Ravitch suspects, with good reason, that her favorite teacher, the intelligent, exacting, and highly literary Mrs. Ratliff, would languish under NCLB. But would Mrs. Ratliff even have become a teacher in today's world? Would someone who is "stifled by the jargon, the indifference to classical literature, and the hostility to her manner of teaching" last through even one week of ed school pabulum, projects, peer-group activities, and proselytizing about Balanced Literacy?
An excerpt of my review of Diane Ravitch's latest book at the Nonpartisan Education Review. You can access the entire review here.
In this book Ravitch brings up her next most recent book: The Language Police. Intrigued (and embarrassed that I hadn't yet read it) I devoured that one a few days ago. If you haven't read it yet, it's a great read.
Some adults lack a sense of the "equal distance of 1" between the whole numbers (the numbers on a number line). Without this concept, addition makes no sense. All math including basic addition is learned by rote as a mechanical process.
I have a memory of Dehaene arguing that people have an "innate" number line inside their minds.
[pause]
yup
It was Dehaene:
I propose that the foundations of arithmetic lie in our ability to mentally represent and manipulate numerosities on a mental “ number line ”, an analogical representation of number ; and that this representation has a long evolutionary history and a specific cerebral substrate. “ Number appears as one of the fundamental dimensions according to which our nervous system parses the external world. Just as we cannot avoid seeing objects in color (an attribute entirely made up by circuits in our occipital cortex, including area V4) and at definite locations in space (a representation reconstructed by occipito-parietal neuronal projection pathways), in the same way numerical quantities are imposed on us effortlessly through the specialized circuits of our inferior parietal lobe. The structure of our brain defines the categories according to which we apprehend the world through mathematics. ” (TNS, p. 245).
I had the following brainstorm at an embarrassingly advanced age:
For a long time, I knew there were two formulas that were somehow relevant to circles, namely 2πr and πr2, but I could never remember which one was area and which one was circumference.
I finally realized that πr2 must be the formula for area, because area is described in square units.
The question I missed was number 4 out of 16, which means it was super-easy. It was so easy, that I'm not going to tell you what the question was. Too embarrassing.
I had brain freeze. Number 4 was one of those "which value can't be the answer?" items. I took a quick look at the 5 possibilities, spotted the one value that was glaringly different from all the other values, and then eliminated that answer because it was different from all the others.
aaarrghh!
Then I spent precious minutes trying to figure out how all the other answers, which obviously could be the answer, could conceivably not be the answer.
I asked my daughter today. She took the SAT this fall and got a score in the range you mention.
She said the questions are all routine exercises.
She would agree the AMC questions and AIME questions are problems.
One of her favorite areas of math is counting. :-) I remember covering permutations and combinations in high school math. However, what I learned was just a small fraction of what's covered in Art of Problem Solving's Intro to Counting and Probability course or book.
Achieving a perfect score on any math exam is quite simple. Though this may sound cliched, all it takes is practice. Practice by taking as many mock tests as you can, and take the time to go through and correct all of your incorrect answers. Keep your mistakes in mind as you take your next mock test.
Since 1992,1 have personally helped more than 50 students each year achieve perfect scores on the SAT Math, SAT II Math I & II, and AP Calculus AB & BC exams. As you might imagine, during my many years of teaching, I have gone through almost every single SAT Math test preparation book out there. I have come to realize that every book is loaded down with explanations and not enough tests! What a waste of money!
Therefore, it is my honor to introduce to you my first test preparation book, Dr. John Chung's SAT Math. There are no tricks or fast-track methods in this book. I have put together 20 mock exams, complete with answers and explanations, to help you PRACTICE your math test taking skills. These are the mock exams that I have used in my private tutoring sessions with my own students, most of whom have gone on to achieve perfect scores on the SAT Math exam.
Special thanks to my latest star students, Angela Lao, Priya Vohra, Devi Mehrotra, Donna Cheung, Jennifer Wong, Amos Han, and Shalini Pammal, who provided invaluable feedback on the format of this book and assisted in the final proofreading session. They all achieved a perfect score on the math section of the PSAT, SAT Math, and SAT II Math I and H.
I hope this book helps you as much as it has helped my students.
