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Integrated Algebra – easy and hard – and bias

January 30, 2009 pm31 6:07 pm

The questions on the January 2009 Integrated Algebra exam were all over the place. What did you find easy? What did you find hard?

Let’s get some explanations and answers for the ones you have most questions about.

I’m going to start with the bias question. I know what the State intended, but I think they blew it. Read, and see if you agree:

#23 A survey is being conducted to determine which types of television programs people watch. Which survey and location combination would likely contain the most bias?

(1) surveying 10 people who work in a sporting goods store
(2) surveying the first 25 people who enter a grocery store
(3) randomly surveying 50 people during the day in a mall
(4) randomly surveying 75 people during the day in a clothing store

I don’t know that there is enough information, but I lean towards (2) or (4) having the greatest bias. I know that’s not what they wanted. Do you see how they blew it?

Integrated Algebra: how will the scores be?

January 30, 2009 pm31 5:42 pm

This may be a case of “mediocre” being a step up. Or will it be a test that is too hard, even with a pass point around 35%?

Yesterday afternoon NY State high schoolers took the third Integrated Algebra regents exam. The exam replaces the widely ridiculed “Math A” which now has quietly faded into retirement.

But today, across New York State, math teachers are grading thousands and thousands of Integrated Algebra exams. The scale is at the bottom of this post, but also all the scales can be found on this NYSED page. It is a strange scale, with 31 out of 87 points passing (65), but 68 out of 87 being an 85. This reflects New York State’s failure: they cannot successfully build a high school exit exam that also successfully measures achievement in an oddball hybridy course (that contains many skills that should be irrelevant to graduation).

I need to be a little careful. I had a very small, specially selected group of students take this exam, with the aim of getting very high scores. They are mathematically strong freshmen, taking a hard Algebra 1. All of them did some of these topics in middle school (though not quite as hard as what they do with me). And we ran a couple of quick sessions to patch up the State’s weird vocabulary and the odd topics that I don’t teach.  I asked them to finish the test, take a break, and then redo most of the test, covering up their previous answers. And most of them did, showing, I thought, good self-discipline, staying over two hours.

In other words, this is not in any way a typical group. My initial reaction to the questions has more to do with how my dozen were likely to respond than with the interests of the students across the state. I’ll wait to hear more before I weigh in on individual questions.

(Scale is below the fold) –> Read more…

Math A – out with a whimper

January 29, 2009 pm31 5:57 pm

This afternoon at 4:15 Math A will be history. And very few of us will care. Surprising?

Seven  years ago, as Course 1 was being offered for the last time, displaced by Math A, schools across the state scrambled to get their kids into Course 1. There was wild overtesting in some poorer-performing schools as every kid without a 55 (that was passing, for a while) took or retook that Regents, ready or not. The schools were, in a way, right. Course 1 had predictable content. A weaker student could be trained to take it, could learn to identify different types of questions, could be taught enough math.

Many schools in New York State, perhaps most, adopted Math A only when forced to. And they were right. First June administration after Course 1 was gone? Boom. Statewide disaster. It took 6 more years to dump the mess. But here we are.

The replacement is “Integrated Algebra” but it’s not really algebra. It’s a shortened version of Math A. Doesn’t tell us how much a kid really knows. Same stupid math in (poorly constructed) context. Same wide-ranging vocabulary. Same ideosyncratic New York math questions. Same arbitrary scoring guide, with unfair deductions. But less content overall.

Both these exams were designed to do double duty: to tell us if a kid is ready to graduate (high stakes tests) and to tell us if a kid is ready to move on to the next course. They do a horrible job of both. So bad, that the State now denies that they tell us about readiness to move on.

These exams tell us nothing about top kids, but do create a graduation hurdle for weaker kids. So we sigh, and choose the shorter one. And no one will miss Math A.

