kitchen table math, the sequel: 9/16/12 - 9/23/12

Saturday, September 22, 2012


For example, in Prince v. Massachusetts, 321 U. S. 158, 164 (1944), the Court wrote:

"If by this position appellant seeks for freedom of conscience a broader protection than for freedom of the mind, it may be doubted that any of the great liberties insured by the First Article can be given higher place than the others. All have preferred position in our basic scheme. Schneider v. State, 308 U. S. 147; Cantwell v. Connecticut, 310 U. S. 296. All are interwoven there together. Differences there are, in them and in the modes appropriate for their exercise. But they have unity in the charter's prime place because they have unity in their human sources and functionings."
No. 83-812. Argued December 4, 1984-Decided June 4, 1985
Why "differences there are" instead of the customary "there are differences"? (Assuming, of course, that "there are differences" was the customary written form in 1944.)

Friday, September 21, 2012

Glen on Daniel Boone

on the subject of using historical documents to teach reading and writing, Glen writes:
I find the writing in Daniel Boone's autobiography interesting. Here is a man who was raised on the frontier in "Indian country," who had some of what today we would call homeschooling but very little formal schooling. His father justified the state of Daniel's formal literacy by saying that his daughters did the writing and Daniel did the shooting.

So what did a frontiersman with nothing but some homeschooling and Bible study write like, back before the state took over the job of education? Here's how his autobiography begins:

"Curiosity is natural to the soul of man and interesting objects have a powerful influence on our affections. Let these influencing powers actuate, by the permission or disposal of Providence, from selfish or social views, yet in time the mysterious will of Heaven is unfolded, and we behold our conduct, from whatever motives excited, operating to answer the important designs of heaven.

"Thus we behold Kentucky, lately an howling wilderness, the habitation of savages and wild beasts, become a fruitful field...."

Using speeches and other historical documents to teach reading comprehension and writing:
In the Event of Moon Disaster: parallelism, cohesion, the semicolon
Karen H recommends the Gettysburg Address for a lesson in parallelism
Jen on teaching the Star Spangled Banner to her 10-year old (and see Comment thread for more)
Glen on Daniel Boone's autobiography

In the Event of Moon Disaster

Another terrific historical document for use in reading and writing classes, particularly on the subjects of parallelism,  cohesion, and punctuation:* Bill Safire's "In the Event of Moon Disaster." Transcript and image of the original at Letters of Note.
To: H. R. Haldeman
From: Bill Safire
July 18, 1969.



Fate has ordained that the men who went to the moon to explore in peace will stay on the moon to rest in peace.

These brave men, Neil Armstrong and Edwin Aldrin, know that there is no hope for their recovery. But they also know that there is hope for mankind in their sacrifice.

These two men are laying down their lives in mankind's most noble goal: the search for truth and understanding.

They will be mourned by their families and friends; they will be mourned by the nation; they will be mourned by the people of the world; they will be mourned by a Mother Earth that dared send two of her sons into the unknown.

In their exploration, they stirred the people of the world to feel as one; in their sacrifice, they bind more tightly the brotherhood of man.

In ancient days, men looked at the stars and saw their heroes in the constellations. In modern times, we do much the same, but our heroes are epic men of flesh and blood.
Others will follow, and surely find their way home. Man's search will not be denied. But these men were the first, and they will remain the foremost in our hearts.

For every human being who looks up at the moon in the nights to come will know that there is some corner of another world that is forever mankind.


The President should telephone each of the widows-to-be.


A clergyman should adopt the same procedure as a burial at sea, commending their souls to "the deepest of the deep," concluding with the Lord's Prayer.
Each of the widows-to-be.


* Semicolons!

Using speeches and other historical documents to teach reading comprehension and writing:
In the Event of Moon Disaster: parallelism, cohesion, the semicolon
Karen H recommends the Gettysburg Address for a lesson in parallelism
Jen on teaching the Star Spangled Banner to her 10-year old (and see Comment thread for more)
Glen on Daniel Boone's autobiography

Thursday, September 20, 2012

onward and upward

The poll...asked human resource professionals to identify the greatest “basic skills” and “applied skills” gaps between workers age 31 and younger compared with workers age 50 and older.
  • Basic skills – more than half (51 percent) of human resource managers indicated they find older workers to have stronger writing, grammar, and spelling skills in English;
  • Applied skills – more than half (52 percent) of human resource managers said older workers exhibit stronger professionalism/work ethic.
SHRM-AARP Poll Shows Organizations are Concerned about Boomer Retirements and Skills Gaps | 4/9/2012
I've been talking to a Manhattan teacher who has a late-afternoon class in the room where I teach. When she learned that I teach freshman composition, she wanted to know whether I was seeing deterioration in students' writing. She expects the next wave of students to have no writing skills at all, and she wondered whether those kids are already showing up in colleges.

