kitchen table math, the sequel: 6/5/11 - 6/12/11

Saturday, June 11, 2011

No WUG is too DAX to be ZONGED

Another fabulous grammar puzzle from Language Log:
No WUG is too DAX to be ZONGED.
Does this sentence say that a WUG should be ZONGED?

Or that a WUG should not be ZONGED?

And why haven't I been reading Language Log for lo these many years?

6 in 10 people get this one right.

Dedicated Teacher on differentiated instruction

Dedicated Teacher writes:
I agree that differentiated instruction* presents a tremendous challenge to the classroom teacher. I currently teach at a school that has time built in for differentiation in reading, but I've been trying to devise a plan to implement the same practices in math, but I just don't have enough instructional time in the day. When I do try to work with a small group of students, I find that the others do not engage in anything meaningful or that I can't teach the small group because I'm having to constantly intervene with the other groups. I find that my differentiation comes when I'm sitting with a couple of children at recess reteaching a concept or by keeping students in during Music or P.E. This not only keeps them from their much needed recess, but I'm often giving up my much needed planning time. If you come up with a way to make differentiated instruction work....let us all know.
* the arithmetic of differentiated instruction

writing = sentences

In her book The Writing Life (1989) Annie Dillard tells the story of a fellow writer who was asked by a student, "Do you think I could be a writer?" "'Well,' the writer said, 'do you like sentences?'" The student is surprised by the question, but Dillard knows exactly what was meant. He was being told, she explains, that "if he liked sentences, he could begin," and she remembers a similar conversation with a painter friend. "I asked him how he came to be a painter. He said, 'I like the smell of paint.'" The point, made implicitly (Dillard does not belabor it) is that you don't begin with a grand conception, either of the great American novel or a masterpiece that will hang in the Louvre. You begin with a feel for the nitty-gritty material of the medium, paint in one case, sentences in the other.

But wouldn't the equivalent of paint be words, rather than sentences? Actually, no, because while you can brush or even drip paint on the canvas and make something interesting happen, just piling up words, one after the other, won't do much of anything until something else has been added. That something is named quite precisely by Anthony Burgess in this sentence from his novel Enderby Outside (1968):

And the words slide into slots ordained by syntax, and glitter as with atmospheric dust with those impurities which we call meaning.

Before the words slide into their slots, they are just discrete items, pointing everywhere and nowhere.

How to Write a Sentence: and How to Read One
Stanley Fish
page 1 - 2
Until this year, I did not know that the sentence is the basic unit in writing.

Not the word.

That's 'cause I was educated by wolves.

help desk - grammar

Inspired by an SAT question C. and I answered yesterday --
All of the editors at the magazine agreed.
All the editors at the magazine agreed.
What happens grammatically when you omit the preposition ('of')?

In the first sentence, 'all' is the subject.

Is 'all' the subject of the second sentence, too? Is the preposition ('of') implied?

Or does 'all' become an adjective modifying 'editors,' making 'editors' the subject of the sentence?

Friday, June 10, 2011

teach the sentence

Close on the heels of Katharine's post about reform writing and Debbie's on the lost art of sentence diagramming, I came across this study mentioned on Language Log:
Research into grammar by academics at Northumbria University suggests that a significant proportion of native English speakers are unable to understand some basic sentences.


The project assumed that every adult native speaker of English would be able to understand the meaning of the sentence:

"The soldier was hit by the sailor."

Dr Dabrowska and research student James Street then tested a range of adults, some of whom were postgraduate students, and others who had left school at the age of 16. All participants were asked to identify the meaning of a number of simple active and passive sentences, as well as sentences which contained the universal qualifier "every."

As the test progressed, the two groups performed very differently. A high proportion of those who had left school at 16 began to make mistakes. Some speakers were not able to perform any better than chance, scoring no better than if they had been guessing.

Dr Dabrowska comments: "These findings are ground breaking, because for decades the theoretical and educational consensus has been solid. Regardless of educational attainment or dialect we are all supposed to be equally good at grammar, in the sense of being able to use grammatical cues to understand the meaning of sentences.


The supposition that everyone in a linguistic community shares the same grammar is a central tenet of Noam Chomsky's theory of universal grammar. The theory assumes that all children learn language equally well and that there must therefore be an underlying common structure to all languages that is somehow "hard-wired" into the brain.

Dr Dabrowska has examined other explanations for her findings, such as limitations to working memory, and even so-called "test wiseness," but she concluded that these non-linguistic factors are irrelevant.

She also stressed that the findings have nothing to do with intelligence. Participants with low levels of educational attainment were given instruction following the tests, and they were able to learn the constructions very quickly. She speculates that this could be because their attention was not drawn to sentence construction by parents or teachers when they were children.

