Puzzle – Walking stick
Another gem from Bertie Taylor:
I accidentally dropped my straight walking stick into a buzz saw, which neatly cut it into two pieces. I was so angry I picked up one of the pieces at random and threw it at the saw. It cut that piece into two. What is the probability that I could make a triangle with the three pieces?
New term, New course
Most of our classes are annualized, but not some electives. For me? Goodbye Combinatorics, Hello Logic.
I met the new class today. All were there, talkative, mildly interested. They liked the book cover.
We want the kids to do 8 credits (four years) of math, but know that not every kid can handle the high end of algebra-geometry-trigonometry-precalculus. So senior electives that carry math credits are a reasonable option. But logic is not only kids avoiding precalc. Some seniors, and a few juniors, choose it as what they hope will either be an interesting or a fun elective. In fact, I don’t intend to disappoint any of them (except for anyone who is thinking of not showing up). And a few are in there since nothing else fit their programs. I would complain (except I am the programmer).
Is it a math class? We use a college text that would usually accompany a logic course in a philosophy department. Perhaps the last 40% is mathematical logic. So it’s a stretch. The other stuff is fun, too. Informal fallacies. Categorical syllogisms. But when we hit the symbolic stuff and breeze through the old Course I and Course II material, and move on to validity testing and indirect proof…
When we meet first period in late May, with senioritis rampant, that’s when the attendence will tell if Logic has proved interesting. I’ll keep you posted.
Puzzle – Circus
A group of children totalling less than a hundred go to the circus and sit in one long row of seats. There are five brothers there, and a girl at each end of the row, and the probability of that happening is 1/3. How many boys and how many girls are there?
Credit
goes to Bertie Taylor, a regular at compuserve’s SCIMAT forum puzzles section. The forum is gone, and I last saw Bertie’s signature a decade ago, but he provided some gems.
Challenge
Standing challenge for any problem on this website: Take a kiddie problem, already solved, and make it challenging for strong high school students or even math teachers. Or, take a problem for advanced high school students, and twist it to make it a good challenge for middle school kids. In any event, this is a standing challenge:
Take a good problem, and rewrite it into a good problem for someone else.
Puzzle – Consecutive integers 1, 2
Two little puzzles for today:
1) Find nine conscutive integers whose sum is 6.
2) How many ways can 1000 be written as the sum of consecutive integers?
Teacher Pay Scale – Darien 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.
Darien, Connecticut is an affluent town on Long Island Sound, just east of Stamford, south of New Canaan, and west of Norwalk. It is very white (96%) and very rich (average family income is over $150,000).
Darien’s salary schedule is below the fold ———–> Read more…
Restructure this
Bloomberg and his chancellor are restructuring again. What are they doing? Why are they doing it?
The New York City Department of Education is involved in a campaign of disorganizing the school system, generating failure, generating demoralization.
Structure
Four years ago the 5 high school districts and 30 odd local districts and the chancellor’s district and (what else) were replaced by 10 Regions .
Last year a way was offered for schools to get out of the regions: Empowerment. The name is intentionally misleading. In return for a little extra control over some local issues, and one fewer meeting each month, schools lost DoE support and had to contract for services. Salami-style, empowerment was the first slice of privatization.
The new proposal marks an acceleration of the same. The regions are being collapsed into 4 theme-based regions (whatever that means) to provide support, and more schools are being forced into empowerment. A new option – finding a ‘partner’ to provide services (for public consumption: “partner;” internally “vendor”) is a quicker route to privatizaion. See Leo Casey’s post on Edwize for more details and some response.
(Below the fold, more on Reorganizing Schools, Reorganizing Personnel, Curricular Issues, Conclusions, and Response) ————> Read more…
I wish I were…
not using the subjunctive?
No.
in Washington DC?
Yes.
Today there is a (I hope very large) demonstration in Washington against the war in Iraq. I can’t be there, but let me add my [small] voice to those who are pressing shoe leather to pavement right about now.
My union, btw, which supported the war in Viet Nam, opposes the war in Iraq, and has even resolved to support today’s mobilization.
Pedagogy: Outlook on teaching math (3rd of 3)
Dave at Mathnotations wrote this big ideas about teaching math post. It got me thinking.
I maintain a resume. Years ago I added to it an “Outlook on Teaching Mathematics” page. I jammed as much of what I thought was most important as I could into one page (without using small fonts or obnoxiously narrow margins). I started posting it here last weekend. The first part is here. The second part is here. Read on for the last and final piece.
