Home stretch! back soon--

Down to the last 100 pages of Debbie's book, which is fantastic.

So still no blogging, but ----- I have bullet points!

• The tuna cure: Surfer and Abby now eat tuna, lentils, and olive oil (plus, starting in the past week, a few carrots). Basically: a low-rent version of palisadesk's high-protein diet for mast cell cancer in dogs. Surfer--who, it turns out, can't tolerate chemo--appears to be fine. (But we'll see.) The younger vet told me mast cell cancer is the dog equivalent of pancreatic cancer: Surfer, with a Stage 3 diagnosis, was a goner unless the Kinavet worked. Older vet, back now from his own brush with death, says: "It's not a death sentence." (Ed says: Can we always see the older vet?) Funnily enough, we encountered the same division of labor during the two years my mother was sick. The younger doctors would waylay my siblings and me for The Talk (Your mother is dying. Let her die with dignity. If she doesn't want to die with dignity, persuade her.) Then the older docs would say things like "In intensive care we support your mother's organs until her body is strong enough to handle those functions again." The older docs were always right. And they never mentioned death with dignity, which was wise because my mother didn't give two figs for dignity.
xxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxx
• Common Core illustrative texts v. what 7th graders read in my districtxxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxx
• 4.6% tax increase proposed (I'm voting no, thank you for asking)xxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxx
• Borrowing to pay teachers: the tax-cert loopholexxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxx
• SAT score decline (also in bullets)xxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxx
• Erica Meltzer's book is out!!!xxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxx
• New high school principal for Irvington who worked for TFA

One board member told me that when the board met the new principal he must have used the word accountability in every other sentence.

Are we the first affluent district ever to hire a TFA person?

We may be. A TFA alum certainly seems out of place here in Westchester, where affluent districts are snapping up superintendents fleeing New Jersey's salary cap.

Our new super replaces the superintendent against whom a number of us waged a running battle for 5 long years (or was it 6?). He is a man in his late 30s or early 40s, trained in elementary education, whose only previous experience--in New Jersey, where his wife and son continue to live--was heading a tiny K-5 district.

We are paying him $250K per year on a 5-year contract. During a minor depression.^* (Did I mention I'm voting no on the budget?)

I think it's possible, perhaps likely, the TFA hire would not have happened without 6 years of citizens' op eds on the Irvington Parents Forum.

Ed told me, when I started the Forum, that revolutions always have writers.

I believe him, and All revolutions have writers has been my essential reason for carrying on. Well, one of the essential reasons, the other essential reason being that both sides of my family came from Ulster.

That said, I don't expect a revolution. The new superintendent has thus far been more of the same, and he was supposed to be The One; all 5 board members said so. The new principal will come into a gatekeeping culture that has been in place for many, many years.

The single best observation anyone ever made to me concerning my district's unshakeable self-regard:

...[W]e're great because 10 kids do spectacular things by senior year. The other 150 will get by and there are no glaring inadequacies.

That's not going to be easy to change.

^* Depression at historinhas

Holistic College Admissions

I'll scream if I hear the word "holistic" at a college info session again. What it really means is that the admissions people love their own sensibilities and power. This might be fine if the choice was between two applicants for one open slot, but it's now a choice between 5 or 10 applicants at some colleges. They claim that there is no merit function that they use, but they don't tell you that the intangible factor has now risen to well over 50 percent of the admissions judgment. Since so many students meet some basic level of ability to handle the rigor at the college, one application out of 5 or 10 is selected based on the judgment of admissions people. They don't even turn some of their holistic decisions over to individual departments that know about academic content. They can't tell whether an applicant is at a base camp or a mountain top.

The admissions judgments are based on essays, recommendation letters, and character intangibles rather than academic intangibles. The admissions person we saw yesterday talked about their criteria of whether you would be an interesting person to have a cup of coffee with. They claim that they can see right through all applicants to tell if they are "authentic", "genuine", and "consistent". I think it just means that you have to be less authentic and hire better admissions prep people. They tell us that the essay and letters of recommendation are critical, but do they really think that the people they select did not get professional help? Sure, they can see through some applications, but what about the difference between authentic students who get help and authentic students who do not?

The other problem is that admissions people seem so anti-math and science. I'll scream a second time if I hear another admissions person or tour student tell us that the general education requirements allows you to not have to take another real math class; that there are other classes that will fulfill the requirements (ha ha). These are Ivy League schools. So here is this engaging English major tour guide who appeals to admissions more than a bookish math student who might have qualified for the AIME test.

We talked with a professor of music who said that they don't get audio portfolios of students to evaluate unless there is a final tie-breaking issue. He was having trouble getting a chance to evaluate and comment on an applicant who was a Presidential Scholar in the Arts. The holistic intangibles are closely held by the admissions people. It's OK, however, to select applicants who are clearly at the top of their math career. Then again, the admissions people may not know the difference.

teacher humor at Pinterest

In bed it's 6am you close your eyes for 5 minutes it's 7:45.
In school it's 1:30, close your eyes for 5 minutes it's 1:31.

Making it as a Middle School Teacher

I find this joke much funnier coming from a kid, I have to say.

This one's funny, though: Should I ask the teacher my question?

thinking of Boston....

If I were a carpenter....

An "unfortunate analogy" from the first SAT, administered in 1926.

A nostalgic trip down memory lane with the SAT [SLIDESHOW]

The tragedy of histogeomegraph continues

In the news today: another botched attempt at interdisciplinarity in our public schools:

ALBANY — High school is full of hypotheticals, like “How does one solve for x?” and “What happens if I skip class?” But this week, students at Albany High School were given an alarming thought puzzle: How do I convince my teacher that I think Jews are evil?

[snip]

“Your essay must be five paragraphs long, with an introduction, three body paragraphs containing your strongest arguments, and a conclusion,” the assignment read. “You do not have a choice in your position: you must argue that Jews are evil, and use solid rationale from government propaganda to convince me of your loyalty to the Third Reich!”

[snip]

Dr. Vanden Wyngaard, who met with Jewish leaders in Albany and made a public apology on Friday, said the assignment was apparently an attempt to link the English class with a history lesson on the Holocaust. The assignment itself seems to back up that theory, telling students to use “what you’ve learned in history class.” It also suggests using “any experiences you have.”

It echoed another recent, controversial assignment in Manhattan, where an elementary school class was given math problems featuring the whipping and killing of slaves, according to The Associated Press. That assignment was an effort to combine math and social studies lessons.

Students Told to Take Viewpoint of the Nazis
By JESSE McKINLEY
Published: April 12, 2013

I always thought the problem with teaching all subjects as one was that the results would be superficial and pointless. Like histogeomegraph.

It's always worse than you think.

checking in--and decline and fall

I'm doing a very rushed polish of Debbie S's SAT book -- which is wonderful -- and we're around-the-clock, so no blogging!

But I'm amassing beaucoup SAT factoids, so I'll put some up as I go.