Many English Speakers Cannot Understand Basic Grammar
ScienceDaily (July 6, 2010)
Turns out grammar needs to be taught.

pop quiz, part 5

How many people do you think answer this question from the Wason test correctly:
[Four] cards are placed on a table to show 3, 8, red and brown....The rule is: “If a card shows an even number on one side, then it is red on the other.” Which cards do you need to turn over to tell if the rule has been broken?
And how many people would you expect to get the answer right on this one:
“If you borrow the car, then you have to fill the tank with petrol.” Once again, you are shown four cards, one side of which says who did or did not borrow the car and the other whether or not that person filled the tank:

Dave did not borrow the car
Helen borrowed the car
Brianne filled up the tank with petrol
Kirk did not fill up the tank with petrol

Does learning math make you more likely to know the answer?

Or, alternatively, does being able to answer these questions make it easier for you to learn math?

I'll put the percent-correct in the comments.

Here is Language Log on the Wason test. (Haven't read yet.)

Thursday, June 9, 2011

Impostor Questions

Any thoughts as to whether or not it's helpful (or harmful) to use non-College Board material when studying for the SAT?

I'm suspicious, and they feel like impostors (though there are notable exceptions, including PWNtheSAT and UltimateSATVerbal), but I'm open to the possibility that these impostors make the knowledge more flexible.

Thoughts? Experiences?

(Cross-posted on Perfect Score Project)

Best Wishes in Your Search for Truth

Truth in American Education

Americans rightly have voiced these concerns that we address:

■Operating outside of the system of checks and balances that Americans rely on is dangerous to our freedoms. They are an affront to parents’ rights, the 10th Amendment and our tradition of local control over education.
■The mixing of public, corporate and foundation money without proper accountability is troublesome, as taxpayers contribute a significant portion of education funding.
■A one-size-fits-all set of national standards, curriculum and testing controlled by a few will affect us all.
■Impacts to public school, private school and home school education will be felt, as mandates increase and curriculum choices will diminish.
■Students are not widgets and require individualized learning. More top-down control is not in the best interests of educating individual students.

Truth in American Education provides information to parents, taxpayers, school board members, educators and legislators who are concerned about these issues. At the heart of it, the disposition of these issues will determine whether the federal government and elite, special interest groups have the right to form the hearts and minds of children and whether we will reject, or affirm, the concepts laid down by our founding principles.

Wednesday, June 8, 2011

$39,000 for tuition - $35,000 for tutors

Siddharth Iyer spent eight Mays cramming for finals, first at Stuyvesant High School and then at Columbia University.

Nine years later, it is still crunch time for Mr. Iyer, a top tutor at Ivy Consulting Group, as his clients face a deluge of end-of-year exams. “He’s been prepping my son all week,” said the mother of one, a senior at Riverdale Country School in the Bronx, speaking on the condition that she not be named because Riverdale discourages both tutoring and talking to reporters.

“Prepping” — in this case for an oral exam in Riverdale’s notorious Integrated Liberal Studies, an interdisciplinary class laden with primary sources instead of standard textbooks — did not start the week before the exams, the mother pointed out. She said she had paid Mr. Iyer’s company $750 to $1,500 each week this school year for 100-minute sessions on Liberal Studies, a total of about $35,000 — just shy of Riverdale’s $38,800 tuition.

Last year, she said, her tutoring bills hit six figures, including year-round SAT preparation from Advantage Testing at $425 per 50 minutes; Spanish and math help from current and former private school teachers at $150 an hour; and sessions with Mr. Iyer for Riverdale’s equally notorious interdisciplinary course Constructing America, at $375 per 50 minutes.

Push for A’s at Private Schools Is Keeping Costly Tutors Busy
Published: June 7, 2011
Elite New York schools like Riverdale and Dalton hire teachers with Ph.Ds -- not Ed.Ds*-- in the fields they teach. Very likely, what has happened here is that these teachers have created advanced college-level courses high school students can't handle.

We need micro-schools.

* When we looked at private schools 3 years ago, we found that the math teachers in nearly every private school had Masters degrees in education, not math.

diagramming the Preamble

redkudu left a link to this diagram of the Preamble to the Constitution of the United States, and I had to post it:

We the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defence, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America.

The Lost Art of Sentence Diagramming

I really do not know that anything has ever been more exciting than diagramming sentences. --Gertrude Stein

After reading this amusing article in the American Educator, I think sentence diagramming has a bad rap. It sounds like fun.

