kitchen table math, the sequel: 5/29/11 - 6/5/11

Saturday, June 4, 2011

SAT #4 Impressions

I just got back from taking the SAT for the 4th time in 2011.

Spent the month of May working with a tutor named Stacey Howe-Lott who taught me so much about math and grammar I hardly know where to begin; and she has excellent test taking advice (which may seem obvious to a lot of people, but it was new to me).

I'm hoping my score reflects the progress.


(Cross posted on Perfect Score Project)

Crowds vs. herds

In my book I draw a distinction between "cooperation" and "collaboration," defining the former as people working while interacting, and the latter as people working on joint projects, but not necessarily in one another's presence or with much productive interaction. In collaborations, after the work is divvied up, participants might spend the majority of their time working independently. 
I argue, furthermore, that this is what typifies most successful real-world collaborations. Except for those of us working on construction sites or film sets, we tend to get most of our work done at desks in private offices or cubicles; not at conference tables.

It turns out that there is a good reason for this. In an article in last weekend's Wall Street Journal, Jonah Lehrer reports that:
The good news is that the wisdom of crowds exists. When groups of people are asked a difficult question—say, to estimate the number of marbles in a jar, or the murder rate of New York City—their mistakes tend to cancel each other out. As a result, the average answer is often surprisingly accurate.

But here's the bad news: The wisdom of crowds turns out to be an incredibly fragile phenomenon. It doesn't take much for the smart group to become a dumb herd. Worse, a new study by Swiss scientists suggests that the interconnectedness of modern life might be making it even harder to benefit from our collective intelligence.

The experiment was straightforward. The researchers gathered 144 Swiss college students, sat them in isolated cubicles, and then asked them to answer various questions, such as the number of new immigrants living in Zurich. In many instances, the crowd proved correct. When asked about those immigrants, for instance, the median guess of the students was 10,000. The answer was 10,067.

The scientists then gave their subjects access to the guesses of the other members of the group. As a result, they were able to adjust their subsequent estimates based on the feedback of the crowd. The results were depressing. All of a sudden, the range of guesses dramatically narrowed; people were mindlessly imitating each other. Instead of canceling out their errors, they ended up magnifying their biases, which is why each round led to worse guesses. Although these subjects were far more confident that they were right—it's reassuring to know what other people think—this confidence was misplaced.

The scientists refer to this as the "social influence effect." In their paper, they argue that the effect has grown more pervasive in recent years. We live, after all, in an age of opinion polls and Facebook, cable news and Twitter. We are constantly being confronted with the beliefs of others, as the crowd tells itself what to think.
...

This research reveals the downside of our hyperconnected lives. So many essential institutions depend on the ability of citizens to think for themselves, to resist the latest trend or bubble. That's why it is important, as the Founding Fathers realized, to cultivate a raucous free press, full of divergent viewpoints.
The ideal, then, isn't group think, but independent thinking followed by a compilation of people's thoughts. 

Jonah Lehrer, however, neglects to mention one reason why the social influence effect has grown in recent years:  all the time that today's students are forced to work in groups in K12 classrooms, and, increasingly, in college classrooms as well.  In this case it's not the hyperconnectedness of our wired and wireless lives that's responsible, but the group think of the education world, with its systematic confusion of "cooperation" with "collaboration."

(Cross-posted at Out In Left Field).

Wednesday, June 1, 2011

SAT Love

dangling modifiers at PWN

brand new!

Now I have to get Mr. PWN to write some SAT geometry questions.

Top 10 List of What I Learned in May

I spent the month of May doing SAT Test Prep with Stacey Howe-Lott. She's the person with the largest score improvement that I was able to find.

I *feel* like I learned a lot. Let's hope the feels are more reality based this time around.

Next SAT in 4 days.


Cross Posted on Perfect Score Project.

dangling modifiers at the Fed

Despite having cut interest rates by 100 basis points in January, layoffs were increasing, inventories were up, and consumer confidence had fallen to its lowest level in more than four years.

A Term at the Fed: An Insider's View
Laurence H. Meyer
A Term at the Fed : An Insider's View

lgm on back to the future

re: Diane Ravitch writing in today's Times--
If every child arrived in school well-nourished, healthy and ready to learn, from a family with a stable home and a steady income, many of our educational problems would be solved.

