Showing posts with label I Don't DO Math. Show all posts
Showing posts with label I Don't DO Math. Show all posts

Thursday, May 12, 2016

Ego of the Ignorant

Self-centered world-view ("I don't need it so neither do you.") coupled with ignorance of the many negative effects on those children who could have accomplished something.

It's the evil twin of "I don't DO math."

Having taught SATprep for many years, I can tell you that the English side of this test isn't very hard - and easier for adults than for teenagers who haven't had as much experience in literature nor the practice in writing. The math side does contain topics that are obscure if you aren't currently enrolled in Algebra II, so I can understand that part.

Tragic, really. What strikes me the most is that this was retweeted so much with comments like "You're my hero!" 

I call shenanigans.

Wednesday, January 29, 2014

Embedded Content and the Foreign Language Paradox

Bumped to the top from August of 2010:


Joanne Jacobs: Kids Don't Know Grammar. Although neither of those quoted (perhaps misquoted) can spell "embedding," their point is good. Embedded curriculum doesn't work.
Less than 10 percent of Robert Archer’s 10th graders know grammar. A 14-year veteran teacher in Spokane, Archer doesn’t blame middle-school teachers. He blames curriculum developers for “imbedding” grammar in the curriculum.
"in my experience, the term “imbedded” is nothing more than educationalese for “not ever specifically taught.” Somehow, this grammar-is-imbedded movement is supposed to help students naturally take in what proper grammar is (i.e., grammar by osmosis). It’s very much a hyper-constructivist approach to education; the students are supposed to “discover” proper grammar on their own as they read good pieces."
He's right. They don't pick up on the proper forms of grammar, nor do they pick up much of anything that isn't specifically presented and what is, doesn't last.

Maybe I'm an old-school fart but it seems to me that if the students really could do this type of learning by assimilation, they would be miles ahead of where they are now. I do SAT prep classes and the grammar skills are terrible -- except for the kids in Spanish or French III or IV.

I call this the "Foreign Language Paradox." When learning English in an English class, grammar and basic forms are not supposed to be explicitly taught. Literature reigns supreme and some limited essay forms are required. Grammar and proper sentence structure are supposedly understood as 5th graders. Then we are all surprised that no one seems to know them.

In any foreign language class on the other hand, noun and verb declensions, grammar and sentence structure are specifically taught; then drill, drill, drill. Every student learns through actual work and walks out with an understanding of the language and a better understanding of English, too. "I never understood the subjunctive mood until SeƱor told us." "Past, imperfect, pluperfect - wow! Then, a couple of present tenses and more than one future tense? Damn."

It's not just Latin that builds English skills, although Latin does have power in its rigid simplicity and endless lists and mnemonics. It's specifically teaching grammar to students when they are finally sophisticated enough to really understand and appreciate it in all its nuanced glory.

Hello? Is my curriculum coordinator listening?

Apparently not.

Joanne chimed in with her own anecdote:
On Back to School Night, my daughter’s eighth-grade English teacher told parents she was going to go off curriculum for two weeks to teach grammar and punctuation. She got a standing ovation.

It's not just English, but math as well. Bunches of my students go off to the tech center for a one or two year program and then return. They have me for algebra I and then go to forestry or woodworking or something. Invariably, I hear about the embedded math credit. They are then placed in the next class and have no clue about the missed material. What's worse is that they are in my class for the eleventh grade and thus on my roster for the NECAP tests in November. I think of myself as a good teacher, but that's just not fair to either of us.

Bottom line: No matter how smart, no matter how motivated, all kids need some instruction. Unless you are specifically making things clear, you are allowing kids to construct any old thing, and it's usually flawed.

Tuesday, January 21, 2014

I don't DO math.

This article:
Is math ability genetic? Sure, to some degree. Terence Tao, UCLA’s famous virtuoso mathematician, publishes dozens of papers in top journals every year, and is sought out by researchers around the world to help with the hardest parts of their theories. Essentially none of us could ever be as good at math as Terence Tao, no matter how hard we tried or how well we were taught. But here’s the thing: We don’t have to! For high school math, inborn talent is just much less important than hard work, preparation, and self-confidence.

Sunday, January 19, 2014

It's not Psuedocontext, it's just wrong.

