E-Accountability OPINION

Many years ago several very wealthy and powerful individuals got together and discussed what to do with the problem of not having enough math and science teachers to teach rigorous, higher-level math courses in our nation's high schools and colleges. Also under discussion was the issue of the high fees 'expert' mathematicians could expect if hired from scientific think-tanks, and their non-union status (as in UFT, NEA, etc).

A brilliant solution was decided upon: a political-public relations-textbook industry-teaching college partnership that would design a curriculum supporting the notion that true learning came from children who felt comfortable working out problems and finding information without being told by a teacher what the 'facts' were. Children would, this partnership decided, be graded on how well they thought up their own answers and how well they 'understood' math processes, rather than just getting the right answer. In fact, this new 'constructivist' doctrine declared in the quickly published textbooks for teachers, the 'right' answer was not something that should be considered important at all. In other words, if a child understood that multiplying 16 "times" 19 meant the same as 16 "added" 19 times, then he or she was right, and must be given credit for constructing the reality around the process. It didn't matter whether the child arrived at the "real" answer, 304, or not, as long as they provided an understanding of the process, that
16 X 19 actually meant:

16+16+16+16+16+16+16+16+16+16+16+
16+16+16+16+16+16+16+16 = 304, or 305, or 310, or 204, or.....

Baloney like this has swept the US for years. In New York City, the District 2 miracle"started by Tony Alvarado funded the dumbing down of elementary school children. Teachers and Principals who did not want to go along were forced to, and still are today. Stuyvesant High School, a premier High School for very smart kids, two years ago started a new math course to accommodate those 9th and 10th graders who could not do the traditionally challenging math curriculum.

Several years ago my 9-year old daughter Marielle, a busy professional opera singer and very strong math student at a premier elementary school that was the leading proponent of the TERC constructivist nonsense, got upset with the time needed by her math homework and decided to write a letter to the NY SUN newspaper. Her letter was published on August 29, 2002. Below is the unedited version:

WHY TERC?
by Marielle Combier-Kapel
4th Grade, PS 6

Parents are making tutors crazy calling them all the time because of TERC math. Kids don't have time to do anything because all they do after school is get tutored in math. There is no one to have playdates with anymore!

Citywide math scores are falling, but Board Of Education officials say that the District 2 math scores on the Standardized tests are high, therefore the TERC math curriculum is a good thing. Many District 2 parents are spending lots of money on tutoring, which brings up the scores, giving the impression that TERC is good for us kids.

Tutoring is great if your parents have money to spend on this. TERC math shouldn't be the only kind of math schools teach to their students. Just because some students aren't that smart, the schools are sending flyers home to parents saying that they should not teach their child traditional math which includes long division and algorithms. I like long division!

My mom says:
"Fuzzy math condemns our kids by not allowing them to establish an understanding of base computations which will empower them as they reach higher levels of problem-solving. The Board of Education policy to implement TERC math and ONLY this curricula is assuring our kids an immediate future of confusion, or worse, boredom, and a long-term disability in math achievement and academic performance in non-math
subjects as well. Learning traditional math as a reference is similar to having a Spanish dictionary when you are trying to write something in Spanish."

Parents are now calling other parents to find out if they tutor their children in math or not, and are signing up my friends. One of my sisters' teachers at Stuyvesant told my mom that the math at the Freshman level may have to be changed to a lower achievement level, as kids from District 2 who are getting in
are having trouble with the traditionally rigorous math program. A teacher at my other sister's honors program told my mom that she has never seen children in 7th grade who are not able to do long division.

What may happen is that I may be unable to compete for college places because the math teaching I have received is not teaching me what I should know. Is that fair?"