Waiting for a School Miracle
By DIANE RAVITCH
Published: May 31, 2011
lgm writes:
Our nation and NY have many students who can be described as ideal. They have been placed in fully included classrooms with students who have severe issues and [they have been] denied access to an appropriate education. Remove that barrier, place by instructional need with competent teachers, and we as a nation will see education succeed. Continue to mainstream, and pretend to teach at an instructional level several years below the grade level over the door if it all, and we'll continue headbanging.

Yesterday's home and careers assignment for my 8th grader was similar to his 1st grade assignments before full inclusion: Take the alphabet. Under each letter, list two careers that start with that letter.

The majority of this school meets Ravitch's definition of ready to learn. But the idealists won't let the majority of children learn at their instructional level.
back to the future with Diane Ravitch

Molly on back to the future

re: Diane Ravitch writing in today's Times--
If every child arrived in school well-nourished, healthy and ready to learn, from a family with a stable home and a steady income, many of our educational problems would be solved.

Waiting for a School Miracle
By DIANE RAVITCH
Published: May 31, 2011
Molly writes:
My children meet all those lovely criteria, but somehow our educational problems remain. My child's good health and nutrition didn't help her when her algebra class spent an entire week singing karaoke followed up by 12 minutes graphing the results. Her stable family with a steady income was of no use when her English class spent 4 weeks studying poetry but never read a single poem that wasn't written by one of her 8th grade classmates. My child's good fortune doesn't do a damn thing to protect her from a crappy curriculum indifferently taught.
back to the future with Diane Ravitch

back to the future with Diane Ravitch

Diane Ravitch writing in today's Times:
If every child arrived in school well-nourished, healthy and ready to learn, from a family with a stable home and a steady income, many of our educational problems would be solved.

Waiting for a School Miracle
By DIANE RAVITCH
Published: May 31, 2011
I can tell you definitively that a child arriving at school well-nourished, healthy and ready to learn from a family with a stable home and a steady income does not solve the educational problem of a high school junior needing to learn precalculus inside his actual school.

how much does a B on a precalculus final cost?

Approximately $500 for private tutoring at $100/hour.

Now we'll see how much it costs to pay said tutor to re-teach precalculus over the summer.

help desk - precalculus
lsquared on what you must know to take calculus
Crimson Wife's online tutoring recommendation

Tuesday, May 31, 2011

Agressive Distraction

I'm days away from starting an Online SAT course and am more than a bit nervous. Not sure if I have the self-control to push through "Compare the Two Passages" with the internet at my fingertips.

We shall see.


(Cross Posted on Perfect Score Project)

Monday, May 30, 2011

dangling modifiers on SAT writing

Say you're taking the SAT next Saturday, and you want to know the one thing you can do to improve your writing score.

For my money, the answer is: figure out dangling modifiers.

Dangling modifiers are ubiquitous on the test, and they are especially ubiquitous in the multiple choice selections. Not infrequently, you can identify the correct answer simply by identifying the only answer that is not a dangling modifier.

This is so often the case that I now routinely read through the multiple choice options and cross out all the dangling modifiers (and the comma splices) before I even bother thinking about what's wrong with the sentence. I don't know whether that's a good idea for everyone, but it's a shortcut for me.

My goal with C. is to get him to the point where dangling modifiers 'jump' off the page at him, which is what they do with me. 

Here's an example of what I mean (based on College Board materials, but clunkier):
One of the first women to serve in Congress, more than twenty significant laws were introduced by Jane Doe, making her a leader in her era.

(A) more than twenty significant laws were introduced by Jane Doe, making her

(B) Jane Doe's introduction of more than twenty significant laws made her

(C) introducing more than twenty significant laws made Jane Doe 

(D) her introduction of more than twenty significant laws led to Jane Doe being considered 

(E) Jane Doe introduced more than twenty significant laws, making her
Choices A, B, C, and D all contain dangling modifiers. You don't have to read the final sentence to make sure it's correct because a dangling modifier is always wrong. Choice E has to be right, and it is.

The problem with a dangling modifier is that it isn't close enough to the thing it modifies, which is presumably why it is said to be 'dangling.' A dangling modifier is not firmly attached to the thing it modifies.

(Modifies means adds information to.)

When I get further along with Martha Kolln, I'll come back to this, but for now I'll say that generally speaking a modifier needs to be directly 'next door' to the thing it is modifying.*

Since the phrase "one of the first women" modifies (adds information to) Jane, Jane has to come next in the sentence -- and just Jane, not Jane-apostrophe-s. Jane-apostrophe-s isn't Jane-the-person; Jane-apostrophe-s is a modifier, too.