For starters, here are the basics on the 16-year decline in SAT scores:

• SAT scores declined from 1963 to 1980
• Verbal mean: dropped from 475 to 425
• Math mean: dropped from 500 to 470
• By 1990, the Math mean has gone back up to 475, but Verbal mean has not budged
• By 1980 College Board perceives a “definite need” to “realign the verbal and math scales”
• SAT V and SAT M averages are 50 points apart
• “there was a clear need to repopulate the top end of the score scale, especially for SAT V”

The Recentering of SAT® Scales and Its Effects on Score Distributions and Score Interpretations

And get your SAT I Score Equivalents right here:
CONVERT INDIVIDUAL AND MEAN SCORES FROM THE ORIGINAL SCALE TO THE RECENTERED SCALE

automated essay grading

In the Times today:

Essay-Grading Software Offers Professors a Break By JOHN MARKOFF
Published: April 4, 2013 | New York Times

I'm actually in favor of essay grading software, in theory. I've been interested in automated essay scoring ever since reading Richard Hudson's paper Measuring Maturity in Writing (which I need to re-read, so nothing more on that at the moment):

Abstract
The chapter reviews the anglophone research literature on the 'formal' differences (identifiable in terms of grammatical or lexical patterns) between relatively mature and relatively immature writing (where maturity can be defined in terms of independent characteristics including the writer's age and examiners' gradings of quality). The measures involve aspects of vocabulary as well as both broad and detailed patterns of syntax. In vocabulary, maturity correlates not only with familiar measures of lexical diversity, sophistication and density, but also with 'nouniness' (not to be confused with 'nominality'), the proportion of word tokens that are nouns. In syntax, it correlates not only with broad measures such as T-unit length and subordination (versus coordination), but also with the use of more specific patterns such as apposition. At present these measures are empirically grounded but have no satisfactory theoretical explanation, but we can be sure that the eventual explanation will involve mental growth in at least two areas: working memory capacity and knowledge of language.

Maturity of writing, in this sense, can be measured by software, and I would be using automated scoring software myself if I could buy essay-scoring software on Amazon. EdX says it's giving software away free to 'institutions' (does that leave out individuals?) so I'll have to see if my department might throw its hat in the ring.

That said, a lot of this is nonsense:

Anant Agarwal, an electrical engineer who is president of EdX, predicted that the instant-grading software would be a useful pedagogical tool, enabling students to take tests and write essays over and over and improve the quality of their answers. He said the technology would offer distinct advantages over the traditional classroom system, where students often wait days or weeks for grades.

[snip]

“It allows students to get immediate feedback on their work, so that learning turns into a game, with students naturally gravitating toward resubmitting the work until they get it right,” said Daphne Koller, a computer scientist and a founder of Coursera.

[snip]

“One of our focuses is to help kids learn how to think critically,” said Victor Vuchic, a program officer at the Hewlett Foundation. “It’s probably impossible to do that with multiple-choice tests. The challenge is that this requires human graders, and so they cost a lot more and they take a lot more time.”

None of these things is going to happen. Students aren't going to write essay responses "over and over again;" if they do write essay responses over and over again it's not going to feel like a fun game; and nobody's going to learn to think critically from automated essay scoring software.

Oy.

words page

In honor of the latest bulletin from palisadesk, I've started a new Blogger page.

uh oh

A note from palisadesk:

Unfortunately, it is true that using Lucy Calkins' methods can raise test scores, due to the design of the current generation of "authentic assessments" (aka holistic assessment, standards-based assessment, performance assessment). I know several schools (including my own) where test scores rose substantially when they STOPPED doing systematic synthetic phonics and moved to a workshop model instead.

So to prove the instructivist stuff works you also need to have in place testing that assesses actual skills -- phonemic decoding, vocabulary, grammar, spelling, arithmetic, etc.

It's really not all that unbelievable, if you consider how the testing has 
changed. Schools used to use norm-referenced measures (like the IOWA, the
 CTBS, Metropolitan Achievement Test, etc.) which also have definite 
limitations, but different ones.

Once they replaced those (as many states
 have done) with "constructed-response" item tests, variously known as 
performance assessments, holistic assessments, standards-based assessments 
and so on, a more fuzzy teaching approach also yielded benefits. These 
open-response items are usually scored on a rubric basis, based on anchor 
papers or exemplars, according to certain criteria for reasoning,
 conventions of print, organization, and so forth. These are variously 
weighted, but specifics like sentence structure, spelling, grammar,
 paragraph structure etc. generally carry less weight than such things as
 "providing two details from the selection to support your argument."

The 
open responses often mimic journal writing -- it is personal in tone, 
calls for the student to express an opinion, and many elements of what we
 would call good writing (or correct reading) count for little or even 
nothing.



The same is true in math. A local very exclusive private school which is 
famous for its high academic achievement recently switched from 
traditional math to Everyday Math and saw its test scores soar on these assessments (probably not on norm-referenced measures, but they aren't
 saying).



Another school where I worked implemented good early reading instruction 
with a strong decoding base (and not minimizing good literature, either),
 but saw its scores on the tests go down almost 25%. I think the reason
 for that is that teaching children to write all this rubbish for the "holistic assessments" is very time consuming, and if you spent your 
instructional time teaching the basic skills -- which aren't of much value 
on these tests -- your kids will do poorly.



So yes, you can post [my email], not referring to me of course. You can say -- 
because I don't think I've mentioned it publicly anywhere -- that I have 
been involved in the past in field-testing these assessments so have a 
more complete picture of how they are put together and evaluated, and what 
they do and do not measure.

Different states have made up their own but 
they share many similarities.

I was surprised when I read this ..... somehow I had assumed that, basics being basic, absence of basics would make any test hard to pass.

Apparently not.

seeking Tiger Mom

At the WSJ (not sure whether it's behind a pay wall): "To (All) the Colleges That Rejected Me" by Suzy Lee Weiss.

Like me, millions of high-school seniors with sour grapes are asking themselves this week how they failed to get into the colleges of their dreams. It's simple: For years, they—we—were lied to.

Colleges tell you, "Just be yourself." That is great advice, as long as yourself has nine extracurriculars, six leadership positions, three varsity sports, killer SAT scores and two moms. Then by all means, be yourself! If you work at a local pizza shop and are the slowest person on the cross-country team, consider taking your business elsewhere.

What could I have done differently over the past years?

[snip]

Having a tiger mom helps, too. As the youngest of four daughters, I noticed long ago that my parents gave up on parenting me. It has been great in certain ways: Instead of "Be home by 11," it's "Don't wake us up when you come through the door, we're trying to sleep." But my parents also left me with a dearth of hobbies that make admissions committees salivate. I've never sat down at a piano, never plucked a violin. Karate lasted about a week and the swim team didn't last past the first lap. Why couldn't Amy Chua have adopted me as one of her cubs?

This girl is a fabulous writer!

ABSTRACT

This paper shows that although the top ten percent of colleges are substantially more selective now than they were 5 decades ago, most colleges are not more selective. Moreover, at least 50 percent of colleges are substantially less selective now than they were then. This paper demonstrates that competition for space--the number of students who wish to attend college growing faster than the number of spaces available--does not explain changing selectivity. The explanation is, instead, that the elasticity of a student's preference for a college with respect to its proximity to his home has fallen substantially over time and there has been a corresponding increase in the elasticity of his preference for a college with respect to its resources and peers. In other words, students used to attend a local college regardless of their abilities and its characteristics. Now, their choices are driven far less by distance and far more by a college's resources and student body. It is the consequent re-sorting of students among colleges that has, at once, caused selectivity to rise in a small number of colleges while simultaneously causing it to fall in other colleges. I show that the integration of the market for college education has had profound implications on the peers whom college students experience, the resources invested in their education, the tuition they pay, and the subsidies they enjoy. An important finding is that, even though tuition has been rising rapidly at the most selective schools, the deal students get there has arguably improved greatly. The result is that the "stakes" associated with admission to these colleges are much higher now than in the past.

