose 3 numbers on a given interval. We will get lots of non-triangles this way. On the other hand, dividing a given number into 3 pieces may skew the results – the constraint makes the process non-random.
- Coordinates. Randomly choose 6 numbers on a given interval: (a,b), (c,d), (e,f). Perhaps we can integrate? multiple integrals?
- Angles. Three numbers from (o,2π). And plot them as points on a unit circle. Will the constraint do something funny. It feels like a relative of my mad carpenter or walking stick puzzles.
Ideas? Thoughts? I can’t believe that any is worse than what the article reported.
Back to School Teacher Food Event
For those who teach and pretend to cook, Ms. Whatsit’s teacher potluck carnivals are 
a pleasure. She’s been hosting them for three months now, with plans to continue. The September back to school edition has my cucumber tomato salad as the lead dish!
Click the pioneers in the orangey painting to visit the Potluck. Here’s a year old post on my salad, or click this link to read about salad’s better than the one above and to the right.
The food in this picture is from the Muslim Students Club at Indiana University. Maybe I’ll make one of those dishes for the next potluck. I think we have felafel and humus, back left, but I’ll pass on the helal bratwurst.
JD2718 