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

Reading and the SAT

I'm a glutton when it comes to books. I finish most within a day or two. I read in gigantic eye gulps.

I like "E," "P," and "A" (audio) editions -- but if I have my druthers, I choose "P" (print -- especially if there's nice paper involved).

I'm a cocktail party reader -- not the proofreading type -- and I am great at skimming, notating, highlighting, connecting, marinating, and synthesizing. I am decidedly not perspicacious.

These skills have served me well....in real life...

On the SAT, they are a liability.

I've decided that the SAT is, for all intents and purposes, a reading test.

My mistakes often come down to one word missed, transposed, or possibly just eye-gulped down the wrong hatch without even realizing that I missed something. The questions are often dressed up in someone else's outfit (especially the math) -- so you must summon every iota of punctiliousness* you have at your disposal.

As Catherine and I were saying the other night, the future copy editors of the world will probably have an easier time with this test, than the mathematicians.

*I've stumbled across this word twice in two days on the SAT.

Illustrations by Jennifer Orkin Lewis

Cross-posted on Perfect Score Project

Glen on legalistic reading and Venn diagram problems

In an earlier post, I asked why the sentence "Thirty students take geometry, and 25 students take Spanish" seems, to me, an acceptable -- and typical -- way of saying: "Thirty students take geometry, and another set of 25 students take Spanish."

I think Glen has explains it:

Out of context, there is an implicit contrast: "Two students do X, and three students do Y" is a common sentence pattern in English, which implies that you are talking about five students and how they divide up. If X and Y aren't obviously alternatives, this form implies that they are. "Two students take Spanish and three take French" would be natural English if talking about five students. If talking about four students, it would be odd. "Two students take Chinese, and three students are hispanic" might prompt an exasperated, "What, hispanic students can't take Chinese?", because it does seem to contrast X, taking Chinese, with Y, being hispanic.

If you didn't mean to contrast one group of students from another, you would probably say it differently. For example, "The geometry class has 30 students, the Spanish class has 25, and some students could be in both classes."

But in the context of a math problem, all of that changes. Math problems written in natural language still require you to make disambiguating assumptions--it is still natural language, after all--but they want to you put more weight on what is literally said and less on other factors ("bayesian priors").

In such a context, you are trained to interpret "Two students do X, and three students do Y," without assuming two disjoint groups. You learn to be literal and legalistic in a math problem context, which is a context-based re-weighting of the factors involved in interpretation of language.

I'm glad Glen has used the term "legalistic": that's exactly what I was thinking.

I'm not a legal reader by any means, but when I do read legal documents -- or, more to the point, when I read a legally vetted explanation of a state of affairs to which I object -- I instantly switch to a literal-minded, 'legalistic' mode. I take it as a given that legally vetted statements count on readers to make inferences that aren't in fact true, and to be mollified by those inferences to boot.

In short, legally vetted public relations statements, which is what I'm talking about, practice a particular form of lying by omission, which is lying via exploitation of the conventions of natural language. (I'll have to be on the look-out for examples...)


Further:

I have an email from Katharine asking whether I'm thinking of the Gricean maxims (pdf file). I hadn't been, because I'd never heard of the Gricean maxims, but I think she's right.

question for Katharine

I've been meaning to post something about the wording of Venn diagram problems for a while now.^*

e.g.:

Thirty students take geometry, and 25 students take Spanish.

I have finally begun to divine fairy rapidly that what this sentence really means is: 

Thirty students take geometry, and 25 students take Spanish. Of those students, some may take both geometry and Spanish. Then again, maybe not.

I divine it, but I don't like it. I would never, ever write the first sentence if what I meant was the second sentence(s). (So no one's going to hire me to write Venn diagram problems any time soon, but never mind.)

I've called this post "question for Katharine" because I'm pretty sure that, as a writer, I'm following an implicit rule I know but can't name.

I might write the first sentence if I meant:

Thirty students took geometry, and another 25 students took Spanish.

Actually, I probably would write the more explicit two-sentence passage because I specialize in spelling things out. But I wouldn't think it was wrong if someone else wrote Thirty students take geometry, and 25 students take Spanish when what they meant was Thirty students take geometry, and another 25 students take Spanish.

But I perceive Thirty students take geometry, and 25 students take Spanish as an incorrect way to express Thirty students take geometry, and 25 students take Spanish. Of those students, some may take both geometry and Spanish. Then again, maybe not.

In short, according to my non-conscious rulebook: 

Thirty students take geometry, and 25 students take Spanish ≅
Thirty students took geometry, and another 25 students took Spanish.

but

Thirty students take geometry, and 25 students take Spanish ≠
Thirty students take geometry, and 25 students take Spanish. Of those students, some may take both geometry and Spanish. Then again, maybe not. 

Why is that?

I started to think it through the other day, but then it struck me that Katharine, who is a linguist, may already know.



^* awhile? a while? I'm going to figure that out soon.

If you want to score 800, shoot for 900

I mentioned in the comments that I'm sick today, but I was just emailing back and forth with Debbie about the SAT -- we're down to the wire here; C. takes it for the last time on October 1.

Here's what I have learned -- and I hope I'll find time to put together a proper post.

Working memory, attention, focus, executive function: all of these faculties are limited resources. Period. In that sense, your brain is exactly like a muscle: fatigue and stress lower performance. (Anxiety lowers performance, too, but for somewhat different reasons.)