For those of you taking Math A – good luck. If you don’t know a multiple choice, bubble in something. And for 31 – 39, write down something, even if you are not sure. Can’t figure out how to write the equation? Write another one, and solve that instead. Give us something. When you leave, there should be absolutely no blank pages.

For those of you taking Integrated Algebra – same thing. It’s really just a shortened version of the same test. And good luck. (I have a few students sitting for this one).

To the Math B students who have been visiting

January 29, 2009 am31 10:02 am

Thanks for coming by. I appreciate that there are kids who care about this stuff, who want to know.

First things first:

maybe you only saw one post here, there are a few:

  1. B Minus 4 (right before the test)
  2. Let the complaints begin (that’s what most of you saw. 100+ comments)
  3. What was the matter with #13? (I complain)
  4. #33 – Unfair (I complain more)
  5. Some good questions (#2, #4, #20, #21, #25, #26, #28, #31, #34)
  6. Weak gravity and other Math B oddities (bad context in questions:  #7, #30, #10)

A lot of you who believe you did poorly think the exam was hard. Many others did well and think the exam was easy. It would be better to indicate that you did well, or did poorly. Easy or hard is in the mind of each student. That 88 that you are proud of, that’s in black and white.

Don’t put your names, or even your schools. But I can see that you are coming from all over NY State. It might be nice to mention what region you are in.

Most of you didn’t notice, but this is a math teacher’s website. I teach in the Bronx, but my students didn’t take Math B.

I think that A and B were horrible exams, and I am glad they are going away. Integrated Algebra is not much better, though. And I worry about Geometry and Trigonometry.

Actually, I don’t think that the test writers in Albany are talented enough to be creating ‘high stakes’ tests. Fortunately for you, Math B is not high stakes. It can make the difference between a regular and an advanced diploma, but I don’t know if anyone outside of New York State really cares about that.

Unfortunately for many of your friends and relatives (and my students) Integrated Algebra is high stakes.

There’s more problems. IA is an algebra exam, to see if you are ready for geometry? No. Way too easy. Way too much extraneous probability and stats, and silly obscure vocabulary. Is at an exit exam, a minimum bar to see if someone is ready to be graduated from high school? No way. Grab a copy, or click over to the NYSED website. Those aren’t the questions that you’d ask to see if someone can function out there.

The conversion charts stink. You should know going in how many points you need.

Congratulations on taking an annoying, and for some of you, challenging exam. If you have to do it again, you’ll have a few more chances. And if not, no more math regents ever. Hooray. But enough with you, for now.

Tomorrow is Algebra.

Listen to the old guy with the scratchy voice

January 29, 2009 am31 9:07 am

Themes run through Pete Seeger’s life and music, like trains run through cities, tunnels, and the long, flat gap between towns. I don’t know what ‘freedom’ means to him exactly, but it’s one of those themes. I’ll leave you a hint for another…

And the voice wasn’t always so scratchy…

He doesn’t name Elizabeth Cotten, but that’s who he’s giving the credit to. Here they are together:

I really wanted to show you him as a young man, singing John Henry. My first train song, and I still have the vinyl, pressed in the late 60’s. Settled for Springsteen:

Jmap posts January 09 Math B and key

January 29, 2009 am31 7:42 am

The link is here.

Weak gravity and other Math B oddities

January 28, 2009 pm31 6:05 pm

We already saw the busiest shop in the world (# of customers approach infinity when it gets real cold).

How about #7:

How strong is gravity in Albany?

#7 The height of a swimmer’s dive off a 10-foot platform into a diving pool is modeled by the equation y = 2x^2 - 12x + 10 , where x represents the number of seconds since the swimmer left the diving board and y represents the number of feet above or below the water’s surface. What is the farthest depth below the water’s surface that the swimmer will reach?

Physics or sports folks out there – how horrible is that model? I assume that when the diver hits the water, the acceleration changes dramatically, right? And for the part before the water an acceleration of 4ft/s per s is more like moon gravity than Albany gravity (even though I hear there is strange stuff up there). Can anyone supply more detail?