I'm really wishing for a national curriculum right now--or at least a series of textbooks that goes K-10 instead of K-6 and another for 6-8.
I'm doing math with a friend's daughter. She's homeschooling, so I get to pick the book, and we're using a Singapore text. Our most recent section is converting units of area: cm2 to m2 and that sort of thing. So, I thought to myself, this is the US, we should also do problems with in2 and ft2--I'll go look through the elementary and middle school texts in my library (I have 2-3 full series of each sitting outside my office door at work). Guess what? None of the books teach the topic at all. Aargh! Everyone is assuming someone else is teaching it, and no one is.
The first time I saw anything about area conversions was in the Saxon Math books I used to teach myself math a few years ago.
I learned inch-to-centimeter and inch-to-foot-to-yard conversions in school, but I learned nothing about area or volume conversions, and I continue to find volume conversions slightly confusing.
Speaking of Saxon Math, I've been thinking I need to get back to my books. I had almost finished the second book in the high school series when I was diverted to whatever I was diverted to. At the time, I was finding logs difficult to deal with in the "shuffled" organization of Saxon Math, especially since I wasn't studying every day.
Speaking of logs, I was emailing with Barry G. earlier today and I compiled a list of all the topics I was never, ever exposed to in high school math or college statistics.
I'll post tomorrow when I'm at my other computer.
The list is too long to remember off the top of my head.
Just 28% of the Portuguese population between 25 and 64 has completed high school. The figure is 85% in Germany, 91% in the Czech Republic and 89% in the U.S.
Ireland
There is substantial evidence from elsewhere that education confers broad economic benefits. Ireland was one of the EU's poorest countries a generation ago. But it threw EU subsidy money into technical education and remade itself as a destination for high-tech labor, made doubly attractive by low corporate taxes. Ireland is now, even after a brutal banking crisis, among the richest nations in Europe.
"They had an educated-enough work force that they could move into a technology industry, and they rose out of nowhere," says Eric Hanushek, a Stanford University professor.
Portugal
Prof. Hanushek and a professor from the University of Munich have linked GDP growth with population-wide performance on standardized tests. They calculate that Portugal's long-term rate of economic growth would be 1.5 percentage points higher if the country had the same test scores as super-educated Finland.
Education long was an afterthought here. "The southern countries like Portugal and Spain and the south of France and Italy, we have always had some problems related with education," says António Nóvoa, a historian who is rector of the University of Lisbon. "That's been like that since the 16th century."
The repressive dictatorship that ruled Portugal from 1926 to 1974 had the idea "that people should not have ambition to be something different than what they were," Mr. Nóvoa says. The result was widespread illiteracy and little formal schooling; just three years were compulsory. Huge leaps have been made since the 1970s, he says, but "it is not easy to change a history of five centuries."
Portugal has just begun phasing in 12 years of required schooling; now, Portuguese can leave school after ninth grade. Many do.
[snip]
A push to evaluate teachers triggered searing strikes and demonstrations in 2008, souring relations between powerful teachers' unions and the government. The political life of education ministers is measured in months: since the dictatorship ended in 1974, there have been 27.
parents protest cuts to quasi-private schools
To the system's critics, a fight that has developed over quasi-private schools is emblematic of what's wrong. With budgets tight, the government has imposed deep cuts on schools that are at the margin of the state's control—no matter that some are among the best.
[snip]
In one town, A Dos Cunhados, the local school isn't run or owned by the government. It is managed by the Catholic Church, in an arrangement that dates to the end of the dictatorship, when the new Portuguese state found it didn't have enough facilities.
At the school, Externato de Penafirme, as at 90 others with what are called "association contracts," the state pays a management fee to a private entity, which broadly follows the state curriculum but hires its own teachers.
The deputy principal, Carlos Silva, once taught chemistry in the public school system. He was shuffled through four schools in four years. Frustrated, he quit and enrolled in a seminary. Afterward, as a priest, he asked his bishop about returning to the classroom, and was assigned to Externato de Penafirme.
