Puzzle: one over one plus … harder and easier variations
This is the place to offer *easier and harder variations for the puzzle below:
What is the value of 
A month ago Dave Marain ran a discussion of 
I know this one has been done many many times before. But he generated a nice discussion.
There are also places for:
What makes these two problems so similar?
*For my money, writing easier variations is the greatest challenge that I am offering. It’s easy to make something harder….
Teaching math: Balance and discrete topics
I am a big fan of balance in teaching mathematics. I don’t much appreciate the extremes that either the constructivists or the back to basics folks are currently offering us. And, honestly, most math teachers, most good ones, find ways to balance between the two extremes.
Let’s remove some discrete topics from K-12 mathematics
So in response to my old new math post, when e wrote: “I just don’t understand why the concept of balance seems to be foreign…” I was mostly inclined to agree with her. But there is a bit more here.
In this case there is a question of whether the topics should be taught at all. Topics from discrete mathematics were not traditionally part of the K-12 mathematics curriculum in the United States.
(more below the fold –>) Read more…
Restoring a link
Synctactic Gymnastics is back, at least occasionally, and I’ve restored the link in the teacher section. Apparently she’s having a rough time of it in her mini-school, and is wondering what to do for next year. The rough time explains (in part) the blog-break.
The old new math
In the early 70’s everyone learned a little bit of new math in elementary school. Sets, Venn Diagrams, different bases… Little did we know, little did we care where it came from, or that it had not always been part of the curriculum…
(*You can read a bit more about New Math all the way at the bottom of this post.)
(Follow up: discussion on what topics to add and remove from the curriculum right here.)
I know they stopped teaching it. Kids don’t know what a set is anymore. Still, it’s one thing to know, another to see the blank looks on their faces. Strange.
Thursday I was planning to teach compound inequalities to my freshmen. My (excellent) Algebra text (Dolciani et al) has a little side unit on union and intersection. So I decided to squeeze my lesson into the last 5-10 minutes, and teach some old new math instead.
I started by putting a big
and a big
on the board. I asked if anyone knew what the symbols were.
In my school the kids come from a wide variety of middle schools, and many from honors or accelerated programs. So there was a chance. I expected about a third of the hands to go up. Only three did. I asked who would be willing to wager some points on the next test that they really knew.
Would they wager some points? All the hands went down.
UFT Elections – results (I)
Preliminary results are in. Unity won overall, with around 80%. ICE/TJC was second in every division except retirees, and carried almost 20% of the active teachers, but 13% overall. New Action took about 8%. The most competitive races were for high school executive board, where the joint Unity/New Action slate took about 65% of the vote.I will publish fuller numbers when I find them.
Organizing needs to be at the top of our priorities. 80% of our active members did not vote.
In the meantime, the most important numbers to come out are turnout numbers. Voting was down compared to 2004. I think it was down in every division, down 15% in high schools, more everywhere else. Among active members, turnout was around 20%. This sets the agenda. Clearly the continuing rapid turnover has left us with thousands and thousands of teachers who passively pay dues (they come out of their checks) but feel no connection to the UFT. The multiplication of mini-schools, in combination with this turnover, has left us with schools with either no chapter, or effectively no chapter.
Every member who did not vote sent us a message: the UFT needs to reach out to its newest members, to its weakest chapters, and rebuild the union from there. We have started. In my district, the District Rep has helped start chapters in every single mini-school, though they are not all functioning at the same level. We have an Organizing Committee that helps with weaker chapters. (Some of?) the borough offices have adopted an approach that puts more staff in the field. But no fooling ourselves here. Organizing needs to be at the top of our priorities. 80% of our active members did not vote.
Puzzle: diagonals in a polygon
One of my favorite little puzzles is “How many diagonals are there in a polygon?”
For solvers here I have three questions:
- What is the answer? (answers here)
- How many different routes of solution can we find? (different solutions here)
- How can we modify this problem to make it easier? (easier versions, here)
Puzzle: diagonals in a polygon – methods of solution
How many diagonals are in a polygon?
There are at least a few different methods of solution, more if you count variations. How many methods can you find? This is the place to post them.
Puzzle: diagonals in a polygon – simpler versions
How many diagonals are in a polygon?
This space is for the most challenging task: designing easier versions (or variations) of this problem. Post them here.
Puzzle: diagonals in a polygon – answer
How many diagonals are in a polygon? (This place is for answers).
Puzzle: probability of matching dice
I threw three identical dice on the table and looked at the outcome. If I throw them again, what is the probability I get the same outcome?
Note: the language is intentionally ambiguous. What are the two possible interpretations? Make certain you know which interpretation of the problem you are solving before you solve. Use the comments, section, below, to talk about the problem without solving it. Use this solutions page to provide solutions.