The Changing Selectivity of American Colleges Caroline M. Hoxby
NBER Working Paper No. 15446
October 2009
JEL No. H75,I2,J24

Not sure what she means by the 'deal' students get at a selective college.

Will let you know once I've skimmed the study....

What are standards for? What do they have to do with curriculum?

Q: Why do schools need standards? What are standards for? What do they have to do with curriculum?

A: A set of standards is a *minimum set of requirements* that a product must meet. Let's imagine a house; the building codes are standards. An individual standard says something like "a wall must withstand straight line winds of up to 75 mph" or "studs must be places at least every 24 inches." Standards tell *what* you need to do, but don't tell you how to do it. They are used so that in the event of a serious risk, the whole structure stays standing. The building code for homes applies whether building a tiny townhouse or a 5 bedroom multi-story rambler. They are meant to force people not to cut too many corners. Standards here in math education are similar: they tell you what must be taught to a student, when, year over year. They are still *minimum set of requirements*, the ones that need to apply to every classroom, every school, every student.

A set of building codes aren't plans for a building. They are not a complete design.

A design tells you what *this building* going to look like. It answers the question of what purpose this house serves. It shows you how the floors and rooms fit together, how space is utilized. Architectural plans are a design for a home. They explain what the floor plan is, what the foundation is shaped like, where the plumbing goes, where the electricity goes, how the building will maintain even temperatures, etc. It's a map for everything that needs to be built.  A solid design takes into account the what the end result should be like and plans the structure accordingly. A good design is also relatively easy to build, because it anticipates what elements of the design depend on the other elements.



In math education, this design is the curriculum. The curriculum is the plan for each year of math education, starting with a foundation, then the walls, the plumbing, the electrical, the floors, the roof, the interior. Like a good design for a building, a good curriculum is easy to implement, anticipating not just the end product, but how to ease the building of the elements as they are put in place.

A design is necessary for a home, but we don't live in an architectural drawing. The home must still be built So there are builders. Clearly the builders need to know the standards, and build according to them, so the structure is safe. But they build according to the standards while the build up the plan, starting with the foundation, and then moving on through the structure. They complete the plan.

Teachers are the builders. They are building the house of mathematics that students will live in. Some teachers are like builders who just doing the efficient thing, putting the pieces up in order. Others are like exquisite craftsmen. The most experienced teachers are like the most experienced builders who are able to look at the plans and figure out what won't quite work in this context, and where changes should be made. They know how long the job will take, and where the hard parts are before they start. They make very few mistakes, and correct them before they cause more problems. A great math teacher is building above and beyond the minimum standards where and when she can; she is on the lookout for the pitfalls in the curriculum, ready to point them out and rework them; she is improving her own skills, employing new innovations, and producing beautiful results.

Bad standards mean the structure is unsafe. Unfortunately, this isn't always visible to the eye. The owner may not find this out until a minor tremor comes and the whole house collapses. Likewise, a bad plan means the house is not a comfortable or useful place to live, or worse, could be dangerous. If the house was designed incorrectly, then the second story may not be able to hold up the third story, and it could collapse. A truly terrible design usually can't be rebuilt, but needs to be torn down. And a bad builder means things go wrong and break in your home, and again, if bad enough, the errors could mean that the house collapses. 

Likewise, in math education, bad standards means the whole structure of math that a student is building up is faulty, and sooner or later, it is going to collapse. But good standards aren't the same as a good design. Students themselves don't need to learn the standards, any more than a homeowner needs to know the building code. Schools need to have a design, a curriculum, for their teachers, the builders to work from. A bad design won't support another story being built on top, year after year after year. And a bad builder on a floor means nothing can be built on top of it until a great builder comes in and rips out the bad work and rebuilds.

Every part of the process matters. Good standards, good curriculum, good teachers.

Cross-posted at www.msmi-mn.org/home/mathqanda

MOOCs, the doomsday scenario

More from the Times on MOOCs:

That the acronym MOOCs rhymes with “nukes” seems apt. Massive open online courses, or MOOCs — led by two profit-making start-ups, Coursera and Udacity, founded by entrepreneurial Stanford professors — are a new disruptive force in education.

[snip]

The MOOC skeptics have a variety of qualms, but especially about what is lost in the retreat of face-to-face teaching — a point eloquently made by Andrew Delbanco, a professor of American studies at Columbia University, in an article in the current New Republic, “MOOCs of Hazard.”

Michael A. Cusumano, a professor at the Sloan School of Management at M.I.T., raises a different issue in an essay published this week: the economics of MOOCs and the implications.

His article appears in Communications of the ACM, the monthly magazine of the Association for Computing Machinery, and he had circulated a version of it earlier to his M.I.T. colleagues. After reading it, L. Rafael Rief, M.I.T.’s president, asked Mr. Cusumano to serve on a task force on the “residential university” of the future, including online initiatives.

“My fear is that we’re plunging forward with these massively free online education resources and we’re not thinking much about the economics,” Mr. Cusumano said in an interview.

The MOOC champions, Mr. Cusumano said, are well-intentioned people who “think it’s a social good to distribute education for free.”

But Mr. Cusumano questions that assumption. “Free is actually very elitist,” he said. The long-term future of university education along the MOOC path, he said, could be a “few large, well-off survivors” and a wasteland of casualties.

Mr. Cusumano’s concerns grow out of his study of the software and media industries in the face of price pressure from free, open-source software and digital distribution over the Internet. Two-thirds of the public companies in the software industry disappeared between 1998 and 2006, as companies failed or were acquired. In the media world, Mr. Cusumano contends that newspaper and magazine companies — including The New York Times Company — made a strategic mistake by giving away their publications free on the Web....

Give-away pricing in education, Mr. Cusumano warns, may well be a comparable misstep. The damage would occur, he writes in the article, “if increasing numbers of universities and colleges joined the free online education movement and set a new threshold price for the industry — zero — which becomes commonly accepted and difficult to undo.”

Beware of the High Cost of ‘Free’ Online Courses
New York Times | MARCH 25, 2013, 5:04 PM

1.
"Massive open online courses, or MOOCs — led by two profit-making start-ups, Coursera and Udacity, founded by entrepreneurial Stanford professors — are a new disruptive force in education."

Really?

We have disruption now?

As far as I can tell, "creative disruption" is occurring when a new business is actually winning. MOOCs aren't a business, and they aren't winning, not at the moment.

And I don't recall distance learning being a disrupter back in the 1990s.

As far as I can tell, the only reason we're even talking about MOOCs is that we are 5 years into a depressed economy, and "free" is sounding like an awfully good idea right about now.

But as for disruption....I fear that the kind of disruption people seem to have in mind when they use the word already happened in the 1990s, and MOOCs are the least of it. Lots more administrators, lots fewer full-time professors, and now MOOCs. Swap in videos of Harvard professors, swap out the adjuncts. More for me!

I suppose you could characterize the bureaucratization of colleges and universities as creative disruption that benefits the administrators, but that's not what Clayton Christensen had in mind when he developed the concept.

2.
"Mr. Cusumano’s concerns grow out of his study of the software and media industries in the face of price pressure from free, open-source software and digital distribution over the Internet....Give-away pricing in education, Mr. Cusumano warns, may well be a comparable misstep."

Right, but.

People like music and news; people listen to music and read news instead of getting down to work.

College courses, on the other hand, are work. A college course is the activity you listen to music and read news to avoid. MOOCs are going to be hard to give away, not easy.

For most of the MOOC discussions I come across, executive function is the Great Unsaid. That, and the fact that Free is not a business model.

