kitchen table math, the sequel: 6/19/11 - 6/26/11

Thursday, June 23, 2011


Last summer I learned that heat and math don't mix.

Yesterday I learned that heat, humidity and no sleep are catastrophically incompatible with a timed 25-minute math section in the Blue Book.

Sitting outside in the heat and humidity, not consciously feeling the effects of a short night's sleep, I missed: 6 questions out of 20. Six. All of them rated E (for Easy) or M (for Medium).

I answered question 20 correctly. Question 20 is the one tutors tell you not to even attempt unless you're trying for an 800. That I could do.

Number 19, I got right, too.

But the question where all you had to do was read the y value on the y axis --- no. Got that one wrong.

Or the question where you were supposed to find the absolute value of the sum of two negative numbers. Wrong again.

For years I've been reading about all the bad things that happen to people who don't get enough sleep. Sleep loss causes inflammation; sleep loss causes weight gaint; sleep loss screws up your memory; etc., etc, etc.

After yesterday, I'm a believer:
When researchers put test subjects in environments without clocks or windows and ask them to sleep any time they feel tired, 95 percent sleep between seven and eight hours out of every 24. Another 2.5 percent sleep more than eight hours. That means just 2.5 percent of us require less than 7 hours of sleep a night to feel fully rested. That's 1 out of every 40 people.

When I ask people in my talks how many had fewer than 7 hours of sleep several nights during the past week, the vast majority raise their hands. That's true whether it's an audience of corporate executives, teachers, cops or government workers. We've literally lost touch with what it feels like to be fully awake.

Great performers are an exception. Typically, they sleep significantly more than the rest of us. In Anders Ericcson's famous study of violinists, the top performers slept an average of 8 ½ hours out of every 24, including a 20 to 30 minute midafternoon nap some 2 hours a day more than the average American.

The top violinists also reported that except for practice itself, sleep was second most important factor in improving as violinists.
Sleep is more important than food.
Tony Schwartz
The Official SAT Study Guide, 2nd edition

Tuesday, June 21, 2011

Cost of College - new blog

I have a new blog - Cost of College.
"A blog about the various costs that we face in the years BEFORE, DURING AND AFTER college. Focus is on the financial as well as the academic factors, with an eye for exploring the trends in higher education that may profoundly affect our lives in the coming years."

Today's post is about taking student loan obligations very seriously.
You can discharge your student loan obligation . . . if you die or become quadriplegic

help desk - Dr. Chung

I think the solution manual may be wrong on this one.

I'm a huge fan of John Chung's SAT Math, btw. This is the first time I've encountered an answer that struck me as wrong.

source: Dr. John Chung's SAT Math

Dr. John Chung's SAT Math

SAT Compare Two Passages

They're the most excruciating for me.

There is a method, and apparently it works for me as I'm getting better, and they are becoming less painful by the day.

(cross posted on Perfect Score Project)

Monday, June 20, 2011

Katharine Beals on King James

There were giants in the earth in those days; and also after that, when the sons of God came in unto the daughters of men, and they bare children to them, the same became mighty men which were of old, men of renown.
Genesis 6, Verse 4
While the other translations are also confusing here and there, there are a number of things that make the KJB sentence especially so.

1. The placement of the semi-colon suggests that the biggest break is between the first clause and the rest of the sentence. But there really shouldn't be a break between it and "and also after that." Cf the oddity of: "There were giants in the earth in those days; and also after that."

2. What does the "when" clause modify: "those days", or "after that", or both? (The disruptive placement of the semi colon does not help in sorting this out)

3. Is "and they bare children to them" part of the when-clause? Semantically, this would make the most sense. But the immediately preceding comma, the overt subject ("they") and the change from present to past tense (from "came" to "bare"), make this interpretation more difficult. Cf:

"when the sons of God came in unto the daughters of men and bore children to them."

3. The tense change seems to serve no purpose other than to obfuscate.

4. What follows, as far as I can tell, is a comma splice. "the same became mighty men which were of old, men of renown" should either be its own sentence, or should be conjoined to what precedes it by "and."

5. Why "the same" instead of "they"?

6. An additional comma could reduce the additional obfuscation at the end: "which were, of old, men of renown"

This seems to me to be a classic case of iconicity in language: using linguistic form iconically to express or alter content. (onomopeia is another example). Here, the obfuscating punctuation, syntax, and morpho-syntax may serve to lend an aura of mystery to what might otherwise seem (to the writers of old? or the translators of new?) to be too straightforward for a religious text.

It would be interesting to see the original Hebrew, which, according to what little I've read, involves less embedding and more simple parataxis (sentences connected with "and"). That still leaves plenty of room for obfuscation.

