I took a sabbatical 2013-14, to study. But I did other stuff, too. Including learning more about teaching. It wasn’t required (Just the graduate math classes were required). I did it for me.
Even before Labor Day, even before the first day of staff meetings that I did not have to attend, I was using my sabbatical. It was early July when me and a friend hopped in his car, and after sampling our way through one brewery in New York (meh) and one brewery in Ohio (nice), and one brewery in Michigan (very nice), landed in South Bend, for a Math Circle Summer Institute.
Math Circles are… well it can be tricky to generalize. They are extra-curricular. They are sometimes led by non-teachers. Some are free, some cost money. Some are geared towards contest preparation. In this country, they are far more often geared towards curiosity and enrichment.
The summer institute drew teachers and non-teachers. The founders/leaders/patriarchs, Bob and Ellen Kaplan, couldn’t make it. A math circle/math community in South Bend organizes the event, and brings kids to play with the participants, and to participate in little circles. I knew in advance myself, my friend, Sue, and Owen. The rest were new to me.
Each day began with a math circle type problem for the adults. The instructor modeled posing the question, but not giving too much information, and letting the teachers and kids play with the problem, ask questions, explore. We worked individually, together, and as a whole room (there must have been 25? altogether. It’s a year ago, I’m a bit fuzzy).
In the afternoons we broke up by level (high school, middle school, upper elementary, lower elementary). There were kids at each level. And we ran daily “math circles” with each participant getting a turn to lead or co-lead.
How was it?
We were playing math all day. You can guess, but I’ll tell you. I had a ball. One of the interesting bits was how few actual teachers there were. I mean, motivated parents who run or want to run circles and university types who want to run or facilitate circles, or people who might become teachers – they were there in larger numbers. That meant there was a sort of freshness and newness to some of the conversation. The mix meant there were people to engage in math with at all levels. But it also meant that there were people trying to rediscover or discover stuff that you figure out pretty quickly in the classroom. It was… interesting. And it was … different. And it was … engaging in a new sort of way. Plus, I made a math-y friend, which was nice for me.
Return to NY – Any impact?
And since? I’ve kept thinking about how the Math Circles organized time, and allowed kids to explore, and to bang their heads against hard problems, without rushing to the answer. I already do some of that, would like to incorporate more of the “feel” into some of what I do.
My friend kept thinking about how fun the circles were. He played with ways to set one up. And he ended up spending time at the NYC Math Circle, hanging around with instructors, volunteering for the summer.
How do you sign up? Should you?
So it’s fun. And you’ll learn stuff. And meet interesting people. And exchange ways of thinking. And get to try stuff out. But it costs money. I paid, but most people… I’d recommend it more for people who can get at least partial funding by their district.
But if you are going to go ahead, it’s a week in July, e-mail Bob Kaplan at email@example.com and get more info directly from him.
I took a sabbatical 2013-14, to study. But I did other stuff, too. Especially travel.
With my classes only on Tuesday and Thursday, I thought I would be out of town just about every other weekend. All of those weekends, by the way, four days long. Didn’t happen. I traveled a lot, and loved it, but cost and reality held down the number of long weekends by quite a bit.
Anyhow, I didn’t know this when I more or less threw a dart at a map, and decided to go to Pittsburgh in September (this is last Fall). With a long weekend a peaceful ride on Amtrak was possible. I used PriceLine to get a downtown hotel for a pretty good price. But I hit a snag. The uptown IND was really out of service Friday morning, September 13 (you can look it up, something bad, just don’t remember what) and despite my creative efforts, I missed the train. Got the next one, but it cost me. And the connection in DC was late… The good news? This was the Cardinal, one of the most scenic trains in the east. My seat mate was a young woman with a minor political job in DC, who loved trains. I had great company right up to her stop,
The rest was a two day blur. I picked out a hotel on Trip Advisor without knowing what one it was. Good deal. Turned out to be the Marriott. And now it is so long ago, that I am having trouble putting my “sights” in order:
- PNC Park. The Pirates lost, but I had a very good seat in a truly great stadium, sitting with intense, yet friendly to out-of-towner, fans.
- The Warhol Museum. Pretty cool.
- Bridges. I think I crossed the Allegheny on two, the Monongahela on one.
- Inclines. Up the Monongahela. Down the Duquesne. With a drink on a terrace at the top, looking over the city.
- Point Park. Lovely. And the Ft Pitt Museum. Too fast.
- Wandered the Strip, the old dock district, and took a distillery tour.
- A walk along part of the Three Rivers Heritage Trail System
And then a return Amtrak train, daytime, lucked out and had nice company again, and a helluva view around “Horseshoe Curve” in Altoona.
It was not as much as I meant to do, and done a little too fast. But what I did, I enjoyed. And if I had thought carefully, I might have wondered if this was going to be a common pattern during my sabbatical year.