Credit for the Bad parts, too.
There are many errors in the packaged, bought and paid for, courses from Florida Online. Unfortunately, the "developers" seem to have taken that "Beta" software approach ... if it isn't "Threatening-the-President-bad", then we won't bother fixing it.

Take this problem, from the Semester Exam:
Triangle ABC is congruent to triangle DEF. In triangle ABC, side AB measures 9, side BC measures 3x+18, and side CA measures 7. In triangle DEF, side DE measures 9, side EF measures 2x+26, and side FD measures 7. What equation would help you to solve for the side length of BC and EF? Explain your reasoning using complete sentences. (10 points)
At first blush, you say "They're congruent. BC is congruent to EF, so 2x+26=3x+18. Done."

What's the big deal?

Solve it.

Pretty easy ... x = 8.  So the sides of a triangle are 9, 7, and 42. Shit.

Any student who takes that obvious next step, and thinks for more than a second about a different topic just studied, i.e. comparing sides of a triangle and scissors theorem, is now convinced he's done something wrong.

It's not Psuedocontext, it's just wrong.

Wednesday, April 17, 2013

Education News is having trouble with numbers.

Education News ran this story:
The promise of technology in education has not been fulfilled — at least not in schools like Seminole Ridge High School, according to The Palm Beach Post. When the school spent millions to equip its labs with 25,000 new computers, little did the administrators or students expect that most of that machine time was going to be taken up by nothing else but testing.
Yeah, I get it. Evil testing. Bad, bad, bad. Using up computer time and such.

But then I noticed "25,000" and I wondered because that's a damn big number for a school.  I wondered if that was the entire district but that doesn't seem to be the case - the high school is specifically named several times. I googled it and found it had 2478 students.

Tell me again why I should trust their numbers?


Saturday, November 26, 2011

I Don't Do Math - Accepting False Limits

Seth Godin (Marketing Expert) has this: Accepting false limits and you'll probably guess that I'm about to throw out "I Don't Do Math", but bear with me.

I will never be able to dunk a basketball. This is beyond discussion.

Imagine, though, a co-worker who says, "I'll never be able to use a knife and fork. No, I have to use my hands."

Or a colleague who says, "I can't possibly learn Chinese. I'm not smart enough."
This is a mystery to me. A billion people have learned Chinese, and the failure rate for new kids is close to zero. If a well functioning adult puts in sufficient time and the effort, she'll succeed.

The key to this disconnect is the unspoken part about time and effort and fear. I agree that you will never ship that product or close that sale or invent that device unless you put in the time and put in the effort and overcome the fear. But I don't accept for a minute that there's some sort of natural limit on your ability to do just about anything that involves creating and selling ideas.

This attitude gets me in trouble sometimes. Perhaps I shouldn't be pushing people who want something but have been taught not to push themselves. Somewhere along the way, it seems, I forgot that it's none of my business if people choose to accept what they've got, to forget their dreams and to not seek to help those around them achieve what matters to them.

Not sure if you'll forgive me, but no, I'm not going to believe that only a few people are permitted to be gatekeepers or creators or generous leaders. I have no intention of apologizing for believing in people, for insisting that we all use this moment and these assets to create some art and improve the world around us.

To do anything less than that is a crime.
Not exactly.

There's a huge difference between the picture above (girl being told she isn't good enough, pretty enough, fat enough, skinny enough, smart enough, slutty enough) and a girl making an honest self-assessment of her abilities.  There's a big difference between giving up too early (accepting FALSE limits) and accepting true limits.

Not everyone seems to be able to do math as well as I can. I can't draw or paint as well as my uncle. My uncle can't drive (and doesn't need to) and certainly can't do math. My grammatical sense is better than that of most teachers, if I can believe what I read and hear on the Internet.

I know scads of folks who "can't do algebra" but who consider themselves successes, engineers who could never understand related rates or scale factors, artists who understand percentages and accounting but not much more, actors who couldn't write to save their lives, and scientists who can't speak to an audience or write coherent sentence without endless rewrites and help from their significant other. White Men Can't Jump ... but that didn't stop him from playing basketball and pretty damn well.

The California teachers who signed a letter saying that students should not be required to pass algebra 2 as a graduation requirement are probably spot on with their assessment of the kids' abilities and completely off the mark when it comes to assessing the political and academic climate. Eighth grade math seems to be about the least you can learn and still have a shot at claiming yourself a success in life.