80 mph

My brother showed me this video --- can't remember if we've ever posted it here.

What I love about it is that the girlfriend actually comes up with a guesstimate that's pretty close to correct, which reminded me of something I once read about the difference between really good math students versus the "works hard" variety.

To wit: the really good students devise elegant and efficient solutions and proofs. The 'works hard' students go on wild goose chases.

Works-hard students do get to the answer or the proof eventually, but the process isn't pretty. (Speaking as a person who has spent a lot of time teaching herself math, I relate.)

The process may not be pretty, but it can be funny.



Another thing: this exchange is a brilliant example of "inflexible knowledge" in action. The young woman isn't transferring the meaning of "per hour" to a different phrasing of the same situation.

Speaking of inflexible knowledge, in Atlantic City this weekend we had a semi-galling episode of Failure to Transfer. My father-in-law has been deaf for years, and Ed and I -- and Andrew -- have had iPads for at least two. We use Andrew's iPad to communicate with him via typing (Andrew types, too). Yet it had never occurred to us that we could do the same for Ed's dad.

Two years to make the connection!

Immediately after I'd had the blinding revelation that iPads work for old people with hearing loss as well as young people with autism, we began plotting and scheming how to get an iPad for Ed's dad (would he use it?? Which one should we get?? The big one?? The little one that would take up less space on a dinner table?? Etc.)

It took me a good 5 minutes to figure out that Ed's dad does not need an iPad. He can talk.

We had a chuckle over that & then an hour or so later Ed raised the subject again.

We have spent a LOT of years living with people who can't talk.

"How I Used Math to Beat a Traffic Ticket"

At RealClearScience

Very fun.

Gone fishing, plague edition

Sorry to be AWOL - we flew to Chicago, where I contracted an epic case of stomach flu (still recovering), then drove down to Atlantic City this weekend for bar mitzvah -----

Today I'm trying to figure out if I'm on Spring Break. You'd think I'd know these things. (I'm tutoring in the Bronx this semester & don't know whether the Learning Center stays open during break.)

Back in a bit.

SAT Essay

My son is in the middle of preparing for his first (and hopefully only) official SAT test. He took the PSAT in the fall and did very well, so we do have some ideas of what to work on. However, the PSAT does not have an essay portion, so he is starting from scratch for that. I had him do the Blue Book essay for test 10, but I don't know how the scores are calibrated. Was it a 6, a 9, or a 12? How does one improve? Also, I was told that even professional writers might get 10's and not 12's. The problem is that there is way too much advice if you just search online.

Since I have used and liked Mike McClenathan's PWN the SAT book for math, I thought I would download his new Kindle "Essay Guide". Like his math book, it gets right to the point. (It's also so inexpensive that buying it is a no-brainer.) It uses a five-point star diagram to explain how there are five areas that one has to improve upon to get a better score:

1. Development and support of point of view

2. Organization and focus

3. Grammar, usage, and mechanics

4. Variety of sentence structure

5. Use of vocabulary

The document explains each of these and then talks about a general approach to writing the essay, starting with the body. OK. we are on the same wavelength. I've always thought that your examples will define your position. Of course, Mike goes into much greater detail, but he still keeps the document short.

One issue that I talked with Mike about was how, even with this information, some students might go backwards before they go forwards. He agreed that that can happen. I don't want to shove his document in front of my son and say: "Read this!" My goal is to see the big picture and focus on the things that will most likely improve my son's score. I'm more apt to show him parts of the document that will help him.

Mike's book does put this into perspective. Since it's so hard to improve from a score of 10 to 12, you will be better off improving on the multiple choice section. If you get all of those questions correct, you can perhaps get a '9' on the essay and still get an 800 score. If you get one wrong, then you need to get an '11' on the essay to get an 800. If you get two wrong and a '10', you could drop down to 760! This analysis can be extended to those not up at that lofty height, but you come up with a different answer. On BB test 1, if you get a raw score of 41 (about 7 wrong), the difference between an essay score of 8 and 9 changes your writing score from 630 to 660! At that level, it would be better to work on your writing rather than the multiple choice questions. And, as Mike points out: "Colleges you apply to might read your SAT essay."

So, my question was where is my son located on this map. I had to have some calibration for the multiple choice questions and the essay. His PSAT score told me about the multiple choice questions, but I needed to have some real feedback on his essay. I was told that robo-readers tend to give high scores. Some talk about getting 12's from them, but 10's from real people. Mike offered to give me real feedback for my son so that we would know where in the ballpark he was. I think this is a good process. Don't just dive in and work without knowing what to work on. It turns out that my son is in the '10' ballpark with no studying, so I will probably just pick and choose parts of Mike's document to show him. I think I will start with having him organize his experiences and references in terms of larger ideas, like morality, technology, and creativity. Then I will have him practice reading questions and determining his examples and position. The biggest risk for him is to read a question that stops him cold. Apparently, a "reality TV" question once did that for a lot of people. It would be tough to fit The Great Gatsby into that.

From all of this, I found out that my son does not need to spend as much time as I thought on the essay, and we know specifically what to work on. Now, where did we put Erica's grammar book? We are also waiting for pages 26+ in her new "The Critical Reader" book.

budget season

Sorry to be missing in action -- budget season is upon us, and I've been writing posts for the Irvington Parents Forum.

The Forum has also had an interesting discussion of kids learning Mandarin Chinese, including an email from a mother who is living in China so her daughter can learn the language. I'll get links posted as soon as I've read everything.

For New Yorkers and anyone else who is interested in school funding:

Per pupil spending $28,517

and

Why the tax cap passed in New York state
Pension contribution rises 37% for 2013-2014
New York State School Board Association opposes Triborough Amendment

and

English Language Arts scores 

The insanity in my state is that a school district can have nearly $30K per pupil funding and still be laying off teachers, cutting programs, laying off more teachers, threatening to cut French, Latin, and Greek, threatening to cut French, Latin, and Greek again, etc., etc., on and on.

Each and every year since the crash, we have a budget crisis: the same crisis, over and over again. It's like Groundhog Day, only not fun.

The reason we have a budget crisis each year without fail is that the budget is capped, but the contracts are not. The cap is 2%, but our contract calls for roughly 4% annual increase in compensation, and 4 is not 2. Plus pension payments will rise by 37% next year, and tax certs are through the roof (nearly $2 million this year, assuming I'm reading the Powerpoint correctly). Apparently tax certs always will be through the roof, forever. So we have a crisis.

Surreally, the solution is simple, but impossible.

All of our problems would be over if the union simply agreed to index raises to inflation. But that option is unthinkable.

The 4-is-not-2 dilemma is unthinkable even as a description of the problem. Instead of "labor costs are too high," the problem is understood to be Cost Escalation Beyond Board's Control.

Pension contributions! Health insurance! Special ed! Mandates!

True enough, all these things are expensive, but "mandates" obscures the fact that the only mandate that matters, and the source of our woe, is the Triborough Amendment. And that is here to stay.

So we are living in the land of zero-sum, where 4% raises for some mean lay-offs for others.

Sometimes kids know *less* than adults realize

A few nights ago, I was having dinner with a friend and her very smart fourteen year-old son.

My friend told me the story of how her son, who is in *eighth grade*, had come home from school with an assignment to write an 8-10 page paper. 

The exceedingly nebulous instructions included brainstorming a "guiding question" and due dates for various drafts, but other than that, there was not one iota of specific information about how these thirteen and fourteen year-olds were supposed to go about writing this paper. 