It’s usually enough for a bad administrator to leave the system – we are rid of them and their behavior – though for the sheer numbers of abusive and/or incompetent principals and assistant principals in New York City today, one at a time seems hardly enough.
And if they reappear, but elsewhere, as the disgraced former principal of Bronx Science recently has, we might like to point it out, but it does not become our immediate problem.
However, we know that issues of abuse, incompetence, and less than forthcoming statements often accompany each other. And when we can document statements that seem in hindsight to veer from the facts…
Last year, a scandal over hazing of younger athletes by older athletes broke at Bronx Science. There were allegations that administrators, up to the top, were aware. And in the midst of the investigation, the principal announced her retirement.
Now, it wasn’t as if that was the first controversy she’d encountered. Under her stewardship, the atmosphere for teachers at the elite school at deteriorated. Faculty turnover was far higher than at any other specialized high school in NYC. Teachers, bristling under her arbitrary and authoritarian leadership, and noticing that she used an honorary degree to start adding “Doctor” to the front of her name, ran a quack campaign – with ducks, that was then repeated in several versions as student pranks. A special complaint of harassment was brought against the principal and one of her assistants – and an arbitrator found for the teachers. She weathered those storms, though it seemed that she continued to stay out of spite for her subordinates.
In any event, you have a chance to compare what she says today, as she takes a new job, with her reasons for leaving, which she claimed had nothing to do with controversy or an investigation:
“This July I was appointed as principal of Maria Regina High School. I am honored to accept … after spending thirty-five years at the Bronx High School of Science where I was the principal for twelve years, an assistant principal of science for three years and a science teacher for twenty years … As an educator, my goal has always been to excite students about learning and support them as they work to attain their educational goals. As an administrator, I know that I cannot and do not work toward this end alone. I, as principal, am a member of a community. It is only with the work of gifted teachers, involved parents and motivated students that success can be achieved … What I have learned through my years as an administrator is that leadership is a humbling experience…
The principal, Valerie J. Reidy, who took over in 2001 after 23 years of teaching and managing at the school, said she was under no pressure from city education officials and was “not under investigation” in connection with the arrests of three track team members, all juniors, in March.
“Was I happy about the track debacle? No,” Ms. Reidy said in a telephone interview on Thursday. “But is there ever going to be a perfect time?”
Ms. Reidy cited her age — she will turn 65 on Nov. 28 — and financial and family concerns for her decision. Her husband, James, retired two years ago from the federal Environmental Protection Agency, and one of her sons is set to wed in September. She wants to sell her house in Westchester County and travel more….
A great math teacher deals with dicey math, because it is on the test
“I’m providing Test Prep for students who have to confront this type of language regardless of its mathematical validity!”
One of the trickiest topics in K-12 mathematics is probability. It’s tricky for a number of reasons:
- It’s not a traditional topic. There are not decades of practices to use, improve, or rail against.
- Probability relies heavily on fractions, the gateway between arithmetic and algebra, the single aspect of grade school mathematics that we screw up (in this country) the most
- The subset of probability we teach, simple combinatorial probability, is not a standard part of college probability courses – we don’t have the usual crowd of post-secondary math people poking around and complaining about mistakes.
- Most people teaching probability learned their probability k-12, or from math ed classes that were based in k-12 curriculum. In other words, what we do poorly, we pass down not only to students, but to the next generation of teachers.
So this twitter exchange is with a great math teacher, retired. As department chair he took some of the most advanced classes (everyone does that) and some of the least advanced classes, full of kids who struggle (no one does that). Currently he is doing SAT prep. He prepares SAT-type questions, and I think he solicits the occasional comment.
Great Teacher: A pt is chosen randomly inside larger of 2 concentric circles. If the prob the pt is outside smaller circle is 84%, larger rad:smaller rad=?
JD: Is “random” smooshy here? If I randomly choose an 0 < angle < 360 and a radius 0 < radius < BIG Radius, is that not random?
3rd Party: Good point – ‘random’ doesn’t necessarily mean ‘uniformly random’
GT: Excellent pt re random. The language I used is common on stand’zed tests where “uniform” is implied. Pls reword it in <=140 char!
JD: Why use “random”? Why make it a probability q? 2 conc circ, Large and small. 84% of area of L is not in s. Radius(L) / Radius(s) ?
GT: Agreed but I’m providing Test Prep for students who have to confront this type of language regardless of its mathematical validity!
I took a sabbatical 2013-14, to study. I mean I did other stuff too, but studying came first. And the first class I walked into was Mathematical Logic.
I teach “Logic” – but it’s a high school course, based on the first logic course that might show up at the 100 or 200 level in a philosophy department. Hurley is my text. My content barely touches the beginnings of what we were about to study.
