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Thursday, September 23, 2010
Modern math is a river in Egypt
It's been decades since any sort of traditional math has been taught in most K-6 schools, but we still hear the same arguments. Our schools have used Everyday Math for years, and before that, they used MathLand. When schools and the state look at the testing numbers and whether they go up or down, it has nothing to do with any sort of traditional approach to teaching math.
Kids get to middle school and high school and still can't show mastery of very basic skills. Even those who favor discovery methods claim that mastery is needed. It still doesn't happen even though mastery of basic skills is much easier to check and correct than vague critical thinking skills.
My conclusion is that it's a huge case of denial.
It's Anti-Math. It's anti-hard work because hard work and expectations separate kids. They claim that kids will learn when they are ready, but that just keeps them from the hard work of figuring out whether there are other causes. It allows them to avoid working on things they don't like. That's why we parents get messages telling us to work on math facts with our kids.
In 5th grade, my son's Everyday Math teacher realized that many kids were struggling with simple things like adding 7+8. She knew these kids were "ready". She tried to fix the problems, but then didn't get to 35% of the material in the course. She believed in mastery, but the other teachers were happy enough to "trust the spiral".
Everyday Math facilitates this denial. They want math to be a pump and not a filter, but what they are doing is pumping along the failure until its too late and then dumping that guilt trip on the kids.
Kids get to middle school and high school and still can't show mastery of very basic skills. Even those who favor discovery methods claim that mastery is needed. It still doesn't happen even though mastery of basic skills is much easier to check and correct than vague critical thinking skills.
My conclusion is that it's a huge case of denial.
It's Anti-Math. It's anti-hard work because hard work and expectations separate kids. They claim that kids will learn when they are ready, but that just keeps them from the hard work of figuring out whether there are other causes. It allows them to avoid working on things they don't like. That's why we parents get messages telling us to work on math facts with our kids.
In 5th grade, my son's Everyday Math teacher realized that many kids were struggling with simple things like adding 7+8. She knew these kids were "ready". She tried to fix the problems, but then didn't get to 35% of the material in the course. She believed in mastery, but the other teachers were happy enough to "trust the spiral".
Everyday Math facilitates this denial. They want math to be a pump and not a filter, but what they are doing is pumping along the failure until its too late and then dumping that guilt trip on the kids.
Wednesday, September 22, 2010
LexAequitas on SAT Critical Reading
LexAequitas:
satreading
And fascinating on many levels....
“As an instructor for TPR for several years, I had a breakthrough on the reading passages at one point after I made a realization. I was good at verbal sections before, generally able to complete them in just over 20 minutes with a 750+ score, but after the instructor training I could complete them in 11 minutes with a perfect score.This is fantastically helpful.
The SAT is rigorously vetted, and constantly challenged. For every answer, there needs to be a detailed explanation that ETS can just mail off to every student who challenges the question. They come up with these before the test is ever given. This means there *has* to be something that can be pointed to in order to differentiate answers. On difficult questions, it will be minor, even picayune. And I don't mean picayune in the normal sense, I mean picayune in the sense that you'd better start thinking like a 13-year old with Asperger's syndrome. Don't accept generalizations that people use in speech and writing all the time just to make communication more efficient.
It's also worthwhile to note that the SAT does not typically select great literature. The writing is often clumsy and arcane, and this is part of the challenge. I suspect a better exercise if you want casual reading that mimics the SAT is to pick foreign translations.”
satreading
And fascinating on many levels....
David Kaplan on Sal Khan
In an undistinguished ranch house off the main freeway of Silicon Valley, in a converted walk-in closet filled with a few hundred dollars' worth of video equipment and bookshelves and his toddler's red Elmo underfoot, is the epicenter of the educational earthquake that has captivated Gates and others. It is here that Salman Khan produces online lessons on math, science, and a range of other subjects that have made him a web sensation.