Never mind high school, it looked like the assignment sheet for a college term paper.  

My friend, a teacher herself, was a bit concerned that the assignment was unclear and emailed his teacher. She couldn't figure out whether the paper was supposed to be thesis-driven or whether it was just a research project, but the teacher wouldn't give her a straightforward answer.

She asked her son whether he'd been given clearer instructions in class.

He shook his head.

"Do you know whether you need to have a thesis, or is it just research?" she asked.

He shrugged. 

"Wait," I said. "M., do you know how to write a thesis?" 

He hesitated and looked confused. "What exactly do you mean by thesis...?"

Even if boys score higher than girls on standardized tests, they get lower grades

Boys score as well as or better than girls on most standardized tests, yet they are far less likely to get good grades, take advanced classes or attend college....

The sometimes controversial Christina Hoff Sommers wrote about this problem of "Boys at the back" in our public schools, illustrated in this chart posted by Mark Perry.

A reason is differences in 'noncognitive skills'

Boys score as well as or better than girls on most standardized tests, yet they are far less likely to get good grades, take advanced classes or attend college. Why? A study coming out this week in The Journal of Human Resources gives an important answer. Teachers of classes as early as kindergarten factor good behavior into grades — and girls, as a rule, comport themselves far better than boys.

The study’s authors analyzed data from more than 5,800 students from kindergarten through fifth grade and found that boys across all racial groups and in all major subject areas received lower grades than their test scores would have predicted.

The scholars attributed this “misalignment” to differences in “noncognitive skills”: attentiveness, persistence, eagerness to learn, the ability to sit still and work independently. As most parents know, girls tend to develop these skills earlier and more naturally than boys.

That last sentence, which I've highlighted, may hold a key to the gender gap in school performance.  Boys lag girls in developing both noncognitive and literacy skills. Over time schools have pushed down more rigorous academic and organizational requirements to younger grades, making it more likely for boys to develop early gaps that often persist into the college years.

A related reason for the gender gap may be what David Brooks called the lack of cultural diversity.

… The education system has become culturally cohesive, rewarding and encouraging a certain sort of person: one who is nurturing, collaborative, disciplined, neat, studious, industrious and ambitious. People who don’t fit this cultural ideal respond by disengaging and rebelling.

Far from all, but many of the people who don’t fit in are boys....

I wrote about this last year.

Brooks is describing what is often called the “feminization” of public schools.  This term is distasteful to some, probably because it reinforces gender stereotypes.  Whatever the label, it does appear that schools have become “culturally homogeneous” in a way that hurts boys more than girls.  It starts in elementary school when an early reader is told that he got the wrong answer because he picked “mad” instead of “sad” to describe how the boy in the story feels after he doesn’t get the bike he wanted for his birthday.  It continues through high school where group discussions in history class only allow expressions of compassion for victims of war but no praise for brilliant military maneuvers.  The message is clear – only certain types of behaviors and thoughts are welcome in the classroom.

There’s no doubt that students do need to be ”studious and industrious” to perform well academically.  It just seems that public schools are misguided in the methods they use in trying to develop those qualities in all students, particularly in boys.

Suggested reforms

Sommers points out that this gender gap should motivate schools to find ways to promote boys' academic achievement, as they have done for girls in recent cases when the gender gap has been reversed.  She suggests some changes that the British, the Canadians and the Australians have implemented.

... These include more boy-friendly reading assignments (science fiction, fantasy, sports, espionage, battles); more recess (where boys can engage in rough-and-tumble as a respite from classroom routine); campaigns to encourage male literacy; more single-sex classes; and more male teachers (and female teachers interested in the pedagogical challenges boys pose).

One example of how poor noncognitive skills can create a misalignment between grades and test scores

I know of a case where a middle school boy consistently earned almost perfect test scores in his social studies class and who reached the finals in his state's geography bee contest.  However, his overall grade was significantly lowered by his poor class notes, likely due to a deficit in "noncognitive skills".  Because of his grades, and because "behavior and work habits" counted so heavily in the admissions process, he was shut out of his high school's honors history track.  If not for his parents' intervention to override the school's policies, allowing him to enroll in the honors course, he might have languished in courses that were too easy and boring for him.  As it happened, he went on to graduate with honors and enroll in an elite university.

(A version of this post previously appeared on Cost of College.)

Are Grading Trends Hurting Socially Awkward Kids?

There's a rather spirited discussion going on at the TheAtlantic.com regarding various questions raised by my article there. Some people are claiming that the demands of the 21st require students to work in groups and be graded on their presentation skills. Please weigh in if you have an opinion on this!

South of the border

In the Times today:

A few years back, I spoke with the education secretary of my home state, Nuevo León, about reading in schools. He looked at me, not understanding what I wanted. “In school, children are taught to read,” he said. “Yes,” I replied, “but they don’t read.” I explained the difference between knowing how to read and actually reading, between deciphering street signs and accessing the literary canon. He wondered what the point of the students’ reading “Don Quixote” was. He said we needed to teach them to read the newspaper.

When my daughter was 15, her literature teacher banished all fiction from her classroom. “We’re going to read history and biology textbooks,” she said, “because that way you’ll read and learn at the same time.” In our schools, children are being taught what is easy to teach rather than what they need to learn. It is for this reason that in Mexico — and many other countries — the humanities have been pushed aside.

The Country That Stopped Reading
By DAVID TOSCANA
March 5, 2013

I'm having a queasy feeling about Common Core's requirement that English teachers devote 60% to 80% of their time to shepherding students through "informational text."

Informational text.

Yeesh.

I write informational text (see here). I read informational text. But I never, ever, call what I write and read informational text.

If I did, I wouldn't be a writer.



source:
The Common Core Standards: What You Need to Know | June 4, 2012
Orange Public Schools

Not to belabor the point, part 3

Is there a person on the planet who thinks "Change Password" is the tab to click if you want to Lock Myself Out of the System?

AND SEE:
Not to belabor the point, part 1
Not to belabor the point, part 2

Not to belabor the point, part 2

Also, is there a person on the planet whom honks ^* who thinks "Change Password" is the tab to click to Not Change Password"?

^* Damn you, Autocorrect!
AND SEE:
not to belabor the point, part 1
not to belabor the point, part 3

scratch Columbia off the list

From The Fundamentals of College and University Teaching
by Steven Mintz, Director, Graduate School of Arts & Sciences Teaching Center Columbia University:

In recent years, a model of higher education that emphasized the transmission of knowledge and skills has given way to a new paradigm, which shifts the focus from the instructor and toward the student. This is a shift from transactional to transformative teaching.

In transactional teaching, an instructor conveys information and students are expected to assimilate and synthesize new knowledge on their own.

Transformational teaching, in contrast, is much more self-conscious about its objectives and methods. It adopts a learner-centered rather than an instructor-centered approach...It gives students assignments that they find meaningful, involving case studies, real-world data and problems, research and inquiry, and encourages them to public display their findings.

[snip]

Teaching can be didactic, emphasizing the transfer of information. It can be philetic, in which the teacher serves as role model and mentor. It can be evocative, assisting students in discovering the personal meaning of a topic or text, rather than seeking some larger truth. Then there is heuristic teaching, which engages students in a process of inquiry and discovery to help them develop the habits of a particular discipline.

Didactic, philetic, evocative, heuristic --- killer list!

But...is that it?

Only four kinds of "teaching"?

Aren't there others?

Other kinds of teaching, like .... off the top of my head ... irresponsible.

Irresponsible teaching. That's one, definitely.