[snip]
Faced with the cuts, students and parents organized. In December, 4,000 people held hands in a big ring around the Penafirme campus. The pictures hit television. A Facebook group sprang up. In January, students walked out of dozens of the privately run schools for three days. To dramatize a claim the cuts would mean the death of their schools, students and parents from 55 schools ferried mock coffins to Lisbon and put them on the median strip outside Ms. Alçada's ministry.
Last month, the education ministry eased somewhat, agreeing to restore part of the lost funding for this semester.
Two new posts from the temporarily dormant Throwing Curves on religion in the schools and the ongoing legislative efforts to revamp teacher evaluation procedures.
The National PTA partnered with experts on the Common Core State Standards to create grade by grade guides that reflect the Common Core State Standards. The site also has a brief powerpoint of additional materials for mathematics describing focus and coherence. Slide #5 caught my attention:
Having one son in a charter school and sports means plenty of driving. Yesterday, I was taking three boys from the high school to the baseball fields a couple of miles away and was lucky to hear this nugget of wisdom:
C: The principal was observing Mr. X (the Latin teacher) today. Class was so much better than usual, we didn't just sit there and read like we usually do.
T: Totally.
J: Yeah, teachers really seem to have better lessons when Principal Y or Mr. Z (Headmaster) is watching them. It's like they think it though better and try to make it more fun to show-off or something.
MSMI 2011: Fractions is a 5 day (plus 5 day followup) institute, June 20-24, 2011 in downtown Saint Paul, MN. MSMI 2011: Rational Numbers is a 4 day (plus 5 day followup) institute, June 27-June 30, 2011. Both institutes will be held at the CoCo Coworking and Collaborative Space. Local arrangements are available at the Crowne Plaza in St. Paul, a short walk from CoCo.
These institutes are designed to develop fractions and rational numbers in a coherent, sequential, and precise manner that builds both conceptual understanding and procedural fluency. Teachers will learn how to help their students increase the depth of knowledge by providing the scaffolding needed for abstract mathematical reasoning. Teachers will develop a better understanding of how they math they teach relates to the math taught prior to and beyond their classroom. By teaching this material in a coherent, precise fashion, teacher will be able to lead students to understand and master this mathematics, enabling their students to achieve a solid foundation for Algebra 1.
Why fractions and rational numbers? MSMI concentrates on fractions and rational numbers following the National Mathematics Advisory Panel's recommendations on "Critical Foundations for Algebra". Fractions are the first abstractions in school mathematics. Fractions prepare students because they depend on precise definitions in order to be well defined. Fractions are handled best by thinking symbolically, not by analogies (no more pie pieces, pizza slices, etc.) Negative numbers have no grounding the way counting numbers do. They are best handled by thinking symbolically and working with definitions. Learning to work with fractions and negative numbers helps students because if they can handle these elements for fractions and negative numbers, they can handle them in algebra.
Institutes are not geared toward any specific textbook or pedagogy, but provide deeper content knowledge immediately applicable to any classroom. The textbook for these institutes is Hung-Hsi Wu's Understanding Numbers in Elementary School Mathematics . This material is aligned with both Minnesota state standards and Common Core standards.
Allison Coates will teach the Fractions institute. UC Berkeley Professor Emeritus Hung-Hsi Wu will teach the Rational Numbers institute.
Topics covered in Fractions Institute include: —
Formal definitions of Fractions and Decimals
— Equivalent Fractions and the Fundamental Fact of Fraction-Pairs
— Addition and Subtraction of Fractions and Decimals
— Multiplication of Fractions and Decimals
— Division of Fractions
— Complex Fractions
— Percent
— Ratio and Rate
Topics for Rational Numbers institute include:
The Two Sided Number Line
— A Different View of Rational Numbers
— Addition and Subtraction of Rational Numbers
— Multiplication of Rational Numbers
— Division of Rational Numbers
While the summer session of 4 or 5 full days provides the bulk of the mathematics content, 5 follow-up Saturday sessions are provided throughout the school year. Saturday sessions review material from the institute and provide time for teachers to discuss implementation of institute material in their classes. In these sessions, teachers work together to determine what works best for their students in their classrooms, and provide feedback to each other.
Looking back at my own junior high experience and comparing it to my kids' middle school experience, I think momof4 has hit the nail on the head. Junior high was about academics, and the adults trusted that the adolescents were cable enough to work through their personal growth issues on their personal time. Middle school seems to be about everything but academics.
