Math A Regents – out with a whimper
And so ends the far-too-long, quite unhappy life of the Math A Regents. Sure, there will be a test in August, and another in January. And maybe half the state will still be using it next June, but that’s it. And last week was the last massive administration.
I don’t know if performance standards (rather than content standards) could ever be appropriate in high school mathematics. Probably not. But I know that NY State’s Performance Standards were miserable. Perhaps the idea works in English and Social Studies; teachers who were paying attention knew that they were a disaster in mathematics, well before they were implemented.
Mathematics, as we teach it, is a set of skills. A student who acquires these skills should be able to apply them, with some guidance, to a variety of situations. We test the skills. The skills are central to what we do. We tell the students what skills we are going to test.
The State (Cssr Mills?) decided to test the application. Problems in context. Unusual combinations. Vocabulary. Content-based standards (solve a quadratic using the quadratic formula) became secondary to process-standards (translate real-world situations to mathematical symbols). Performance is much harder to test, and much harder to perform well on. Not enough people paid attention.
(continues below the fold —->) Read more…
No room at the inn?
Thinking about another summer option, I recalled that my union (the United Federation of Teachers) had a notice out sometime in the Spring looking for teachers to go to New Orleans for part of the summer, to help out (something with schools). So, you know what, just in case I decided Iceland was too expensive this year, I decided to find out. And I found out alright. Many more teachers volunteered than there is space for. I can get on a wait list. Maybe.
It’s a nice reminder there’s a whole lot of good folks out there.
Exam question – Precalc
It looks like most of my students did not reach the bonus question on the final exam. They had 2 hours and 15 minutes for 12 questions, and several were quite engaging. Deriving the quadratic formula is old hat, as is finding the locus of points equidistant from two given points, and pretty much as is finding all solutions (real and complex) to a cubic. However I thought this one clever, and am impressed by some of the solutions:
a) Consider a system of a cubic and a circle. How many solutions are possible?
b) Create such a system that has the maximum number of solutions.
(more commentary, and info about those graphs, below the fold –>) Read more…
These last two years
(Warning: self-indulgent, navel-gazing post)
As teachers wrap up a school year, we usually think forward to the summer. There’s always some consideration of the past year. But today, as I avoid grading final exams for another moment, I am thinking of the past two years.
At the end of the 2004-2005 school year I was finishing my 3rd year in a 3-year-old school. I was the original math teacher, the only scheduler, and the union rep. I was having trouble (and feeling stress) with a very difficult principal. I was also on the exec board of the state professional association for mathematics.
- June 2005. I investigate leaving my small school (for 2006-07, not 2005-06, giving it one more year). I get two positive responses and one “Jonathan, when you need to come here, come. You have a job.” I never left, but that was the closest I ever came to doing it.
(much, much more, below the fold —>) Read more…
Math Carnival X is up
Here, at Dave Marain’s MathNotations. Dave has a nice descriptive paragraph for each of this edition of the carnival’s links. And while you are there, scroll through some of Dave’s own older posts. He’s only been blogging for half a year, but already has a treasure trove of problems for you to try, or ideas to use in the classroom.
Exam bonus question: Precalc
What do you make of this time-eater for a bonus on a precalc final?
Find the locus of points, the sum of whose distances from a given point and a given line are constant.
- I think my wording is awkward. Better ideas?
- I am not sure what the figure is, though I am fairly confident it does not have corners.
- I was looking for any progress: a loose sketch, some application of the distance formula, almost anything graphic, analytic or algebraic.
So what do you think?
Exam Question – Logic
I asked the following on my final exam. I like this question quite a bit:
Convert each statement into a standard form categorical proposition. Identify the conclusion. Identify the major and minor premise. Move the statements, if necessary, to form a standard form categorical syllogism. Identify the mood and the figure. Is this catgorical syllogism valid? If not, explain what rule is being violated.
The Bushs aren’t Democrats, so the Bushs aren’t big spenders since big spenders are Democrats.