Or unaccountable. That's another.

Irresponsible .... unaccountable .... ineffective ..... oppressive .... depressive ..... unsound .... unhinged .... harebrained....

I could go on.

NY state technology standards

I've just heard from a parent here....

My district is considering cutting French, Latin, and Greek --- and adding a technology teacher to K-5 in order to meet NY state's "technology standards."

I had no idea we had "technology standards," but come to find out, we do.

I do remember, back when David Steiner had first been appointed Commissioner of Education, attending a lecture at which he told us that the Board of Regents considered 'technology' very important. I think he may have said that he'd had some debate on the subject with one particular member of the Board, but I'd have to check my notes to make sure. Since checking my notes would entail finding my notes, that may not be happening. (Was I still using my AlphaSmart then?)

Does Common Core have "technology" standards?

New York State Technology Standards

Elementary and Intermediate Grade Levels

Standard 1 – Analysis, Inquiry, and Design
Students will use mathematical analysis, scientific inquiry, and engineering
design, as appropriate, to pose questions, seek answers, and develop solutions.

Standard 2 – Information Systems
Students will access, generate, process, and transfer information using
appropriate technologies.

Standard 5 – Technology
Students will apply technological knowledge and skills to design, construct, use,
and evaluate products and systems to satisfy human and environmental needs.

Standard 6 – Interconnectedness – Common Themes
Students will understand the relationships and common themes that connect
mathematics, science, and technology and apply the themes to these and other
areas of learning.

Standard 7 – Interdisciplinary Problem Solving
Students will apply the knowledge and thinking skills of mathematics, science,
and technology to address real-life problems and make informed decisions.

The whole megillah

Meyer, Steiner, & Bauerlein on Thursday at CUNY

Peter Meyer is moderating Steiner & Bauerlein!

The ELA Common Core Standards: The path to a better educated America?

The ELA Common Core has been called the most radical change in American public education in the last 50 years. On the eve of the introduction of these standards into thousands of classrooms , join Dr. David Steiner and Dr. Mark Bauerlein for a provocative discussion about how the ELA Common Core will transform our schools.

Thursday, February 28
Roosevelt House at CUNY
Reception: 5:30 PM
Discussion: 6:15 PM
Where: 47-49 E. 65th St., New York, NY, 10065
65th between Madison & Park

Register here

I just signed up to go.

preview of Erica Meltzer's SAT book

Erica has posted a Preview of her forthcoming book on SAT reading: The Critical Reader: The Complete Guide to SAT Critical Reading.

Erica's book is going to be the book on SAT reading.

Her book is going to have a great deal to teach students about reading, period.

From the Introduction:

Eight years elapsed between my last SAT, which I took as a senior in high school, and the first time I was asked to tutor Critical Reading. I distinctly remember sitting in Barnes and Noble, hunched over the Official Guide, staring at the questions in horror and thinking, “Oh wow, this test is hard. How on earth did I ever get an 800 on this thing when I was seventeen?” Mind you, I felt completely flummoxed by Critical Reading after I had earned a degree in literature.

Somehow or other, I managed to muddle through my first Critical Reading tutoring sessions. I tried to pretend that I knew what I was doing, but to be perfectly honest, I was pretty lost. I had to look up answers in the back of the book. A lot. I lost count of the number of times I had to utter the words, “I think you’re right, but give me one second and let me just double-check that answer...” It was mortifying. No tutor wants to come off as clueless in front of a sixteen year-old, but I was looking like I had no idea what I was doing. Grammar I could handle, but when it came to teaching Critical Reading, I was in way over my head. I simply had no idea how to put into words what had always come naturally to me. Besides, half the time I wasn’t sure of the right answer myself.

Lucky for me, fate intervened in the form of Laura Wilson, the founder of WilsonPrep in Chappaqua, New York, whose company I spent several years writing tests for. Laura taught me about the major passage themes, answer choices patterns, and structures. I learned the importance of identifying main point, tone and major transitions, and the ways in which that information can allow a test-taker to spot correct answers quickly, efficiently, and without second-guessing. I discovered that the skills that the SAT tested were in fact the exact same skills that I had spent four years honing.

As a matter of fact, I came to realize that, paradoxically, my degree in French was probably more of an aid in teaching Critical Reading than a degree in English would have been. The basic French literary analysis exercise, known as the explication de texte linéaire, consists of close reading of a short excerpt of text, during which the reader explains how the text functions rhetorically from beginning to end – that is, just how structure, diction, and syntax work together to produce meaning and convey a particular idea or point of view. In other words, exactly the skills tested on Critical Reading. I had considered explications de texte a pointless exercise (Rhetoric? Who studies rhetoric anymore? That’s so nineteenth century!) and resented being forced to write them in college – especially during the year I spent at the Sorbonne, where I and my (French) classmates did little else – but suddenly I appreciated the skills they had taught me. Once I made the connection between what I had been studying all that time and the skills tested SAT, the test suddenly made sense. The close reading skills I had spent four years being forced to hone came remarkably in handy. I suddenly had something to fall back on when I was teaching, and for the first time, I found that I no longer had to constantly look up answers.

Erica's website: The Critical Reader

Erica's other books:
Eight Multiple Choice SAT Writing Tests: The Companion Workbook to The Ultimate Guide to SAT Grammar
The Ultimate Guide to SAT Grammar

More slave math

Watching local news tonight.

Today's story: parents being interviewed about a new slave math scandal in school.

The mom who is head of School Council, trying to go easy on the teachers involved, said she thinks it's a very good idea to bring "social studies" into math.

Which reminded me of Histogeomegraph and the tragedy of content isolation. And of the middle school model. And of my own middle school, back when they were bringing in the middle school model here.

With the middle school model, we parents were told, wondrous connections amongst the disciplines would be made:

• In math class, the teacher could point out that Pythagorus was a Greek 
• In English class, the teacher could point out that the father in The Miracle Worker was a patriarchal male who is ashamed of his handicapped child
• In science class, the teacher would take POINTS OFF!!!! for misspelling

The problem with "bringing social studies into math" is that a person who has spent a great deal of time and energy learning math has not spent a comparable amount of time and energy learning "social studies." So the social studies that gets 'brought in" is superficial (Pythagorus was a Greek), wrong ("ashamed of his handicapped child"), obnoxious (POINTS OFF!!!),^* or, in the case of slave math, upsetting and weird.

From 1999, here's Nancy Granstrom:

During our eldest daughter's eighth-grade year in junior high school, I wrote a letter to the editors of the local newspaper praising the education in our school district. The teachers were highly knowledgeable, dedicated individuals, who imparted their expertise so well, and did an exceptional job of preparing students for high school. I was convinced that the Community Consolidated School District 21 in Wheeling, Illinois had cornered the market on how to truly deliver a quality education. Two years later, however, it was welcome to Jack London Middle School for our second daughter.

Our daughter had not been looking forward to all the spelling, vocabulary, history, pre-algebra, and reading of the classics she had seen her older sister do. It turned out that she did not need to worry because little of that took place at her middle school. The explanatory pamphlet from the district stated that middle school theory includes: "Integrated thematic instruction, cooperative learning, problem-based learning, multiple teaching styles, flexible block scheduling, and authentic assessment."

Under this system all teachers taught all subjects, even if they were not qualified to do so. The philosophy was and is that they should be able to teach anything. The reality is they have to, because the majority of the classes are extremely integrated.

A Parent Criticizes "Middle School Theory"
by Nancy L. Granstrom

Funny thing here in my district: we had two years of strife over the middle school model, then they brought in the middle school model, and then...nothing.

