add this problem to the curriculum

re:

r² is a multiple of 24 and 10. What is the smallest value?

Here, from a few weeks ago, is Stanislaus Dehaene on multiplication:

[O]ur intuition of quantity is of very little use when trying to learn multiplication. Approximate addition can implemented by juxtaposition of magnitudes on the internal number line, but no such algorithm seems to be readily available for multiplication. The organization of our mental number line may therefore make it difficult, if not impossible, for us to acquire a systematic intuition of quantities that enter in a multiplicative relation. (This hypothesis is supported by the fact that patients can have severe deficits of multiplication while leaving number sense relatively intact; in particular, patient NAU (Dehaene & Cohen, 1991), who could still understand approximate quantities despite aphasia and acalculia, was totally unable to approximate multiplication problems).

This passage precisely captures my experience learning arithmetic.

Addition and subtraction make intuitive sense to me; multiplication and division do not. It's really that simple. For me, "math" - math as opposed to simple counting - begins with multiplication and division.

This observation brings me to a corollary: people always say kids fall off the math cliff when it's time to learn fractions, but I think the math cliff comes sooner. I think the math cliff is multiplication, only nobody knows it.

Nobody knows it because falling off a math cliff isn't like falling off a real cliff; with a math cliff, you can walk right over the edge and just hang there for awhile, suspended in mid air, like Wile E. Coyote.

The real drama comes after the fall, which is when kids finally get to fractions. Fractions aren't the cliff, and they aren't the fall. Fractions are the crash-landing at the bottom.

At least, that's my guess for the moment.

Setting metaphor aside, though, if it's true that we are not equipped with an intuitive understanding of multiplication and division, and I believe it is true, why don't more people know this?

Everyone knows fractions are hard; why doesn't everyone know multiplication and division are hard?

It's true most people perceive that certain aspects of multiplication and division are hard. Namely: memorizing the times tables is hard (for many children) and learning to do long division is hard (for many children). But I've never seen anyone take these facts to mean that there is something intrinsically challenging about multiplication and division in a way that is not the case with addition and subtraction.

Why?

I don't know, but I have some thoughts.

Which.... will have to wait. It's getting late, and I'm still trying to edit the body of this post into shape, so I'm going to set that aside and skip to the end, and just say that I think children should probably be taught to solve problems like the one above, which appeared on the October SAT. I'm pretty sure problems this can be used to find out whether students are suffering associative interference between addends and factors, which I bet an awful lot of students are no matter how quickly and accurately they can construct factor trees.

I'm also thinking more attention should be paid to teaching young children the terminology of arithmetic: addends, subtrahends, factors, and the like. I think -- I don't know -- that fluency with the terminology might help reduce associative interference. "All math looks alike": the 5 and the 2 in 5+2 look exactly like the 5 and the 2 in 5x2. But the words addend and factor have nothing in common whatsoever.

More later.

what is SAT math?

I'll be interested to hear from all of you if I'm wrong about this, but as far as I can tell, SAT math is middle school competition math.

It's hard math for middle school.

If C. and I had worked our way through Art of Problem Solving's Competition Math for Middle School, neither of us would have gotten stuck on the factoring problem we both got stuck on:

r² is a multiple of 24 and 10. What is the smallest value?

Competition Math for Middle School, a book for mathematically gifted middle schoolers, explicitly teaches the answer to this question:

441, 256, and 576 ... are all perfect squares. If a number is a perfect square, each of the prime factors will have an even exponent in its prime factorization.
J. Batterson, p. 139

Leafing through the two books, I am struck by the the amount of explicit, procedural teaching directed to mathematically gifted students. No one's asking them to figure these things out or to "problem solve." Instead, they're being directly told that all of the prime factors in a perfect square will have even exponents.

Ditto for the how many diagonals in an n-gon, a perennial favorite amongst SAT math writers these days, it seems.

correction: My wording above -- explicit, procedural teaching -- implies that these books teach procedures instead of concepts. That's not at all the case and isn't what I meant to convey.

What I meant to convey was the fact that gifted middle school students aren't being asked to figure out  concepts for themselves; they're being explicitly told how the problems work, and why.

Courtney James

re: what to do about C. and calculus, Crimson Wife writes:

I have no personal experience with him, but I have heard numerous raves about Courtney James' tutoring from fellow moms in our local homeschool support group. He tutors AP Calculus BC according to his website. 

Exciting!

help desk help desk help desk help desk help desk help help help

arrghh

First of all: once again, I'm sorry to be MIA -- I'm looking forward to becoming a regular on my own blog some time again soon.

Second: help! help!

C's second calculus test came back today: a disappointment, and a Bad Sign. And I am fresh out of enthusiasm for dealing with another year of high school math. Meaning: I am fresh out of enthusiasm for dealing with high school math teaching and high school math grading and high school math hiring of high school math tutors to remediate high school math grading and high school non-learning of high school math and on and on and on and then further on and on some more.

I'm done.

Also: calculus tutors are few and far between. I found only one last year, and the lone session he had with C. didn't help. Other parents have told me they couldn't find calculus tutors, either, and for years I've been hearing things like: "My son did well in BC Calculus. We were lucky because his father can teach it." As I recall, the mom who told me her husband could re-teach BC Calculus at home also told me that her husband's first cousin was an economist who had won the Nobel Prize. I'm pretty sure I'm not making that up.

Nobody in this house can teach calculus. I haven't even finished taking algebra 2, and Ed has forgotten the calculus courses he took in high school and college and doesn't care to revisit them.

So here we are.

Also - and this is a repeat - last year's math class was a total, effing disaster. The teacher was and is seriously ill but is still teaching, and the kids were and are dropping like flies. A huge percentage of last year's AP Calculus AB students got 1s on the AP test. Ones. And when I say "huge percentage," I mean eighty-five or ninety percent: the guy broke the bell curve. This was the teacher C. had for pre-calc, so C. is bringing to this year's calculus course an epic level of non-preparedness.

The teacher C. has this year is supposed to be fantastic and in fact told us he was fantastic on Back to School Night (he actually said: "I am it," which was exhilarating at the time), but if the grades are not great then the learning is not great, either. Fantastic is as fantastic does.

Ed is thinking we should just transfer C. to AP Stat (or maybe it wouldn't even be AP Stat - maybe just "Stat Honors," a class in which, according to C., students recently took a test on bar charts after completing a bar chart project) and be done with it.

That's pretty much how I feel, too, but it leaves the problem of algebra 2 and calculus, neither of which C. will have learned in high school -- and neither of which I want him taking in college since he'll likely be attending a school with kids who are a lot better than he is in math. At this point it is crystal clear to me that there is no reason on Earth to take a math course in college, pay for it, get a bad grade in it, and not learn any math. And I'm thinking the same principle holds true for high school. Why spend a single second of your (child's) life in a non-required math course so he can not learn math?

Last data point: C. did fine on the first test in the class and thought he did well on this test, too. He did great on the diagnostic test going in, and is doing well in physics. His mistakes on this test appear to be mostly "careless errors" (I have a whole new take on the nature of careless error thanks to the SAT) and a failure to follow correct notation, etc. In short, he appears to understand the material, not that I would know.

