Retesting factoring – some success
It is my intent not to allow students to leave my algebra class not being able to factor trinomials. To that I end, I employ the “retest.”
Factoring comes in November and December in my (fairly traditional) algebra text. The results on our first factoring test were about as expected: 60% of the students scored 80 or better. I wish that it would be higher. I worked for it to be higher. Every year I adjust. I wonder if we start too easy. But answers don’t matter at this moment for the 40% who scored below our expectations.
They studied over vacation (no regular assignment), and took a retest when they came back. Now, this retest is tricky. I make it similar to the original test, but shorter, with the points only adding up to 90. I also pick a slightly easier subset of questions. The goal remains 80 points. So on the retest, 20% broke 80, and 20% were assigned more tutoring.
Friday we retested again (the actual questions are posted beneath the fold). And every last student qualified. Pheww.
Seems a bit cruel, I know. I combine teaching for understanding with teaching skills, but this test is all about skill. No way to reason yourself clear, just practice and repeat. But they gain a sense of accomplishment. It makes me feel good that they eventually succeeded. And now I can say “Yes [whatever new topic we are studying] is hard. But you are a student who learned to factor, which was much harder, so I know you can do it…”
Primaries
(I don’t plan on writing much on this topic)
This season of primaries seems exciting. They are coming fast and furious, and both races are still open. The Democrats are down to two frontrunners, with Edwards just hanging on. The Republicans have, hm, right now it’s two or three in front, but I think all five, not including the internet guy, are still in it. For those who enjoy horse races, they have two.
But what of the choices? On the Democratic side, it looks like style over substance, in a very serious sort of way. The (partial) exception is John Edwards, who has sounded a more populist, labor-ish them. But a pile of not so bad speeches don’t make him a working class hero (note to self, good name for a sandwich shop, bet it already exists). Look at this position grid. Edwards and Clinton, on the big issues? 24 out of 25 matches. And the last is a maybe.
Actually, Fred Klonsky’s hohum response seems about right. Where Obama differs from the other two, like the possibility of US military action against Iran, or NCLB, it makes me cringe. He was one of the 23 Senators to vote no on the resolution authorizing the invasion of Iraq, but given his statements on Iran, that looks tactical, not a matter of principal.
Change, change, change. Change don’t mean jack. I have been watching these things long enough to remember Gary Hart’s energetic centrism catching the pundits fancy in the face of Walter Mondale’s plodding Minnesota liberalism. Change change change.
Teacher Pay Scale — Bridgewater, NJ
It’s time to update the pay scales here, and add a few more. To kick things off, earlier this week an anonymous commenter sent a link to the current Bridgewater/Raritan, NJ pay scales. Here’s the link, and here’s a few notes about the area: (the scale is reproduced, below the fold)
The two places (a township and a borough) are in Somerset County, New Jersey, about half way from Staten Island, NY to Allentown PA, near where I-78 and I-287 meet. Combined population is about 50,000. There are about 6 elementary schools, 3 middle and intermediate schools, and one high school. Larger Bridgewater has a median family income near $90k, while smaller Raritan’s is closer to $60k. Both towns are about 85% white, 10% Asian.
The scale starts near NYC, has lots of steps for education (BA+15, +30, +45, MA +15, +30, +45, +60, +75, PhD), but the advances are smaller amounts. The extra money for experience is very small in the first few years. After year 8, the increases become quite large ($3 – 4k, every year) until year 15.
CoM 24 at Ars Mathematica
I don’t like skipping Carnivals of Mathematics, and I really wanted to make this one, but managed to post 5 or 6 posts with flubbed html. Embarassing.
Anyhow, lots of good stuff. Go visit.
Ars Mathematica, the host, has a, for me, fairly meaty mathematics blog. I need time and patience to read the posts there, but when I invest the time, I find it worthwhile.
Gazinta – two remainder puzzles to kick things off
I promised divisibility in January, and have yet to deliver. In fact, I’ve posted almost nothing about anything since the New Year. But my energy returns, and things will start rolling again. Now.
This is classic. I tried to divide my collection of rocks into two equal piles, but there was one left over. Then I tried to divide it into three equal piles, but there was one left over. When I tried to divide it into four equal piles, there were three left over. When I tried to divide it into five equal piles, there were three left over. When I tried to divide it into six equal piles, there was one left over. Then I divided it into seven equal piles. Can you imagine doing all this dividing with almost a thousand rocks? How many did I have?
This (I believe) is not classic: Consider the sum of the remainders when a number is divided by 1, 2, 3, 4, and 5. Under what conditions will the number be a multiple of this sum?