Also note the subtle error in the description of y.

(for kiddies: answer is the vertex of the parabola – (3,-8) so 8 feet below the water’s surface.)

#30 [ corrected the wrong #: #8] Farmington, New York, has plans for a new triangular battlefield park. If plotted on a coordinate grid, the vertices would be A(3,3), B(5,-2), and C(-3,-1). However an evil wizard a tract of land has has seized control become available that would enable and the wizard the planners to plans to turn it into a strip mall increase the size of the park, which is based on the following transformation of the original triangular battlefield park, R_{270} \circ D_2

  • my version would at least make it amusing. Theirs is stupid.
  • they treat their notation as standard (not requiring explanation). I have seen enough transformational geometry texts to know that it is not. having New York State official (but not accepted by the wide world) mathematical nomenclature is unacceptable.
  • they don’t specify the center of dilation. they don’t specify the center of rotation.
  • this question fails to assess something that matters: whether kids understand how to compose. If they do the rotation first, no problem… (although, in defense of Albany, there is a multiple choice item, #9, that did exactly that, and with the trap answer.)

kiddies, they meant the center of each transformation to be at the origin, and we work from do the first to the second, iow, the dilation comes first:

(x,y) \mapsto (2x,2y) \mapsto (2y,-2x) and the coordinates become (6,6), (-4,-10), (-2,6).

#10 A central angle of a circular garden measures 2.5 radians and intercepts an arc of 20 feet. What is the radius of the garden?

Stop right there! We don’t measure angles on the ground in radians. When we do use radians, they appear as multiples of π!

The answer is 50 feet. The author is an idiot.

1/09 Math B, some good questions

January 28, 2009 am31 9:34 am

Even though Math B is winding down, I didn’t expect a good exam. And New York State did not fail to disappoint. 13 had ridiculous context. 33 included math from outside of the curriculum. Some reasonable questions, and answers:

2 .The expression \frac{5}{3+\sqrt{2}} is equivalent to…

Normal solution: multiply numerator and denominator by 3 - \sqrt{2} (the conjugate)

Cheat solution: plug the expression into a calculator. Equals about 1.1. Check the four answers. Only choice (3) is close.

Correct solution: \frac{15 - 5\sqrt{2}}{7}

4. What is the solution of the inequality x^2 - x - 6 < 0 ?

Cheat. Check a couple of numbers.  0 works, and eliminates 2 choices. 2 works and eliminates another choice.

Normal solution: Factor the quadratic: (x-3)(x+2) < 0. Sign changes at 3 and -2.

Correct solution: -2 < x < 3

20. The accompanying diagram [not here, just imagine] shows part of the architectural plans for a structural support of a building. PLAN is a rectangle and \overline{AS} \perp \overline{LN}

My comment: The context, as usual, is contrived, silly, and distracting. LN is a diagonal. AS is an altitude to LN at S.

Which equation can be used to find the length of \overline{AS} ?

(1) \frac{LS}{AS} = \frac{AS}{SN} (3) \frac{AS}{SN} = \frac{AS}{LS}

(2) \frac{AN}{LN} = \frac{AS}{LS} (4) \frac{AS}{LS} = \frac{LS}{SN}

I’ve got no cheat here. \triangle ASL ~ \triangle NSA. Sides are in proportion, so choice (1).

21. Solve for x: \sqrt{x+18} - 2 = 2

Transpose: \sqrt{x+18} = 4

Square both sides: x + 18 = 16, and x = -2. Checks, too.