We received this admonition from her teacher about the 4th Grade math homework:
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Dear Family,
In mathematics, our class is starting a new unit called Arrays and Shares. This unit focuses on multiplication and division. Students begin the unit by looking at things that are arranged in rows, for example, juice packs, egg cartons, and rows of chairs. Through examining these rectangular arrangements (or arrays), they begin to visualize important aspects of multiplication, for example, that the solution to 7 X 6 is the same as the solution to 6 X 7.
As students go on to work on two-digit multiplication and related division problems, it is critical that they visualize how to pull apart the numbers they are working with. To solve these harder problems, students learn to use related problems they already know how to solve. For example, the problem 7 X 23 can be solved by breaking the problem into more familiar parts: 7 X 10, 7 X 10, and 7 X 3.
While our class is studying multiplication and division you can help in the following ways:
Look for items around your house or at the grocery store that are packaged or arranged in rectangular arrays. Tiles on the floor, egg cartons, window panes, and six-packs of juice cans are examples of rectangular arrays. Talk with your child about the dimensions (rows and columns) and discuss ways to figure out the total number.
Play the Array Games that your child brings home for homework.
Help your child practice skip counting by 3's, 4's, 5's, and so forth.
When your child brings home problems, encourage your child to explain his or her strategies to you. Ask questions, such as "How did you figure that out?" and "Tell me your thinking about this problem", but don't provide answers or methods. Show that you are interested in how your child is thinking and reasoning about these problems.
Please don't teach your child step-by-step procedures for computing multiplication and division. Too often we find that children at this age memorize the multiplication and division procedures but cannot recognize situations in which multiplication and division are useful. We will gradually support students this year in developing several strategies for carrying out multiplication and division problems, but we would prefer they not memorize procedures at this time.
Thank you for your interest in your child's study of mathematics. We are looking forward to an exciting few weeks of work on multiplication and division.
Sincerely,
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Marielle was subsequently told that she could not do math, and in 5th grade she was not put back onto the Math Team. She agreed to try for the Johns Hopkins Center For Talented Youth, and was a high scorer in Math, becoming one of the top 3% of 5th Graders in the United States. Her self-esteem was pushed back up, despite the comments from her teacher.

...then there is the textbook industrial complex:

Imagine the textbook industry's happiness with a new market for their publications (we have not seen them, but they must be out there) such as " The Math Classroom: Designing Desk Groups To Optimize Constructing Comfortable Math Thinking" or "Desk Arranging To Assist Teachers in Student Conversations During Math Class". Chapter after chapter must provide colorful pictures of where rugs could be placed, what size rocking chair to use, and how to arrange desks in the most creative way to encourage student discussion, in case the teacher has to go to another room, to the bathroom, a retreat in the country, etc.

In conclusion, we congratulate Rocky Mountain News reporter Linda Seebach, and NYU Professor Alan Siegel, in their exposure of the false claims of constructivism!

Betsy Combier

Seebach: An illusory math reform; let's go to the videotape
by Linda Seebach, Rocky Mountain News, August 7, 2004

American children come off badly in international comparisons of mathematics performance, and they do worse the longer they're in school.

One such comparison, the Third International Mathematics and Science Study, tested more than 500,000 children in 41 countries, starting in 1995. As part of the study, researchers videotaped more than 200 eighth-grade math lessons.

These lessons have been studied intensively in an effort to figure out why Japanese students do so well in math while American students do so badly. Alan Siegel, a professor of computer science at New York University, has reviewed the videos and calls the teaching "masterful."

He also believes that many of the TIMSS studies contain "serious errors and misunderstandings." If you have doubts, he says on his Web site, "go review the tapes and check out the references. After all, that's what I did" (www.cs.nyu.edu/faculty/siegel/). His paper also appears in a recent volume of essays on testing published by the Hoover Institution, Testing Student Learning, Evaluating Teacher Effectiveness.

The eighth-grade geometry lesson Siegel discusses is based on the theorem that two triangles with the same base and the same altitude have the same area, and it is framed in nominally "real world" terms as a problem in figuring out how to straighten the boundary fence between two farmers' fields so that neither farmer loses any land.

This is of course highly relevant to urban Japanese youngsters, who are likely to be called upon frequently to accomplish this task.

The teacher first primes the class by reminding them of the theorem, which they had studied the previous day. Then he playfully suggests with a pointer some ways to draw a new boundary, most of them amusingly wrong but a couple that are in fact the lines students will have to draw to solve the problem (though they aren't identified as such).

Then he gives the students a brief time, three minutes, to wrestle with the problem by themselves, and another few minutes for those who have figured out a solution based on his broad hints to present it. Then he explains the solution, and then he extends the explanation to a slightly more complex problem, and finally assigns yet another extension for homework.

As Siegel describes it, "The teacher-led study of all possible solutions masked direct instruction and repetitive practice in an interesting and enlightening problem space.

"Evidently, no student ever developed a new mathematical method or principle that differed from the technique introduced at the beginning of the lesson. In all, the teacher showed 10 times how to apply the method."

But that's not the way the lesson has been described in the literature. A 2000 commission report from the U.S. Department of Education, Before It's Too Late, gushes that in Japan, "teachers begin by presenting students with a mathematics problem employing principles they have not yet learned. They then work alone or in small groups to devise a solution. After a few minutes, students are called on to present their answers; the whole class works through the problems and solutions, uncovering the related mathematical concepts and reasoning."

How could Japanese children solve problems based on "principles they have not yet learned"? Why, in the same way that Meno's slave solved a mathematical problem on the exact same day that Socrates happened to be asking him questions.

As to how this confusion might arise, Siegel notes that a report by J.W. Stigler and others for the National Center for Education Statistics, The TIMSS Videotape Classroom Study, uses this very lesson as an example of how their data analysts were trained to identify solutions discovered by students.