"I don't DO math" should be an incentive rather than an excuse, I know, but I also have to accept that not everyone is going to be "proficient" in this topic or any other. We need to tell them "Do your best and don't let the stupidity of youth drive you to deny an ability that you may develop in a field you haven't got a clue about yet" but we also must accept that not everyone can be good at everything.

Even math teachers.

Saturday, October 15, 2011

Circle of Failure

The other day I was in a 504/IEP meeting and a kid was being considered for alternative programs.  The tech center guy was sitting across the table and was discussing the kid's options.

"Well, the Hospitality Program would be a good fit."
"She doesn't want to put in any effort. What would be her options after that?"
"Well, she could work with the elementary school kids.  She really likes kids."


What I wanted to say was "This girl has failed at every possible program we can think of. She is lazy, and spoiled, and even her mother can't bribe her to do well.  She hates math and barely tolerates English and Social Studies. She couldn't care less about academics of any kind.  ... Why would you put her with a bunch of impressionable elementary kids?  How can that possibly work out well?"

Fortunately, I didn't have to say that, but at some point you need to put the majority's needs ahead of the reclamation project.

Thursday, November 11, 2010

Those who can ...

Yeah, I know.  I hate that old saw, too.  But dammit, why do we have to have so many people confirming it?  The Mrs. reminded me of a time last year when she went to a conference. Another teacher stood and spoke of their "adventures" hiring a third-grade teacher. The school required the applicants (13 of them? Number was implied, not specified) to write an essay and take the 8th-grade end-of-course math test.

None passed.

The school had to reopen the application process.

Monday, April 12, 2010

And there's that metric thing.

Other than in the picture ... Can you spot the error?

Event encourages interest in science
By Rachel Warren

Published: Sunday, March 28, 2010

About 125 people enjoyed an afternoon of kid-friendly activities Saturday at the Highland Road Park Observatory as part of NanoDays, a nationwide festival of educational programs.

The events are organized by participants in the Nanoscale Informal Science Education Network and will take place in more than 200 museums, research centers and universities this year, according to the NanoDays Web site. The event in Baton Rouge was hosted by the Department of Physics and Astronomy and the Center for Computation and Technology.

Juana Moreno, physics assistant professor, said the event was organized to inform the general public, not just children, about nanotechnology — the science of manipulating materials on an atomic or molecular scale.

She said she organized the event at the University of North Dakota when she taught there, and this is the first time she has put the event together at LSU.

The event hosted two speakers, Jayne Garno — a University chemistry assistant professor — and Kristen Buchanan from Colorado State University. Garno showed the audience images of nano-objects captured in her lab, and Buchanan discussed “nanomagnetism” and its application to hard drives.

University students also volunteered in demonstrations of nanoscience at tables set up throughout the observatory.

The interactive displays allowed children to play with liquid crystals, dissolve effervescent tablets to learn about surface area and pour liquid onto fabric to show how nanotechnology can be used to protect clothes from stains.

Rebecca Ringuette, physics graduate student, said she and the other students volunteered for the Society of Physics Students. She said the group is dedicated to public outreach and getting people excited about science, and it puts on as many events like NanoDays as it can.

“The next generation of scientists will not be there if we don’t get them interested in science,” she said.

A child’s interest in science is strongly influenced by the enthusiasm of the teacher, Ringuette said.

Will Heitman, a 9-year-old student at Bernard Terrace Elementary, discovered at the event he was 490 billion nanometers tall. His favorite demonstration was of the liquid crystals, which respond to temperature change by changing color.

Heitman said he attended the event because he loves science. He is especially interested in robotics and wants to be a roboticist when he is older.

Christopher Kersey, manager of the observatory, said it’s important children be introduced to physical science as soon as possible. He said the events of the day were geared toward children, but adults learned as well.

“Adults are interested because these kinds of things weren’t around when they were in school,” he said.

original here.

Sunday, February 28, 2010

The Ratio Programmer needs to review his basic facts


Maybe this is the same guy that programmed the progress bar? From XKCD:

Thursday, February 11, 2010

It's not a factory.