Many other religious texts and/or translations, from what I know of them, rely heavily on an obfuscation that is partially linguistic (Zen koans?)

I've suspected the same thing of certain philosophers (Kant, Hegel) and a number of postmodernists as well.

My preference is for maximum linguistic clarity: the best messages, however mysterious, should shine rather than fade away when viewed in the light of a well-written sentence.

Genesis 6 1-4 Jerusalem Bible

the King James version:
There were giants in the earth in those days; and also after that, when the sons of God came in unto the daughters of men, and they bare children to them, the same became mighty men which were of old, men of renown.
Genesis 6, Verse 4

the Jerusalem Bible version:
Sons of God and daughters of men
When men had begun to be plentiful on the earth, and daughters had been born to them, the sons of God, looking at the daughters of men, saw they were pleasing, so they married as many as they chose. Yahweh said, 'My spirit must not for ever be disgraced in man, for he is but flesh; his life shall last no more than a hundred and twenty years'. The Nephilim were on the earth at that time (and even afterwards) when the sons of God resorted to the daughters of man, and had children by them. These are the heroes of days gone by, the famous men.
Genesis 6: 1-4
The Jerusalem Bible passage is just as mysterious as the King James, but I'm not straining to decipher the pronoun referents.

The Jerusalem Bible: Reader's Edition

winner-take-all schools redux

more from the conversation re: public versus private school on College Confidential:

cpt of the house writes:
The fundamental reason for my sending my kids to a private school is that I could see that they got more opportunities for high level academics, sports, music and a lot of other things as compared to their highly regarded high school. Now some kids were able to get those same goodies at their public schools, and that is a wonderful thing. I did not enjoy those years of paying that tuition and if our public school, or any public school in the area could have provided the benefits that the privates could, I would have jumped on it. But they did not. I had kids who could not get into AP programs at our county school districts, but got into them in the private schools and got all 4s and 5s on the tests.
Now in our case, we were taking chances since our kids were not the top grade academic kids in K-12 that are at these private schools and were in the bottom half and even quarter of their class in high school. They needed every bit of positive push we could give them....they would not have had those advantages and choices from our public school. They would not have gotten into the top classes there that are gate kept (I checked), they could not get the number of ECs in terms of performing arts, and they would not have gotten the athletic opportunities. Their peers would not have been the kids who were assuming they were going to go to college as our high school is very diverse in socio economic situations and since they would not be in the classes where college is the main goal.
This is what Paul Attewell documented in his study of elite public high schools. Kids who are capable of earning 4s and 5s on Advanced Placement exams are tracked out of the most advanced courses.

Paul Attewell's Winner-Take-All in bullet points
The Winner-Take-All High School: Organizational Adaptations to Educational Stratification. Paul Attewell. Sociology of Education, Vol. 74, No. 4 (Oct., 2001), 267-295

public versus private high school

interesting discussion at College Confidential

I was struck by this observation:
One thing that I feel was so worth while at that private school where I sent my kids was the Composition course. Every Monday starting with freshman year until the end of first semester of senior year, they have to write an essay on what is usually an unannounced subject. THey have to handwrite the essay in those old blue books used for final exams at colleges. Those essays are scrutinized and corrected and graded. The student then has a chance to rewrite the essay--in class during the week to better the grade. So no out of school help is available for that part of the grade, and the kids really do learn to write. Sometimes a general topic is given and the kids have to research a subject and can bring a page of notes and cites to use for the essay, but still, the exact question is not known.

What makes this work are dedicated teachers who read and grade those essays. One thing I despised about our public school experience were teachers who did not follow up on corrected papers and tests. They would mark off the answers, sometimes not even reading the work carefully, and then just hand back the paper, If they bothered to look in their wastepaper basket, they would find those returned papers for the most part, thrown in there. The kids would learn nothing from the assignment. X School teachers read every single answer and would make the kids redo what they showed they did not know. But that is not always the case for even private schools. The top privates, the selective ones with the top reps tend to offer this as a matter of course.

And here's a parent talking about Rice:
I want to share with you the experience I had going to the last commencement for Rice, a Catholic all boys school in Harlem run by the Christian Brothers. The CB are a dying breed, their extinction accelerated by the priest scandals, and this school never did make any money. The school graduated a group of all African American young men from Harlem, none of them deemed smart enough to be accepted to any of the top magnet schools the NYC city offers to its brightest students. The graduation rate of this school is remarkable, given who goes there, and nearly every single one of those kids is going to college, even more remarkable when you look at the stats for inner city AA young men. Now this is not a school that most middle class folks would want for their kids, but when you look at the accomplishments for those young men, given what the alternatives are, the result are phenomonal. I do not support school vouchers, but this a case that really makes me pause, and would the type of exception that I would support.