The reason she expects the next wave of students to have no writing skills at all is that Manhattan schools are required to use the Lucy Calkins program. The teacher said that everyone in her school hates the curriculum so much they spend every lunch hour venting, and she herself is desperate to find a job in the suburbs because friends have told her suburban schools "let you teach grammar." There's no escaping Calkins in the city. The principal of a neighboring school tried to get rid of the program and was told to reinstate it or find another position. So the program stayed.

In my experience, suburban schools don't teach grammar, either, although I haven't seen the level of micromanaging here that Manhattan teachers are subjected to. If a teacher in my district wants to teach grammar, and knows some grammar, it's not against the rules. But Manhattan teachers are monitored.  Administrators enter their rooms unannounced to inspect the bulletin boards and observe the mini-lessons, and if teachers are found teaching grammar, they're in trouble. Such is educational reform in the big city.

I shared my Geographical Theory of school quality with her: the closer a school's location is physically to Teachers College, the worse it is.

She said, "Well, imagine how bad things are for us."

and see:
Nightmare from Teachers College
Coach Class by Barbara Feinberg

Tuesday, September 18, 2012

Stanley Fish on teaching writing in college

Stanley Fish answers the question Isn't the mastery of forms something that should be taught in high school or earlier?
By all the evidence, high schools and middle schools are not teaching writing skills in an effective way, if they are teaching them at all. The exception seems to be Catholic schools. More than a few commentators remembered with a mixture of fondness and pain the instruction they received at the hands of severe nuns. And I have found that those students in my classes who do have a grasp of the craft of writing are graduates of parochial schools. (I note parenthetically that in many archdioceses such schools are being closed, not a good omen for those who prize writing.)
I really want to start a Catholic school. Really, truly. My building used to be a Catholic school; I'd like it to be a Catholic school again.

By the way, I do realize that if I had actually attended Catholic schools as a child I might feel different. But I was raised a flat-footed Methodist, as I think I once heard Huston Smith say on TV, and to me the Catholic Church was magic. The nuns in their black habits, the priests, the Holy water in the doorways and the crucifixes on the wall ---- and the sign of the cross! Oh my.

A couple of years ago I asked my second to oldest sister whether she had liked the sign of the cross as a child, and she said at once and with great enthusiasm, "Of course!" She had been so taken by the Catholic Church she wanted to be Catholic. I had no idea. Were all 4 of us kids having our own private Catholic crush?

Truth to tell, my own Catholic crush wasn't so private. I took piano lessons from the nuns for years, and my parents made arrangements for me to attend the Catholic school one day each school year.

I remember reading somewhere that charter schools copied Catholic schools, and the observation struck me as true. I bet, if you scratched the surface, you'd find a lot of charter founders who as children pressed their noses against the windows of a Catholic school, outside looking in.

Monday, September 17, 2012

Computerized teaching: the feedback gap

Yet another breathless account of the wonders of computerized learning appears in this weekend's New York Times Magazine in an article entitled "The Machines are Taking Over: advances in computerized tutoring are testing the faith that human contact makes for better learning."

The article opens with a scene of an actual human being tutoring a fellow species member. While her tutee works on a problem (calculating average driving speed), the tutor provides lots of interactive feedback. Neil Heffernan, the tutor's fiance, catalogued the various different types of feedback she gave under such categories as “remind the student of steps they have already completed,” “encourage the student to generalize,” “challenge a correct answer if the tutor suspects guessing”). According the the article, Heffernan then "incorporated many of these tactics into a computerized tutor," which he spent nearly two decades refining. Now called ASSISTments, it is used by by more than 100,000 students "in schools all over the country." The article describes the experience of one of these 100,000 students with the program's interactive feedback:
Tyler breezed through the first part of his homework, but 10 questions in he hit a rough patch. “Write the equation in function form: 3x-y=5,” read the problem on the screen. Tyler worked the problem out in pencil first and then typed “5-3x” into the box. The response was instantaneous: “Sorry, wrong answer.” Tyler’s shoulders slumped. He tried again, his pencil scratching the paper. Another answer — “5/3x” — yielded another error message, but a third try, with “3x-5,” worked better. “Correct!” the computer proclaimed.
In other words, it's the same old binary right-or-wrong feedback that nearly every educational software program has been using for decades. As the article notes:
In contrast to a human tutor, who has a nearly infinite number of potential responses to a student’s difficulties, the program is equipped with only a few. If a solution to a problem is typed incorrectly — say, with an extra space — the computer stubbornly returns the “Sorry, incorrect answer” message, though a human would recognize the answer as right.
True, the program is still a work in progress. But what's being refined, according to the article, isn't the feedback. Rather, it's the program's ability to detect when a student is getting bored, frustrated, or confused (via facial expression reading software, speed and accuracy of responses, and special chairs with posture sensors "to tell whether students are leaning forward with interest or lolling back in boredom."):
Once the student’s feelings are identified, the thinking goes, the computerized tutor could adjust accordingly — giving the bored student more challenging questions or reviewing fundamentals with the student who is confused.
Or "flashing messages of encouragement... or... calling up motivational videos recorded by the students’ teachers."