Khan Academy, with Khan as the only teacher, appears on YouTube and elsewhere and is by any measure the most popular educational site on the web. Khan's playlist of 1,630 tutorials (at last count) are now seen an average of 70,000 times a day -- nearly double the student body at Harvard and Stanford combined. Since he began his tutorials in late 2006, Khan Academy has received 18 million page views worldwide, including from the Gates progeny. Most page views come from the U.S., followed by Canada, England, Australia, and India. In any given month, Khan says, he's reached about 200,000 students. "There's no reason it shouldn't be 20 million."
Sal Khan: Bill Gates' favorite teacher by David Kaplan
David Kaplan is one of the best writers on the Irvington Parents Forum. Probably the best, as a matter of fact, and that's saying something, because there are a lot of good writers on the Forum.
Tuesday, September 21, 2010
why is SAT reading so hard?
I've just recently focused on SAT reading ---
It's hard.
Until two weeks ago, I took SAT reading for granted. I had high verbal scores in high school, and when I took a sample SAT test a couple of years ago, I missed two questions on the reading, only one of which was a real miss in the sense that my answer was clearly wrong. On the other miss, I disagreed with the CollegeBoard's answer.
So I hadn't thought about the verbal section until I started working with C. and a couple of other juniors on SAT prep.
Now I find that working through the verbal section is a wretched, miserable experience, and this is true in spite of the fact that I get the answers right.
Here's Hack the SAT
:
True!
Working through a Critical Reading passage - especially a 'compare two passages' section (those are death) - I feel the brain equivalent of eye strain.
Why is that?
It's hard.
Until two weeks ago, I took SAT reading for granted. I had high verbal scores in high school, and when I took a sample SAT test a couple of years ago, I missed two questions on the reading, only one of which was a real miss in the sense that my answer was clearly wrong. On the other miss, I disagreed with the CollegeBoard's answer.
So I hadn't thought about the verbal section until I started working with C. and a couple of other juniors on SAT prep.
Now I find that working through the verbal section is a wretched, miserable experience, and this is true in spite of the fact that I get the answers right.
Here's Hack the SAT
:You know how some people have a gift?
[snip]
No one has a gift for Critical Reading.
Sure, plenty of people have a gift for reading.... [but] no one is particularly natural at critical reading, this seemingly endless stuff that jams the SAT full of tiny blue print and passages about the subtle revelations of medieval scientist nuns.
[snip]
[E]ven those students who get high scores on Critical Reading find it more draining than the Math or Grammar sections.
True!
Working through a Critical Reading passage - especially a 'compare two passages' section (those are death) - I feel the brain equivalent of eye strain.
Why is that?
Monday, September 20, 2010
a man after my own heart
Glen wrote:
I have my fourth grader do a hundred fraction problems while I do his "cut pictures out of magazines" homework for him. I have him work through middle school math contest problems, tossing him hints when he gets stuck, while I draw on his poster board. I had him learn every country in Europe while I built miniature teepees in a shoebox diorama.
He gets good grades on his schoolwork, but other parents--I mean kids, of course--often cut and paste better than I do.
His teacher thinks he's a "natural" at math, but there's nothing natural about it. It's man-made. It's training--the same sort of training you'd do if you needed to teach someone to cut hair or build birdhouses: show them how, help them a few times, and put them to work.
She would be shocked if she actually knew the level of difficulty of the math and science work he can do, but we're careful not to let her find out. Last year the teacher found out and was nasty to him for the rest of the year. She liked him when she thought he was a natural, but when she found out that he had to work at math, she was outraged.
"It's not fair to me that you are willing to do that much work for your father, but aren't doing the same for me!" I thought that I--I mean my son, of course--was cutting enough pictures out of enough magazines for her, but she apparently thought she deserved more.
She wanted to discuss the "problem" with me. She was concerned about how I was using his time. (How ironic.) She said that their Everyday Mathematics emphasized "conceptual understanding" and was concerned that my approach might not lead to "actual understanding." The previous night he had solved,
"We have four times as many cows as horses on our ranch. If we sold 280 cows, we'd end up with twice as many horses as cows. How many cows do we have?"
He was in third grade. I almost asked her to go to the board and show me how SHE would have taught him to solve it, with "actual understanding," but that would have been cruel. I held my tongue to keep my son out of trouble and said that I tried my best to help him understand. We left it at that.