What do you think?
jd2979
Progress has been slow, yet progress it is. Not so long ago it was jd3016. But the category is still, of course, The Wide World. JD2718 would be post-smoking normal. Slimmer values of e? Let’s not get ahead of ourselves.
Puzzle: circle geometry – stumped!
A friend offers me what he warrants is a famous puzzle:
given three circles, how would you construct a circle tangent to all three?
I’ve been going around in, well you know, not getting very far. I have managed to pose 2 additional questions, which I thought would help, but not yet!
- describe the circumstances in which this would be impossible
- instead of constructing the tangent, throw the whole problem onto the coordinate plane, and determine the equation of the circle tangent to the other three.
Geometry is a weak point for me, and constructions especially so.
I like trips
I like doing extra stuff with my school. I mean, I like teaching the best, but there’s more. Being Chapter Leader and programmer guarantees that I will be involved in some extra aspects… but there is more. I go to most PTA meetings, sometimes to listen, sometimes to schmooze, sometimes because I am still in the building and there is free coffee and cake, once or twice to pitch UFT stuff.
I’ve attended some afterschool stuff – the dodge ball game (didn’t perform well, but who cares?), karaoke (didn’t perform well, but who cares? plus the kiddies sang along with The Yellow Submarine, so who really noticed how bad I was?)
But I love trips. This fall I went on a day trip to Old Sturbridge Village, in Massachusetts. In the winter I went with a group of seniors ice skating in Central Park (didn’t fall down). There was an overnight trip to Boston in the Spring. Also, a play with my service aides a few weeks ago. And another play last week with some juniors and seniors. Does prom count as a trip? [edit: I left off the Spring trip to the Metropolitan Museum of Art. And just last week I went with a student to the Shanker Scholarship awards.]
(last trip below the fold —>) Read more…
Looking to transfer schools in NYC?
I’ve got a question for you. You probably have already thought about level, about location, about reputation. You may have thought about safety, about parking. At the high school level you may have considered curriculum in your content area. If you are clever/web savvy you may have checked out the UFT’s “Grapevine,” (though it is not big enough yet) or Inside Schools, or the DoE’s website, or the school report cards.
But the big question should be: are last year’s teachers coming back?
Think about it. There is no better measure of morale than the proportion of teachers who stay. And teacher morale will tell you if this is the school you want to be in.
(and incoming new teachers, including Fellows, this goes for you, too)
Summer Vacation Planning 2007 – I – Iceland?
If (just if), if I were to fly to Europe this summer on Icelandair,
- is a stopover in Iceland worth it?
- for how long? (figure max is less than a week)
- what’s worth seeing? (and what’s not?)
- where does one stay? (is Reykjavik fine?)
- better on the way to Europe, or the way back?
Tropical Storm Gonu
Every once in a while a little science creeps into this blog. Tonight I noticed that blogger khloud, who was a math major, a teacher, now does some sort of IT but still touches math-y things, and who once sent me a “thinking blogger award,” khloud is in Arabia and has she has been blogging about Tropical Storm Gonu.
A tropical storm hitting the Persian Gulf? Yup. There haven’t been any since WWII (and I don’t know when they had one before that).
It’s crossing the gulf from Oman to Iran now, and max winds have dropped from 111 mph down to the 70s.
Side effect of Global Warming? I don’t know.
Here’s a few links: Weather.com, Islamic Republic News Agency (Iran). Amazing.
Puzzles: 4, 3, 2, 1 and maybe (())
The Four fours puzzle is famous. I learned the annual variation (edition 2007) from Denise, and that was fun.
Every once in a while I try another variation, and here’s todays. Use 4, 3, 2, 1 in exactly that order, and combine them with +, -, * and /, not necessarily in that order. (operations may be repeated, parentheses may be inserted). How many distinct numbers can you create?
Before you start, quiz yourself:
- How many do you expect to get?
- What percentage do you expect to be negative?
- What percentage do you expect not to be integers?