• An effective instructor is also a learner. I continue to take courses in mathematics and to study on my own. I am an avid problem-solver. I have never stopped trying new techniques in the classroom, and modifying, or rejecting them based on actual experience. As a role model it is necessary to share this love of learning with students. I freely admit when I do not know, and gladly share with students how I intend to search for “the answer.”
It is not acceptable to know just a bit more than the students.
(more below the fold) —> Read more…
Puzzle: Area = 1 (refined)
Find the set of all points (x,y), such that the figure formed by (1,0), (0,0), (0,1) and that point, not necessarily in that order, has area = 1. The figure formed should be a closed, non-intersecting polygon.
Bonus: Find the additional set of points (x,y) that taken with (1,0), (0,0), (0,1) and that point, not necessarily in that order, form a self-intersecting polygon with area = 1.
Teacher Pay from far away: Las Vegas
I will be concentrating on pay in the New York metropolitan area, but a reader sent a link from Clark County, Nevada, so why not share it? Remember though, the cost of living is significantly lower there – their numbers and ours are not directly comparable.
2006-07 ANNUAL TEACHER SALARY SCHEDULE
|
CLASS A |
CLASS B |
CLASS C |
CLASS D |
CLASS E |
CLASS F |
CLASS G |
|
|
STEP |
B.A. |
B.A. + 16 |
B.A. + 32 |
M.A. |
M.A. + 16 |
M.A. +32 |
PH.D. |
|
1 |
$30,299 |
$32,084 |
$33,855 |
$35,641 |
$37,417 |
$39,192 |
$39,692 |
|
2 |
31,687 |
33,462 |
35,243 |
37,021 |
38,800 |
40,811 |
41,311 |
|
* 3 |
33,073 |
34,845 |
36,624 |
38,403 |
40,184 |
42,438 |
42,938 |
|
4 |
34,453 |
36,227 |
38,010 |
39,786 |
41,573 |
44,059 |
44,559 |
|
5 |
35,835 |
37,618 |
39,391 |
41,173 |
42,953 |
45,681 |
46,181 |
|
6 |
37,222 |
38,999 |
40,775 |
42,555 |
44,330 |
47,297 |
47,797 |
|
7 |
38,600 |
40,380 |
42,159 |
43,939 |
45,716 |
48,921 |
49,421 |
|
8 |
41,768 |
43,554 |
45,321 |
47,100 |
50,541 |
51,041 |
|
|
9 |
44,926 |
46,706 |
48,485 |
52,162 |
52,662 |
||
|
10 |
46,310 |
48,088 |
49,866 |
53,783 |
54,283 |
||
|
11 |
47,694 |
49,476 |
51,250 |
55,402 |
55,902 |
||
|
12 |
57,125 |
57,625 |
|||||
|
13 |
58,641 |
59,141 |
|||||
|
14 |
60,596 |
61,096 |
|||||
|
15 |
61,808 |
62,308 |
|||||
|
16 |
63,044 |
63,544 |
Class G (PhD) is cutting off on my screen. It is just Class F + $500.
Source: Clark County School District
(Notes from my correspondent, below the fold) —-> Read more…
Puzzle: Area = 1
Dave Marain has been posting engaging problems for use with (mostly) middle school students (some are ok for upper elementary, others for algebra or geometry students). Today he put up a coordinate geometry problem in this group of questions,which made me think.
The problem was along the lines of: Find x such that the area of the polygon formed by (6,7), (12,-2), (15,-2), (x,7) is 117. (He had different numbers, but same idea). Decide what figure is formed, and use a well-known formula to decide what x is. When you click the link and look at Dave’s problem, please make sure to read the comments. He has a talent for generating rich discussions.
I do a lot of “what if” as I solve problems, to see if I can come up with generalizations, or interesting alternates. Try this one, but be warned, I think it is hard:
Find all possible values of (x,y) such that the area of the polygon formed by (0,1), (0,0), (1,0), (x,y) is 1.
Pedagogy: Outlook on teaching math (part 2)
Dave at Mathnotations wrote this big ideas about teaching math post. It got me thinking.
I maintain a resume. Years ago I added to it an “Outlook on Teaching Mathematics” page. I jammed as much of what I thought was most important as I could into one page (without using small fonts or obnoxiously narrow margins). I started posting it here last weekend. The first part is here. Read on for the second piece. (I’ll post the last later this week).