25. What is the solution of the inequality |2x – 5| ≤ 11/2 ?

Abnormal solution: Factor out a 2: |x – 5/2| ≤ 11/2 This is the interior of a circle with center 5/2 and radius 11/2, so -3 ≤ x ≤ 8

26. The volume of Earth can be calculated by using the formula V = \frac{4}{3}\pi r^3 . Solve for r in terms of V.

Multiply both sides by 3/4pi, then take the cube root: r = \root 3\of{\frac{3V}{4\pi}}

28. Perform the indicated operation and express in simplest form:

\frac{3x^2+12x-15}{x^2+2x-15} \div \frac{3x^2-3x}{3x-x^2}

A former student of mine explained this one well: You factor, you cancel. She used to abbreviate it on the board, and her kids never forgot (UF, UC). I choose not to write that in class. Here goes:

\frac{3(x+5)(x-1)}{(x+5)(x-3)} \div \frac{3x(x-1)}{x(3-x)}

\frac{3(x+5)(x-1)}{(x+5)(x-3)} \times \frac{x(3-x)}{3x(x-1)}

Everything cancels. That x-3 over 3-x gives -1. The answer.

31. Find the roots of the equation x^2 + 7 = 2x

Cheat solution. Complete the square. x^2 - 2x + 1 = -6

(x - 1)^2 = -6

x - 1 = \pm \sqrt{-6}

x = 1 \pm 6i

34. Given PROE is a rhombus, \overline{SEO}, \overline{PEV}, \angle SPR \cong \angle VOR

Prove \overline{SE} \cong \overline{EV}

Ok, I am missing the diagram, but the description is sufficient.

Take those congruent angles, subtract the congruent opposite angles from the rhombus, that gives us a pair of congruent angles (SPE and VOE)

PE = OE (sides of a rhombus)

\angle SEP \cong \angle VEO (opp angles)

Now the two little triangles are congruent by ASA, and what we want is congruent by corresponding parts.

Math B #33 – a model of an unfair question

January 28, 2009 am31 7:45 am

33. The accompanying table shows wind speed and the corresponding wind chill factor when the air temperature is 10 F

Wind Speed (mi/h) Wind Chill Factor (F)
4 3
5 1
12 -5
16 -7
22 -10
31 -12

Write the logarithmic regression for this set of data, rounding coefficients to the nearest ten thousandth.
Using the equation, find the wind chill factor, to the nearest degree, when the wind speed is 50 miles per hour.
Based on your equation, if the wind chill factor is 0, what is the wind speed to the nearest mile per hour?

First, let’s get a science/physics/meteorology guy here. Does the context make sense?

But here’s the bad news: Logarithmic regression… calculator-trained kids can plug into the calculator (maybe). But e, the base of the natural logarithms, is not part of the curriculum associated with this exam. Talk about unfair!

Another NYS teacher wrote:

Although logarithmic regression is in the curriculum, ln and e are not.  Based on the regression options of the TI-83/84 it makes logarithmic regression questions impossible to answer without developing base e or the natural logarithm.

A student is not able to get full credit on this 6 point question unless he or she has a full understanding of ln and e.

What was the matter with Math B #13?

January 28, 2009 am31 6:53 am

It didn’t make sense. They wanted the kids to set up inverse variation, solve, get 256, move to the next question.

But the problem didn’t make sense!

Carol notices that the number of customers who visit her coffee shop varies inversely with the average daily temperature. Yesterday, the average temperature was 40 and she had 160 customers. If today’s average temperature is 25, how many customers should she expect?

(1) 100    (3) 256
(2) 145    (4)  1,000

They wanted 256. (40)(160) = (25)(256).

But look kiddies, you are right to jump through the hoops they set for you. That’s your job. But if you are smart, you will ask, as you fly through the air, “why?”

And on #13, there is a number, but no reason why. Inverse variation must be the wrong model for this problem. Think about it. How much data did she need to “notice” that relationship? Jeez, I hope you’d fail an economics exam or an earth science exam if you tried to use inverse variation as a model here. What happens in Chicago? (think about it, the temp regularly gets near 0). What happens when it rains? Day of week?

Oh, “average daily temperature” – what exactly does that mean? The average daily temperature in July…. oops. I think they meant the average temperature for that day… but we don’t take those averages… how would we calculate them? what would they mean? People want the high, want the low.

When something makes no sense, someone should say something.