Of course, if that's the case then he needs more practice - but how do we swing that? The teacher doesn't seem to use a textbook, and I'm not going to be able to scrounge useful practice sets this go-round as I did for the 3 years when C. was in middle school.

(Could I talk to the teacher? Why, yes indeed I could talk to the teacher. But seeing as how talking to a math teacher has yielded exactly zero results over lo these many years, talking to the teacher wasn't my first impulse. Writing a help desk post was my first impulse.)

So...any thoughts?

We had a great, great precalculus tutor last spring at the very end of the school year; if we'd hired him at the beginning of last year, C. might have learned pre-calculus. We could hire him again (I assume) and decree that this year C is actually going to learn pre-calculus, which means we could pay tuition for C. to study bar charts at his Jesuit high school and pay tutoring fees for him to study pre-calculus here at home --- who says Americans have to de-leverage?! If you've got kids in school and you want them to learn math, deleveraging is not for you!

Or....or what?

What else is out there?

He could enroll in a community college precalculus course -- when?

Now? While he's in high school? (While he's in high school commuting 15 miles there and back every day?)

Then take calculus over the summer?

Another question: are there solid precalculus and calculus courses online? I took all of the ALEKS geometry course and part of the ALEKS Algebra 1 course, and as much as I want to like ALEKS, as much as I do like the tone and feel of the site, I don't think ALEKS replaces a good teacher or a good textbook. But do others out there think that might be the way to go?

What about online schools and colleges? I know there are universities that offer online math courses that kids take when they've been expelled or can't physically attend their local schools for some reason. Is that a possibility? Any recommendations?

And while we're on the subject, can anyone out there explain to me how in this country does a smart student with no discernible learning, attentional, motivational, or emotional difficulties whose talents and interests lie in history/social science actually learn some damn math?

What does it take?

'10 Reasons to Skip the Expensive Colleges'

On the heels of CassyT's post on America's Ten Most Expensive Colleges, here are some ideas on why you might want to avoid them.

'10 Reasons to Skip the Expensive Colleges'

America's Ten Most Expensive Colleges

America's Ten Most Expensive Colleges—And How Much Financial Aid They Provide
Via Good Education.

My husband is a 1985 graduate of #6 - Claremont McKenna,  where the average student currently pays $20,423 of the $55,865 sticker price.

Front page articles on the edtech bandwagon

Fast on the heels of a front page New York Times exposé on how education technology has failed to raise test scores comes a front page Education Week article on the virtues of replacing teacher-centered lessons at school with technology-centered lessons at home.  The technology in question is that of the Khan Academy, whose library of lectures and problem sets is impressive in its vastness but not in its instructional feedback. If you input a wrong answer to a math problem you are told that your answer is wrong, but not why, nor how to fix it. Despite this, the Khan Academy has empowered teachers like 10th grade biology teacher Susan Kramer to skip over direct, structured instruction, and instead to watch her students "weave through rows of desks, pretending to be proteins and picking up plastic-bead 'carbohydrates' and goofy 'phosphate' hats as they navigate their 'cell.'"

To be fair, the Khan Academy (1) hasn't been around that long and (2) is the creation of a former hedge fund manager with degrees in math, computer science, and engineering but not in, say, cognitive science and child development. As such, the Khan Academy hasn't profited from the "over 20 years of research into how students think and learn" that underpins more established educational software programs like Carnegie Mellon's Cognitive Tutor.

So it was a bit disconcerting to find, fast on the heels of the Edweek's Khan Academy article, a front page article in Sunday's New York Times on Cognitive Tutor, and how it, too, has turned out to have no statistically significant impact on test scores. While I'd never had a chance to try it out (unlike the Khan Academy, Cognitive Tutor gates access to demos and charges big bucks instead of nothing at all), I'd heard only good things about it, and J enjoyed soaring through its algebra lessons during middle school. But as soon as I read the Times' description of its pedagogy, its limitations became crystal clear:

When the screen says: “You are saving to buy a bicycle. You have $10, and each day you are able to save $2,” the student must convert the word problem into an algebraic expression. If he is stumped, he can click on the “Hint” button.

“Define a variable for the time from now,” the software advises. Still stumped? Click “Next Hint.”

“Use x to represent the time from now.” Aha. The student types “2x+10.”

A math buff would soar right through this; for anyone else, the hints seem way too much of a crutch. There's no mechanism here for ensuring that you're working things out to the best of your ability before resorting to "hint"---i.e., nothing to stop you from clicking "hint" the moment you're not sure what to do. And what if your answer is almost right: say you forgot to include the initial $10, or let x stand for hours rather than days? As far as I can tell (I've now tried it out a bit), you're either right or wrong, and that's it. The program simply isn't sophisticated enough to highlight exactly what needs adjustment. And there's a very simple reason for this. As I discovered in creating a software  program that highlights grammatical errors in English phrases and sentences, this kind of perspicuous feedback takes a huge amount of coding (of the sort that you don't find in any other language teaching software program, thank you very much). Programming in the analogous feedback for mathematical expressions and equations strikes me as even more prohibitive.

On closer inspection, therefore, Cognitive Tutor seems inevitably to foster--in all but the brightest, most motivated students (the ones most able to basically teach themselves)--far too passive of a learning environment for lasting learning. Indeed, the only truly active learning environment that I've ever seen in any software program for any academic subject is that which a computer programming language platform provides for--what else?--computer programming. Only here does the feedback--the error messages or the unexpected outputs--precisely reflect what you've done wrong.

Will these recent exposés about the limitations of educational technology for subjects other than computer science have any effect whatsoever on the edtech bandwagon?

We might as well ask whether recent cognitive science findings have had any effect on how schools teach "higher level thinking." Or whether mainstreaming kids on the autistic spectrum has had any effect on mandatory group work and personal reflections. Or whether parental concerns have had any effect on schools choosing Reform Math. Or whether, for that matter, the Pope is Jewish.

(Cross-posted at Out In Left Field).

Who is Christopher Columbus? (Ask an Aspie)

"I don't know."

The revelation in question happened in late August, but I share it today in honor of someone who appears to be fading from America's k12 classrooms.

I actually wasn't that surprised when, while reading with J about the Age of Exploration in The Story of the World, Volume 2, it emerged that he didn't know who Christopher Columbus was. After all, one of the main reasons I've been working my way through this four-volume series with him is that I know he's picked up very little world history in the course of his 15 1/2 years. But, while he's still mostly oblivious to the incidental factoids that float all around him, he's increasingly attending to school, and increasingly sitting in the same classes, doing the same assignments, and taking the same tests, as everyone else.

So while I'm guessing that most (all?) of his schoolmates not only have heard of Christopher Columbus, but also know something about what he's famous for, I'm also guesssing that none of them learned these things from a social studies class or reading assignment that made them their focus.