I was at Queens College, and this was a 600 level course – it was designed as a first real course – and it was. In college I’d only done a philosophy department logic, similar to what I teach. This was new.
I want to describe the course and the people and what I did and didn’t do, briefly. The text was Enderton “A Mathematical Introduction to Logic.” Professor showed an earnestness, an excitement about the subject. Looked vaguely like a cross between Dr. James Wilson and Lt. Reginald Barkley. There were a few complaints that he was unclear, or explained poorly – but they were off-base. The subject was very hard – the professor spoke clearly, used vocabulary carefully, introduced ideas well, offered great board notes, provided illustrative examples – but the subject was just that hard.
There was one auditor for the first two or three weeks who seemed to be a retiree – but he got bored and disappeared, leaving me probably the oldest in the room. We lost about a quarter of the class before the mid-term. Maybe more. And we were down to about half by the end.
The text for this class was divided into four chapters. We covered the first two, and part of the third.
I made it through “Sentential Logic” relatively unscathed, running an A, and while I felt shaken a bit by the level of difficulty, more or less stayed on top of everything. Professor was really good with office hours, available, and wanting to help. We used induction, but differently than I had encountered it before. It took real getting used to. The concepts were fairly familiar, or I picked them up. Or struggled through them. I had to study, which is something I did precious little of when I was younger.
The second unit, First-Order Logic tripped me up. I lost my way with “substitutability” and never fully recovered. What’s a language? What’s a Theory? What’s a model? What does it mean to “satisfy”? What does it mean to be “definable”? I have answers for all of these, but I’m not 100% sure when I answer. And sometimes I know what to say, and I’m not sure what my words mean.
We touched incompleteness and undecidability at the end. I certainly did not follow all of what we were doing there.
My final exam was weaker, and I ended up with a B+. Which doesn’t sound great. In fact, I think there were only 3 or so A’s in the class; my grade’s no embarrassment. And I learned enough that I would love to do this class again (or read something, but I doubt I could do it without a smart, clear professor, like this guy). It’s a situation where I know something between half and three-quarters, and where I am well-positioned to to boost that to 90+%.
It may have untangled some vocabulary issues for my teaching, but hardly. It was good to struggle against hard material. And it was fun to study with much younger students (I worked with a teacher, two grad students, and an advanced undergrad), some of whom ran academic rings around me.
Side-note. While I was taking this class, this blog got linked by a guy who shares my initials and probably teaches the exact same class at a different campus in the same university.
I don’t follow baseball as closely as I once did. I go to Yankees games, and have to ask the names of some of the players – back in the day that’d never happen.
But I still enjoy the game, and do get to games, and every once in a while check box scores or standings.
That, by the way, is a remarkable admission from someone who used to buy one or two daily newspapers during my 20s, and would turn to the box scores first. I gained much facility with arithmetic, back before I was ten, as I saved the Sunday paper, and updated the leaders during the week, adding in ABs and Hs from the box scores, and dividing to get the new averages. I studied pitchers’ ERAs and tried to find the match-ups that would lead to the shortest games. And at a certain point, I would look at an average, and find possible AB and H combos that would have led to that average (rounded to the third decimal place), or would look at an ERA and a number of innings to calculate the number of earned runs, and recalculate the ERA with the new box score (websites give you all of this instantly today, but it used to take a week before new stats were published).
Anyway, I’m looking at the standings today, and it turns out that the two best records in baseball, and the two worst records in baseball, they are not extremely good or extremely bad, and all live in one division of one league: the American League West.
First, the lack of extremes is interesting. Over half the teams are between .450 and .550. But only two are over .600, and only one is over .400.
But the AL West looks different. The Oakland As are 25 games over 500, the
California Anaheim Angels are 22 games over, the Houston Astros are 20 games under, and the Texas Rangers are 22 games under. See that California vs Texas thing? Cool.
Is anyone else close? On the high end, no. In fact, they are the only two teams are above .560, the Tigers, Orioles and Dodgers are 12 games over, each. On the low end its closer. Rockies are 19 under, Cubs are 18 under, and the Diamondbacks and Phillies are both 14 below 500.
But the two best, and the two worst, in one division of only five teams. If this was independent, it would be weird. But here’s my question: how much is this due to the Angels pounding the Rangers and the Athletics pummeling the Astros? I could ask someone, or I could look it up:
5 – 2
7 – 5
10 – 3
8 – 2
Interesting, without the two doormats, the Angels would be just 10 games over .500, and nothing special. Without losing to the top two teams in baseball, who the are forced to play frequently (currently about a fifth of their games), the Astros and Rangers would be ten and fourteen games under, or pretty much mediocre. In other words, the high quality of the competition in the division hurts the two from Texas, while the (weaker) divisional opponents boosts the Angels’ record.
But the As are 12 – 7, .632 against the Astros and Rangers, 53 – 33, .612 against everyone else. They are just really good.