In junior high, I had really solid instruction in writing,including extensive grammar instruction. We did science labs that required the exact same sort of write-up that my high school labs later required. We studied actual history and civics (as opposed to the nebulous social studies).
In middle school, my daughters don't write, they produce power point presentations. The few writing assignments are given as group projects - my oldest was recently assigned a group poem to write. While they do science experiments, these seem to be purely for demonstration value as the students are never required to record observations in any standardized form.
My middle school daughters frequently miss class in order to attend assemblies during which some nominally well-known person tells them how important it is to stay in school and get an education. The irony of cancelling class to have an athlete extol the virtue going to class seems lost on middle school administrators.
and "docent science," which is what my colleagues and I call it. Science appreciation is another good term. I guess I can see that they figure that most students won't actually go on and do STEM in college, but they are really limiting their students' options. Plus, I can't tell you how many students come to college thinking that there are careers in science appreciation.
I've always had a simmering interest in math, and for years I bought 'math appreciation'-type books, which I always found somewhat unsatisfying and never finished reading.
Finally, after writing ktm for awhile and teaching myself math so I could re-teach math to C., I realized I didn't want to appreciate math. I wanted to learn math.
"Understanding math" - which I think of as a kind of feeling I have at times - is tremendously fun, but it's not fun when I can't actually do the math I'm "understanding." Hard to explain.
I've also learned the importance of "getting used to" math as opposed to understanding it. Or, at least, I've had the experience of learning to do something I can't understand and then, after awhile, coming to feel that it's "natural" and "logical" to do whatever it is I've been doing.
This process is starting to happen a bit with counting, which I have found utterly mystifying. Recently I discovered that a great deal of what I've been doing in counting problems involves the commutative property and the definition of multiplication.
Who knew?
I can't tell if all this self-teaching I've been trying to do is a good thing or a bad thing.
Misconception 2: Value-added scores are inaccurate because they are based on poorly designed tests. Most standardized tests are indeed flawed, but this is not a problem created or worsened by value-added. Seven Misconceptions About Value-Added Measures by Douglas N. Harris Harvard Education Letter - March|April 2011 p. 8
Is that correct?
As I understand it, New York's state tests can't be used for value-added purposes. The tests are shorter in some years, longer in others, and somehow don't correspond to a one-year measurement of learning. Or so we were told. Certainly they don't provide any sense of where a child might be within a year's worth of content. New York tests are scored 1 to 4, so if your child scores a middling 3, what does that mean on a scale of 10 months? Nobody knows.
I had been assuming that in order to use a standardized test as a value-added measurement, the tests had to be normed month-by-month as the Iowa Test of Basic Skills is normed:
Grade Equivalent (GE)
The grade equivalent is a number that describes a student's location on an achievement continuum. The continuum is a number line that describes the lowest level of knowledge or skill on one end (lowest numbers) and the highest level of development on the other end (highest numbers). The GE is a decimal number that describes performance in terms of grade level and months. For example, if a sixth-grade student obtains a GE of 8.4 on the Vocabulary test, his score is like the one a typical student finishing the fourth month of eighth grade would likely get on the Vocabulary test. The GE of a given raw score on any test indicates the grade level at which the typical student makes this raw score. The digits to the left of the decimal point represent the grade and those to the right represent the month within that grade.
When your child takes the ITBS from one year to the next, it's simple to see whether he's made a year's progress in a year's time. If, at the end of grade 3, he scored a 3.10 on computation (grade 3, month 10), he should score a 4.10 on computation at the end of 4th grade.
But how would you make that determination using the New York tests?
Or is there some other comparison you make from year to year?
Vendors everywhere, technology, no books, Smartboards (it's the 20th anniversary of the invention of the Smartboard!), and, during plenary sessions, constant calls for Parent Responsibility, each one met with thunderous applause. Parents were not a popular group amongst the Celebrants.
During the session on bullying, three teachers asked plaintively, "Why is bullying our responsibility?" "Why is everything on us?" They were aggrieved.