Indeed, in this age where it's anyone's guess which facts our schools are making it their responsibility to teach, it occurs to me that students like J--with their narrow interests and their tendency to tune out most of the ambient information that others soak up without deliberate instruction--are a valuable resource. Next time you wonder whether your school is actually teaching (rather than merely mentioning in passing) the Bill of Rights (say), or the Cold War, or the Silk Road, ask an Aspie. That is, look for a spaced-out, narowly focused child on the autistic spectrum who hasn't made the topic their personal specialty, and see what he or she can tell you about it.

(Cross-posted at Out in Left Field).

the college admissions process

Do you ever get the feeling that there's something going on that we don't know about?
Timothy Fenwick, Jr. in Diner

MSMI Saturday Session: Singapore 1 & 2

I just returned from MSMI's Saturday Session on Singapore Math 1 & 2, hosted by our very own Allison Coates.

Turnout was great and lots of important material was covered, with a particular focus on the importance of NUMBER BONDS.

I'm looking forward to next month's session on grades 3 & 4, which should be pretty bar model intensive.

Thank you, Allison, for a very useful and informative session!

Unemployed and $87,000 in student debt . . .

Maybe he should be occupying his university in addition to Wall Street.

Read more at Cost of College.

SAT reading vs math

If I had to come up with an artificial number of what constituted truly impressive combined scores on the recentered SAT I, I would say over 1,490 or 1,500. Those are still considered very high scores, ones that are not easy to attain, no matter how bright a student is.

I hesitate to give this example, because, as always, it is not the combined score that matters as much as the breakdown. It is still, as it has always been, more impressive to see high verbal scores than high math scores, since most students at the highly selective colleges will be doing much more writing and reading than math. Verbal ability is still a good indicator of how strong a reader the student is. The ability to read well will ultimately have a bigger impact on most college students than the ability to do SAT I math very well, especially since the level of SAT math is not particularly high. There are many students who do terribly on the SAT I math and yet who manage to get the highest score of 5 on the AP calculus exam. If any math is useful at the college level, it is calculus, not the basic math covered on the SAT I. Therefore, SAT I scores of 750V, 630M would be much more impressive for most highly selective colleges than a 640V, 780M, even though the latter score has a higher combined total by forty points.
A is for Admission by Michele A. Hernandez 1997

From what I can see, this view still holds true (though take my observation with a grain of salt).

I do wonder whether the high-end test prep industry may have actually increased the value of a high Critical Reading score, given that the reading test is the one you can't tutor.

I use the words "can't tutor" because those are the words everyone uses: it is extremely difficult to raise the critical reading score via tutoring, and everyone knows it, including college admissions officers presumably.  Nonetheless, I believe there are tutors who do raise reading scores.^*

But it's not easy.

My guess is that college admissions officers at highly selective colleges assume the parents bought 50 points on math, but the reading score came from the kid. 


^* I should probably add that C. wasn't tutored in reading. I have confidence in Erica because I've met her and I like her book.

Steven Jobs, part 2

my neighbor, Steve Jobs

(via Reformed Broker)

Steve Jobs, RIP

He brought the magic.

highly selective colleges

Here's what I've learned. Not earth shattering, but not completely obvious, either.

First of all, highly selective colleges, at least some of the time, are in competition with each other. In recent years Ed interviewed a boy who was accepted by two Ivy League colleges; his parents then negotiated a better financial package on the strength of the second acceptance. Speaking hypothetically, Harvard doesn't want its admits going to Yale, and Yale doesn't want its admits going to Harvard. (I'm not saying those were the colleges involved in this case.)

Second, one department or area inside a highly selective college or university may be faring better than another. That is to say, one department may be losing a disproportionate share of admits to another highly selective college or university than other departments are losing. I gather admissions departments track these things.

If that's the case and your child is interested in that area, he or she might have a better chance of being accepted than the global admit rate implies.

I don't know whether this information is "actionable," but I think it might be. For instance, it might be possible to find out figures on the number of majors a department has had going back over the past 10 years, say. If the department has seen a drop in majors, it is probably looking for students. (Obviously, academic departments don't make admissions decisions. Nevertheless, it appears to me that colleges want all departments to have students.)

I suspect college magazines may have useful information to share as well. Retirements of famous professors, for instance. When a well-known professor retires, the department loses a drawing card.

Another thing to look for: new programs being developed. It strikes me that new programs might imply a higher admit rate early on for interested students. And new programs will almost have to pull majors away from other departments, which may shift the odds for students headed towards those departments as well.

No other thoughts at the moment.

Dartmouth testing profile for perfect scores

Critical reading - 800
8.2% of applicants have 800 CR
32.0% accepted

Writing - 800
9.4% of applicants have 800 on Writing
30% accepted

Math - 800
16.2% have 800 on math
18.7% accepted

source: Dartmouth College Undergraduate Admissions

I wonder if there's a case of left-digit bias in these scores.

first-serve Debbie and death-march Cathy

As an aside: Cathy is my real name, the name I grew up with. I changed to Catherine when I was hired to teach at UCLA at age 27, I think it was. I looked the same age as my students, who called professors by their first names, so I switched to Catherine and have been Catherine ever since, except in Illinois, where everyone I know calls me Cathy.¹ Ed calls Illinois "Cathy-land."

Anyways, I am lollling reading Debbie's SAT post this morning:

"Not sure if those were the words that inspired my unplanned, last second, impulsive shift in strategy -- but I took SAT #5 in 2011, all in first-serves. I was aggressive. There was not one iota of perseveration in my game that day....I had a blast and enjoyed every second of the experience. I distinctly remember thinking as I colored in those first bubbles with that deliciously soft and perfectly sharpened #2 pencil, "This feels soooooo good."

Of course, I already knew this. Saturday afternoon, 2pm or so, as I was sitting at my kitchen table (where else?) in a stupor, Debbie called and said, re: the SAT we had both taken that morning, "Did you love it!?! I loved it!!!!"

Debbie is the single most enthusiastic person I have ever met in my entire life, and I say that as a person of extremely high enthusiasm myself. I have so much enthusiasm - my real name is Cathy !! - that until I met Debbie, I was the most enthusiastic person I had ever met in my entire life. Now I'm number 2.

Which brings me to: did I enjoy it?

Taking the SAT: did I enjoy it?

Answer: No.

I did not.

Not one bit, except for the guaranteed peace and quiet during the timed test sections: as a person working at home, I can see the value in having your own personal time-and-space proctor enforcing silence and an appropriate seating arrangement in 25-minute increments. I've always thought I needed an assistant, but I was wrong. I need a proctor.

The SAT, for me, was not a tennis match. Not that I've ever played a tennis match.² Where tennis is concerned, I am apparently a permanent taker of tennis lessons, not a player of tennis games.

The SAT, for me, was more like a death march, which seems to be what it is for a lot of actual high school juniors and seniors.

A death march to, I dunno, SUNY New Palz, maybe.<sup>3

1</sup> Well, everyone I know except for people I know through ktm.
²Debbie, btw, is an extremely good tennis player. Not that she will tell you this.
³ The only thing I know about SUNY New Palz is that's the college Anthony Weiner attended; I hope I'm not hurting people's feelings, and I'm very sorry if I have.