1/2009 Math B Regents – let the complaints begin

January 28, 2009 am31 1:03 am

13. Carol notices that the number of customers who visit her coffee shop varies inversely with the average daily temperature.

I’m not going any further. This is horrible.

6. What is the translation that maps the function f(x) = x^2 - 1 onto the function g(x) = x^2 + 1

(1) T_{0,2}

(2) T_{0,1}

(3) T_{1,-1}

(4) T_{-1,1}

B minus 4

January 27, 2009 pm31 5:35 pm

Counting down to the end of New York State’s Math A and Math B exams.

Thursday afternoon Math A will be administered across New York State. For the last time.

In an hour students will sit for Math B. There will be 4 more exams: June and August 2009, and January and June 2010.

No one will cry over the end of A and B (though some will cry over this week’s exams. High stakes exams place high pressure…)

Math A was introduced in 1999. It replaced Course I. and a little of Course II? It marked the beginning of the end of the RCTs (the easier route to a diploma). Teachers knew on Day 1 that something was wrong. Too much reading. Too much math in (artificial) context. Too much rounding. Too many topics (it was keyed, roughly to a year and a half of material. In many places that meant two years.) And no depth. Because it wasn’t measuring anything, it was unreliable. In June 2003, the first time the entire state had to take it, boom, failures all over, including fancy suburbs. And they rescaled it so that the suburbs would pass. And they appointed a committee that recommended a committee, that… Well, 6 years later, and we’ve reached the end.

The foot-dragging commissioner responsible for this “standards-based assessment,” Mills, is gone. But the damage he wrought lives on.

The replacement exam, Integrated Algebra, is neither really integrated, nor algebra, but schools quickly made the switch (unlike a decade ago, when the vast majority of schools tried to get as many kids into the last administrations of Course I as possible). Integrated Algebra is a lot like Math A lite, with a year’s worth of material, but the same shallowness, and far too much breadth. Some of the worst of A is gone, but…

Anyway, this week we celebrate the end of A. To those students this morning taking (or retaking) B, working on those Advanced Regents diplomas, good luck. And to my readers, we’ll come back to these topics a few more times this week.

Say goodbye to Eduwonkette…

January 27, 2009 am31 9:28 am

she’s hanging it up. I don’t quite get it… a real job or something…  I didn’t believe it at first, but it was a good ride.

Quick area/perimeter puzzle

January 26, 2009 pm31 11:50 pm

Can you find all the rectangles for which the perimeter equals twice the area? (just the numbers. Ignore the fact that the units don’t match)

Clever exam bonus question

January 25, 2009 am31 4:05 am
tags:

Nope, not a cute puzzle. Not a deep brain teaser. Just another, beautiful use of the 2009 game.

We give long final exams. The period lasts two hours and twenty minutes. It is possible to write an exam that takes the average kid two hours, allowing those who move a bit slower an opportunity to finish without time pressure. But what to do with the early finishers?

If they were perfect, they would check their work twice, take a crack at one or two little bonus questions, and then have nothing to do. Even perfect kids get fidgety, and my kids are not necessarily perfect. Whispering, chairs creaking, papers rustling, it all gets tough on those still working.

So we kept them engaged. The 2009 game is, at their level, open-ended. I offered one tenth of a point per number correctly found. Big give away? Nah. Even teachers, with 20 minutes, most would pick up 4 – 6 points. Glancing at the exams (not graded yet), it looks like the kids picked up 1 – 4. And in return? They were engaged with a puzzle that forced them to play with numbers. Also in return? The slower test-takers had a much quieter testing environment than they might have had otherwise.

Thanks Denise!

(note, I did this last year as well. Don’t remember if I wrote about it, though.)

Brief post-inaugural hiatus is over

January 25, 2009 am31 2:28 am

I took a little break from blogging this week. As final exams arrived and programming for the Spring term continued and preparation for Regents ran apace… anyway, 2718 is back. New car, new hair, new bathroom, new term… all just days or weeks away.