(There is a hint below the fold —>) Read more…
Puzzle: probability of matching dice – solution page
I threw three identical dice on the table and looked at the outcome. If I throw them again, what is the probability I get the same outcome? Post solutions in the comments section, below.
Against redbaiting in the UFT
The following are excerpts of a piece written in response to a Unity Caucus mailing about Kit Wainer. Although it is authored by David Gurowsky, its condemnation of the campaign tactic used by Unity Caucus is representative of New Action policy. It is available in its entirety at the New Action website. Regular readers may note that I wrote about this same issue in “UFT Election Campaigning” a bit over a week ago.
It’s an old expression that “all’s fair in love and war,” but it seems that Unity Caucus has extended that idea to include election campaigns. Unity stooped to new lows when it mailed to members a post-card entitled, “The Man with No Plan.”
The piece was directed at Kit Wainer, presidential candidate of ICE-TJC. We at New Action have our differences with Mr. Wainer, and in this 2007 UFT election have endorsed Randi Weingarten for UFT president, but we cannot condone literature that stoops to red-baiting.
(there is more below the fold –> ) Read more…
First Ban
Less than a week ago, in comments, I boasted about never having banned someone from this blog.
And then, on his blog, Norman of EdNotes OnLine demanded that I identify which organizations leftist teachers belong to. Read that again, or read his words: “The next time jd2718 gives a report, I suggest he name names and true affiliations”
The context is simple: On February 19th I wrote about the UFT Delegate Assembly in “UFT – My Union and War.” A guy (who I know) who is running as ICE made a motion. Two or three other people (who I don’t know) spoke in favor of the motion. I identified them all as ICE supporters. The guy who made the motion, I know he is a leftist, but I didn’t know which group. And certainly in the context of the DA debate his caucus affiliation is of primary interest.
A month later Norman wrote on his blog, “Red-baiting from New Action Supporter? You Decide” (which I won’t link to, but it’s not so hard to find.) If you get there, the top two thirds is him blathering on, then excerpts from me, then his coup de grace: No one accuses Norm of being rational; I am, according to him, a red-baiter for not naming names.
Since Norm learned I support New Action he has made a series of scurrilous attacks, with escalating seriousness, and when he gets called on it, just runs away, then slinks back a few weeks later. I have not been able to shame him into an apology, into identifying what has been wrong with his behavior, or into controlling his own outbursts. And now, he wants names named? The results can be dangerous. What will he do next? This is more serious than I can deal with. He’s banned from this site.
New Carnival of Mathematics
and I forgot to submit! Doh! It’s a very punchy version over at Evolution Blog. Lot’s of good teaching stuff mixed in with the normal spread of serious stuff, business math, and computers. Don’t miss the Rubix Cube or the teaching little kids stuff. There is even an art post. For me, I look for puzzles and numbers, and the closest approximation is Michael Tang’s riff on the last two digits of 
Eleventy-first…
…Carnival of Education. Hosted at the Education wonks.
(I should have worked in the appropriate literary reference. Too bad.)
Teaching Math: Homework Review
Over at dy/Dan there has been an interesting discussion of why Dan doesn’t assign homework. At some other point I may blog about my differentiated assignments. But not today. I’d like to briefly touch on another aspect of homework: how it is reviewed.
If homework is assigned, then it should have value. And if it has value it should be reviewed and acknowledged.
Students put up homework problems when they enter my classroom. There are four circumstances:
- to show off great work.
- to get feedback on hard work that they attempted, but are unsure about as to form or one or more details
- to learn how to do a problem that they were unable to complete (or even attempt)
- to complete an unanswered question that another student has put up
So at the beginning of class several students go to the side board. Who? Whoever wants to. They get credit. They get credit if they are correct. They get credit if they are incorrect. And they get credit for putting up a problem that they were unable to complete (or even start). And we review those problems on the board; rarely more than they put up; rarely fewer.
(more discussion, beneath the fold —->) Read more…
UFT elections: New Action/Unity Joint HS Slate
The UFT Executive Board is up for election. TJC and ICE are running a joint slate. Unity and New Action are running independent slates, but have cross-endorsed several candidates. Among the at-large seats, Unity has cross-endorsed 5 New Action candidates. They appear on the ballot as New Action/Unity. And in the high school division New Action has 3 candidates cross-endorsed by Unity, and Unity has 3 candidates cross-endorsed by New Action. In addition, New Action cross-endorsed Randi Weingarten for President.
I am particularly pleased with the high school cross-endorsement. If I didn’t cast a “slate” vote the first Unity member I would have voted for would have been my District Rep, Lynne Winderbaum. And now she’s on my slate!