Also being refined is the "hint" feature, which users click on when stumped. Human beings (particularly teachers) track common wrong answers and have other human beings (particularly students) come up with helpful hints. These hints are then incorporated into the next generation of ASSISTments.

Cognitive Tutor, a more established software program that is "used by 600,000 students in 3,000 school districts around the country," also limits its feedback to hints and right-or-wrong responses.  And it, too, is being refined based on data from human users:
Every keystroke a student makes — every hesitation, every hint requested, every wrong answer — can be analyzed for clues to how the mind learns.
Ultimately, this data will be put to use not to refine feedback on particular student responses, but to help decide how to space out material and schedule periodic reviews.

But it's carefully tailored feedback on particular responses by particular students that makes human tutoring--the inspiration for all these programs--as powerful is it is.

In my earlier post on Cognitive Tutor, I wrote that programming sufficiently perspicuous feedback for mathematical problems "strikes me as even more prohibitive" than the feedback I labored for years to provide in my GrammarTrainer program. Last night I ran this impression past a mathematician friend of mine who cares a lot about effective math instruction. She emphatically concurs.

When it comes to educational software developers--as opposed to educational software users--there is some somewhat perspicuous feedback on whether their answers (answers to students' educational needs) are on track. As I write earlier, that feedback isn't particularly encouraging.

(Cross-posted at Out In Left Field).

Sunday, September 16, 2012

writing by ear

On the question of 'picking up' grammar through reading, Jean writes:
I think many people--like you--can learn general grammar rules by reading. I am also one of those people, BUT I have always felt insecure in my writing. There are many fine points that I did not absorb and that I make mistakes in. I have also noticed that my daughter, who reads no more than I did at her age but who is made to do a rigorous grammar course, can read at a higher level than I could at her age.
Reading Jean's comment, I'm thinking ... I probably would have been insecure about the fine points of grammar IF I had ever thought about the fine points, or cared. But I didn't! I didn't think about grammar at all, I thought about writing (comma splice intentional).*

I write by ear. I don't recall ever consulting a grammar book, not once in an entire career of professional writing. In fact, I didn't even own a grammar book until a little over 10 years ago, when an editor told me that all the editors in New York liked The Grammar Bible. I bought it, but I didn't read it. (Hope to do so one of these days.)

I always wanted to be a writer, from the time I knew what writing was, and I was an obsessive reader (and still am). And I simply never gave grammar a second thought. I learned grammar through reading, and I practiced grammar through writing.

I wish now I had been taught grammar -- sentence diagramming in particular -- as I would have loved every minute of it, and I think formal instruction in sentence syntax would have made me a better writer sooner.

But I wasn't taught grammar, and I learned to write without thinking consciously about grammar and punctuation.

Back to the question of missing the fine points: I distinctly recall, from time to time (especially back when I discovered my affection for the semicolon) not knowing what 'the rules' said to do. But uncertainty about the rules never caused me to think I ought to actually go out and look up the rules.

Basically, I had just one ironclad rule: does it sound right? If it didn't, I rewrote; and I rewrote over and over and over again. One of these days I should count how many versions some of my sentences (and passages) go through. It has to be in the hundreds. Many hundreds, in some cases.

I'm sure that, like Jean, I was making subtle errors all those years. In fact, I know I was. After I finally started to learn the formal rules, just 2 years ago, I discovered one in particular that I hadn't picked up through reading, which is the prohibition against placing a comma between an independent clause & a dependent adverbial clause.


I went home because I felt sick.


I went home, because I felt sick.