Schools matter quotes a letter to the editor of the NYTimes:
"The Times notes that No Child Left Behind was unpopular "partly because it requires schools to administer far more standardized tests …". ("Experts Say a Rewrite of Nation’s Main Education Law Will Be Hard This Year," January 28). Education Secretary Duncan has announced that the Race to the Top national standards plan will include national tests linked to the standards, which means far more testing than we had with NCLB."
Okay. Let's stop here and discuss this for a second. NCLB was not vilified because it required testing, but because it mandated changes to the schools based on those tests, changes that would not fix the issue that those tests were thought to identify but didn't.

more:

Sunday, February 7, 2010

A million points of extra credit

Here’s a classic idea from 360:
Suppose you teach a course and you want to have 3 exams each worth 20% of your grade, homework worth 10%, and a final worth 30%. One way to do this is to set the midterms at 100 points each, the final at 150 points, and homework scaled to 50 points for a total of 500 points in the class.

So far so good, right? The problem with this is that if you offer extra credit you have to be careful not to give too much — you wouldn’t award 10 points for being the first to speak in class, right? (OK, you might, but that would be pretty generous.) So if you want to be able to offer smaller amounts but not have them sound small, you need to have a larger total number of points.

How large? How about 1 trillion points! That ties in nicely to the scale of the national debt, which you can tie together with mathematical literacy and/or an interdisciplinary math/political science activity. Tests are now worth 200 billion points. The final is 300 billion. And now, if a student gives a good answer in class you can off the cuff award them one million points of extra credit! The student feels good — who doesn’t like to receive a cool million points in extra credit? — and you don’t even have to bother remembering to enter it in your gradebook. On the other hand, if there are little errors on an exam that you want to point out but don’t necessarily want to penalize (forgetting to write parenthesis, for example, so that 2·(3x+5) is written as 2 · 3x+5 ) you could take off 50 million points. That’s enough to get anyone’s attention.

I think in some of our classes this would be intimidating, so it’s probably not the best scheme in general. But in other classes, especially the upper level ones, I think our majors would see this as amusing and, perhaps, a help in internalizing the scale of some of these numbers.

Like I said, tempting.
If only gradequick allowed for it.

Saturday, January 30, 2010

The State of the Climate Debate

Is this the best they can come up with?
Temp is -12 global warming degrees F up the mountain at Killington today. Think I'll just ski half a day, have a couple of beers and some chili, and drive back to NYC.
or:
Late Thursday evening, in the hour before midnight, I found myself driving home from the airport amidst howling winds, blowing-and-drifting snow, and rapidly-falling temperatures. Watching the temperature dropping on the display of my truck's exterior-monitoring thermometer, an interesting and possibly didactic exercise occurred to me:

Ponder the following three factoids:
o The long-term average high temperature for this time of year (at the BTV airport reporting station) is 27F;
o Monday, the temperature reached into the low 50s;
o Friday (yesterday), the temperature struggled to reach into the low single-digits.

Do the math and ponder what these things tell you about the nature of the underlying "system"....

I know that this is supposed to be a clever rebuttal of the Climate Change theory, but I just can't bring myself to do anything but laugh at it. What a pathetic attempt.

I'm glad I don't live near the ocean in one of those low-lying cities like New York or Los Angeles. Though, to be able to travel by ship through the Northwest Passage which has opened for the first time in memory would be cool ...

Monday, December 28, 2009

Juxtaposition, Graphics, Lying Like a Rug

It's amazing what you can do with statistics. ("Lies, Damned Lies, and Statistics.") Here's a sample:



Funny how the addition of a graph makes a point stronger, while not necessarily making anything clearer or more correct.

The problem with this graph is its simplicity - those are not the only pertinent bits of information at play.

Teachers often can be incredibly one-sided and have too much effect on students by asking questions that require agreement with a false premise before answering. I have heard variations of all of these questions as I have passed by open classroom doors ...
  • Did Clinton cause that improvement on his own or did the computer age have more of an effect on the economy?
  • Did Bush really destroy the economy or were these events out of his control?
  • Did Bush know that his failures, including "Mission Accomplished", would come back to haunt him and his legacy?
  • What should Bush have done differently in the last six months of his Presidency?
  • Why didn't Bush do something while the economy imploded?
  • Is it a coincidence that Democrats have grown the economy while Republicans have not?
  • Since Democrats grow the economy,as seen in the graph above, why shouldn't we pass Health Care reform and save the lives of those less fortunate?
Why is this okay? Is it just because too many people are innumerate (to use Paulos's word for it) that this kind of thing is promoted and passed on?