Harvard Admissions Meeting

This might go well with the discussion on getting perfect SAT scores. I realized from the SAT averages of Ivy League schools that they must go way out of their way to accept students with (relatively) lower scores. That's why many students with top scores don't get in. A friend of mine was in charge of an open meeting, sponsored by our state's Harvard Club, that talked about Harvard and the admission process. It also included a discussion by some current students from our state.

It started with a 20 minute video presentation that seemed to go out of its way to talk about how Harvard students are really just regular people - not some sort of elite. Well, they are elite regular people. That's the community they are trying to put together, and above a certain level of grades, other things become much more important.

So here is the issue. What does Harvard look for in a student? They don't want kids to apply just because it's Harvard or an Ivy League school. But after the meeting, I can't say that I know the answer to this question. They want a well-rounded school, but the admissions officer for the state claimed that each student can be "oblong". If you don't know what you want to concentrate in (they don't call it a major), then why would you want to go to Harvard? Because it's an Ivy League school? The admissions officer said that all Ivy League schools are different, but she didn't explain how Harvard might be different than Yale. It seems to me that if you made a case about wanting to be part of the work being done in one specific department at Harvard, that wouldn't be enough. Since most students don't know what they want to concentrate in, that's not really part of the admissions equation. They don't want you to apply because of their name or because it's an Ivy League school, but what else is there? They will decide if they want you based on their needs, not your needs. One of my grandfathers went to Harvard and one went to Yale. Why? Because one lived in CT and one lived in MA.

Someone once told me that the reason to go to an Ivy League school is for the people you'll meet and for the opportunities you might get. I realized when the students spoke that they were just talking about undergraduate courses. They were still figuring out what they wanted to concentrate in. Do they transfer to another Ivy League school when they figure it out? No. They wait for grad school.

In music performance, the goal is to find the best teacher to work with. You don't just blindly apply to Juilliard or Curtis. But then again, name, connections, and opportunities matter. It seems that the top schools want it both ways. They recruit based on their reputations, but students are supposed to pretend that it doesn't matter.

It's a "Math Flavored" Test

That's what PWNtheSAT told me after I screamed on the top of my lungs for the umpteenth time because I'd fallen again for some deception in the "Math Section" that wasn't even "math."

"Does that make you mad?" he asked.

"YES," I screamed.

"Good, then don't let them do that to you again."

And then he told me to think of the Math Section like shrimp flavored Ramen Noodles: there could be some shrimp in there, but really it's a lot of other "stuff." "That doesn't mean it's any less hard," he clarified, "Just different."

Not sure if those were the words that inspired my unplanned, last second, impulsive shift in strategy -- but I took SAT #5 in 2011, all in first-serves. I was aggressive. There was not one iota of perseveration in my game that day.

Last Saturday morning, at DeWitt Clinton High School in the Bronx, NY -- I discovered my inner "don't mess with me" self.

No idea what this means for my score, and thank god this doesn't really count for anything. I am very curious though, as to how this "backwards-Debbie" plan worked out, and I'd be lying if I didn't admit that I woke up the next day just a little bit scared.

Here's what I know for sure:

I had a blast and enjoyed every second of the experience. I distinctly remember thinking as I colored in those first bubbles with that deliciously soft and perfectly sharpened #2 pencil, "This feels soooooo good."

I will also say this: Every day I'm less sure about what, exactly, the SAT is testing. More and more it feels like a test of how not to be messed with -- especially the math (and least of all the writing).

And if that be the case (and I do believe that be the case), I'm going to highly recommend a book that I've highly recommended before: PWN the SAT Math Guide.

From the introduction:

"The SAT is not a math test........it's full of booby-traps, misleading diagrams, and intentionally difficult phrasing. Even questions that look a lot like straightforward algebra questions are put there not to see if you can do the algebra, but to see if you can spot the shortcut that lets you avoid the algebra.

.....Taking the SAT like you'd take a regular math test is like bringing a knife to a gun fight......

.....The SAT is a test, above all, of how good you are at taking the SAT......

Illustrations by Jennifer Orkin Lewis

Cross-posted on Perfect Score Project

death by calculator

So on Saturday I took the SAT, all 4 hours of it: another supposedly fun thing I'll never do again!

Over on College Confidential there are, currently, 65 pages of my fellow test-takers debriefing each other re: the Critical Reading passages.

How is management different from handling? jpegslayer wants to know. I don't recall management being a choice on the Ella Baker passage,^* but I do recall, dimly, selecting handling.

Also, there's a protracted debate over vehement vs caustic and emphatic vs disparaging. I have no memory of vehement vs caustic appearing anywhere on the test (apparently I was in a trance for parts of it), and I chose emphatic over disparaging.

People thought the Fleece passage was HARRRRDD (Akil found it here), which it was. Hard and odd...pretty much hard because it was odd. Odd and truncated, which made the thing odder still.

Question: was Fleece urbane or eccentric?

Answer: he was eccentric. I say he was paranoid, too, but the College Board and I may not see eye to eye on that one.

As to the rest of the test, C. and I both had math calamities, sad to say. C. choked on the one hard section of the three: got stuck on an early problem, lost track of time, and ran out the clock without even having read 5 of the problems, let alone tried to answer them. Classic, and so frustrating.

My own difficulties were self-inflicted.

I started down the path to ruin on Tuesday, when Debbie told me about the math frac function on the TI-83: PWN says you have to have it! Well, if PWN says you have to have it, then you have to have it because PWN knows everything about the SAT. (Really. He does.)

Trouble was: I didn't have it. A TI-83, that is. I have a lowly TI-36 I've been using for years and know so well I can practically touch-type the thing.

So I called Ed at NYU and asked him to pick me up a TI-83 on the way home. He said he would, but for some reason or other he didn't, which meant one less day to get up to speed on the TI-83 assuming he managed to get one on Wednesday.

He did, but it was sealed inside one of those monster pressure-sealed jobs that are impossible to open, and I didn't get around to dealing with it 'til the next night - Thursday - when the plastic proved so tough I actually cut myself with the scissors I was trying to jam through the packaging. In hindsight, that was a sign.

By the time the TI-83 was finally liberated from its packing and I had staunched the bleeding, it was 8:30 or so, and I was in no mood. At which point it emerged that C. didn't know anything about the math frac button(s) and couldn't show me how to use them.....so Debbie stopped over on the way home from her daughter's back to school night and spent 10 minutes explaining the thing.

That left one day - Friday - to practice.

In my defense, I did try reminding myself that one day of practice on a calculator with a different keyboard, different functions, and different locations for the same old functions (different notations, too) was not going to overwrite 5 years of practice with my trusty TI-83: I know this! I am a science writer, for god's sake! I write stuff about the brain! Stuff about the brain and learning and memory!

But I just kept thinking: math frac. Got to, got to, got to have math frac.

Oh, man.