Add comments and questions below.
Add solutions by clicking this.
Solutions – two remainder puzzles
- I tried to divide my collection of rocks into two equal piles, but there was one left over. Then I tried to divide it into three equal piles, but there was one left over. When I tried to divide it into four equal piles, there were three left over. When I tried to divide it into five equal piles, there were three left over. When I tried to divide it into six equal piles, there was one left over. Then I divided it into seven equal piles. Can you imagine doing all this dividing with almost a thousand rocks? How many did I have?
- This (I believe) is not classic: Consider the sum of the remainders when a number is divided by 1, 2, 3, 4, and 5. Under what conditions will the number be a multiple of this sum?
Add solutions below.
Add comments and questions by clicking this.
A colleague who I will miss
The teacher in my department who plans with me is leaving.
It’s good for her. Her husband got a much better job out to Alaska, moving from flying small planes to jumbo jets. And they had been waiting for years. It’s a good move. She’ll land a job, quick, teaching math.
we split the prep. I can’t tell you what it’s like to be able to pick up materials Monday morning, never having laid eyes on them, and know that you can teach with them.
But I am miserable. We have worked together four years. She arrived as a second year teacher, and I was nervous. We team taught an algebra class her first term. I should do a study. The kids from that class, I think they mathematically outperformed their peers in mathematics for the balance of high school. It went that well.
She started out ok. Every year she got better. She brought patience to the classroom, combined with a real interest in math, and a real knowledge of math. She had this knack for making math “non-scary” for kids, while keeping strong content. I brought my set of games to the classroom. And she brought hers.
more beneath the fold —>
Gazinta January
As in, 11 gazinta 99, but 8 doesn’t ga’inta 23.
January math posts will deal with divisibility. We will look at
- what divisibility means
- division and long division
- checking divisibility without dividing
- divisibility rules (base 10)
- divisibility rules (other bases)
- teaching tips and tricks,
- and of course, little puzzles along the way.
Let’s start: When we talk about divisibility, we’ll be talking about whole numbers only. I will write “number” and we will understand that we are only discussing positive integers. These topics won’t make sense for fractions or decimals or square roots… We won’t talk about negative numbers either. And we’ll set aside some time to briefly discuss zero and division.
We can say 3 goes into 15, or we can say 3 divides 15, or we can write 3|15. All of these mean that there is some number (no mystery here, it is 5), but in general some number, such that 3 times the number is 15. Remember, number means positive integer in these posts.
We can say that 2 does not go into 17, or we can say 2 does not divide 17, or we can write 2∤17. All of these mean that there is not a number we can multiply 2 by to make 17. (Eight and a half? Remember, we are talking about whole numbers. Fractions don’t count).
Challenge for the United Federation of Teachers
Early this month, the United Federation of Teachers designated a number of schools, every level, every borough, where administrative abuse was rampant and where we would collectively, including UFT Central, including members from neighboring schools, would target those school, would engage in a full court press. Excellent idea. Overdue, even.
But when I heard the list of schools, I was shocked. Where were the Bronx small high school hellholes? I can think of five for the top of the list without thinking. There must be more than a dozen that should be there… But I was wrong. The kind of assistance that we are providing, it requires that an engaged chapter be in place. We are helping those who are already fighting. This makes sense. It is a good and positive initiative. It is needed.
Organize functioning chapters in every school.
But what of the small high school hellholes? The ones with 50%+ turnover each year? With incidents unreported? With members working 4-in-a-row or lunches? Where chapters do not meet? Where principals are abusive and teachers are afraid? (continued –>) Read more…
New Year’s Potluck…
…over at Meeyauw’s place. Buttermilk pie. Southern food. Pizza. Fruit faces. Various teacher stuff. And of course, soup.
Click the carrots to get inside.
Carnivallette of Marrow
A carnivallette of bone marrow recipe and dishes blog posts from the last few months.
Pork “ossobucco” from the Reluctant Gourmet, left.
Bone Marrow, St. John, from Eating with Jack (an elegant dish, right).
How do you like bone marrow? A discussion from just a week ago on ChowHound (listed under my NY links) and a NY marrow recommendation from a few weeks earlier.
An English roast bone marrow and parsley salad recipe from Married with dinner.
Bone marrow dumplings from KQED Bay Area Bites (sort of their chowhound?). It’s the last in the list of 2007’s top meat dishes.
Lee Anne Wong includes NY’s Blue Ribbon and its bone marrow marmalade on her top 10 (#8).