This is one of the top 5% of elementary schools in Silicon Valley, so almost all the kids are performing at grade level--and that's where they want to keep them.
And I've now found out that at higher levels, middle school and high school, it's almost standard practice for parents to take the mindless homework load off their kids' shoulders to free up time for them to do the portion of homework that is actually useful.
If I have to do even more mindless homework, I may have to outsource it to India.
Using sentence combining to improve reading scores
from Arthur Whimbey and Myra Linden
:
*prototype-construction method
** I'm not holding my breath
:Let us now examine the problem mentioned at the beginning of this chapter: the difficulty that some students have comprehending textbooks containing sentences with relative clauses. Here is a paragraph from the Encyclopedia Americana.
Infectious diseases are the only ones that can be transmitted. They may be spread by infected animals, infected people, or contaminated substances, such as food and water. Infectious diseases that can be transmitted to humans from infected animals are known as zoonoses. Zoonoses may be transmitted by carriers, such as insects; by the bite of an infected animal; by direct contact with an infected animals [sic] or its excretions; or by eating animal products.
College freshman were asked to read this paragraph and then answer the following questions.
Zoonoses are:College students with weak reading skills often pick alternative b. When asked why they picked b, some reply that zoonoses sounds like zoo and animals are kept in zoos, so they figured zoonoses are animals. This explanation reflects the thinking style of nonanalytical readers. They base their conclusions on superficial associations among bits of information rather than on careful step-by-step interpretations of chunks of information and gradual reconstruction of total meaning.
a. insects that carry diseases.
b. infected animals that transmit infectious diseases to humans.
c. infectious diseases that man gets from animals.
d. carriers that transmit infectious diseases.
Other students who chose b explained that they got this answer from the last six words of the third sentence: infected animals are known as zoonoses. This, too, reflects the thinking style of weak readers. They read a little bit here, a little bit there, and then jump to a conclusion.
The correct answer is based on the third sentence, which reads:
Infectious diseases that can be transmitted to humans from infected animals are known as zoonoses.
This sentence contains the following relative clause:
that can be transmitted to humans from infected animals
Good readers work step-by-step through the sentence in obtaining its correct meaning. They begin with the subject: infectious diseases. Then they go on to the relative clause, an essential relative clause that indicates the type of infectious diseases being considered; those that animals can transmit to humans. Finally, they come to the predicate: are known as zoonoses. Therefore, in answering the question they pick alternative c.
Research studies have found that students with weak analytical skills can understand only simple sentences, just as they can solve only one-step math problems. They have difficulty understanding complicated sentences, just as they have difficulty solving multi-step math problems. In other words, they can handle just small chucks of information because they have not developed skill in working step-by-step through complicated information. They can understand sentences such as this:
Some infectious diseases are known as zoonoses.
But they cannot understand Sentence 3 in the paragraph.
Other research studies (reviewed in Why Johnny can't Write: How to Improve Writing Skills) have found that having students construct complex sentences from simple ones improves their scores on standardized reading tests. these studies have not explored whether having students add relative clauses to sentences improves their ability to comprehend specifically sentences with relative clauses. They have only found that constructing various types of complicated sentences from simpler ones (using the types of exercises shown in this book) improves overall reading comprehension ability, with the weakest readers making the greatest gains. As the P-C Approach* is used more widely in our schools,** we can expect the average reading comprehension ability of the nation to improve. And as this improvement becomes evident, researchers may conduct additional studies to determine exactly how and why having students manipulate, construct, and write sentences improves their reading skills.
Teaching and Learning Grammar: The Prototype-Construction Approach
pp. 90-92
*prototype-construction method
** I'm not holding my breath
help desk - sentence diagram
In the passage below, Terkoz the ape has kidnapped Jane; Tarzan is tracking Terkoz through the treetops.
This was a fantastically difficult sentence for my college composition students to read; it was difficult for me to read, too.
Can someone diagram the first sentence?