And there’s lots I meant to say that I need to get to. Charters. Gotham Schools. Teaching off topic. The end of my math wars story…

All coming. All soon. Probably.

Inauguration in my school

January 21, 2009 pm31 4:48 pm

We have a small school. An advantage is flexibility. We shortened periods yesterday so that we ran 1-2-3-4-5-inauguration-6-7. After 5 students reported to pre-assigned rooms. Call it around 11:40.

We’d been working on live feed into each classroom. And I’d been predicting that we would end up listening. We were set with the radio over the PA (we never intended to pull audio off the live feed).

One of the rooms never went up. Around 11:30 – 11:45 another room went down, and then another. We shifted kids into rooms with video. We lost more rooms, and more shifting. Just before noon we lost more. We were down to half our rooms. But the kids packed in. And then we watched.

With the words “congratulations Mr. President” there came applause over the PA. But it was drowned out by the applause in the room. Then the speech started. Some kids slept. Most listened. A few fidgeted. Some listened intently.

I have heard Obama give inspirational speeches. Yesterday’s was not one of them. But then again, it’s just a speech.

It’s a new day

January 20, 2009 am31 10:07 am

From red to blue. Out with the VW, in with the Toyota.

My school is going to try to broadcast the inaugural, live. The sign in the lobby says “Inaugurationalism” But bandwidth? I think we will end up listening to it over the PA. I might like it better that way anyway.

Last winter soup from my old kitchen. Very parsnippy today, and substituting white for yellow onions left a pleasant sweet contrast to the parsnip and black pepper. And great bones.

Teaching off topic 2

January 19, 2009 pm31 8:20 pm

I go off topic all the time; it’s how I teach. But I was miles away twice last week, and both may make interesting stories. I wrote about the first earlier. Here’s the second:

I’ve been doing math stuff in the Bronx for years. I taught, eventually gave a few talks, did a Saturday enrichment thing for a while, picked up the college gig, got involved with pre-service Teaching Fellows for a few years…

There was a pause. I might have been in trouble. They were thinking.

Sometimes things come together. I encouraged a neighbor, Numbers Guy, to become a math teacher. Huge personality, a natural. And last fall he was accepted to the Teaching Fellows. One of my math campers from a few years ago, Early Riser, rises from his school’s Siberia, the trailers, and step by step, out of teaching: he is now an AP. Numbers Guy was looking for a job. It took a little convincing, since Early Riser does middle school and Guy wanted high school, but it has worked, exceptionally well, as a matter of fact.

So Numbers Guy picks up math team. And invites me to come. And Early Riser thinks it’s a great idea. Plus, their school sends my school a few kids every year. And last week I did middle school math team. What to do? Numbers Guy was open to anything. This was going to be fun.

1. For a warm up, an old standby: Read more…

Teaching off topic 1

January 19, 2009 am31 5:27 am

I haven’t written about teaching all term. Don’t know why. Just wasn’t moved, I guess. Classes are similar to previous years: Algebra I, a half-year-advanced Algebra I, College Algebra (at the college), and my first term senior elective: Combinatorics.

I go off topic all the time; it’s how I teach. But I was miles away twice last week, and both may make interesting stories. Here’s the first:

Combinatorics wrapped up. We counted in September, October, and November, learned a little probability in December, and then expected value. This month we analyzed a few games, including roulette. I don’t think the kids did spectacularly, but, most of them really calculated the expected values for each bet in roulette, and were surprised by the result. There’s a big deal hidden in there: each kid had enough confidence in both their ability and in the mathematics that they did not challenge their result, or question their result, they were simply surprised. That sort of big deal can pass unnoticed, but it shouldn’t. It makes me smile.