The Hawaiian blog, onokinegrindz, visited London and took a wonderful photo of roasted marrow bones.
And then there’s me (soup bones above left), Fred (cabbage soup), and Spamwise (roasted bone, at the Beacon in NY, right).
Fred wraps it up neatly in his Chronicle of Bone Marrow.
(ps, there’s a ton more out there. This site has medieval recipes for marrow pies (“sluberkens” in some form of Dutch) and marrow-stuffed quinces. Tip of the iceberg.)
C o Math 23
Winter Soup – the photo array
I’ve often boasted about my winter soup. Here, live on this blog, you finally have a chance to see this gross-looking, olive brown colored glop.
Unpeppered marrow broth, left, parsnips and carrots (hiding other stuff) right.
The basic idea: boil the hell out of barley, split peas (yellow and green) and lentils, about a pound, pound-plus altogether (1 hour). Throw in marrow bones (can add neck bones with some meat, if you want), and boil them hard (1 hour). Then pepper, spice, and throw in chopped carrots, parsnips, onion, and celery, and boil a bit, then simmer.
After an hour, hour and a half, you have edible soup. Reheat repeatedly (adding water), and you thicken it to porridge. Just reheat what you want, and you get to keep it at the soup stage. I do a bit of each.
More beneath the fold, mostly pictures —> Read more…
Puzzle – sum of the angles
I wish I could make nice diagrams…
Consider rectangle ADEH with side ABCD and side EFGH such that AB = BC = CD = DE = EF = FG = GH = HA.
Find the sum of ∠FAD, ∠GAD, and ∠HAD ∠EAD, ∠FAD, and ∠GAD.
Questions in the comments section, above.
Answers? Over here.
Solutions – sum of the angles
(Way cool that this image is fine for illustrating my problem, but is really from a fairly advanced seeming math blog (on game theory?), on a topic that I do not understand: Bosker Blog.
Consider rectangle ADEH with side ABCD and side EFGH such that AB = BC = CD = DE = EF = FG = GH = HA.
Find the sum of ∠FAD, ∠GAD, and ∠HAD ∠EAD, ∠FAD, and ∠GAD.
Answers in the comments section, above.
Questions? Over here.
Some bloggish notes and updates
The Grinchy edition of Teacher’s Potluck went up at Whatsit last week. Take a look. And the deadline for submissions for Friday’s Carnival of Mathematics at The Math Less Traveled is rapidly drawing near. If you are planning to submit…
There are more link changes than I can remember. The last few include
- adding Lynet (Elliptica, math, and other stuff, from Australia),
- Miss Brave teaches elementary here in New York City,
- Miss George teaches middle school English (in the suburbs? in NYC?),
- Sol does all kinds of tricks, some on video, at Wild About Math,
- I’ve been commenting on Rolfe’s blog forever,
- and the Columbus Education Association.
- Brown-eyed girl was cute, but I got bored.
- Kimberly Moritz maintained a great principal’s blog at G-Town Talks, but she got promoted and the blogging went by the boards.
- The best addition is eduwonkette. When she showed up a few months ago, bloggers were falling over each other to say nice things about her. Not me. I was waiting to see what was wrong, what the secret angle was. Answer? That was silly of me. Eduwonkette writes a smart, well-directed blog that covers mostly education issues, focussed on New York City. Typical is a series of related posts on a topic over the course of a week. She’s weighed in intelligently and sharply, without feeling caustic, on the progress reports, merit pay, etc. I think she’s a teacher, but I’m not positive. And if you hurry over, she’s on break, but you can read her stand-in, skoolboy, with a series of posts on class size.
Double tag, + delay
I got hit with the 7 things meme last week and the week before, but I let it sit before responding (I have another, several months delayed meme, that I might get to this week). My taggers were Homeslice, then Frizzle.
- I’ve only eaten goose once in my life. Mid-December, 1991. After an 18 hour train journey from Bratislava, in the dead of the winter, I arrived in Lvov and was greeted with roast goose and potatoes cooked in greasy goose fat. Amazing.
- I only became a regular driver as an adult, just a few years ago. I am quite pleased that I can drive, but I do not enjoy it in the least. If I have a passenger, I usually offer them the keys.
- Famous people? I was introduced to Grant Hill’s dad when he was a college running back and I was 3. Had you asked me then, I would have said Calvin Hill was my favorite football player. But pick me up so I can say hi to him? I burst into terrified tears when I came eye level with this huge man. I went to school one year with one of Bill Cosby’s kids. I don’t think we said more than a couple of words all year (open classroom, so we were in the same room, but not really any of the same groups). I saw Kim Carnes on the street when Bette Davis Eyes was at #1. “Are you Kim Carnes?” “yes” and I just kept walking. I knew a quite notable physicist, and a mathematician, but I doubt readers would recognize the names.