You hear constantly that sentence diagramming doesn't help with writing, but I'm wondering whether it would help with reading. I'm tutoring a high school junior on the SAT, and the sentences are fantastically complex. The reading passage we worked on this weekend actually contained two sentence fragments in a row, both of which modified the complete sentence before them.
At boughs’ ends, where the anthropoid swings from one tree to another, there is most to mark the trail, but least to point the direction of the quarry, for there the pressure is downward always, toward the small end of the branch, whether the ape be leaving or entering a tree. Nearer the center of the tree, where the signs of passages are fainter, the direction is plainly marked.
Tarzan of the Apes
Edgar Rice Burroughs
The Compact Bedford Introduction to Literature
p. 74
This was a fantastically difficult sentence for my college composition students to read; it was difficult for me to read, too.
Can someone diagram the first sentence?
You hear constantly that sentence diagramming doesn't help with writing, but I'm wondering whether it would help with reading. I'm tutoring a high school junior on the SAT, and the sentences are fantastically complex. The reading passage we worked on this weekend actually contained two sentence fragments in a row, both of which modified the complete sentence before them.
Saturday, September 18, 2010
LD enrollment drops
After decades of what seemed to be an inexorable upward path, the number of students classified as learning-disabled declined from year to year over much of the past decade—a change in direction that is spurring debates among experts about the reasons why.
The percentage of 3- to 21-year-old students nationwide classified as having a “specific learning disability” dropped steadily from 6.1 percent in the 2000-01 school year to 5.2 percent in 2007-08, according to the most recent data available, which come from the U.S Department of Education’s 2009 Digest of Education Statistics. In numbers, that’s a drop from about 2.9 million to 2.6 million students.
A learning disability—a processing disorder that impairs learning but not a student’s overall cognitive ability—is the largest, by far, of the 13 disability classifications recognized by the main federal special education law. Forty percent of the approximately 6.6 million students covered under the Individuals with Disabilities Education Act, or IDEA, fall into that category.
The decrease in the category goes hand in hand with a decrease in special education enrollment overall, though that change is not as large. The percentage of all students covered under the IDEA fell from a high of 13.8 percent in the 2004-05 school year to 13.4 percent in 2007-08—from about 6.7 million students to about 6.6 million students. Enrollment in the categories of emotional disturbance and mental retardation also went down, but students in those groups make up a far smaller slice of the IDEA pie. At the same time, though, enrollment of students classified as having an autism spectrum disorder or “other health impairment” rose.
[snip]
About 80 percent of children who are classified as learning-disabled get the label because they’re struggling to read. So, scholars say, the dropping numbers could be linked to improvements in reading instruction overall; the adoption of “response to intervention,” which is an instructional model intended to halt the emergence of reading problems; and a federally backed push toward early intervention with younger students before they’re labeled.
Learning-Disabled Enrollment Dips After Long Climb Up
by Christina A. Samuels
Education Week
12-week column on drawing
in the New York Times
Before I got sidetracked teaching myself math, I was learning to draw --- Loved it.
Also, I used to knit. I used to knit a lot. A friend of mine told me that knitting and math yield the same pleasures, and she turned out to be right. So I haven't knitted anything in 5 years, either.
I need a couple more lives besides just the one I've got.
Before I got sidetracked teaching myself math, I was learning to draw --- Loved it.
Also, I used to knit. I used to knit a lot. A friend of mine told me that knitting and math yield the same pleasures, and she turned out to be right. So I haven't knitted anything in 5 years, either.
I need a couple more lives besides just the one I've got.
Wednesday, September 15, 2010
safety first
Coincidentally, we were discussing the "security" system here in my district at the very moment Ed and I were trekking back and forth to the U.S. Open.
At the Open, the threat level appears to be permanently set on orange and security is always high. Security is so high that, when I presented my bag for inspection, the gal behind the table said, "Is that a Kindle? You can't bring that in."
What?
As Ed said, if you can take a Kindle on an airplane, which you can, you should be able to take a Kindle to the Open.
But no. I was supposed to hike two blocks -- uphill and in the sun -- back the way I came in 'til I got to a tent where I could pay another employee five bucks to check my Kindle.
