kitchen table math, the sequel: 8/28/11 - 9/4/11

## Saturday, September 3, 2011

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

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

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

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

On the SAT, they are a liability.

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

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

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

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

Illustrations by Jennifer Orkin Lewis

Cross-posted on Perfect Score Project

## Friday, September 2, 2011

### Glen on legalistic reading and Venn diagram problems

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

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

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

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

In such a context, you are trained to interpret "Two students do X, and three students do Y," without assuming two disjoint groups. You learn to be literal and legalistic in a math problem context, which is a context-based re-weighting of the factors involved in interpretation of language.
I'm glad Glen has used the term "legalistic": that's exactly what I was thinking.

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

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

Further:

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

## Thursday, September 1, 2011

### question for Katharine

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

e.g.:
Thirty students take geometry, and 25 students take Spanish.
I have finally begun to divine fairy rapidly that what this sentence really means is:
Thirty students take geometry, and 25 students take Spanish. Of those students, some may take both geometry and Spanish. Then again, maybe not.
I divine it, but I don't like it. I would never, ever write the first sentence if what I meant was the second sentence(s). (So no one's going to hire me to write Venn diagram problems any time soon, but never mind.)

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

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

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

In short, according to my non-conscious rulebook:
Thirty students take geometry, and 25 students take Spanish
Thirty students took geometry, and another 25 students took Spanish.

but

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

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

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

### If you want to score 800, shoot for 900

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

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

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

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

2. If you want to score an 800, shoot for a 900. Ditto for 700: shoot for 800. Which is another way of saying number 1.
The reason to shoot for an 800 if you want a 700 is that anything that knocks out mental resources will drop your score by that much.

Now I'm going to go crawl in bed.

overlearning by WiseGeek

### Smart Teachers in Stupid Schools, part 2

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

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

### words to live by

Amy P on class projects:
nobody in the history of man has ever bought a school project kleenex box

## Wednesday, August 31, 2011

### Smart Teachers in Stupid Schools

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

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

## Tuesday, August 30, 2011

### two-pack

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

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

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

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

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

## Monday, August 29, 2011

### let's not and say we did

Imagine replacing the sequence of algebra, geometry and calculus with a sequence of finance, data and basic engineering.
How to Fix Our Math Education
By SOL GARFUNKEL and DAVID MUMFORD
Published: August 24, 2011
Robert Pondiscio responds.

For the most part, it appears, Joanne Jacobs' readers aren't impressed. I'm especially partial to this comment:
I’m currently teaching quantitative literacy at the community college level. The vast majority of students who take it need either this class or a basic stats class to fulfill a graduation requirement.

I have taught this class for several semesters over the past few years. My impression: Most students don’t really care for the class, despite its “relevancy.” It seems that not a few felt misled by their advisers, thinking that they were enrolling in an “easier” math class. They tend to wish that they had enrolled in the basic stats instead, because it is more straightforward as a math class.
That reminds me of the time C. said, back when he was age 10 or so: "They don't understand, Mom. When you make math more fun, it's more boring."

## Sunday, August 28, 2011

### Taming the Math Perfectionist

(I was going to make this a comment on another post but it got so lengthy and unwieldy that here I am making it a full-on independent post. Pardons.)

Speaking of perfection/distraction/panic/etc, we've finally made a bit of headway with a problem we've been having at our house for some time: my daughter is a pretty bright girl, enough that, well, I really haven't had to teach her anything yet. (My son, I teach; my daughter, I expose and she just does it.)

The dark side to this behavior is that if she comes across something she doesn't just "get" immediately, she shuts down and panics.

[[Small digression for background:

We cruised through Singapore 1 with no hiccups, and I put the brakes on Singapore 2 when it was clear (starting multi-digit addition/subtraction) that she didn't have her single digit facts down cold enough yet. That didn't seem to bother her because while she didn't have immediate recall of the facts, she certainly "got" simple addition, it wasn't a conceptual issue for her. We spent a couple of months working through just Math-U-See Alpha which is nothing but hammering well-grouped math facts until she made significant progress. We're starting back to Singapore 2 tomorrow morning, in fact.

OK, enough digression.]]

A. happens to greatly enjoy computer games, so while we were hitting the math facts hard, I spent some time looking at various math practice sites for her. I ended up giving Math Whizz (based in the UK) a try and we had a bit of a break-through with it.

It started with an evaluation, in which I told her that it was (by definition!) going to ask her questions that she could not answer, because it had to know at what point she could no longer answer questions. She freaked out a little when it got to multiplication and asked me for help, I told her I couldn't help her because that would goof things up -- if it thought she knew multiplication well, then it would be giving her even harder multiplication that she definitely couldn't do. We talked about the fact that she was required to fail in order for it to work. She eventually got used to this idea.

Then, later when the assessment was all over, she was doing one of the lessons which was something she was "sure" she couldn't do and she panicked, asking me how she could get out of it. I came over and said:

"Well, let's take a look at this. You know if you get the wrong answer, it'll just give you slightly easier stuff next time, so no big deal."

"OK, let's just put in all zeroes!"

"Well, sure, we could do that, but let's see if we can get as far as we can with this, and then maybe it can see *how* we got it wrong and use that information to figure out what you need practice with."

So, I left her alone to Fail With Style ... and wouldn't you know she got most of the questions right. When freed to "get them all wrong" because the system needs her to fail if she doesn't understand it, the stress and panic went away, and she went on to figure 8 of 10 of them out. And she was excited by that, instead of freaking out that it wasn't 10 out of 10. (It was 3 digit subtraction with regrouping, which we sure haven't covered officially yet. And, now that I think about it, I'm a little mind boggled that she placed high enough for them to try that in the first place. Hmm.)