I had never heard of this rule, and never conceived of it, either. (I had also never heard the rule about using a comma after a FANBOYS, or the rule about not putting a comma after "rule" 2 sentences ago.) Where commas were concerned, I had always followed my own rule, which was to use a comma if it sounded right. So sometimes I used a comma, and sometimes I didn't use a comma, depending.

After I learned the No Commas Before Subordinate Adverbial Clauses rule, I started to follow it .... but then, not too long afterward, I stopped. The rule doesn't work! Sometimes a sentence needs a comma, rule or no rule, and there's an end to it.

All of this said, I feel pretty strongly today that I would have been better off if I had learned formal grammar, including sentence diagramming, in K-12. But that is a subject for another post.

* The fact that writing is grammar, pretty much, escaped my notice.

Magister Green on how the Greeks and Romans taught

Magister Green on the question of whether you can "pick up" the grammar of writing through reading:
Going back to ancient times, the Greeks and Romans taught their children not rules of traditional grammar but rather the works of the great poets and thinkers who had come before. In particular, emphasis was placed on memorizing and modeling one's own schoolwork on the works of past masters. If we accept that students can learn grammatical rules through exposure as opposed to explicit instruction (which I do accept), the fact that schools in general (public and private) refuse to teach, much less acknowledge, the works of "masters" would go a long way towards explaining why students today know so little of the rules of traditional grammar.
I've been only vaguely aware of the 'copy work' practices of the ancients (and of the Well-Trained Mind people), but I've come to be a fan.

I think Magister Green is right.

One reason students don't write (or punctuate) grammatically today is that they aren't spending enough time reading, studying, and 'mastering' important works under the direct guidance of their teachers.

I think there's probably something missing in terms of fluency training in the early grades, too: possibly just basic fluency practice in writing and punctuating simple Subject+Verb+Object and Subject+Verb+Complement sentences. But I don't know.

I speculate that 'basic fluency training' is missing because C. was reading important works under the direct guidance of teachers in high school (though not before then), yet his writing still had lots of comma splices. I asked him how he finally got rid of them, and he said he thinks his dad just corrected so many of them that he finally started to see them himself.

Which reminds me: I need to get a post up on Morningside and "discrimination training."

Morningside does not seem to teach "grammar" at all, really. They teach writing via sentence combining, and they don't teach sentence parsing or sentence diagramming. Kent Johnson told me he teaches grammar terminology after students have learned to write, and he teaches the terminology at that point because students have to know it for state tests.

I don't know how I feel about that. I gainsay nothing Morningside does; I've seen the results with my own eyes (and in a writing class, too). But the idea of 'withholding' or avoiding the vocabulary of grammar bothers me nevertheless. I wish somebody had taught me how to diagram a sentence back in the day!

On the other hand, I may be looking at it the wrong way. The Morningside program doesn't avoid teaching the vocabulary of grammar so much as it delays formal instruction in grammar.

Maybe that's the right sequence. Reading and writing first, grammar second.

I'm going to come back to this later.

SAT math is puzzle math

Ed and I had an amazing conversation last night with an SAT math tutor. He told us that for him SAT math is super-easy, so easy that the first time he saw the test he wondered whether it was a joke. He estimates that in his years of tutoring he has encountered 20,000 SAT math items: for each item, he instantly knew the answer.

At the same time, he's not adept at other aspects of math, particularly anything to do with spatial reasoning, which predicts success in math, science, and engineering. He has trouble doing problems like this one:

His brain, he said, works exactly like the brains of the people who write the SAT, and nothing like the brains of other people who are good at math. He himself is good at math, spent most of his life writing software for Wall Street and briefly taught math. As to the latter, he told us US math teaching would be much better if schools cut the curriculum by 2/3 and had students learn the remaining 1/3 really well. He'd never read Schmidt and had never heard of mile-wide-inch-deep.* It just seemed obvious to him that a good 2/3 of US curriculum should go.

Naturally I was keen to know what kind of brain he and the SAT people have, and the answer was: a puzzle brain. He loves, loves, loves puzzles; puzzles are his thing.

That's SAT math, only the puzzles are too easy for him.

A funny moment: he said his ex-wife told him she was reading a book that explained his brain: "You have no right brain at all," she told him, or words to that effect. When he read the list of right-brain characteristics, he agreed.

I wish I'd asked him how he fares on find-the-hidden-right-triangle items specifically.

* Schmidt: "[A]t eighth-grade [we're] telling teachers to teach 35 topics. Other countries are telling their teachers to teach 10 to 15."