Or, alternatively, I could walk a couple hundred yards back to the ladies' room, secrete my Kindle on my person, present my bag for inspection a second time, and enter the grounds without further ado. Which is what I did.
I told Ed, "Any security system that relies on terrorists to pay some guy five bucks to check his explosive device isn't a security system."
More anon.
At the Open, the threat level appears to be permanently set on orange and security is always high. Security is so high that, when I presented my bag for inspection, the gal behind the table said, "Is that a Kindle? You can't bring that in."
What?
As Ed said, if you can take a Kindle on an airplane, which you can, you should be able to take a Kindle to the Open.
But no. I was supposed to hike two blocks -- uphill and in the sun -- back the way I came in 'til I got to a tent where I could pay another employee five bucks to check my Kindle.
Or, alternatively, I could walk a couple hundred yards back to the ladies' room, secrete my Kindle on my person, present my bag for inspection a second time, and enter the grounds without further ado. Which is what I did.
I told Ed, "Any security system that relies on terrorists to pay some guy five bucks to check his explosive device isn't a security system."
More anon.
Tuesday, September 14, 2010
Another rude awakening
Last year, my first-born was in enrolled in our local public school in second grade, and although he spent 6 or 7 hours there each day, he came home with tons of homework and a good deal more learning remaining. I started to think, “Why am I sending my kids to school, when the school sends them back to me to educate?” A friend later complained to me that when they gave her son a book report, it meant at least 5 hours of her own time working on it with him. Another parent told me how great the tutoring was at the chain store down the street from her. All this got me to thinking: if I’m ultimately in charge of my kids’ education, why do I feel so powerless? . . .
I assumed that the government knows best what, and how, to teach my kids. It’s an assumption I was raised with, one I never challenged, until now. Well, you know what they say about you when you assume…
“It’s always worse than you think?” Well, that’s what we often say around here.
Another parent gobsmacked by our public schools
Back to School: Part One
I assumed that the government knows best what, and how, to teach my kids. It’s an assumption I was raised with, one I never challenged, until now. Well, you know what they say about you when you assume…
“It’s always worse than you think?” Well, that’s what we often say around here.
Another parent gobsmacked by our public schools
Back to School: Part One
Monday, September 13, 2010
Testing in Basic Math in Community College
I finally got a copy of Teach Like a Champion. Since I teach at a community college, not everything applies. But I do teach a basic math class. And the book has inspired me to start taking data on my tests. This led me to analyze my tests to see what and how much I test on each topic.
At the end of the summer semester, I used the department written final to see if I could determine how much mastery my students had on each topic that I taught. Unfortunately, I don't have data from the beginning of the semester. But what I found wasn't very good: I measured the mastery on 15 topics by calculating a percent correct for each topic. For example, there were 5 problems on whole number operations and 11 students. This gives a total of 55 problems. Only 76% were answered correctly. If I had to take a guess, I would say that the class probably had over 70% mastery on whole number operations before they came into class. My highest % mastery was decimal operations, fraction operations and dimensional analysis with 93%, 85% and 93% mastery respectively. My lowest topics were divisibility tests and lowest common multiple and prime factorization. I then analyzed each incorrect answer to see what the most common errors were. 66% of the errors were concept errors: either the student didn't answer the question or did not use the correct mathematical technique. 19% of the errors were process error. In this category are errors like the following: a student knows that when multiplying mixed numbers, he must turn the mixed number into an improper fraction, but he does this incorrectly. 7% of the errors were mathematical. Another 8 % were divided evenly between not reducing fractions and sign errors.
So I'm teaching basic math again this semester, and I am trying to determine what I should be doing to ensure mastery. I am going to try curriculum based measurement. This is a technique I read about that is used in some elementary schools. You give students very short exams on a particular topic. Instead of counting the number of problems that are correct, you count the number of correct digits. For example, if a student has to add 99 and 49, there is a possibility of 3 correct digits, not one correct problem. You then do some number crunching and adjust your teaching accordingly. (I realize I'm gliding over this.)
It doesn't seem like any of the other instructors at my community college are collecting and analyzing data like this. If anyone has any links or resources on this topic, I would love to hear about it.