"Altogether, this lesson is counted as having 10 student-generated alternative solution methods, even though it contains no student-discovered methods whatsoever," Siegel says.

Furthermore, the mathematicians who wrote about the study subsequently didn't see the original tapes; they relied on the misleading coding done by the data analysts.

Why does it matter? Because so-called "discovery learning" is the promised land of mathematics reform, and if only we follow the prophecies of the National Council of Teachers of Mathematics across the River Jordan, all our failings and failures as a nation will vanish away. And we know the prophecies are true, because the Japanese have gone before us.

Only they haven't. This is teaching in the traditional mode, beautifully designed and superbly executed, but nothing like the parody of instruction that goes by the term "discovery learning" in math-reform circles in the United States.

The videotape shows, Siegel says, that "a master teacher can present every step of a solution without divulging the answer, and can, by so doing, help students learn to think deeply. In such circumstances, the notion that students might have discovered the ideas on their own becomes an enticing mix of illusion intertwined with threads of truth."

Illusion prevails in far too many American classrooms.

The New York Sun • August 6, 2004
The Answer Goes Back To Basics
By ANDREW WOLF
awolf@nysun.com

The National Endowment for the Arts recently released a report on our nation's literacy. Americans are not reading as much as they used to. This trend has been accelerating in the past two decades. There has been a lot of anguish over this news, which has drawn much comment on both the left and right, and no shortage of theories attempting to explain how we came to this. Everything gets blamed, from television to videogames to the Internet. I have my own theory.

It is curious is that the movement of our young people away from the joy of reading for pleasure appears to coincide with the rise of the whole language (often labeled "balanced literacy") method of teaching reading, and the associated content-poor "progressive" teaching model that encourages students to "construct" their own knowledge.

This pedagogy, now the predominant way American (and as we shall see, British) children are taught, is supposed to instill a love of reading and literature. "Libraries" are placed in every classroom, part of an effort to create a "literature rich" environment. Small groups of students are organized into "book clubs."
Meanwhile, the role of the teacher as a conduit of knowledge has been subverted. Here in New York City, teachers have been directed to arrange classroom desks in clusters, in which groups of children face each other to facilitate the group projects that have replaced direct instruction by teachers. "Authentic literature" has supplanted textbooks as the tools of learning subject matter.

All this is done to promote the love of independent learning, made possible by promoting the love of reading. This is at the center of the ideology promoted by literacy gurus such as Lucy Calkins of Columbia University Teachers College, Diane Snowball of the Australian United States Services in Education, or AUSSIE, and Lauren Resnick of the University of Pittsburgh Institute for Learning. Our Department of Education is funneling tens of millions of dollars to these theorists, spending perhaps a quarter of a billion dollars in the past year to enforce compliance with this approach. This is wasted money.

As more American children are taught by these methods, the love of reading is apparently not increasing, but diminishing at an alarming rate, as the NEA study demonstrates. Can the way children are taught in school actually be the cause of this? I believe it is.

The idea that children learn to read and develop a love of reading from merely immersing them in a "literature rich" environment is akin to teaching the children of Gary, Ind. how to play musical instruments using the "think" system. Prof. Harold Hill and the storyline of "The Music Man" is, I believe, fiction. Knowledge is not acquired by osmosis. It is a process of building, one fact upon another. Those children who develop a love of reading don't do so for its own sake. It is because these children thirst for more knowledge.

That quest is not triggered by being surrounded by books such as the ones in the classroom libraries mandated by the Department of Education. Most of these books are works of fiction, mostly carefully scrubbed and filtered, with content largely designed to build self-esteem rather than impart knowledge. I submit that this kind of literature is the least likely to encourage children to become voracious readers.

Are textbooks obsolete? They are now much maligned and in danger of becoming extinct. But in the real world, I have found that they often were motivators for further reading. They provided overview and context, and in my distant youth often lured me into further study.This is not to say that the textbooks of today are without problems. Censors from the left and the right have attempted, and in many cases succeeded, to remake textbooks to advance their political and even religious agendas, undermining their value.
America is not alone in exhibiting a rising concern over the anti-intellectual proclivity of the teaching methodologies that have become so widespread. In Britain, the same debate is raging. Even the Prince of Wales has recently weighed in.

In a speech to teachers of English and history in state-run secondary schools in late June, Charles lamented that the "faddish" curriculum is resulting in students who are becoming "culturally disinherited." The prince suggested that the content-poor British curriculum could be a "potentially expensive and disastrous experiment with people's lives."

The traditional instruction apparently favored by the prince is more in line with the thinking of Professor E.D. Hirsch Jr., whose Core Knowledge curriculum is based on the idea that knowledge is like Velcro – its acquisition is facilitated by the previous knowledge already accumulated.