Nobody ever heard a word about it again, and except for some scheduling changes, things seemed to be pretty much business as usual.

Two or three years later, they brought in Lucy Calkins' reading workshop.

__________________________________________________________

^* I say "obnoxious" because the school was not teaching spelling at all. C.'s spelling was so bad that I had purchased a spelling curriculum I was using at home, and now, in the name of the middle school model, we were being told that the only help our kids would receive in the spelling department would come in the form of a cranky science teacher, nearing retirement, punishing the kids into better spelling by taking POINTS OFF!!! (That's what we always called it, back in the day: POINTS OFF!!!)

I wish now I'd kept a journal of those years. Ed attended that meeting....

Oh, wait! It's coming back to me.

Ed of course was strenuously lobbying against adoption of the "middle school model," and was playing a prominent and vocal role in the parent meeting convened to educate us in the nature of the coming changes. So when the science teacher said her contribution to Subject Integration was going to be taking POINTS OFF!!! Ed said forcefully & without a trace of irony, as if the POINTS OFF!!! plan explained everything (which it did), "That's very helpful to know. The science teacher will integrate English and science by docking points on science tests for spelling errors. That's the kind of information we need."

He told me later the science teacher glared at him.

Really, the best parents can hope for is to get these people's goat every once in a while.

online courses: "decrements" in performance for all students

ABSTRACT
Using a dataset containing nearly 500,000 courses taken by over 40,000 community and technical college students in Washington State, this study examines how well students adapt to the online environment in terms of their ability to persist and earn strong grades in online courses relative to their ability to do so in face-to-face courses. While all types of students in the study suffered decrements in performance in online courses, some struggled more than others to adapt: males, younger students, Black students, and students with lower grade point averages. In particular, students struggled in subject areas such as English and social science, which was due in part to negative peer effects in these online courses.
Adaptability to Online Learning: Differences Across Types of Students and Academic Subject AreasDi Xu and Shanna Smith JaggarsFebruary 2013CCRC Working Paper No. 54

all MOOC all the time

The Times ran a terrific editorial on MOOCs yesterday:

The Trouble With Online College
Published: February 18, 2013

Stanford University ratcheted up interest in online education when a pair of celebrity professors attracted more than 150,000 students from around the world to a noncredit, open enrollment course on artificial intelligence. This development, though, says very little about what role online courses could have as part of standard college instruction....

...First, student attrition rates — around 90 percent for some huge online courses — appear to be a problem even in small-scale online courses when compared with traditional face-to-face classes. Second, courses delivered solely online may be fine for highly skilled, highly motivated people, but they are inappropriate for struggling students who make up a significant portion of college enrollment and who need close contact with instructors to succeed.

Online classes are already common in colleges, and, on the whole, the record is not encouraging. According to Columbia University’s Community College Research Center, for example, about seven million students — about a third of all those enrolled in college — are enrolled in what the center describes as traditional online courses. These typically have about 25 students and are run by professors who often have little interaction with students. Over all, the center has produced nine studies covering hundreds of thousands of classes in two states, Washington and Virginia. The picture the studies offer of the online revolution is distressing.

The research has shown over and over again that community college students who enroll in online courses are significantly more likely to fail or withdraw than those in traditional classes, which means that they spend hard-earned tuition dollars and get nothing in return. Worse still, low-performing students who may be just barely hanging on in traditional classes tend to fall even further behind in online courses.

A five-year study, issued in 2011, tracked 51,000 students enrolled in Washington State community and technical colleges. It found that those who took higher proportions of online courses were less likely to earn degrees or transfer to four-year colleges. The reasons for such failures are well known. Many students, for example, show up at college (or junior college) unprepared to learn, unable to manage time and having failed to master basics like math and English.....

O brave new world!

more MOOC

Letters to the Times

The President of Dickinson College has this to say:

MOOCs are separate from that highly desirable and precious residential degree. Online courses represent auxiliary income to support bricks and mortar and to increase brand recognition globally. New wine for an old bottle.

The high cost of a degree at M.I.T. — or most universities — is not lowered. That would be a revolution.

Devlin's Lament: the symbol barrier

(Cross-posted at Out In Left Field)

In an article in the most recent issue of American Scientist entitled "The Music of Math Games," Keith Devlin (head of the Human-Sciences and Technologies Advanced Research Institute at Stanford University and NPR's "math guy") says that learning math should be like learning to play the piano. In doing so, he recalls (but does not credit) Paul Lockhart's Lament ("A piano student's lament: how music lessons cheat us out of our second most fascinating and imaginative art form"), which I blogged about here.

Though Devlin is no literary virtuoso, not all of what he writes here is mushy metaphor. He begins with a discussion of educational software, and here his points are clear and consistent with my own experience. Most "math games" and "math education" software programs I've seen don't make mathematics an organic part of the games or activities. Instead, math problems--mostly arithmetic problems of the "mere calculation" variety--are shoe-horned into non-mathematical situations. Here they serve simply as tasks you must complete before moving through the current non-mathematical activity or on to the next non-mathematical activity.

As Devlin writes:

To build an engaging game that also supports good mathematics learning requires... understanding, at a deep level, what mathematics is, how and why people learn and do mathematics, how to get and keep them engaged in their learning, and how to represent the mathematics on the platform on which the game will be played.

The same is true of language learning. Most linguistic software taps only superficial aspects of language, and, as I know from personal experience, it takes great effort to build a program that does more than that.

Where I begin to part ways with Mr. Devlin is in his discussion of traditional math and what he thinks is an excessive emphasis on symbols:

Many people have come to believe mathematics is the memorization of, and mastery at using, various formulas and symbolic procedures to solve encapsulated and essentially artificial problems. Such people typically have that impression of math because they have never been shown anything else...

...

By and large, the public identifies doing math with writing symbols, often obscure symbols. Why do they make that automatic identification? A large part of the explanation is that much of the time they spent in the school mathematics classroom was devoted to the development of correct symbolic manipulation skills, and symbol-filled books are the standard way to store and distribute mathematical knowledge. So we have gotten used to the fact that mathematics is presented to us by way of symbolic expressions.

This approach to math, Devlin suggests, is at odds with the resolutions of a "blue-ribbon panel of experts" serving on the National Research Council’s Mathematics Learning Study Committee ("Adding it Up: Helping Children Learn Mathematics," National Academies Press, 2001). In Devlin's words: these resolutions hold that math proficiency consists of:

the aggregate of mathematical knowledge, skills, developed abilities, habits of mind and attitudes that are essential ingredients for life in the 21st century. They break this aggregate down to what they describe as “five tightly interwoven” threads. The first is conceptual understanding, the comprehension of mathematical concepts, operations and relations. The second is procedural fluency, defined as skill in carrying out arithmetical procedures accurately, efficiently, flexibly and appropriately. Third is strategic competence, or the ability to formulate, represent and solve mathematical problems arising in real-world situations. Fourth is adaptive reasoning—the capacity for logical thought, reflection, explanation and justification. Finally there’s productive disposition, a habitual inclination to see mathematics as sensible, useful and worthwhile, combined with a confidence in one’s own ability to master the material.

Ah, "21st century skills," "habits of mind," "conceptual understanding," "real-world situations," "explanation," "disposition"...--all this makes me wonder about the ratio of mathematicians to math eduation "experts" on this blue-ribbon panel. (It should be noted that Devlin himself is not, strictly speaking, a mathematician; he holds a Ph.D. in logic from the University of Bristol, and, while affiliated with Stanford, is not a member of the Stanford math department.)