If your child is shooting for a high score on the SAT, he or she needs to do two things:

1. Automate everything he or she can automate. SAT Math is supposed to be a test of problem solving, but I am now positive that the 800 scorers are not solving problems. They're getting right answers on exercises they can do 'in their sleep.' In short: overlearning.

2. If you want to score an 800, shoot for a 900. Ditto for 700: shoot for 800. Which is another way of saying number 1.

The reason to shoot for an 800 if you want a 700 is that anything that knocks out mental resources will drop your score by that much.

Now I'm going to go crawl in bed.

overlearning by WiseGeek

Smart Teachers in Stupid Schools, part 2

more from teacher Christine:

Progressive educators would like to promote a more democratic society advocating greater equity, justice, diversity and other democratic values, yet their methodologies do just the opposite, with "Fuzzy Math" and "Whole Language" causing lesser privileged students who can't afford tutoring to fall way behind. NYC has 70% of its student population in this category. Imagine how devastating to the morale and sense of self-esteem the use of poor curriculums can have on a child's psyche. These students subjected to these methods grow to believe they can't do anything; they are labeled as special needs children and become distraught that they are not mentally capable of becoming educated. Many are just pushed through the system because there is no where else for them to go. Progressivism which is trying to enforce some kind of social agenda, rather than purely impart knowledge, is causing many students to fail and teachers to become distraught and despondent.

What do teachers who refuse to follow the leader do? Many shut their doors and pull out the curriculum they know works. I know of teachers who, when whole language is being implemented by the district, will use their phonics programs undercover. Teachers will set up look-outs in the hall to see if supervisors are coming and drill students in what to do should a supervisor show up. I have had my students open their "readers" and put in the phonics books I'm using inside. "If someone comes you take the book slide it in your desk and pretend you're reading." I've instructed.

Smart Teachers in Stupid Schools

words to live by

Amy P on class projects:

nobody in the history of man has ever bought a school project kleenex box

Smart Teachers in Stupid Schools

Christine writes:

I'm sitting in yet another meeting for staff development on the common core curriculum. This meeting is for Special Ed Teachers, the Special Ed supervisor for the district is talking about "hotspots" – "And one of the "hotspots" as you know, is that our students must tell us where they are academically and how they intend to move to the next level." I raised my eyebrows and made a face in her direction. "What?" she questioned, "We're all professionals here, and do you have something to add?" "Not really" I replied, "No, I insist, you obviously have something on your mind and we'd like to hear it." "Look" I stated firmly, "I don't know many adults who can tell you where they are academically and how they expect to get to the next level, no less children, no less special needs children! Now, the kids can tell you what they like to do and what they don't like to do, but to ask them to present their academic portfolio on the spot is simply not appropriate. The professionals in the classroom must discern and administer efficient methodologies to teach the kids and get them to the next levels; this should not be a concern of the students." We're seated in a big square table; the other teachers are all within my sight. As I look around seeking support, most remain mute not daring to question the status quo, only one strong dynamic teacher nods her head feverishly in agreement and asserts "Exactly!" "Well," maintains the supervisor, "This is what is coming down the pipe all our kids have to be 'proactive learners'." "Yes, well," I quipped, "it's simply not appropriate." "'Proactive learners'" I rolled my eyes thinking, "These people love to use phrases that have snappy ideals with little meaning in the classroom."
by Christine

It's amazing how fast the jargon turns over in public education. I've been paying close attention for years, and every time I turn around a whole new...hotspot...pops up. Now the new hotspot is HOTSPOTS, for god's sake.

I'm going to go out on a limb and predict that special-ed parents are not going to take kindly to the notion that their kids will now be required to proactively take charge of their own education.

two-pack

 Ralph Gardner on shopping for Irene:

[M]y wife sent me out to provision Friday morning. I stocked up on all the staples—beer, vodka, milk (which will surely spoil if we lose power for days, as some predict) ice cream (ditto), a bushel of tomatoes (I may do some canning if I get bored bailing out the basement) and, most importantly, batteries. We checked our supplies and even though we're well stocked in the C, AA and AAA varieties, we appeared to be all out of the D size, the workhorse behind many flashlights.

I returned home triumphant, every item on the shopping list my spouse had assembled bought and ready to rally for our survival. All except the batteries. It wasn't as if they didn't have any D batteries at our local hardware store. It was just that they only came in the pricey two pack. I'd had my heart set on the Armageddon size—the kind you find at Lowe's or Home Depot and come eight, 16, 32, even 64 to a box.

I wanted enough batteries to see us through anything nature threw at us; I wanted the confidence of knowing we had light through the 2012 elections if need be; I wanted enough candle power to throw a party. And at a couple of bucks a pop, I didn't see any way that was going to happen, at least not without bankrupting us.

Needless to say, Debbie was not happy when I got home. She had her hands full trying to book our daughters on one of the last trains out of the city even as Amtrak was canceling them faster than one could hit the refresh button. The last thing she needed was to worry that we'd be roaming around in the dark (the local news warning about the danger of candles, which I was looking forward to lighting all over the house in homage to the 19th century).

She accused me of being cheap on a vast and unprecedented scale. Indeed, she insinuated that I was perfectly willing to squander the safety of our family just because I couldn't get a deal on batteries, wondering whether I'd ever heard the expression "opportunity cost."

The whole thing is hilarious.