Long story short, I got to the test, took the first math section, the hardest of the three (well, four in my case since my experimental section was also math) and stumbled and tripped over one problem after another when I couldn't remember where the Enter key was (or even that there was an Enter key), or which side the Power key was on, or how you do square roots on the TI-83 (hit the 2nd key; square root key is on the left, not the right) or exponents (use parentheses), etc., etc., etc. And since working memory can hold only 3 or 4 things at a time, plus or minus two, and "where's the Enter button?" counts as one (at least), I'd have to forget some key part of the problem I was trying to solve in order to clear enough mental space to remember how to work the calculator, so then I'd have to re-read the problem to re-remember whatever I was remembering before I had to forget that to remember the calculator, and then when I was done re-reading and re-remembering the problem, I might discover I had now re-forgotten how to work the damn calculator, which meant I would have to re-forget the problem to clear space to re-re-remember the workings of the TI-83 ----- aaaaaauuuugggh! Stuck in an infinite forgetting and remembering loop! Help! Help!

I switched back to my old calculator for the other three sections, and things went much better.

Later, hearing the story, Ed said, "I was afraid of that."

^* The Ella Baker passage made my eyes bleed.

Wu on Common Core State Mathematics Standards

Phoenix Rising

Opening:

Many sets of state and national mathematics standards have come and gone in the past two decades. The Common Core State Mathematics Standards (CCSMS), which were released in June of 2010, have been adopted by almost all states and will be phased in across the nation in 2014. Will this be another forgettable standards document like the overwhelming majority of the others?

Perhaps. But unlike the others, it will be a travesty if this one is forgotten. The main difference between these standards and most of the others is that the CCSMS are mathematically very sound overall. They could serve -- at long last-- as the foundation for creating proper school mathematics textbooks and dramatically better teacher preparation.

http://www.aft.org/pdfs/americaneducator/fall2011/Wu.pdf

Wash U professor on Reed Hastings' really bad idea

As a physicist, educator and father of five, I can say that Messrs. Duncan and Hastings do not understand education or the role of computer and Internet technology in it. A well-thought-out textbook or a live classroom demonstration does a much better job of conveying understanding than anything that can be done with computer or Internet technology.

Anyone who has watched students using these technologies will recognize that they are distractions from the hard work of education.

Jonathan Katz
Professor of Physics
Washington University
St. Louis

More technology isn't the answer to our educational needs
WSJ | September 24, 2011

Speaking of well-thought-out textbooks, one of the most oppressive aspects of "technology" in the schools is the replacement of textbooks by packets, which are fantastically difficult to keep track of, not just for the student but for the teacher, too. I speak as a creator of packets: I'm driving myself crazy.

It wasn't always thus. Back in the day, teachers ran off those damp, great-smelling, purple-print mimeographs. But mimeos were a limited production; teacher packeting didn't take off until the advent of the Xerox machine. I predict things are only going to get worse as people start buying personal scanners.

Add Google to photocopiers and scanners and you get all-packets-all-the-time. What a mess. Yet another rolling calamity on the horizon!

I tutor a boy in a neighboring town who doesn't appear to have a math textbook at all, and not because the school is using Terc. Last I heard, the school is using Terc, but the only book the teachers are actually using (it appears) is a test prep book from one of the test prep book companies. The teachers Xerox one-page review lessons out of the test prep book for the kids to collect in their binders. The paper-punch holes last a couple of weeks, then the sheets tear loose and slip out of the binder and down to the bottom of the backpack, where they live until the summer, when Mom goes through the crumpled wads of paper and tosses it all out.

Or, alternatively, when Mom goes through the crumpled wads of paper and discovers her child has failed two out of six units in math this year. On fractions! tofix to revise to fix torevise

Speaking of worksheets, does anyone know where to get a complete set of Prentice-Hall's fantastic grammar worksheets? (pdf file)

and see:
the founder, chair, and CEO of Netflix has a really bad idea
Larry Summers has a really bad idea
Wash U professor on Reed Hastings' really bad idea

David Brooks has a really bad idea
David Brooks has a really bad idea, part 2
David Brooks has a really good idea

why students have to memorize things
extremely fast learning & extended working memory

'you can't hide from math and statistics and be a good marketer'

In the growing field of data analytics, finding "qualified candidates has proven difficult" for employers.

Is data analytics the new 'plastics'?

A different view of first grade Readiness

A recent post at Free Range Kids led me to this post,
which has a checklist for testing if your child is ready for first grade.

1. Will your child be six years, six months or older when he begins first grade and starts receiving reading instruction?

2. Does your child have two to five permanent or second teeth?

3. Can you child tell, in such a way that his speech is understood by a school crossing guard or policeman, where he lives?

4. Can he draw and color and stay within the lines of the design being colored?

5. Can he stand on one foot with eyes closed for five to ten seconds?

6. Can he ride a small two-wheeled bicycle without helper wheels?

7. Can he tell left hand from right?

8. Can he travel alone in the neighborhood (four to eight blocks) to store, school, playground, or to a friend's home?

9. Can he be away from you all day without being upset?

10. Can he repeat an eight- to ten-word sentence, if you say it once, as "The boy ran all the way home from the store"?

11. Can he count eight to ten pennies correctly?

12. Does your child try to write or copy letters or numbers?

What jumped out at me from it was the insanity in both directions: 1) academic skills that now indicate readiness for preschool, or at latest, kindergarten, were 30 years ago indications of being ready for first grade, and 2) life skills that now indicate readiness for middle school were indications 30 years ago that a child was ready for first grade.

We're pretty conscious that we've pushed the academics far far earlier on our kids, because by and large, we now value academics as the only path to successful adulthood (whether true or not, who is going to take the risk it's true and not prepare their children accordingly?), but by denying them independence, we're creating perpetual adolescents in the process who won't be successful at adulthood.

What child today would be expected to handle walking or biking 4-8 blocks at the age of 6 or 7? What parent would allow their child to do so? What would happen to that parent? How would a parent even begin to teach their child that autonomy these days?

The list makes clear the prior division of labor: the home was where socialization and citizenship was taught, and school was where the 3 Rs were taught. The expectation was that the family did their job, and the school would do theirs.

It may be causal that the schools now fail because the family failed. It may be a feedback system where the family fails because the schools fail. But we should ask ourselves if we really think the State can succeed where the family has failed, and if so, what it will do to what few functioning families remain. Because the State has no interest in your child having enough autonomy to ride his bike a mile from home at the age of 7--in fact, the State's interests are counter to that proposition.

The founder, chairman, and CEO of Netflix has a really bad idea

In last week's Wall Street Journal: A Digital Promise to Our Nation's Children.

Annotated.

Student achievement and educational attainment have stagnated in the U.S., and a host of our leading economic competitors are now out-educating us. [now?]

[snip]

Imagine, though, an online high-school physics course that uses videogame graphics power to teach atomic interactions, or a second-grade online math curriculum that automatically adapts to individual students' levels of knowledge.

[snip]

At its full potential, technology could personalize and accelerate instruction for students of all educational levels. [or not]

[snip]

Other countries are far ahead of us in creating 21st-century classrooms. South Korea, which has the highest college attainment rate in the world, will phase out textbooks and replace them with digital products by 2015 [note: products, not books]. Even Uruguay, a small country not known for leadership in technology, provides a computer for every student.