- And of the integers, what percent do you expect to be even?
Use the comments section for your guesses, but click here for discussing the actual answers.
Solutions: 4, 3, 2, 1, and maybe (())
The Four fours puzzle is famous. I learned the annual variation (edition 2007) from Denise, and that was fun.
Every once in a while I try another variation, and here’s todays. Use 4, 3, 2, 1 in exactly that order, and combine them with +, -, * and /, not necessarily in that order. (operations may be repeated, parentheses may be inserted). How many distinct numbers can you create?
Before you start, quiz yourself:
- How many do you expect to get?
- What percentage do you expect to be negative?
- What percentage do you expect not to be integers?
- And of the integers, what percent do you expect to be even?
Use the comments section, below, to discuss the actual answers. Click here for questions and general comments.
Sometimes they get to you
It’s not quite the Heart Award that PO’ed Teacher earned, but guess what I read in this year’s yearbook?
This book is dedicated to…
all of our teachers because you have helped us along the path of our journey.
WITH a special thank you to Mr. 2718 for all the extra effort you have taken to help us.
Trivia
What do Catalan numbers have to do with London Plane trees (official tree of the NYC Parks Department) and the Outerbridge Crossing (connecting Staten Island, NY, to some town in New Jersey)?
Puzzle: sum of some numbers
There is a 5-digit number which is the sum of all 3 digit numbers made from its digits. What is it?
Please comment here with questions and observations.
Please click here if you want to share your answer.
Solutions: sum of some numbers
This is the place to post your solutions.
There is a 5-digit number which is the sum of all 3 digit numbers made from its digits. What is it?
If you have comments, questions, or observations, please click here.
Carnival of Mathematics IX
So they handed this thing to a school teacher? What did they expect? A lesson, of course. Today we’ll use the alphabet to study math. (Apologies in advance for the irregular capitalization).
Alane (Math Notes) Addresses why we teach Arithmetic and about how we All can learn the Abcs. (elementary mathematics education)
RandomHacks Broaches Backtracking. (computing)
Michi will be Considering Cohomology in the Caucasus. (and Complains about Connectivity) (travel/conference)
Involutions attempts to Classify Concepts by search engine page Counts. (statistics)
Dy/Dan continues his Discussion of assessment with part Deux. (secondary mathematics education)
E of E‘s Ponderings Expresses some thoughts about her Experiences at a math and math Ed conference. (math wars/conference)
SharpBrains Forces the reader to use their Frontal lobe with the Fork in the road. (recreational mathematics)
John, the Unapologetic Mathematician, Goes to a Grown-up math competition (ARML) and Gives a solution to a power question.
Hal Huntsman has written about How community colleges teach algebra. (post secondary mathematics education)
Brent of Math Less Traveled Instructs us in a most beautiful Identity (in i) and then uses it to Inform simpler Identities in Trig. (trigonometry)
JD2718 (your host) Jogs kids’ memories by forcing them to Join prior knowledge with 
MadKane Laughs with a Lecture error Limerick. (humor)
Dave Marain Mentions Mortgages, and More Mortgages, deeper Meaning from an sat algebra problem, and More problems. (secondary mathematics education)
Math and Logic Play takes a look at the Monte Hall Problem. (recreational mathematics)
Dan at the Exponential Curve gets a Negative response about National Board Certification (also check out his recent series of puzzles). (secondary education)
Julie of Math Trek Offers an explanation of the recent Origami Trisection of an Angle. (geometry)
Grey Matters Proposes and discusses several variations and the Psychology of the Prisoner’s Dilemma. (logic puzzle)
Denise of let’s Play math Posts on Problem solving. (mathematics education)
Hamid Promoted a π Plate. (merchandise; humor)
Rod of Perfectly Reasonable Deviations Reports on a bidding scheme which is not Rational. (recreational mathematics)
The Crazy Math Lady Rants that her students cannot manipulate Rational expressions in their heads (and therefore must show work). (primary/secondary mathematics education)