- I am a (rather strident) atheist. I avoid discussions, since it is so easy to offend. And I do my best not to enter houses of worship, even if they are no longer in operation.
- I like pets. I enjoy the company of cats and dogs. My sister’s dog recognizes me (and treats me as the α-male when her husband is out). But I have never had a pet of my own, except for goldfish that lasted for a week or so when I was a tot.
- I didn’t eat pizza until I was 20. I still don’t eat most food that contains cheese.
- My news memories go back to age 4 and the 1968 primaries, my parents working for different candidates, and sitting on the floor of the den, in silence, as my father watched the news of Bobby Kennedy’s assassination. I think I remember the Apollo moon orbit from later that year, but that is blurry. Viet Nam came later to my consciousness, probably 69 or 70, when I recall not knowing what “casualty” meant and being impressed by highways important enough only to need one digit (as opposed to our local I-91 and I-95). After that, I recall events more easily.
Here are the rules:
– Link to the person that tagged you and post the rules on your blog.
– Share 7 random and or weird things about yourself.
– Tag 7 random people at the end of your post and include links to their blogs.
– Let each person know that they have been tagged by leaving a comment on their blog.
OK, now I need to tag some untagged bloggers? This is tough, since the meme is two weeks old (pretty much stale). Here’s my try: Teaching (smarter) – also known as Rocking the System, Syntactic Gymnastics, HRoman of the Roman Empire, Hal from Hal’s House of Pancakes, Jose (how’d he dodge this so far?) of, of course, Jose Vilson, Andrée from meeyauw, e of e’s ponderings, and Darmok of Ancora Imparo (I miss his comments).
What if they bomb the test?
Math causes anxiety. Tests cause more anxiety. Math tests? Yeah, anxiety, and more than additive.
I tell students that they must pass tests. I tell them what’s on the tests in advance. I advise them how to study. And still, not everyone passes. If it’s one kid, we can handle that individually. But when it is a handful?
My response is 3-pronged, depending on the topic.
- Move on.
- Correct yourself.
- Retest.
Move on. This is both the easiest, and the worst option (at least by itself). In history, you don’t get China? You’ll do better on India. No worry. But in mathematics, skills build on one another. Don’t understand how to manipulate a variable in September? You’ll be crying until June, unless we get you some help.
Correct yourself. This is easy for the teacher, not necessarily for the student. I don’t use it for the most crucial skills. In short, take your exam, rewrite all or part of it, and I will return some credit.
(more beneath the fold —>) Read more…
Animal variables
From left to right, elephant, sea monster, frog, grass, vortex. I don’t know why my algebra students call the middle one “frog,” but it doesn’t much matter. I get squeals when I throw one of these into a problem set.
The elephant was originally oriented to the left, but then the exponents looked like floppy ears, so we had to switch. My breaking the middle on the right is a bit sloppy, but since it involves sea monsters, that shouldn’t be a problem.
Friday, a bunch of kids exchanged elephant or frog socks… And when I come back from Scotland with Nessie chachkas…
Teaching: The Really Big Number (applied)
Ages ago (last Spring), Sharp Brains offered this puzzle: What is the remainder when 
So I worked it into my day-before-vacation algebra lesson, and duplicated it for an algebra class I covered (but only started for the last algebra class of the day, since we had to leave for the holiday talent show)
First we played my “little bit of math magic” (write down a number, square it, save the last digit, square that, save the last digit, multiply by your original number. What do you have? Your answer was…). Only I told them in advance that they could use calculators, if they had them, but they didn’t need them, only without calculators they wouldn’t be able to stump me…. I did a round with each class, then a second round where I restricted them to 10 – 40 or something like that, and suggested they write down all the numbers and answers, and challenged them over break to figure out what was going on…
Second we worked on the really big number. Here’s roughly what I said:
What’s the remainder when 20 is divided by 3? [2]. When 100 is divided by 7? [2] Did you have to do remainder math in middle school? [no] Here’s one way to look at remainder math: What’s the remainder when 100 is divided by 11? [1]. Instead, we can write this as 11n + 1. It doesn’t much matter what n is (but what is it? [9]) since we are only interested in what’s left over.
continues below the fold —> Read more…
Some awfully big schools
See the list of the largest high schools in New York City, using ‘data’ from the NYC Department of Education’s new class size report?