It is no secret that advances in educational technology have been hailed as breakthroughs in the past, only to disappoint. [true] Too often, the market for educational technology has been inefficient and fragmented. The nation's 14,000 school districts, more than a few of which have byzantine procurement systems, have been inefficient consumers and have failed to drive consistent demand. [we have to buy more technology?]

[snip]

To help remedy those gaps, the Department of Education is launching a unique public-private public-vendor partnership called Digital Promise.

Digital Promise is a bipartisan initiative that will be sustained primarily by the private sector [which will be sustained by a more efficient, less fragmented market and consistent demand] ... Federal seed money will fund the program's start-up, but it will be overseen by a board that includes business executives vendors—such as John Morgridge, the chairman emeritus of Cisco, and Irwin Jacobs, co-founder of Qualcomm—who will work with researchers, educators and other private-sector leaders vendors.

Digital Promise's aim is ambitious: to advance breakthrough technologies that transform teaching and learning in and out of the classroom, while creating a business environment that rewards innovation and entrepreneurship [for vendors].

Digital Promise can show leadership in areas such as helping build a more efficient market for [vendors of] education technology.


Arne Duncan and Reed Hastings
September 19, 2011 - WSJ
Mr. Duncan is the U.S. secretary of education. Mr. Hastings is the founder, chairman and CEO of Netflix and a former president of the California Board of Education.

One word: dismal.

and see:
speaking of technology and stagnant scores
oh brave new world!
codswallop, part 2
the founder, chair, and CEO of Netflix has a really bad idea
Larry Summers has a really bad idea
Wash U professor on Reed Hastings' really bad idea
David Brooks has a really bad idea
David Brooks has a really bad idea, part 2
David Brooks has a really good idea

E.D. Hirsch explains cause of decline in SAT scores is content-light instruction

Average SAT scores fell this year, with critical reading results declining to the lowest on record.  E.D. Hirsch writes that the main cause is a move away from content-rich instruction in the elementary grades.

The decline has led some commentators to embrace demographic determinism — the idea that the verbal scores of disadvantaged students will not significantly rise until we overcome poverty. But that explanation does not account for the huge drop in verbal scores across socioeconomic groups in the 1970s.

The most credible analyses have shown that the chief causes were not demographics or TV watching, but vast curricular changes, especially in the critical early grades. In the decades before the Great Verbal Decline, a content-rich elementary school experience evolved into a content-light, skills-based, test-centered approach.

Daniel Willingham on this subject:

More: How Knowledge Helps - It Speeds and Strengthens Reading Comprehension, Learning—and Thinking (Cross-posted at Cost of College)

In a van down by the river

I had to go to the high school with my son last night for a mandatory program for everyone involved with athletics and extracurricular activities. A parent had to attend with a student. It was on "chemical health" and it included a motivational speaker - a basketball coach. At the end, everyone had to sign a "contract". I assumed that the message was going to be more sophisticated than when I had to watch "Refer Madness" in 1969. Only a little. All I could think of was Chris Farley and the SNL skit. A large part of the talk was to emphasize Determination, Respect, Enthusiasm, Attitude, Motivation, and S for something. All of that is fine, but he made a big pitch for how college is now mandatory for success. He gave the usual statistics, except for the ones which show increased college loan defaults because the degree hasn't helped. He made it seem that not going to college was two steps away from living in a van down by the river.

the Oxford comma

For years I have resisted dropping the final comma in a series.

E.g.: lions, tigers, and bears versus lions, tigers and bears

If there are three things, I use two commas. I don't know why.

Now I do.

AWOL!

Sorry to be -- fall now involves three treks to the Open and the start of my composition class, and I'm just beginning to get my bearings.

I am in the process of officially transferring my allegiance from Roger Federer to Novak Djokovic.

Speaking of Novak Djokovic, I think I need a pressurized egg.

Under activist investor pressure, McGraw-Hill to split into two listed companies

The breakup of the mini-conglomerate follows public demands starting in July from the Ontario Teacher's Pension Fund and hedge fund Jana Partners LLC for a broad reorganization. The activists suggested breaking up the company into more than two pieces to highlight the value of its individual equities, commodities and financial analytics units.

http://www.reuters.com/article/2011/09/13/us-mcgrawhill-idUSTRE78B1Y620110913

These activist investors comprise about a 15% (so far) stake in the company. McGraw-Hill, in case you didn't know, is a major publisher of "integrated math" and "Everyday Math" books.

Activist investing is an interesting strategy in educational reform; in this case it appears to be the unlikely alliance of teachers (with educational interests) and a hedge fund (with a financial interest). Even with a small, but significant stake, you can nucleate other shareholders around you and force management votes and proxy battles, and cause massive headaches for management, who will often have a large risk of being voted out.

Even if voting out does not occur, management will often make such concessions to activists as reform of their company policies and educational products, or even various monetary "greenmails"; activists can then use this money to multiply their leverage against other targeted companies.

Time Flies

Hey, remember this kid?

He's starting Singapore Math on Monday.

Free access to expanded version of U.S. News college rankings

Free access is courtesy of Google.  Hurry, because this offer expires  Thursday, September 15!

Today, U.S. News and World Report released their 28th annual ranking of the top higher-education institutions across the nation. While this list of schools represents traditions of academic excellence that span centuries, these institutions also clearly recognize the importance (and value) of modern technology in academia. Google has just announced that 61 of this year’s top 100 universities have chosen Google Apps for Education to improve communication and collaboration on campus.
Free Access To Rankings From Google
To show their appreciation to these schools, and to help students better explore and evaluate their college options, Google is providing a year’s worth of free access to the U.S. News complete rankings for anyone who registers before Friday, September 16. Just sign up and you’re all set.

(Cross posted at Cost of College)

9/11

On 9/11, Jimmy's teacher called and told me to come pick him up. The high school was in chaos, she said; they'd had word that a former member of the staff had died in one of the planes, and teachers and kids were crying. Jimmy, then 14, was big and difficult and had attended the school for just 5 days, the first severely autistic student ever to enroll. His transition was going badly, and there was now no chance they would be making headway on that front today. 

When I got there, the teacher told me her babysitter had called: there'd been an attack on Fort Smith, up near her house. I'd never heard of Fort Smith, and I had no idea where it was, close or far. "Pick up all your kids," the teacher said. So I did.

Christopher was in the lunch room when his name was announced along with the name of our neighbor's son, Christopher's friend. There was a mix-up about who the other boy's teacher was, so Christopher told the grownups the right teacher's name, and then he was sent out to me.

I have no memory of greeting him that day. Where were we? In the school lobby? On the steps out front? Those moments are gone. My memories of 9/11 are like the movie Inception, where one of the signs the characters are dreaming is that they don't know how they got wherever it is they are now. That's 9/11 for me. In one memory I'm standing in front of the high school talking to Jimmy's teacher; in the next I'm walking with Christopher on the sidewalk at the far end of the school parking lot, the end close to my friend K's house, trying to think how to tell him about the airplanes hitting the towers and the towers falling down and realizing I should have come up with a plan about how to do this before I got here. Instead, I'm winging it.