Mark of Good Math/Bad Math Seeks to Seriously Share Some introductory ideas about Set Theory (definitions), Set theory (the need to axioimatize), Set theory (axioms). (set theory – now that’s a useless label. While I’m breaking voice, this guy writes to me. Not private e-mails, just his blog posts, but I am a high school math teacher who’s dabbled here and there, and forgotten as much college level stuff as I’ve ever learned, and MarkCC explains fundamental concepts at exactly the level where I can understand everything, but didn’t necessarily before reading it)
Linda of Teens and Tweens sends her kids to public school, and supplements with math Teaching at home, but her Text choice has recently changed. (enriching elementary mathematics education)
Measure Theory Talks about the Trials and Tribulations of Tutoring Two calculus students. (post secondary mathematics education)
mrc from Understanding has an Unusual scheduling question. (algorithm)
Text Savvy Writes on the Wason Selection Task, and again here. (elementary logic)
XKCD’s latest: The Power of One. (humor)
Out of the archives: Ms. friZZle (stretching to use those Z‘s) bemoans her middle school students’ difficulties with mathematics, a – Z, and again. (primary/secondary mathematics education)
3. Three Standard Deviations to the Left does the math for his school’s suspension rate, and makes his students try their estimates as well. (secondary mathematics education)
– – — — —– ——– ————- ——– —– — — – –
Apologies to K, Q, V, Y, 1, 2, and all the other numbers.
The next carnival opens in 13 days at Dave Marain’s Math Notations. Submit via the submissions tool.
Thanks to all for your current submissions.
And a final thanks to Alon Levy, blogger emeritus, for setting all of this up.
under construction
the carnival of mathematics will appear in this space in a few hours.
Sorry for the delay
y = 1/x
What a nice way to end the year! My Algebra II/Precalc group, coming off conic sections, were confronted with this. I asked them to create a table, and hand-graph. Lots of reasonably interesting discussion about getting more data points, then about the discontinuity and asymptote (first time they have run into a vertical one), and that horizontal asymptote. We digressed to talk about point discontinuities (eg, 
Someone asked about a horizontal stretch. We looked at 
And then 
Transforming functions? Taught so much earlier? It sunk in.
9th Carnival of Mathematics
is coming tomorrow. Get those submissions in, today!
E-mail me at jd2718 (at) gmail [d0t] c0m, or
fill out the form at http://blogcarnival.com/bc/submit_1049.html.
Whose schools? Our schools.
There has been a discussion running on Fred Klonsky’s blog (me, Leo Casey, and Fred) (and continuing on Edwize) about Green Dot and tenure and our attitude to “hybrid forms” (semi-public charter schools). Leo is excited, it seems, to have found a charter-operator who is not anti-union. Fred is more cautious. I am still listening, but I think I go beyond caution. It’s still a charter, and while a unionized charter is better than a non-unionized charter, real public schools are better than either.
In the course of the discussion, Leo says:
your [jd’s] argument is based on a serious conceptual and strategic mistake: the identification of public schools with a late 20th century organizational form of public schooling — hierarchical, bureaucratically organized and centrally run public schools, each one a ‘factory model’ school. …
Fred later puts this question to me:
JD
If the other side owns charters, who owns the schools I work in? Who owns the Chicago, NY or LA public schools?Do you think it is us? The people of Chicago, NY or LA?
While I would think that Leo would be more skeptical about charters, I think his point about the present nature of traditional forms of public education has a lot of merit.
And here’s my response (just below the fold –> ) Read more…
Carnival of Mathematics – submit your submissions!
The next Carnival of Mathematics (mean old #9) goes live this Friday, right here.
There are two ways to submit:
- Official Carnival Submission Webform, or
- e-mail the link directly to me at jd2718 at gmail d0t com
A
s always, anything math-related goes:
- math teaching,
- advanced math,
- not so advanced math,
- math history,
- computer science,
- math humor,
- statistics,
- math-related economics, or
- other stuff
JD2718 