(Cross Posted at Perfect Score Project)

Tuesday, June 7, 2011

a bad economy depresses math scores

Given the magnitude of the recent recession, and the high-stakes testing the U.S. has implemented under the No Child Left Behind Act (NCLB), it is important to understand the effects of large-scale job losses on student achievement. We examine the effects of state-level job losses on fourth- and eighth-grade test scores, using federal Mass Layoff Statistics and 1996-2009 National Assessment of Educational Progress data. Results indicate that job losses decrease scores. Effects are larger for eighth than fourth graders and for math than reading assessments, and are robust to specification checks. Job losses to 1% of a state’s working-age population lead to a .076 standard deviation decrease in the state’s eighth-grade math scores. This result is an order of magnitude larger than those found in previous studies that have compared students whose parents lose employment to otherwise similar students, suggesting that downturns affect all students, not just students who experience parental job loss. Our findings have important implications for accountability schemes: we calculate that a state experiencing one-year job losses to 2% of its workers (a magnitude observed in seven states) likely sees a 16% increase in the share of its schools failing to make Adequate Yearly Progress under NCLB.

Children Left Behind: The Effects of Statewide Job Loss on Student Achievement
Elizabeth Oltmans Ananat, Anna Gassman-Pines, Dania V. Francis, Christina M. Gibson-Davis
NBER Working Paper No. 17104
Issued in June 2011
NBER Program(s): CH
Here's the Curious Capitalist: Is the Economy Hurting Your Kid's Report Card?.

Perceptual Learning

There was a story in the New York Times yesterday about perceptual learning, and it brought up two things for me:

a) I was surprised (relieved?) to hear that I wasn't the only one who has trouble with fractions.

b) I had a breakthrough moment a few weeks ago when Catherine told me to break out the number line.

(Cross posted on Perfect Score Project)

Monday, June 6, 2011

Remind me not to travel in space

Lieberman’s joint research with medical school faculty, other colleagues, and Brown University graduate and undergraduate students have revealed a “syndrome” – a pattern of speech motor and cognitive deficits occurs [sic] that derive from impaired subcortical basal ganglia structures. Ongoing studies of Parkinson’s disease, childhood developmental verbal apraxia, Rolandic epilepsy, autism, hypoxic insult to the brain arising from exposure to extreme altitude as climbers ascend Mount Everest, and focal brain lesions provide an opportunity for both graduate and undergraduate students to participate in research. Other studies on speech production have synthesized the vowels that Neanderthals could have uttered. The findings of these studies have been applied to the diagnosis and treatment of these conditions as well as monitoring systems for exposure to high-intensity radiation in space travel, which produces damage to neural circuits involving the basal ganglia.
Philip Lieberman at Brown
I've spent the past year trying to figure out the basal ganglia. (pdf file)

In case you were wondering.

Bonus factoid: Here's what it sounds like when a Neanderthal tries to pronounce a long 'e.'

The Pleasure of Problem Solving

Willingham's article, Why Don't Students Like School, describes perfectly why I love working on SAT problems:

There is a sense of satisfaction, of fulfillment, in successful thinking......It's notable too that the pleasure is in the solving of the problem. Working on a problem with no sense that you are making progress is not pleasurable. In fact, it's frustrating. And there's not great pleasure in simply knowing the answer either.

And why I find them so challenging:

There's a final necessity for thinking: sufficient space in working memory. Thinking becomes increasingly difficult as memory gets crowded.

(Cross-posted on Perfect Score Project)

Sunday, June 5, 2011

at Google

re: crowds vs herds, jtidwell writes:
I worked at Google. I was based in the Cambridge (Mass.) office, but its architecture is comparable to the NYC office. I spent my share of time working as a visitor in the NYC office, too, and also in Mountain View.

What they are doing at Google is TOTALLY different from guess-the-number problems. :-)

But, first, the architecture. There are large rooms with an open layout, but these aren't generally huge. Most that I visited only held about 20-30 people, and the people working in them were respectful about a quiet environment. There are countless meeting rooms, both large and tiny, that one can retreat to when necessary. And truth be told, I never spent much time at my desk! I was frequently working in one of these meeting rooms, either in F2F meetings, or on videoconferences, or some hybrid thereof, or by myself when I needed serious quiet.

Plus, everyone is issued laptops instead of (or in addition to) one's desktop computer. Googlers are encouraged to take their work anywhere they please, as long as it's secure. Working from home is fine, too.

The nature of the work there is quite collaborative, as all good software product teams are. But once decisions are made, or questions formulated, everyone scurries off and does individual work. Very intense individual work. (In my case, it was UX design, with occasional programming or online research to figure something out.) And let me tell you, if you weren't extremely competent at self-directed work and individual achievement, you didn't last long in that environment. :-)

Following the crowd's opinion, just because you don't have the nerve to state your own differing opinion, isn't looked well upon either.

Red Horse Tutoring

Stacy Howe Lott has a website!

the arithematic of differentiated instruction

Concerned Teacher on differentiated instruction:
Differentiated instruction is a total scam. You MUST teach in order for students to learn, and you must offer practice time during which you are available to lend assistance. No superteacher can do both at multiple levels and through multiple modalities daily in the course of a single 55 minute period class, and do it well.