Just sayin'.

Thursday, December 24, 2009

Politicians can't Do Math, or Risk Analysis

Based on absolutely no evidence other than a nagging feeling that there might be something in that whiny voter's complaint, a Maine senator wants force companies to put a warning sticker on the back of all cellphones, warning of radiation.

Let me summarize:
1) Some low-grade moron has a vague feeling that the tiny bit of radiation from the cellphone is dangerous because you held it to your head for 400 minutes a month (0.8% of the time for a radio transmission that MIGHT travel 3 miles) yet the radio transmissions from all those radio stations are okay (for signals that travel a couple hundred miles and are broadcasting 24/7/365 -- right through your head).
2) No one has been able to show causation in studies. In fact, most of them show that cellphone users have a LOWER brain cancer rate than non-users.
3) Handheld or not, the cellphone is as dangerous to use while driving as four shots of whiskey in a teenager. (DUI crash rates are on par with cellphone crash rates)
4) texting while driving is something like 25times as dangerous as driving with friends piled in the car, and 6-8 times as dangerous as DUI.
5) the sound levels on iPods and other MP3 players drastically reduce the attention and awareness of the teenage driver. Surprisingly, playing the radio does not have nearly the same effect.

Given all that, they want to warn about cancer.

Spare me.

reposted Yahoo article below the fold:

Wednesday, December 9, 2009

Closing Schools - Now what?

Pissed Off: Out Of The Mouth Of Babes says:
The kids were all abuzz about some of the borough's schools being closed. They were worried that these kids will now be coming to Packemin. They didn't understand why these schools were being eliminated. I told them about the school's poor academic records and their failure rates. The kids immediately piped up with "Bad kids are bad kids. So now they will all come here and bring our school down too. I bet we will be the next school closed."
Toles had it best:

Saturday, September 26, 2009

Time for Testing ... but not academics?


I'm worried about my kids' workloads.  I'd like to suggest that we trim some things from their to-do lists so they can concentrate on what's important.

I refer, of course, to the TEST.

I don't know about most of you, but here in the VT-NH-RI NECAP regions, we have AYP testing in the fall of the junior year. Many schools around here are getting antsy because their "didn't-make-the-grade"-checkmarks are being checked. Accumulate checkmarks in two consecutive years and you're on notice. Continue to not make AYP for any subgroup and your school is on double-secret probation. Administration might be forcibly changed. Schools might suffer sanction.

A school to the south of us is having eight days of one-hour delayed-openings ... for PRACTICE TESTING. Then they'll have six days of two-hour delayed openings for the actual tests. 9th, 10th and 12th have no school and are home sleeping for the extra hours. 11th are cramming for the test.

When did actual teaching take a backseat to the state-wide testing pogrom? When the principals started fearing for their jobs.

Few people other than the teachers and students make the connection that one of the major reasons that education is on the ropes is the tremendous number of things students miss a class for. I have kids with 10 excused absences already and it's only the 18th day of class. Sure, they're excused, but they're still not there.

Doctor's appointments, valid sicknesses (and the cough-cough days-off, Mommy calls the school), vice-principal call-downs for discipline, counselors who talk to them about their "issues" or who counsel them on getting into college (miss class to talk about going to college - don't you just love it?). Field trips and other teacher's projects. Assemblies for anti-bullying and harassment, watching the President, pepping up the cheerleading section, Prepping for the NECAP tests, staying off drugs (as presented by seven steroid-laced muscle-bound men who stress that they've 'never done drugs'), not driving drunk, watch out for STDs and creepy Internet pedophiles. MADD, SADD, SMILE and WORLD OF DIFFERENCE taking various kids for one, two or three full days.

Then you've got in-class suggestions to "drop everything and prepare for the NECAP test" three weeks from now, not to mention the idea of giving the 9th, 10th and 12th graders time to sleep while the 11th graders practice test-taking strategies, and then six more days when they're actually taking the test. And the principal opines that it's not fair for anyone to give homework during the testing days -- and then reinforces his opinion with a direct statement "I don't want you to give homework in any class that has an 11th grader in it." For math teachers, that's quite a few of them.

Throw in the random interruptions, sports excuses, part-time job, ill parents and kids in a pissy mood cause they're teenagers with active glands. Add the nurse call-downs for swine flu, or regular flu, or the school-based physicals.