In the next memory, I can hear myself saying, "Something bad happened," and after that there's another jump cut, and now Christopher is asking me anxiously what the country can do. I don't have a plan for handling this part of the conversation, either, so Christopher, sensing he's on his own, is trying to figure it out for himself.

We go back and forth a little bit about the things America could do, nothing I say providing the slightest reassurance or comfort, until finally he asks: "Do they have any really tall buildings?" Meaning: Do they have any really tall buildings we can knock down? His little face, ringed with curls, is tense and worried, but his voice is hopeful. He is seven, he has been in second grade for five days, and if we have lost two buildings, then it is right for them to lose two buildings, too. But the buildings have to be really tall.

"No," I say, "they don't," and he looks stricken. I am stricken, too. Something bad has happened.

Later on, that day or another day, Christopher worries that something bad will happen to the Statue of Liberty, too. What if the terrorists crash an airplane into the Statue?

I wonder what was my answer. Something with too many words, I'm sure. They probably won't try to hurt the Statue, but even if they do try the army is watching, and they won't let any planes crash into the Statue, etc., etc. My point being: the Statue is safe. Also, we are safe.

But Christopher isn't listening. He has come up with his own answer.

"If the terrorists crash into the Statue of Liberty," he says, "it will be OK. The French are so nice, they will give us another one."

It is the right answer, and he doesn't worry about the Statue again.

The meaning of an expression?

I have a question about an Integrated Algebra homework assignment:

In 3-10, state the meaning of each expression in part a and in part b, and simplify the expression in each part.

The first two problems:

3.  a.  20 + (6+1)    b.  20 + 6 + 1

4.  a.  18 - (4 + 3)   b.  18 - 4 + 3 

What does "state the meaning" mean?  I suspect it means to write the equation in words, as explained in this Yahoo Answers response offered by a teacher.

Also, I noticed that every homework exercise in the textbook has a "Writing About Mathematics" section.  I wonder if the teacher will correct all the writing assignments.

Lots of writing ahead.

The book is Amsco's Integrated Algebra for New York State.

no change in ACT math scores

speaking of rigged...

change in SAT math scores:

Between 1996 and 2005, the average [SAT] mathematics score increased for all racial/ethnic groups. During this time, the score for Asian/Pacific Islander students increased by 22 points, from 558 to 580. Mathematics scores for White, Puerto Rican, and American Indian/Alaska Native students increased between 12 and 16 points, while Black, Mexican American, and Other Hispanic/Latino students experienced smaller increases, between 3 and 9 points. (p. 77)

no change in ACT math scores:

Unlike SAT mathematics scores, ACT mathematics scores have not increased over time. (p. 81)

geography

The majority of students who take the ACT live in the Midwest, Rocky Mountains, Plains, and southern regions of the country (ACT 2005a). The SAT is more prevalent on the east and west coasts and in the Northeast (SAT 2005a).
p. 76
Status and Trends in the Education of Racial and Ethnic Minorities
National Center for Education Statistics
September 2007

Should American parents have their kids take the ACT?

rigged

Someone I know spoke last night to an admissions person at a highly selective college.

The admissions person said that highly selective colleges here in the U.S. have been admitting numerous students from China because their resumes are so strong. Spectacular scores, spectacular grades.

Then, when the students arrive at the highly selective colleges, their professors discover that they aren't prepared and can't do the work.

What these colleges are seeing, the admissions counselor said, is "systematic cheating." Those were his words.

Another thing: these highly selective colleges have been led to believe that the Chinese government is paying full fare. But no. The students have a bit of money from the Chinese government, but nothing close to what they need, and their parents can't afford to make up the difference.

So there they are, in America, enrolled in the most selective colleges in this country. They can't do the work, and they can't pay the tuition.
  
update: no change in ACT math scores

Functions

I recently added some links for problems to my previous two posts on algebra review and rational roots. Today I'd like to post about functions.

The appropriateness of when to introduce the function concept varies depending on the views of the individual instructor and the student population one is working with. I value the importance of the function concept and notation, but feel that teaching the function notation and the “vertical line test” without follow-up material relating to curve analysis (max, min etc.), composition and inverse, and transformation of functions is of questionable value particularly in the case of a gen. ed. math course that is to be taken by a broad range of students.

I've found that it is possible to discuss many topics related to the behavior of polynomial, rational, exponential and logarithmic functions without the additional two or three days of material required to introduce the function notation to a gen. ed. student population.

Given time, I like to cover functions by introducing the basic notation, followed by curve analysis in which the concepts of increasing and decreasing behavior, as well as maximum and minimum values are discussed. I then like to address function composition and inverse, the transformation topics (which can be somewhat tricky for students) and finish with a unit on the application of functions to a range of optimization problems common in many Calculus courses. I typically have the students use the TI 83/84 calculators to find the maximum and minimum values that will be found algebraically in a Calculus course.

So, I typically spend four to five weeks covering

1) notation

2) increasing, decreasing, max, min

3) composition, inverse

4) transformations

5) applications/modeling

More after the jump...

Common Core math

Apparently, no one is willing to defend the Common Core math standards for Education Next.

help desk - fables and fairy tales

I'm teaching a freshman composition course based on fables, folk tales, fairy tales, and creation myths, and I need some essays or passages for students to read and possibly use for text reconstruction exercises.

Any ideas?

I've amassed a collection of academic papers, but they won't work for my class.

Here's the kind of thing I'm thinking of:

Why did Aesop use animals instead of humans in fables?

Practicing Medicine Can be Grimm Work by Valerie Gribben

9/11

in the Wall Street Journal this morning:

Mr. Schwartz, within a few days of the attacks, was on a train with his family to Florida, where they owned a vacation home. Within a year, they had given up their Manhattan apartment. They had a feeling "possibly that this is the wrong place to be right now with an infant," he said.

His son Calder is 10 now, in the fifth grade in Tampa. The boy has visited New York often, and loves it.

"I said, 'When you go to college, go to college in New York,'" said Mr. Schwartz. "He said, 'So you can come back with me.' "
Refugees From the City Reflect Anew on Their Decision

the rules

from h2g2

Tennis crowds are extremely close to the action so the slightest movement can be off-putting. Of course there will be times you will have to move - too much hospitality is going to play havoc with your bladder control - but do it when it's allowed. For instance, people can move from their seats when the players are changing after every two games, one service game for each player or double partnership. The stewards will be stopping you from returning to your seat once the players are ready to resume play, but before they stop it's up to you to remain in your seat. When the time does come and the second game is over, move swiftly and directly to your nearest exit (they will link up to where you actually want to get eventually), as you only have 90 seconds before play has to resume.

While you are in your seat try not to get too comfortable, especially if you're a snorer and have been queuing or travelling a long time to get in. There's nothing worse than being asked from the umpire's chair to wake up to stop putting the players off.
Etiquette for Tennis Spectators

I'm talking to you, people of Arthur Ashe.