Anyhow, I was getting ready for review, and padding out a few extra lessons. I tossed them some dice games. We did the Monte Hall problem. And then, last day before review, I show up and tell them to put the blackboard away (yes, that’s a story. another story. and I’m not telling it. at least not today). So away goes the blackboard, and I start to talk:

Most of you are waiting to hear back from schools now. You know that there are some objective factors that go into the decisions – grades, SATs. They look at extra curriculars. Right?

[half-hearted nods] Read more…

Carnival of Mathematics 47, where no, well…

January 18, 2009 am31 12:55 am

It has become tradition, at the start of each Carnival of Mathematics, to discuss the number of the Carnival. And here I was, all set for 48, not realizing we’d gone off cycle by a week. (Really, I was kind of hoping for 45. I hosted 9, 18, 27, but missed 36…). (Also, 44 would have been cool. My age. # of the new president…)

47 is more impressive in geeky popular culture than in mathematics. Forty odd years ago something of a cult of 47 developed at Pomona College, devoted to noticing occurences of the number, the digits in that order, multiples, etc. Looking for 47s, they found them.

So, what grabs your attention? 47 is of the form 3n – 1 (yawn). It is odious, it is a lucas number, it is a safe prime? The Pythagorean Theorem is the 47th in Euclid’s elements (but something had to be 47th. And something else 48th, right?). Or the outrageous claim that 47 is the quintessential random number…? Or, even better/worse, the recurrence of 47, the string 47, multiples of 47, and even apartment 4-g in just about every episode of Star Trek: The Next Generation, and each of the spin spin off offs that followed?

Today, all hands, the Carnival of Mathematics is going where, well, hm. Sorry. I’ll limit it to headings.

Wesley Crusher (or how we teach our young)

Dave Marain at MathNotations has a wonderful new math contest for high school (and middle school) kids. Sign up is free. The contest is online, probably February 3. Kate at f(t) found that her students were more interested in bouncing a ball than studying exponents, so they studied the bouncing ball. (with solution). Pissed off Teacher is preparing her students for the AP, an exam with different mechanics.

Jason, the Number Warrior, turns factoring quadratics into a graphic puzzle. Rolfe introduces his sons to binary. Check out this interesting graph of arithmetic knowledge and self-esteem (ouch).

Vulcans (hard stuff)

Rod calculates the distance between two lines in \mathbb{R}^n. David (0xDE) compares two ways of looking at a seating problem (ménages problem). At Quomodocumque we read about a leftover problem: n points in the plane with no 3 collinear. Brent of Math Less Traveled calculates Pi through looking at the integer part of its multiples, and gains digits more quickly than it initially seems likely.

And in the category of “if the pictures look so simple, why is the counting so hard?” David (same as above) describes how several families of combinatorial objects can be generated as the collection of complete subgraphs of a graph.

A New Season

Denise at Let’s Play Math celebrates the new year with the 2009 game. Mike at Walking Randomly explores “What is interesting (mathematically) about 2009” And twopi at 360 (come on, you have to smile for that, right?) has both interesting and trivial exploration of the number 2009.

To boldly go… (new work, exploration)

The Carnival of Mathematics features a first: Polymath has blog-published what looks to be an original piece of work: a new proof in plane geometry. The existing proofs are more complicated, and involve trig. Foxmaths seems preoccupied with calculating values that exist, and some that don’t. The value of omega: 1 = \omega \times e^\omega exists, but it takes so long to find! The solutions to F^1 = F^2 (when we ignore the leftmost digits of F)? The sum of the sin(1) + sin(2) + … + sin(n)?

And Jost a Mon explores the mathematics of sprinting

The Prime Directive

Zeno of Halfway There is all over bad analysis of the problems with the election in Minnesota. And he has a photo of Spock (scroll down). Edmund at Maxwell’s Demon discusses the responsibilities of mathematicians. Political Calculations uses math as a tool to help you: math can help with a little analysis of the unemployment rate? Perhaps. But math certainly can help plan your wedding invitation list. Twopi catches a pop star misnaming variables.

The Holodeck (Games and puzzles and recreational stuff.)
(I thought about calling this one “dabo” but, seriously, who watched DS9?)