Standing in the way of these lofty goals is what Devlin calls the "symbol barrier":

For the entire history of organized mathematics instruction, where we had no alternative to using static, symbolic expressions on flat surfaces to store and distribute mathematical knowledge, that barrier has prevented millions of people from becoming proficient in a cognitive skill set of evident major importance in today’s world, on a par with the ability to read and write.

To the rescue comes... Devlin's math education software program:

With video games, we can circumvent the barrier. Because video games are dynamic, interactive and controlled by the user yet designed by the developer, they are the perfect medium for representing everyday mathematics, allowing direct access to the mathematics (bypassing the symbols) in the same direct way that a piano provides direct access to the music.

Devlin's notion that a well-designed math video game can help students meet the National Academy's goals for math education rests on two assumptions. One is that students can achieve a sufficient level of mastery in mathematics without symbols. The other is that playing such video games is to math what playing the piano is to music.

To address the first claim, Devlin elaborates the analogy to music:

Just how essential are those symbols? After all, until the invention of various kinds of recording devices, symbolic musical notation was the only way to store and distribute music, yet no one ever confuses music with a musical score.
...
Just as music is created and enjoyed within the mind, so too is mathematics created and carried out (and by many of us enjoyed) in the mind. At its heart, mathematics is a mental activity—a way of thinking—one that over several millennia of human history has proved to be highly beneficial to life and society.

But there's an important difference between math and music--and a reason why no one confuses music with a musical score. Music has a privileged place in subjective experience. Along with sensations like color, taste, and smell, it produces in us a characteristic, irreduceable, qualitative impression--an instance of what philosophers call "qualia." Just as there's no way to capture the subjective impression of "redness" with a graph of its electromagnetic frequency, or of "chocolate" with a 3-D model of its molecular structure, so, too, with the subjective feeling of a tonic-dominant-submediant-mediant-subdominant-tonic-subdominant-dominant chord progression. Embedded in what makes music what it is to us is the qualia of its chords and melodies.

Like most other, more abstract concepts ("heliocentric," "temporary"), mathematic concepts don't generally evoke this qualia sensation. What makes math beautiful are things like eloquence, patterns, and power. Unlike a Bach fugue translated homomorphically into, say, a collage of shapes, mathematical concepts can be be translated into different representational systems without losing their essence and beauty.

Devlin argues that while we might write down symbols in the course of doing real-life math, it is primarily a "thinking process," and that "at its heart, mathematics is a mental activity—a way of thinking." I agree. Indeed, math is much more appropriately compared with thoughts than with music. But this makes math symbols the mathematical equivalent of linguistic symbols. While thoughts, like math, can be expressed in a number of different symbol systems, you need some sort of symbol system in order to represent your own thoughts and to understand the thoughts of others.

This is especially true of abstract thoughts--and of abstract math. As Devlin himself admits, "the advanced mathematics used by scientists and engineers is intrinsically symbolic. "What isn't intrinsically symbolic, Devlin claims, is "everyday mathematics":

The kind of math important to ordinary people in their lives... is not, and it can be done in your head. Roughly speaking, everyday mathematics comprises counting, arithmetic, proportional reasoning, numerical estimation, elementary geometry and trigonometry, elementary algebra, basic probability and statistics, logical thinking, algorithm use, problem formation (modeling), problem solving, and sound calculator use. (Yes, even elementary algebra belongs in that list. The symbols are not essential.)

OK, but what does this mean for education? Are we going to decide before the end of middle school which students are going to become scientists, engineers, and mathematicians, and only help those students scale the "symbol barrier"? For a barrier it certainly is, as Devlin himself notes: "people can become highly skilled at doing mental math and yet be hopeless at its symbolic representations."

But Devlin is too busy appreciating the (well-studied) math skills of Brazilian street vendors, who do complex arithmetic calculations in their heads with 98% accuracy, and supposedly without the help of symbols (even mental ones?), to realize the educational implications of the fact that "when faced with what are (from a mathematical perspective) the very same problems, but presented in the traditional symbols, their performance drops to a mere 35 to 40 percent accuracy." No, not everyone is going to become an engineer. But not all non-engineers are going to become Brazilian street vendors.

It's ironic how deeply Devlin appreciates the difficulty that "ordinary people" have with the symbol barrier without appreciating what this says about their educational needs:

It simply is not the case that ordinary people cannot do everyday math. Rather, they cannot do symbolic everyday math. In fact, for most people, it’s not accurate to say that the problems they are presented in paper-and-pencil format are “the same as” the ones they solve fluently in a real life setting. When you read the transcripts of the ways they solve the problems in the two settings, you realize that they are doing completely different things. Only someone who has mastery of symbolic mathematics can recognize the problems encountered in the two contexts as being “the same.”

Instead of seeing this as a reason for exposing children to mathematical symbols early and often, Devlin sees this as reason to create computer games that somehow teach math non-symbolically.

He calls this "adaptive technology," a term that should raise red flags. In a recent blog post, I wrote about how assistive technology often becomes yet another excuse not to teach basic skills. Kids with dyslexia struggle mightily with the symbol system of written language; should they instead learn everything through text-to-speech and speech-to-text devices, and never learn how to read and write?

Devlin makes a few other strained comparisons to the piano:

The piano metaphor can be pursued further. There’s a widespread belief that you first have to master the basic skills to progress in mathematics. That’s total nonsense. It’s like saying you have to master musical notation and the performance of musical scales before you can start to try to play an instrument—a surefire way to put someone off music if ever there was one.

No it's not; it's like saying you have to master simple scales and exercises before you move on to Rachmaninoff.

The one difference between music and math is that whereas a single piano can be used to play almost any tune, a video game designed to play, say, addition of fractions, probably won’t be able to play multiplication of fractions. This means that the task facing the game designer is not to design one instrument but an entire orchestra.

Can one create a video game that functions "as an instrument on which a person can 'play' mathematics?"

Can this be done? Yes. I know this fact to be true because I spent almost five years working with talented and experienced game developers on a stealth project at a large video game company, trying to build such an orchestra.

What does Devlin's software do? The last two paragraphs of this article function as an extended but not very informative infomercial. Here's the most informative excerpt:

Available in early March, Wuzzit Trouble is a game where players must free the Wuzzits from the traps they’ve inadvertently wandered into inside a castle. Players must use puzzle-solving skills to gather keys that open the gearlike combination locks on the cages, while avoiding hazards.

Puzzle solving? As I argue in my last post on math games, existing games already offer some version of this, and it isn't math. This, indeed, is one of the other problems with so-called math education software.

Devlin suggests his software is different:

Unlike the majority of other casual games, it is built on top of sound mathematical principles, which means that anyone who plays it will be learning and practicing good mathematical thinking—much like a person playing a musical instrument for pleasure will at the same time learn about music.

Wuzzit Trouble might look and play like a simple arithmetic game, and indeed that is the point. But looks can be deceiving. The puzzles carry star ratings, and I have yet to achieve the maximum number of stars on some of the puzzles! (I never mastered Rachmaninov on the piano either.) The game is not designed to teach. The intention is to provide an “instrument” that, in addition to being fun to play, not only provides implicit learning but may also be used as a basis for formal learning in a scholastic setting.

If you say so. But I wonder how much it will cost schools (and society) to find out whether this latest incarnation of "math education" software helps prepare students to become mathematicians, scientists, engineers--or Brazilian street vendors.