The details at the end of the second point are from lessons that I use.
• I strongly believe that instruction should be adjusted or modified to meet the needs of the current students. This entails a constant process of carefully planned experimentation, reflection, adjustment, and evaluation. Further, I have found it valuable to share with students information about modifications (pacing, depth, styles of instruction, balance of traditional/non-traditional work), and to solicit additional feedback from them.
(more beneath the fold) —> Read more…
Teacher Pay Scale – Englewood Cliffs 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.
Englewood Cliffs, New Jersey is a very affluent town on on the Hudson River, just north of the George Washington Bridge. Average Household Income is above $100,000. Englewood Cliffs has large Japanese and Chinese populations.
Englewood Cliff’s salary schedule is below the fold ———–> Read more…
Pedagogy: Outlook on teaching math
Dave at Mathnotations wrote this big ideas about teaching math post. It got me thinking.
I maintain a resume. Years ago I added to it an “Outlook on Teaching Mathematics” page. I jammed as much of what I thought was most important as I could into one page (without using small fonts or obnoxiously narrow margins). I’ll post it here, in three pieces, over the course of the next few days. Read on for the first piece.
• Best mathematics teaching inspires. At all levels and all ages it is possible to communicate some of the elegance, power and beauty of this most abstract subject.
As adults we may take “two” for granted, but we have never met it, never touched it, never tasted it.
(more below the fold) —————->>> Read more…
Why teachers unions are good for teachers and the public
Pissed Off Teacher reposted the article. Read it here. (It was originally in the AFT Magazine, The American Educator)
I don’t always care for what Diane Ravitch says, but she’s smart, and she gets some things right. She got this right.
Thanks to POT for putting it up.
I’m running
…in the upcoming UFT elections.
I thought I would be running for delegate to the (is it the AFT convention?). Instead it will be for an officer slot, on the New Action slate.
Vote for me. (Easiest way is to vote New Action slate. But if you split your ballot, I’m probably the only Jonathan running for an officer position – won’t be hard to find .) But do vote. It is a small but important responsibility that all UFT members should take seriously.
I will write more about why I support New Action, and why you should, too, another day. For now: New Action criticizes our leaders when they are wrong, but supports them when they are right. New Action has a unique commitment to strengthening our union from the bottom up, from the chapters. And finally, I continue to believe that the UFT needs a much more vigorous approach to supporting new teachers, (chapter building, but much more than chapter building) and a strong vote for New Action is the best way to deliver that message.
Puzzle – Better fit? (3 questions)
For those of you who don’t want to try to answer, try the question at the bottom.
(Assume everything is snug. No overlaps.)
- Which is a better fit – a small circle in a small square or a large circle in a large square?
- Which is a better fit – a circle in a square, or a square in a circle?
- Where can you produce the tighter fit – with two congruent circles in a rectangle, or two non-congruent circles in a triangle?
How can you compare two “fits” to decide which is better?
Lord of the sweet tooth
Take a look
…at this bizarre production.
Miss(ed) Manners and friend appear to have found an interesting project to occupy them over break, and produced, um…. Do you like candy? Lord of the Rings?
They produced the Battle of Helms Deep, in candy. Too strange too miss.
I wonder which beings they ate first.
MLK Day
I like having this holiday off. But I think we are celebrating the wrong day.
August 28, 1963 was the I have a Dream speech. The first Tuesday after the first Wednesday on or after August 28 would be a good day to celebrate.
March 25, 1965 was the march on Montgomery. Good day for a holiday.
April 4, 1967 Martin Luther King Jr. speaking at Riverside Church in upper Manhattan, delivered Beyond Vietnam: A Time to Break Silence. This was one year to the day before his asssassination. This would be an appropriate holiday.
The day he was born was inconsequential. When he acted, when he marched, when he spoke words brave and true, then he affected us. We are celebrating the wrong day.
Some new blog-links
I’ve been vigorously adding things worth reading:
- Math Notations is Dave Marain, who’s been commenting here. High school math, puzzles, problems, bits of lessons, New Jersey
- The Exponential Curve is Dan Greene, teaching math and blogging math lessons (charter school, in California?)