NOW is when we're taking time off for testing?

Pretty soon the students have no time to spend concentrating on math and really, don't they have enough on their plate without also demanding that they learn that, too? Let's drop the math requirement and replace it with test-taking strategies and test-taking skills. That'll learn them.

Hmmmm ...

Or we could just teach and eliminate all the other silliness. Consistent, steady progress towards a goal. No distractions, just routine.

NAH. It'll never happen. This is education. Homey don't play that.

Wednesday, May 20, 2009

Help ! I'm confused. My math mojo is deserting me ...

Okay, here's the question. NEA sends out this blurb about germs in school and you just know there's stupid people involved. I'm reading the thing and seeing that the water fountain has 2 700 000 bacteria per inch.

Huh? Shouldn't that be "per square inch"?

Okay, maybe a misprint. I read on. "But the very worst, most disgusting, just say no for germ's sake, was the public sandbox, where NSF's analysts found a horrifying 7,440 bacteria per inch!"

Huh? Huh?

How is this the very worst? The water fountain is something like 4000x as much. The cafeteria plate that they eat off is twice the number! What the hell? With mathematical analysis like this, it's no wonder that elementary teachers don't find it necessary to do math or find it embarrassing when they screw up teaching fractions.

"I just don't DO math. Tee-hee-hee. Giggle."

Can't you just hear it now? "Let's make a silly crack about how video games are bad for you - 551 sounds like a BIIIIIG number!" Too bad it's one-third the number of bacteria on a typical student's hand.

"I don't DO fractions, either. Giggle. Snark."

Here's the link. Reposted below.

Eeek! There's a germ on my desk!


The bacteria and germs are out there, just not where you might think.


Even as fears of a flu pandemic fade, it's worth noting where all kinds of germs lurk in your classroom. In 2006, the non-profit NSF International took its microscope to two Michigan elementary schools to measure the general bacteria population on different surfaces.


Water Fountain Spigot
2,700,000

Cafeteria Tray
33,800

Cold Water Faucet
32,000

Hot Water Faucet
18,000

Cafeteria Plate
15,800
Computer Keyboard
3,300

Toilet Seat
3,200

Student's Hand
1,500

Animal Cage
1,200

* Units are number of aerobic bacteria per inch

This year, NSF's microbiologists widened their scope and swabbed surfaces in 26 public places. Thanks to your school custodians, schools starred in the comparison. School bus seats practically sparkled with fewer than 10 bacteria per square inch, as did books and basketballs. Still quite clean were desks, gym mats, and computer mice.

But leaving schools behind, they found a little germ factory on the video game controls in movie theaters-551 bacteria per square inch. (Proof that those games aren't so great for mind AND body.) But the very worst, most disgusting, just say no for germ's sake, was the public sandbox, where NSF's analysts found a horrifying 7,440 bacteria per inch!

Fortunately, your classroom doesn't resemble a sandbox. And it's not too hard to keep it from breeding like one. Check out these tips from veteran custodians on fighting germs in the classroom.

Those who can, do. Those who can't, teach teachers or run their union.

Friday, January 23, 2009

Geometry Fail

In honor of PO'd Teacher's Uniform Geometry Exams being so "clever" ...

 
I thought I'd add a question for it ... Does Mr. AP look good in a tophat?

Wednesday, January 7, 2009

AP Science writer can't do math.

Well, he IS a reporter. He should have known better because he covers science for one of the largest press organizations in the world, but I guess we can forgive him because he writes for idiots - the American public.

Aside from making fun of his idea of percentages, does anyone else gets annoyed by the hyperbole around teen births rates that include adults?

I really don't care about the birth rates for "teenagers" who are adults and who have completed high school and possibly even gotten married. At 19, you're responsible for yourself and should be able to have children if you want without some blowhard decrying your inability to live up to his standards.

Let's break out the 18s and 19s from this data.

Group the kids into 12-13, 14-15 and 16-17, if you insist on grouping. (I'd rather see what happens year-by-year, though). In this way, you have three groups that differ in more important ways and you don't lump adults with children: minors at puberty, minors just under the age of consent, and minors just over the age of consent.

Then I'll get the rage going if it's warranted.

(Those are numbers per thousand. The national average is 41.9 per thousand, or 4.2%)