I personally know a number of young men who graduated with my son. They did not do well in the NYC high school lottery, so their parents, came up with the money to send them to a Catholic high school. It was a difficult 4 years for these families, who even with discounts and transportation vouchers found it very difficult to go to this school that often required transportation transfers to attend. Some of the kids lived in far away boroughs. They were NOT the brightest or best by any public or private school standards. But every single one of them are going to college with enough merit/financial aid to make it work. I talked to the mom of one who told me that less than half her sons' peers who did not get into the great NYC magnet schools are going to college and if they are, are going to community colleges or at best the CUNYS maybe. What a difference in results.

Sunday, June 19, 2011

King James

On the subject of reading and grammar (see here and here), I've been trying to read the Bible -- the whole Bible, start to finish -- for 3 years now.

When I asked C's freshman religion teacher which Bible to read, he said that while the King James edition was the one I should read, the Jerusalem Bible was the one I could read.

He was right.

Why is the King James version so difficult? I'm sure Katharine can tell us, and I hope she will.

For now, my sense is that the problems come down to unfamiliar grammar combined with unfamiliar idiom:
There were giants in the earth in those days; and also after that, when the sons of God came in unto the daughters of men, and they bare children to them, the same became mighty men which were of old, men of renown.
Genesis 6, Verse 4
I don't know what this passage means.

First of all, I don't know what the word giants means in this context. Were the giants the sons of God?

I'm not sure. I don't know how the words and also after that connect the subject of the first independent clause to the subject of the second independent clause: how do the words and also after that relate giants to sons?

Next question: if the sons of God are the giants, are the giants half-God, half-man? (That can't be right, can it? This is the Bible, not The Odyssey.)

The expression came in unto the daughters is unfamiliar, but I can figure it out from context.

As to grammar, the pronouns are an obstacle and have been in virtually every passage I've read:
...when the sons of God came in unto the daughters of men, and they bare children to them, the same became mighty men which were of old, men of renown...
They refers to the daughters of men; them refers to the sons of God; the same refers to the children;  and which also refers to the children. I think. If this passage appeared on the SAT, it would be wrong on grounds that the pronoun antecedents are unclear.

In Abraham Lincoln's day, I gather, children were taught to read using the King James Bible, so presumably the pronoun antecedents were clear enough to readers back then. But the King James has different grammatical rules than the ones we're used to, and that's the problem.

If you don't know grammar, you can read the words, but you can't read the text.


Since my son gets to take the PSAT test as a sophomore in October, I thought that it would be a good place to start. Taking into account the warnings of "imposter" questions, I decided to get some real tests. Unfortunately, they are not offered by the College Board anymore, so I had to get them through Amazon. I got them the other day, and I thought I would share my initial impressions.

First, the real questions are so enlightening compared to a 3rd party PSAT test book I bought. The questions on the test are simple, ... but speed and accuracy are very critical. In the first section, you have 20 questions to answer in 25 minutes. Even though some questions are trivial, it still takes you time to read the question, check to make sure you are not jumping to conclusions (that it really is that simple), and then fill in the bubble. It's one thing to do this informally, but if you try to simulate a real test situation, the seconds slip by very quickly, and the pressure to rush increases.

Second, some of the questions go out of their way to try and trick you into the wrong answer. In one question, you find x+y, but they ask for the average of the two numbers. One answer is x+y and another is (x+y)/2. Clearly, the test is not just about your knowledge of math. I think there were 3 out of 20 questions where they went out of their way to mislead you.

Third, there are certain things you need to know very quickly, like the ratios of the sides of a 45-45-90 triangle and a 30-60-90 triangle. It's not good enough to know the Pythagorean Formula or to find the answer with trig. The formula is too slow and trig gives you the result in decimal, when the answer is in radical form.

One test example was to find the height of a equilateral triangle with a side length of 8. Right now. Fast. With trig, you get 8*sin(60) = 6.928, but the answer is in radical form. With the formula, you get sqrt(64 - 16) = sqrt(48). Quick, what is the reduced radical form? Your brain might start to freeze before you find 4*sqrt(3).

You really need to be able to immediately write down any other side of these common triangles given any one of the sides. One would like to use simple concepts and mathematical understanding to solve many things, but that's not what the test is all about. The test is all about saving seconds. I only finished it with about 3 minutes to spare.

I know this is nothing new to SAT wonks, but I hope to share some of the math shortcuts I find.