Teachers are not the folks who have perpetrated this myth. Teachers have had this myth forced upon them by administrators, and as far as I know, colleges have promoted this nonsense.

Concerned Teacher responding to Protecting Students from Learning
The arithmetic of differentiated instruction doesn't add up.

Put 20 kids at all levels of abilities and interests in the same classroom for 55 minutes.

Seat them in pods.

Have the teacher deliver a 10 minute mini lesson, after which she moves around the class working one-on-one with 20 different children.

While the teacher is making her way around the room, the other 24 children do whatever they've been told to do without being able to ask a question or get feedback. If they've been told to work together, then a lot of them are going to be copying whatever the quickest child in the pod is doing.

The total number of productive minutes an individual child can experience is 12 to 15 out of the 55, max, and that's assuming that the mini lesson was pitched to the child's level.

If the lesson was over a child's head, he or she has just two or three minutes of comprehensible direct instruction from the teacher.

If the lesson was below a child's level, he or she also has just two or three minutes of useful direct instruction from the teacher. If that.

Hunter Writing System

looks interesting:
Is this a whole-language approach to teaching grammar?

Yes and no. Yes, to the extent that whole-language instruction requires involvement of all the senses in learning. It is my recommendation that teachers have students say their rearranged sentences out loud (or, at least, subvocally) not only to test whether they are meeting the criteria for some grammatical element but also to hear what correctly spoken English sounds like. Of course, they do write and read the sentences as they carry out the exercise material.

No, because this system for immersing students in structure does not--and cannot--teach grammar through literature or through the students' own writing. Students must learn the structure of the sentence systematically, building from the known to the unknown in an experience-based and carefully sequenced way. This ownership of structure cannot be learned in random order nor without "interactive" types of exercises.

How does this way of teaching grammar relate to the process approach to teaching writing?

Nancie Atwell, a chief proponent of the process approach to teaching writing for middle school students, recommends occasional 10-minute mini-lessons in grammar primarily for the purpose of fixing some usage error. (Her reasoning is that the indispensable, if not sole, means to becoming a better writer is to do personally meaningful writing--as opposed to learning grammar as a means.)

Although my program would provide ideal subject matter for 10-minute mini-lessons, the primary instruction would have to be in the fundamentals of grammar (not in rules of usage); it would have to be virtually daily, not occasional, in occurrence; and it would have to be accompanied by extensive practice. It would have to include incrementally developed lessons on how sentences and their parts work and interact and would address usage errors only as sufficient background to understand and consistently apply them have been absorbed.

The philosophy of the proponents of the process approach to writing is that improvement in the mechanics of writing will take place with students' heightened desire to make sure that their message is read and acted upon and without formal instruction in grammar. (There remains the troubling question as to whether such experiences can lead to the remedying of most, let alone all or the most serious, mistakes. Then there is the question of permanency of the error-free writing.) Is it not reasonable to believe, too, that any lasting improvement in the mechanics of writing might occur just for the brightest of students or for those immersed in correct usage of English in their homes?

My philosophy regarding mastery of writing on the part of middle school students--in fact, all students--is entirely different. My philosophy is that immersion in grammar--that is, an experiencing of the roles of the key parts of the sentence by means of hands-on strategies, strategies that initially involve the rearrangement of sentence parts--is a prior and, for many (if not most) students, an indispensable means to self-confidence and competence in writing....

It is in light of this that I recommend that my grammar program--in accompaniment with on-going composition work--be the initial component of any foundational writing program (and, therefore, of any middle school program). My teaching suggestions in the next section offer some insights.

Competing Philosophies

help desk - absolute value

Problem 85 in Perfect 800: SAT Math:
In an amusement park, regulations require that a child be between 30" and 50" tall to ride a specific attraction. Which of the following inequalities can be used to determine whether or not a child's height h satisfies the regulation for this ride.

(A) | h -10 | < 50
(B) | h - 20 | < 40
(C) | h - 30 | < 20
(D) | h - 40 | < 10
(E) | h - 45 | < 5

update: The book's answer is C, which is wrong.

Should We Be Worried? (YES)

Core Standards Are Very Different
The new standards are supposed to be internationally benchmarked. Yet Common Core’s eighth-grade math standards don’t match Finland (0.21), Japan (0.17) or Singapore (0.13), primarily because these countries stress performing procedures. On language arts and reading, alignment ranges from 0.09 with Finland to 0.37 with New Zealand.

Should we be worried? Common Core Standards represent “a change for the better” when it comes to “higher order cognitive demand,” Porter concludes, but the “answer is less clear” when it comes to the topics that are covered.

Personally, I would say the "answer" is perfectly clear!

How Big a Change are the Common Core Standards?