This suggests that if we believe that reading is good for society and we want our education system to result in a literate and knowledgeable people, we will not find the answers in whole language, balanced literacy, or constructivist ideology. The answers are to be found in a true "back-to-basics" movement. The kind of instruction that candidate Bloomberg promised us, but Mayor Bloomberg has thus far failed to deliver.

The havoc wrought by today's "modern" math
By Dr. Charles Orms/ Guest Columnist, North Andover Citizen
Friday, September 24, 2004

If you are a parent of elementary school children you've probably seen it: elaborate make-work homework assignments, cutting and pasting extravaganzas, overly complex and roundabout procedures to add or multiply numbers, estimation exercises that won't quit, and the use of calculators in place of traditional arithmetic methods.

You thought: "Of course, the educational professionals must know what they are doing. Once my children catch on to these clever techniques, they will develop into mathematics geniuses!" Unfortunately, what you discover is that they never learn the core facts and methods, their confusion grows, they lose their self-confidence, they decide they just can't do math, and you are stuck paying for tutoring. Even worse, children who might have become exceptional mathematicians, engineers, or scientists are denied their rightful future.

What went wrong? Years ago the educational establishment decided that teaching mathematics had to either consist of rote memorization (without real understanding) or students had to discover mathematics through trial and error because it was assumed that only 'if they discovered it themselves' would they truly understand it. While this view presented a false choice (there are much better alternatives), the educational community was sold on the second alternative because it had an intellectual cache that was lacking in "rote memorization." What resulted are the various "modern" math curricula for our children that under emphasize learning math facts, that bend over backward to avoid teaching standard methods for addition, subtraction, multiplication, and division, and that refuse to teach traditional processes for manipulating fractions.

Almost all our public schools today use one of the "modern" math curricula and millions of promising math-based technology careers are being ruined every year.

Permit me a short excursion. I have a technical/engineering background (PhD MIT '74) that rests largely on advanced mathematics. One reason I followed this path is that, as a student, I always had poor memorization skills and, therefore, subjects such as biology, chemistry, and foreign languages were very difficult for me. I loved math and physics because there was very little memorization; I could derive any formula I needed during a test. "Understanding" was a much more powerful asset for me than memorization. If anyone would be inclined to favor understanding over memorization it would be me. But the modern math is a disaster. I'm convinced that if I had been "taught" math with it 50 years ago, I would probably have become a poet (my English teacher is rolling over in her grave).

So do I favor just rote memorization? Of course not. Successful math education requires that students learn the techniques that true geniuses have developed over the last 3000 years. You may think the standard technique used to add numbers is trivial (place value concepts, carrying, etc.), but it was not obvious to the ancient Greek philosophers. Multiplication, long division, and fractions are even more complex. Teaching the techniques first and then exploring the underlying concepts and why these techniques work is the most efficient way to achieve true understanding. If Socrates and Aristotle couldn't invent our modern arithmetic system, why do we think the typical third or fourth grader can?

The impact of "modern" math on students in the US has been devastating. Just look at how the US stands up against other countries.

Place an equal emphasis on method mastery AND conceptual understanding, and you have the makings of a powerful elementary math curriculum. A curriculum that leads to real learning, that builds self-esteem and, rarest of all, a child that comes home and says, "Hey mom, I really love math!"

This approach to math education is not new. It is what a well-taught traditional mathematics course always emphasized. In some cases, poor teaching may have led to over-emphasis on rote memorization drills, but that is no reason to stop teaching the critically important mathematical methods.

How are we doing with early mathematics education in this area? As the table shows, not very well. While the differences in scores between towns/cities may be accounted for by socio-economic factors, the percent of students who are not proficient (meaning they scored as "Needs Improvement" or "Warning/Failing") in fourth grade (90 percent in Lawrence, 60 percent in Methuen, 50 percent in North Andover, and 34 percent in Andover) cannot be excused. Even worse is the lack of progress after four more years of what passes for math "education".

2003 MCAS SCORES(Percent ADVANCED OR PROFICIENT)

Town/City - 4th Gr - 6th Gr - 8th Gr

Andover -- 66% - 76% - 66%

Lawrence - 10% - 9% - 9%

Methuen -- 40% - 41% - 34%

North Andover - 50% - 51% - 60%

AVERAGE -- 42% - 44% - 42%

The trend towards "modern" math may finally be slowing. Parents are upset with the lack of a rigorous math curriculum and the need to hire tutors or enroll their children in remedial after school programs. A nationwide movement is growing to expose the failures of "modern" math and restore an academically sound curriculum. For information, visit mathematically Correct