So:

Choice A is wrong because "One of the first women to serve in Congress" modifies "more than twenty significant laws," which amounts to saying that the laws were women.

Sometimes you can see this better when you cross out the 'extra' words:

(A) One of the first women to serve in Congress, more than twenty significant laws 

means:

the laws, not Jane, were the first women to serve in Congress

(B) One of the first women to serve in Congress, Jane Doe's introduction of more than twenty significant laws made her

means:

the introduction of laws was one of the first women

(C) One of the first women to serve in Congress, introducing more than twenty significant laws made Jane Doe a

means:

introducing [20 laws] was a woman

(D)  One of the first women to serve in Congress, her introduction of more than twenty significant laws allowed Jane Doe to be considered a

means:

the introduction was a woman

(E) One of the first womento serve in Congress, Jane Doe introduced more than twenty significant laws

means:

Jane Doe was [one of the first] women, which is correct.

I am positive that sentence diagramming would help with SAT writing.

Too bad no one knows how to do it.


update: Martha Kolln on dangling modifiers:

The participle can open the sentence only when its subject is also the subject of the sentence and is located in regular subject position. Otherwise, the participle dangles.

Understanding English Grammar By Kolln & Funk (8th, Eighth Edition)

* I'm sure there's more to it that that. 

Courtney James - math tutoring

Crimson Wife writes:
I have heard really high praise for Courtney James as an online math tutor
update: For some reason, the link works for me only when I cut and paste the address into my browser, so here it is: http://mathperfect.net/Tutoring.aspx

update update:

Andy writes:
The link is broken because there is a trailing non-breaking space in the link (it ends Tutoring.aspx%20 instead of .aspx)
Thanks!



slower math students in Singapore

from the Air report on math education in Singapore:
The topic structure in Singapore’s framework is efficient because topics are not taught and retaught as students move through the primary grades. Instead of repeating topics that students have already learned, teachers simply reintroduce them as a foundation on which to build new mathematical content. This practice, however, may not be suitable for students who have more difficulty with mathematics. The Singapore system recognizes that students who have trouble with mathematics may not attain mastery by following Singapore’s regular program of mathematics instruction and that these students may need special assistance to attain competence.

Beginning in grades 5 and 6, Singapore identifies its weaker students on the basis of a general examination of mathematics and language competency. These students receive special assistance and are taught according to a special fifth- and sixth-grade mathematics framework. This special framework mandates that students in the slower track

• receive approximately 30 percent more mathematics instruction than students in the regular track, and

• be exposed to the same mathematical content as students in the regular track, although at a slower pace.

The mathematics framework for students needing compensatory assistance adds review material to strengthen students’ understanding of previously taught content. For example, topics on numbers and geometry taught in grade 4 are repeated at a faster pace in grade 5. The introduction of some new concepts such as ratios, rates, and averages, which are normally introduced in grade 5, are delayed until grade 6 for the weaker students (Ministry of Education, 2001a). What is important, however, is that because slower students spend extra time studying mathematics, topics usually taught in grades 5 and 6 do not have to be completely sacrificed to make room for repetition.6

To support the framework for slower students, Singapore has developed a Learning Support Program to help educators identify these students and provide them with extra help (Ministry of Education 2003c). Mathematics Support Teachers (MST), who receive on-the-job supervision and specialized training to ensure that they are professionally competent, deliver compensatory assistance.

In the United States, we expect all students to meet the standards in state frameworks, but the standards do not help teachers address the needs of slower students. In fact, U.S. standards do not acknowledge that students learn at different rates. No Child Left Behind addresses the needs of failing schools, but it does not directly require that failing students receive help. Although some research evidence supports the belief that students benefit when the curriculum is adjusted to match their ability levels (Loveless, 1999), a distinct alternative curriculum would raise concerns in the United States about potential harm to students from ability grouping. Singapore’s approach differs from traditional ability grouping in that Singapore establishes a framework that requires students to master the same content as other students, not a watered-down curriculum as often happens in U.S. ability grouped classrooms. Singapore also provides extra assistance from an expert teacher.

What the United States Can Learn From Singapore’s World-Class Mathematics System: An Exploratory Study (and what Singapore can learn from the United States)
Apparently teachers in Singapore do not deliver 10-minute mini lessons followed by 40 minutes of one-on-one work with the students who are "struggling."