The great and the good (Brian Williams, Cory Booker) thought teachers had a lot to be aggrieved about. Democracy is hanging by a thread, they told us: the only reason we have a country at all is teachers. And yet Americans fail to feel "reverence" toward teachers. What is to be done?
Mehmet Oz said pretty much the same thing; then he showed us a graph charting the rise of obesity in America and said rising obesity is the reason "there's no money for education." We need to lose weight! Because we need more money for education!
Also, the NEA wants the government to pay for college and graduate degrees for teachers. We'll need to lose a whole lot of weight for that.
My friend attended a session where there was a group of young administrators seated in the middle of the room. The teachers booed the administrators. Now that's interesting ---- what was going on? I wish I'd been there.
A fellow from the Department of Education told us that DOE is rolling out "an ambitious 5-year initiative": the moon shot of this generation. Which was.....a website. The moon shot of this generation is a Department of Education website.
We watched a lot of student videos, all created with a product called Adobe-something-or-other: raps about Haiti; a geography class in California making soup. In the soup video, a pretty girl who came to America from Nicaragua complained that nobody knows where Nicaragua is or that a person who speaks Spanish and has brown eyes might be from Nicaragua and not Mexico. Another student in the video said somebody thought "Guatemala" was guacamole.
Maybe the reason students don't know where Nicaragua is or that Guatemala is a country not a dip is that they're making soup in geography class.
A high-energy Brit pitched his Teacher Channel, I think it was called: there will be authentic content!! We watched an authentic video of a grade school class in Florida where the kids scotch-taped together little houses and stuck them in a line on a stage. Then the teacher walked along the stage blowing the houses with a leaf-blower to simulate a hurricane. Some of the houses blew apart and some didn't. Shots of fist-pumping little kids; fade-out.
The Brit told us we had just witnessed "learning" and said there would be many thousands such videos available on Teacher Channel, which was being sponsored or hosted or public-private partnered or some such with WNET, the host of Celebration of Teaching and Learning. Applause!
In the session on how to teach counting using a children's book, the Math for America Master Teacher banned the words "permutation" and "order" because "permutation" and "order" are words, not understanding. He told us, repeatedly, that he makes his high school students spend a full test hour drawing the answers to counting problems in order to show them that multiplying 5x4x3 is more efficient than drawing 60 houses with 1 of 3 pigs inside. At the end of the sessions, he advocated the use of children's books for teaching high school counting problems. "How many handshakes amongst the 7 dwarfs?" That was a good counting question we could base on a children's story, he said.
At one point a teacher said she'd made a counting tree, and the Master Teacher said, a look of mock incomprehension on his face, "Tree? What is a tree? Why do you talk about trees?"
Five minutes later he put up a Powerpoint picture of a counting tree -- an actual tree, with a trunk going down to the ground, and branches pointing up to the sky. I don't know why a real tree is good and an abstract tree is bad. He didn't say. The rule seemed to be that everything the teachers said was old-school and wrong, while everything the Master Teacher said was up-to-date and correct.
The Master Teacher had no blackboard, whiteboard, or Smartboard, so you had to try to remember everything he had just finished saying while trying to follow whatever he was saying now, and his Powerpoint drawings were confusing, at least to me. He spoke too fast. He told us over and over again that we needed to hold with our students the kind of conversation he was holding with us: i.e., a conversation for understanding.
I don't recommend it. The "conversation" consisted mostly of our Master Teacher eliciting wrong answers and forbidden vocabulary from his class. There were probably 5 people of 30 who could work the problems, so he focused on them and didn't bother with the rest of us.
I'm actually thinking about writing James Simons a letter.
Description: If three pigs live in five houses and each pig lives alone, how many living arrangements are possible? Participants will learn how a children’s book illustrates a simple way to solve counting problems like this without listing all possibilities. Teachers at all levels, from elementary to high school, will learn how students can find the answers without using confusing words like “permutation.”
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course or book.
. There are no tricks or fast-track methods in this book. I have put together 20 mock exams, complete with answers and explanations, to help you PRACTICE your math test taking skills. These are the mock exams that I have used in my private tutoring sessions with my own students, most of whom have gone on to achieve perfect scores on the SAT Math exam.
. I have a question about this passage: 