Brooklyn Tech, 19601? That’s the school’s population, according to the new report. I’ve listed the top 40, below, and there’s more surprises. Each school is listed at 2, 3, 4 times its actual size.
No, Brooklyn Tech has not moved to Reading, PA 19601
Yes, these numbers make no sense. Is there anyone left at Tweed who knows anything, anything at all, about the school system? No one with any actual experience looked and said, um, we don’t have schools with 20,000 kids?
Brooklyn Technical HS 19601 ⋅Francis Lewis HS 19016
Benjamin N. Cardozo HS 16425 ⋅John Adams HS 15847
James Madison HS 15846 ⋅ Edward R. Murrow HS 15614
Dewitt Clinton HS 15557⋅ Boys And Girls HS 14805
Forest Hills HS 14748 ⋅ Bayside HS 14725
Hillcrest HS 14490⋅ Fort Hamilton HS 14478
Richmond Hill HS 13786⋅ Herbert H. Lehman HS 13603
Franklin Delano Roosevelt HS 13478⋅ Tottenville HS 13251
Midwood HS 12758⋅ Martin Van Buren HS 12557
John Bowne HS 12556⋅ John Dewey HS 12223
William Cullen Bryant HS 11978⋅ Murry Bergtraum HS 11836
Thomas A. Edison Career And Tech Ed HS 11669⋅ Long Island City HS 11632
Bronx HS Of Science 11535⋅ Grover Cleveland HS 11230
Fiorello H. Laguardia HS Of Music & Art A 10745⋅ Flushing HS 10745
Curtis HS 10556⋅ Newtown HS 10478
New Utrecht HS 10294⋅ Louis D. Brandeis HS 10205
Susan E. Wagner HS 10114⋅ Stuyvesant HS 9367
Clara Barton HS 9095⋅ Harry S. Truman HS 8867
Port Richmond HS 8448⋅ New Dorp HS 8227
Sheepshead Bay HS 8144⋅ Franklin K. Lane HS 8122
(Brooklyn Tech’s actual register is a bit under 4500)
Wireless mouse
Having a wireless mouse and a wireless keyboard, that seemed cool. For about 10 minutes.
I haven’t lost either one (which could be scary). In fact, since I never move either far from the computer, there is hardly a reason to be untethered (though not bumping into the wires is probably an advantage I haven’t noticed). I do notice that sometimes the letters don’t appear in the order I typed them….
But these things burn through AA batteries like nobody’s business. Two nights ago, I ran out. And the remote. None in the apartment.
Did I prioritize? Yes. For one night, my CO alarm and alarm clock were without batteries, while I kept the important devices running.
Faking Class Size
The New York City Dept. of Education has released class size data. Hmm. I should say, heavily adjusted class size data. Edwize was happy. They should have known better.
The high school numbers were arrived at by cheating. They excluded lots and lots of classes.
Each school locally designated courses as “core” or not. The general guidelines were that any course that is used for graduation would be core, everything else would not be.
Which categories are excluded? Foreign Language is the biggest category. Then Music, Art.
Individual classes are excluded. Which? In most schools, anything that is not part of the standard graduation sequence. Which means lots and lots of things. And different things in different schools.
In math, any advanced courses? Probably excluded. Precalculus? Probably excluded. Calculus? Probably excluded. Statistics? Probably excluded. Any lower-level post Math A courses (eg, Intermediate Algebra)? Probably excluded. (note that these courses help many kids earn their 5th and 6th credit towards graduation).
English is worse. The guidelines make clear that electives should be excluded. But – “The Modern American Novel” – typical class that could count for elective credit? Probably excluded. And some kids are taking it as an elective, and it is the 8th needed English credit for others. Journalism? Ditto.
And the core/not core designation was made in each individual school, following these vague guidelines.
So how many classes were counted, how many were excluded? That piece of data they are not sharing.
No sense of responsibility
“The A grade, though, may also have something to do with the fact that the progress reports weigh all safety factors as only 2.5 percent of a school’s total grade” said James S. Liebman.
Talk about accountability!
Who weighted safety 2.5%??? Liebman did!
No back door to sneak out? He’s always got the passive voice to duck responsibility.
Post about a NYC small school you must read
This.
One UFT leader told me (on several occasions) that the need to build chapters from scratch at new small schools would help develop new leadership.
Bullshit. We have developed festering sores where teachers’ rights are trampled. Only with dedication of resources from UFT Central can we turn this around. We’re waiting.
JD2718 