400 point gain on SATs

Ms. Xu, who was born and raised in China before emigrating to suburban California at age 9, had high hopes that she would be the first in her family to go to college. But poor results on a practice SAT and a dearth of extracurricular activities convinced Ms. Xu, 17, that she needed a scholastic makeover if she were to make it into a school her parents could brag about to relatives.

ThinkTank sent her to a public speaking camp, helped her improve her college essay and gave her the e-mail addresses of all the members of the Stanford University history department. At the company’s prompting, she found two internships with department professors. She also enrolled in ThinkTank’s college prep courses, which helped improve her SAT score 410 points to 2160 out of 2400. Next autumn, she will start at Harvard University.

Coaching and Much More for Chinese Students Looking to U.S.

By DAN LEVIN
Published: May 29, 2011
NY Times

39,947 Chinese undergraduates

With China sending more students to American colleges than any other country, the competition for spots at the top schools has soared. During the 2009-10 academic year, 39,947 Chinese undergraduates were studying in the United States, a 52 percent increase from the year before and about five times as many as five years earlier, according to the Institute of International Education, a U.S. organization.

Coaching and Much More for Chinese Students Looking to U.S.

By DAN LEVIN
Published: May 29, 2011
NY Times
The admissions people at SUNY Binghamton told us they have undergraduate students from over 100 countries.

the exact science of college admissions?

As a record number of students from outside the United States compete for a limited number of spots at the most selective American colleges, companies like ThinkTank are seeking to profit from their ambitions.

In the United States, students have long turned to independent college counselors, but in recent years, larger outfits have entered the market, offering full-service designer courses, extracurricular activities and focused application assistance. These services have spread to the fast-growing and lucrative market in China.

With China sending more students to American colleges than any other country, the competition for spots at the top schools has soared. During the 2009-10 academic year, 39,947 Chinese undergraduates were studying in the United States, a 52 percent increase from the year before and about five times as many as five years earlier, according to the Institute of International Education, a U.S. organization.

[snip]

Capitalizing on the increasingly globalized education system, ThinkTank Learning has tapped into the market in the United States and China.

The founder of the company is Steven Ma, 32, a former Wall Street analyst who started the company as a business for preparing students for college entrance tests in 2002 before expanding into application consulting in 2006, starting with seven students. In 2010, that number had risen to 300, including 75 from China. The company said it made about $7 million last year, with 50 percent from admission consulting.

ThinkTank said it was able to distill the college admissions process into an exact science, which Mr. Ma compared with genetic engineering. “We make unnatural stuff happen,” he said.

Students, whose parents often pay tens or even hundreds of thousands of dollars, are molded by ThinkTank into well-rounded, socially conscious overachievers through a regimen often beginning as early as the year before entering high school. The company designs extracurricular activities for the students; guides them in essay writing; tutors them for the SAT, the U.S. college admission exam; and helps them with meet-and-greet sessions with alumni.

“There’s a system built by colleges designed to pick out future stars and we are here to crack that system,” Mr. Ma said.


Coaching and Much More for Chinese Students Looking to U.S.

By DAN LEVIN
Published: May 29, 2011
NY Times

Dyscalculia vs Lack of Math Facts

The other day someone emailed me about a new word he'd learned:

Dyscalculia

(He clarified that he didn't think I had it, he just wanted me to know that it existed.)

I have been starting to wonder why it is so difficult for me to improve my math SAT score though.....

.....Which lead me to Daniel Willingham's article about whether or not it's true that some people are "bad at math." After reading it, I believe I fall squarely in the "lack of automaticity" category, rather than "dyscalculic."

Headed to Kumon this summer with my son to brush up on math facts so that I can free up some working memory for the fall SAT. Surprisingly (miraculously?), my son is psyched; daughter is another story.

(Cross Posted on Perfect Score Project.)

Sunday, May 29, 2011

C's SAT writing section minority rule

A couple of weeks ago, C. told me that on the Identifying Sentence Errors portion of SAT writing, sentences pertaining to minorities are error free. The correct choice is always E.

Darned if I haven't seen the same thing ever since he pointed it out.

Then today C. missed an answer because the sentence was about minorities and had an error.

"I used my rule," he said, "and it was wrong."

Starting this week, I am going to re-direct his attention to dangling participles, subject-verb agreement, pronoun antecedent agreement, tense consistency, parallelism, and idiomatic usage, among other things.

If that's possible.