Poker with Venn Diagrams? Read the post, then click Mike’s solution (at Critiques of Libertarianism). My submission is a little dice puzzle. People find conditional probability sooo frustrating.

Enterprise (history and old stuff and strange stuff)

Michi on the Chromatic Number of Lichtenstein. John Kemeny has photos of mathematicians … and more of the same … but is looking for their names. They come from Time/Life’s archives. Ξ at 360 found some polygons in the Smithsonian. Any with 7 sides? Look at the photos closely. Vlorbik is having some issues with WordPress’ implementation of TeX.

James T Kirk (for laughs…
and anything else that can’t be taken too seriously)

Ian at Logic Nest recounts some amazing facts demonstrating the amazing intelligence of Karl Gauss, for example, did you know it only takes Gauss 4 minutes to sing “Aleph-Null Bottles of Beer on the Wall”? (silly, but very funny. Don’t skip it.)  The images below are from Blig Blug and Friends and (x or why) [seems to have wandered off. But the link remains, and is worth it]. Click the images [or non-image] to see more of their math-related (and non-math related) cartoons.

Fantasy Island

If you submitted via the carnival tool, and your submission is not here, well, the tool was broken. Sorry.
The next carnival is due January 30… but I don’t know where. If you are host, link back so that readers might track you. And if you are a reader, watch the comments here, or keep an eye out at the Carnival of Mathematics webpage.

All good things…

Glitchy Carnival of Mathematics?

January 16, 2009 pm31 11:00 pm

The next Carnival of Mathematics (47) was scheduled to appear here early tomorrow (Saturday) morning.

There is a problem with the carnival submission tool – it has not been set to forward submissions to me.

If you submitted via the tool, please resubmit directly to me: [thisblogname] at [gmail] dot [com]. I’ll delay some reasonable amount of time, but the Carnival will come out tomorrow (Saturday).

Summer paid 1 week study for community college faculty

January 16, 2009 am31 8:19 am

Since there’s a handful of you reading this…

Just like for teachers, but for CC faculty… One week summer vacation, paid. The National Endowment for the Humanities runs it. The ones for teachers, I know that they take all licenses – they took me, math teacher, to study industrialization. I would guess they do the same for the Landmarks of American History for Community College faculty.

Deadline is March 16. Stipend is $750. The only bad news, the list of workshops is much shorter:

Encountering John Adams: Boston and Braintree

Concord, Massachusetts: A Center of Transcendentalism and Social Action in the 19th Century

Landmarks of American Democracy: From Freedom Summer to the Memphis Sanitation Workers’ Strike

The American Lyceum and Public Culture:  The Rhetoric of Idealism, Abolition, and Opportunity

Progress and Poverty: The Gilded Age in American Politics and Literature, 1877-1901

Passages to Cleveland: Community Memory and the Landmarks of Migration

Here’s the link.

NYSUT on (lack of) state audits of charters

January 16, 2009 am31 6:29 am

New York State United Teachers wrote:

ALBANY, N.Y. January 15, 2009 – New York State United Teachers today welcomed an appellate court decision requiring charter schools to comply with state audits, saying that the current economic climate underscores that taxpayers deserve accountability for how public money is spent and how charter schools perform.

Read the original article…

I’m not happy with how friendly NYSUT (and the UFT, the NYC public schools affiliate, and my union) is towards the idea of charter schools… but I appreciate that they are paying attention…

Read more…

Inauguration in my school

January 15, 2009 pm31 10:56 pm

Tuesday we are running shortened morning periods, then inauguration, then shortened afternoon periods.

During the inauguration, all the kids will be assigned to classrooms (probably O.C assignments) and, bandwidth allowing, will watch the event on streaming video. I am not at all upset about the possibility of bandwidth overload… I almost like the idea of listening to the address over the PA better – more focus on the words and ideas.

One of the advantages of being in a small, wired school.