At the end of the summer semester, I used the department written final to see if I could determine how much mastery my students had on each topic that I taught. Unfortunately, I don't have data from the beginning of the semester. But what I found wasn't very good: I measured the mastery on 15 topics by calculating a percent correct for each topic. For example, there were 5 problems on whole number operations and 11 students. This gives a total of 55 problems. Only 76% were answered correctly. If I had to take a guess, I would say that the class probably had over 70% mastery on whole number operations before they came into class. My highest % mastery was decimal operations, fraction operations and dimensional analysis with 93%, 85% and 93% mastery respectively. My lowest topics were divisibility tests and lowest common multiple and prime factorization. I then analyzed each incorrect answer to see what the most common errors were. 66% of the errors were concept errors: either the student didn't answer the question or did not use the correct mathematical technique. 19% of the errors were process error. In this category are errors like the following: a student knows that when multiplying mixed numbers, he must turn the mixed number into an improper fraction, but he does this incorrectly. 7% of the errors were mathematical. Another 8 % were divided evenly between not reducing fractions and sign errors.
So I'm teaching basic math again this semester, and I am trying to determine what I should be doing to ensure mastery. I am going to try curriculum based measurement. This is a technique I read about that is used in some elementary schools. You give students very short exams on a particular topic. Instead of counting the number of problems that are correct, you count the number of correct digits. For example, if a student has to add 99 and 49, there is a possibility of 3 correct digits, not one correct problem. You then do some number crunching and adjust your teaching accordingly. (I realize I'm gliding over this.)
It doesn't seem like any of the other instructors at my community college are collecting and analyzing data like this. If anyone has any links or resources on this topic, I would love to hear about it.
Sunday, September 12, 2010
Another article (or two): Is it bad to test students frequently?
Two recent New York Times articles fly in the face of conventional pop psychology and education theory.
An article in last week's Science Section on study habits cites cognitive science research indicating that the act of taking a test can enhance learning:
The process of retrieving an idea is not like pulling a book from a shelf; it seems to fundamentally alter the way the information is subsequently stored, making it far more accessible in the future.
As Henry L. Roediger III, a psychologist at Washington University in St. Louis puts it, “Testing not only measures knowledge but changes it.”
Next we have a front page article in this weekend's Week in Review on Testing, the Chinese Way, written by Elisabeth Rosenthal, whose children spent a year at the International School of Beijing where "taking tests was as much a part of the rhythm of their school day as recess or listening to stories." Citing personal experience, Rosenthal argues that:
>Young children aren't necessarily aware that they are being "tested."
>Frequent tests give children important feedback about how they are doing.
>Frequent tests offer a more meaningful way to improve self-esteem than frequent praise does.
On this past point, Rosenthal cites Gregory J. Cizek, a professor of educational measurement and evaluation at the University of North Carolina at Chapel Hill:
Professor Cizek, who started his career as a second-grade teacher, said the prevailing philosophy of offering young children unconditional praise and support was probably not the best prescription for successful education. “What’s best for kids is frequent testing, where even if they do badly, they can get help and improve and have the satisfaction of doing better."
Cizek's overall take on testing in schools? “Research has long shown that more frequent testing is beneficial to kids, but educators have resisted this finding:”
Rosenthal concludes on a particularly powerful note:
When testing is commonplace and the teachers are supportive — as my children’s were, for the most part — the tests felt like so many puzzles; not so much a judgment on your being, but an interesting challenge. It is a testament to the International School of Beijing — or to the malleability of childhood memory — that Andrew now says he did not realize that he was being tested. Will tests be like that in a national program, like Race to the Top?
When we moved back to New York City, my children, then 9 and 11, started at a progressive school with no real tests, no grades, not even auditions for the annual school musical. They didn’t last long. It turned out they had come to like the feedback of testing.
“How do I know if I get what’s going on in math class?” my daughter asked with obvious discomfort after a month. Primed with Beijing test-taking experience, they each soon tested into New York City’s academic public schools — where they have had tests aplenty and (probably not surprisingly) a high proportion of Asian classmates.
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