- Dr. Homeslice high school teacher, and unionist, California
- Math Teacher Mambo teaches 10th grade in Texas
- Bright Minds (play and problem kids, and I am not sure what else, but it seems well-written)
- Halfway There is a California community college math teacher, really politics, not too much math
I’ve also been interacting with some WordPress bloggers, but haven’t gotten around to linking yet. Darmok is named for a character from a SNG episode (I guessed right) and answers puzzles, right here. He’s also a physician with a scienc-y blog. Daniel Livingstone’s Learning Games looks promising. I had an interesting exchange with Hal of Hal’s House of Pancakes; I’ll keep following it. Denise in Illinois writes Let’s Play Math. She’s homeschooling and motivated.
In the other direction, I’ve delinked EduInsights. What was I thinking when I put him up? Anti-liberal education, based on fuzzy stats. Not a good link for me.
NYCDOE – C30: Why bother?
C-30 is the process by which principals and assistant principals are permanently appointed to schools. The process involves parent, teacher, school staff, administrator union, and Department of Education (through Region, District etc) personnel. (Before a principal or assistant principal is permanently appointed, the DoE often appoints an Interim Acting (IA) principal or assistant principal.)
I don’t know how long C-30 has been around (15 years?) or when it changed (3 years ago) but the change was dramatic.
The part of the C-30 that most of us hear about is the Level I Committee. The Level I includes representatives of all the different groups mentioned above, including two UFTers. It interviews the candidates. I have served on 5 (or is it 6) Level I’s. And with the changed regulations, they have become a waste of teachers’ time.
(more below the fold) —-> Read more…
Teacher pay scale – Westport 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.
Westport, Connecticut is an affluent town on Long Island Sound, just east of Norwalk. It is liberal, white (over 95%) and rich (per capita income over $70,000).
Westport’s salary schedule is below the fold ———–> Read more…
What’s my name?
Jonathan. But my last name? I don’t say. Not on this blog. I don’t claim, however, that this blog is anonymous. You could dig just a bit and figure out who I am (and some of my regular readers do know me) But I have made an effort not to put my name on this site. I write about my school (a little), and while nothing is bad or embarassing, I would still prefer that students not blunder in here, at least not through a one-off casual search.
On the other hand, I am an activist. I am my chapter leader (union steward), and I participate in all levels of union activity that are appropriate for that. Some chapter leaders do the minimum expected of them. Not me. (Others do more than me, but I really do take my responsibilities seriously). Beyond what would normally be expected, I have recently joined a caucus in my union, New Action – UFT, which despite the name gets me to more meetings and discussions (the action will come).
I am an active math teacher, and participate regularly in professional activities, through my union but also through my state professional association. I was even an executive board member for a few years. I have helped organize events, I have been a speaker, articles have appeared in professional journals with my name.
I have written on other websites, and in several cases those sites have used my name, and my blog name, and I haven’t bothered asking them to take it down.
I am out there, and it doesn’t take detective skills to link the name with the blog.
Even so, last week when I noticed that NYC Educator, a Queens high school English as a Second Language teacher/blogger who supports a different UFT caucus, had published my name in a short attack piece in late December, I was annoyed. The reason for the piece (he claimed I am running for Exec Board) was a lie. The point was simply to make insulting reference to me, and to put my full name into the blog.
(more below the fold) ——> Read more…
Puzzle – Overlapping circles
Maybe this one is easier than I will make it seem.
Given three circles, each of radius 3, drawn so that each circle passes through the center of the other 2 (in other words, the centers form a 3-3-3 equilateral triangle), find the area of the portion common to all 3.
(ripped off from an SAT II practice problem. All answers were in terms of pi and radicals, and there were five choices)
UFT – Today’s Delegate Assembly – January 2007
These things bore me, but there is usually at least one thing that makes it worth having gone. Today there were 4:
1. resolution on the closing of schools
2. resolution on January 27 anti-war demonstration
3. Remarks by D32 DR
4. Maria Colon
Let’s start with 4), since it was the best. Maria Colon was the chapter leader at JFK HS in the Bronx. She caught one of the AP’s changing regents grades, landed herself in a full year hassle, and when she stepped down as chapter leader, found herself brought up on ridiculous charges. After a year (was it a year?) in the rubber room, Maria was fully exonerated.
Tonight a delegate from JFK took the mike, sort of at the wrong time, but no matter. She said something about JFK and harassment, and that Maria was in the room. We haven’t seen Maria in over a year. She was greeted with a standing ovation, made remarks thanking the entire UFT, and talking about the need to fight in the schools, and left to a second standing ovation.
(more beneath the fold) —> Read more…
JD2718 