- David Gurowsky- New Action/Unity, Stevenson HS, Chapter Leader
- Douglas Haynes-New Action/Unity, Canarsie HS
- Gregg Lundahl-Unity/New Action, Washington Irving High School, Chapter Leader
- James Vasquez- Unity/New Action, Newcomers HS, Queens HS DR
- Lynne Winderbaum – Unity/New Action, JFK HS, former tough-as-nails Chapter Leader, Bronx DR
- Mark Karwowski-New Action/Unity, Telecommunications High School
UFT elections – ballot problem (resolved)
There was a printing problem with the envelopes, causing some of them to be returned to sender (one guy in my school already got his back, twice!)
The American Arbitration Association is sending out new envelopes (at their expense, not the union’s).
- If you haven’t mailed your ballot yet, use the new envelope.
- If your ballot returned, use the new envelope.
- If you have mailed your ballot and it has NOT been returned to you, no further action is necessary.
The new envelopes will arrive with a letter from the Election Committee. (You can read the text of the letter beneath the fold —>) Read more…
New links, old links
+++
- There is a new puzzle site, called: Math Puzzle. I have only started to explore it. There is a lot there.
- I already mentioned New Action’s website, in a separate post. But it bears repeating. (and if you haven’t voted, get those ballots in).
- The Life and Times of a Rural Math Teacher looks promising. Middle school, with normal frustrations and bad spelling (you are forewarned!)
- Queen of the Quadratic is a Texas HS math teacher, focused on teaching. Posting is a bit sporadic, but interesting when it comes.
—
- Jenny D is very smart. She’s a doctoral candidate, preparing to work in ed policy. But smart doesn’t make up for non-teachers setting policy, especially with such a low experience level.
- 3. 4. I lost interest in Your Mama’s Mad Tedious, NYC Public School Blue, and Miss Malarkey. They have all become fairly infrequent posters as well – since November they have, combined, a total of 6 posts.
===
My blogroll is a work in progress. Feel free to click as many of those links as you see fit. Some of them, if you hover the mouse over them, will tell you a bit about the link. If it is on the list, it caught my interest once. But I will lose interest, regain interest, add, subtract, even reorganize.
More on the roots of i
In this post I mentioned looking for 
![\sqrt[3]{i}](https://s0.wp.com/latex.php?latex=%5Csqrt%5B3%5D%7Bi%7D&bg=ffffff&fg=333333&s=0&c=20201002)
it is the math that holds the authority, not me
I want my teaching to be well-informed, so I dug around a bit (spoke to a professor, dipped through a couple of books, surfed). Check my understanding, if you will.
(Discussion continues, beneath the fold –>) Read more…
Division/0
Check out a cute pic: I Divided by 0 at Hal’s House of Pancakes.
UFT Activists
Yesterday afternoon I watched my high school’s baseball team scrimmage. I try to make sure I get to at least one game a season for each of our school’s teams. Anyway, I have a talk with a parent I haven’t seen in a while (her kid is a senior in my class, but hadn’t had me since freshman year).
The parent retired before the 2005 contract, and had been a TJC supporter. I caught her up on some of the bad provisions of 2005, and we chatted about this election. She is still a TJC supporter, always had been, though she declined to get involved this time, beyond voting their slate; she felt too far removed from UFT politics.
Then we started to talk about individuals. I’ll leave aside the negatives – but there were positives. It was nice, after reading some of the blog stuff and some of the irresponsible leaflets, to talk with someone who I don’t necessarily agree with, and talk about solid UFT activists – from all caucuses.
(more below the fold –>) Read more…
Carnival of Education #110
The new Carnival of Education #110 is up at Eduwonk.
UFT election campaigning
Unnecessarily ugly, but what did you expect?
Norman, in what’s becoming a routine, got caught making scurrilous comments on my blog. What is this, the third, fourth, 
time? When I called him on it (this time he accused me of redbaiting), he ran away. That’s what he does. He’ll be back.
It’s late in the day to point this out, but UFT members deserve a campaign of ideas, not mud. We got creamed in the 2005 contract, and we need to prepare ourselves to take back what we lost. Slinging mud (and worse) doesn’t help.
ICE’s blog published insulting, made-up quotes, to attack their opponents. “…from a High School teacher in Brooklyn…Thanks Randi for watching my school close so we are now all ATRs with no rights to teach.” “…from a Mayor in New York City…Thanks Randi for allowing me to control the schools. I couldn’t have done it without your help!”
Unity just sent out a piece of inflammatory campaign literature. They redbaited TJC, and resorted to name calling, including making up not really amusing new initials for T.J.C. and I.C.E.
ICE’s new leaflet equates the union president with our enemies: Mayor Bloomberg and his Chancellor. They even print little pictures of all three, together, calling them “two lawyers and a billionaire.”
(More, and my linking and banning policies are below the fold —> ) Read more…
Puzzles – a little marble probability
Two bowls contain black and white marbles. The total number of marbles is 25. One marble is drawn from each bowl. The probability of getting two white marbles is 0.54 .
If the marbles are replaced, and the experiment repeated, what will be the probability of getting two black marbles?
JD2718 