I've been worried about what was going to happen once we started hitting things that she just didn't "get" immediately because it was bound to happen at any point and, before, it would have been a disaster for her. I am currently ... cautiously optimistic.

### English literature at Harvard

from "The Decline of the English Department" by William Chace:
Consider the English department at Harvard University. It has now agreed to remove its survey of English literature for undergraduates, replacing it and much else with four new “affinity groups”—“Arrivals,” “Poets,” “Diffusions,” and “Shakespeares.” The first would examine outside influences on English literature; the second would look at whatever poets the given instructor would select; the third would study various writings (again, picked by the given instructor) resulting from the spread of English around the globe; and the final grouping would direct attention to Shakespeare and his contemporaries.

Daniel Donoghue, the department’s director of undergraduate studies, told The Harvard Crimson last December that “our approach was to start with a completely clean slate.” And Harvard’s well-known Shakespeare scholar Stephen Greenblatt also told the Crimson that the substance of the old survey will “trickle down to students through the professors themselves who, after all, specialize in each of these areas of English literature.” But under the proposal, there would be no one book, or family of books, that every English major at Harvard would have read by the time he or she graduates. The direction to which Harvard would lead its students in this “clean slate” or “trickle down” experiment is to suspend literary history, thrusting into the hands of undergraduates the job of cobbling together intellectual coherence for themselves. Greenblatt puts it this way: students should craft their own literary “journeys.” The professors might have little idea of where those journeys might lead, or how their paths might become errant. There will be no common destination.

As Harvard goes, so often go the nation’s other colleges and universities. Those who once strove to give order to the curriculum will have learned, from Harvard, that terms like core knowledge and foundational experience only trigger acrimony, turf protection, and faculty mutinies. No one has the stomach anymore to refight the Western culture wars. Let the students find their own way to knowledge.

### "The Decline of the English Department"

First the facts: while the study of English has become less popular among undergraduates, the study of business has risen to become the most popular major in the nation’s colleges and universities. With more than twice the majors of any other course of study, business has become the concentration of more than one in five American undergraduates. Here is how the numbers have changed from 1970/71 to 2003/04 (the last academic year with available figures):

English: from 7.6 percent of the majors to 3.9 percent
Foreign languages and literatures: from 2.5 percent to 1.3 percent
Philosophy and religious studies: from 0.9 percent to 0.7 percent
History: from 18.5 percent to 10.7 percent
Business: from 13.7 percent to 21.9 percent

In one generation, then, the numbers of those majoring in the humanities dropped from a total of 30 percent to a total of less than 16 percent; during that same generation, business majors climbed from 14 percent to 22 percent. Despite last year’s debacle on Wall Street, the humanities have not benefited; students are still wagering that business jobs will be there when the economy recovers.

What are the causes for this decline? There are several, but at the root is the failure of departments of English across the country to champion, with passion, the books they teach and to make a strong case to undergraduates that the knowledge of those books and the tradition in which they exist is a human good in and of itself. What departments have done instead is dismember the curriculum, drift away from the notion that historical chronology is important, and substitute for the books themselves a scattered array of secondary considerations (identity studies, abstruse theory, sexuality, film and popular culture). In so doing, they have distanced themselves from the young people interested in good books.
William H. Chace
American Scholar
Autumn 2009

### question

From the October 2009 SAT:
There are 100 pieces of candy in a bag, 20 percent of which are wrapped. If a total of 70 percent of the pieces of candy in the bag are chocolate, what is the smallest number of wrapped chocolate pieces that could be in the bag?

C. had trouble with this problem, which led me to doubt my answer.

This brings me to an issue I've been meaning to raise.

Would this problem be easier if you worded it this way:
There are 100 pieces of candy in a bag, 20 percent of which are wrapped. If a total of 70 percent of the pieces of candy in the bag are chocolate, and the other 30 percent are caramel, what is the smallest number of wrapped chocolate pieces that could be in the bag?

### treemageddon, part two

Hell.

C. just looked out the window and saw that we have 4 trees leaning on their sides against the hill out back. I'm pretty sure all of them are toppled, though I can't see whether their root balls are exposed. Doesn't look good.

The ground is saturated from the rainiest August we've had in all the years they've been taking measurements, and a moderate wind was enough to push them over.

It's like the earthquake damage you see in countries without earthquake building codes. An earthquake that wouldn't faze Los Angeles levels Haiti. Right now, where trees and soil are concerned, we're Haiti.

My favorites:
123 (of 236)
162 - “Bring it”
165 - lawn chairs in pool
177 - surfers
196 or 198 – **Hurricane Alert** Mayor Bloomberg states “everyone should have 7 new pairs of underwear"

### the Barstool on Irene

from NYC Barstool:
I haven’t even opened my second box of Pop Tarts yet and this s*** is already over. Unreal. I have 2 pounds of cold cuts and 6 unopened bottles of wine. Looks like it’s gonna be Brown Sugar Cinnamon, Boars Head and a nice Cabernet for my Sunday Funday.
Same here. Ed says in addition to the FIFTEEN CANS of tuna fish he snapped up at Stop n Shop yesterday (the last cans on the shelf!), we have a pound of ham.

Nobody around here eats ham any more, either.

Ed says, "At least I didn't buy Pop Tarts."

Now we're debating whether you can eat Pop Tarts raw. C. says Yes, you can.

### still here

Electricity still on; sump pump working.

Trying to figure out what to do with the FIFTEEN CANS of tuna fish Ed bought yesterday, seeing as how nobody around here eats tuna fish any more.