Oh, man.

We spent yesterday at the Open, which in our house means summer is officially over. I love the Open; we've gone every year since we moved here 13 years ago, and it's just about the only New York ritual we have. But it's getting less and less fun. The upper deck is pretty much bedlam these days. Yesterday we had seats on the aisle and next to the stairwell, and Ed and I and an exasperated lady from France appeared to be the only people present who had heard that you're not supposed to traipse in and out of the stadium during play. The lady from France was a stalwart; she took everyone to task and held people at bay.

But they just kept coming, and going.

errrgh

Routine Builder

A fantastic app: Routine Builder.

I am now watering my plants on schedule, once a week, instead of whenever I remember it, which is about once a month, if I'm lucky.

If my plants are lucky, I should say.

I've just this minute added "Eat An apple" to the daily queue.

Steve H on vocational education

I asked about education and jobs for students who like math but aren't going to major in math, by which I probably mean students who 'like numbers' or 'like arithmetic'...(I don't want to be more specific than that in a post.)

Here is Steve H:

Actually, the vocational path might be best for students who are not so great in math, but want a degree and a technical education. You might get math courses that are more appropriate for your needs.

See New England Institute of Technology. (www.neit.edu) It's all about getting an associate or Bachelor's of Science degree. It it very well regarded, but not cheap. They are very focused on specific careers. You can get the degree piece of paper AND be trained for a specific career.

Here are some of the careers they list.

Clinical Medical Assistant
Surgical Tech
Medical Engineering Tech
Interior Design
Physical Therapy Assistant
Construction Management
Multimedia and Web Design
Video and Radio Production
Digital Recording Arts Tech
Automotive High Performance
Automotive Tech
Auto Collision Repair
Electronics Engineering
Mechanical Engineering
Game Development & Simulation Programming

I found the course catalog and can find math prerequisites for courses, but I haven't found a list of math courses for each degree. I did find that the Electronics Engineering Bachelor's Degree requires a course called Calculus II.

"The Bachelor of Science Degree in Electronics Engineering Technology is accredited by the Technology Accreditation Commission of ABET,..."

I don't know whether businesses worry about who accredited your degree. Those who know about the school would never compare this engineering degree with one from the state's university, but will that difference matter in 10 years in an area that doesn't know about the school?

and:

I should have asked what you mean by "like math"? Lots of jobs might need people who can put together spreadsheets and not have a fit with empirical equations. That is probably the best venue for these people. You probably won't find a posted job that asks for a spreadsheet guru, but you might be able have a job where you can evolve into that person.

There is also computer-aided design that is in demand by architects and engineering firms. If you are really good at 3D geometric modeling (e.g SolidWorks or Rhino), you will most likely always be in demand. I don't know if you would call that math.

In general, I would make a distinction between those who want to do math and those who want a job which will take advantage of their ability to handle math-like attention to sequence and details. I've met a number of people without degrees who have an amazing ability to handle technical details, some of which involves math.

help desk - jobs

I have a question.

What kinds of math-related jobs exist for students who like math but aren't going to be math majors in college?

What kinds of math-related jobs are taught in vocational schools? (I'm thinking of the schools Steve H has mentioned.)

Speaking of technology and stagnant scores

from 1997:

In 1922 Thomas Edison predicted that "the motion picture is destined to revolutionize our educational system and ... in a few years it will supplant largely, if not entirely, the use of textbooks." Twenty-three years later, in 1945, William Levenson, the director of the Cleveland public schools' radio station, claimed that "the time may come when a portable radio receiver will be as common in the classroom as is the blackboard." Forty years after that the noted psychologist B. F. Skinner, referring to the first days of his "teaching machines," in the late 1950s and early 1960s, wrote, "I was soon saying that, with the help of teaching machines and programmed instruction, students could learn twice as much in the same time and with the same effort as in a standard classroom." Ten years after Skinner's recollections were published, President Bill Clinton campaigned for "a bridge to the twenty-first century ... where computers are as much a part of the classroom as blackboards." Clinton was not alone in his enthusiasm for a program estimated to cost somewhere between $40 billion and $100 billion over the next five years. Speaker of the House Newt Gingrich, talking about computers to the Republican National Committee early this year, said, "We could do so much to make education available twenty-four hours a day, seven days a week, that people could literally have a whole different attitude toward learning."
The Computer Delusion
by Todd Oppenheimer
J U L Y 1 9 9 7

the founder, chairman, and CEO of Netflix has a really bad idea
speaking of technology and stagnant scores
oh brave new world!
codswallop, part 2

Oh brave new world!

photo: Jim Wilson/The New York Time

CHANDLER, Ariz. — Amy Furman, a seventh-grade English teacher here, roams among 31 students sitting at their desks or in clumps on the floor. They’re studying Shakespeare’s “As You Like It” — but not in any traditional way.

In this technology-centric classroom, students are bent over laptops, some blogging or building Facebook pages from the perspective of Shakespeare’s characters. One student compiles a song list from the Internet, picking a tune by the rapper Kanye West to express the emotions of Shakespeare’s lovelorn Silvius.

The class, and the Kyrene School District as a whole, offer what some see as a utopian vision of education’s future. Classrooms are decked out with laptops, big interactive screens and software that drills students on every basic subject. Under a ballot initiative approved in 2005, the district has invested roughly $33 million in such technologies.

The digital push here aims to go far beyond gadgets to transform the very nature of the classroom, turning the teacher into a guide instead of a lecturer, wandering among students who learn at their own pace on Internet-connected devices.

“This is such a dynamic class,” Ms. Furman says of her 21st-century classroom. “I really hope it works.”

Hope and enthusiasm are soaring here. But not test scores.

Since 2005, scores in reading and math have stagnated in Kyrene, even as statewide scores have risen.
In Classroom of Future, Stagnant Scores
By MATT RICHTEL
Published: September 3, 2011

Spend first, find out the stuff you bought doesn't work later!

My district, one year after the crash (or was it two? time flies--) bought SmartBoards for every single classroom in the district still remaining SmartBoard-free after the first go-round of SmartBoard acquisition.

The reason?

SmartBoard equity.

Seriously. Those were the actual words our administrators and then-school board members used. SmartBoard equity.

There were kids in classrooms with SmartBoards, and there were other kids in other classrooms without SmartBoards. Not fair!

Hence: SmartBoard equity. Taxpayers had to buy SmartBoards for all the classrooms so all the kids could have SmartBoards all the time.

We've got high school kids who can't do long division (I tutored one such student this summer), but no worries. Our district has achieved SmartBoard equity, and that's what counts.


addendum

I realize I've told the SmartBoard equity story before.

I will probably tell it again, because I can't get over it. Where tales of SmartBoard equity are concerned, once is not enough.


High-Tech Heretic: Reflections of a Computer Contrarian


Oversold and Underused: Computers in the Classroom

the founder, chairman, and CEO of Netflix has a really bad idea
speaking of technology and stagnant scores
oh brave new world!
codswallop, part 2