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Higher Goals for Exit Exams
California cheats its students by expecting too little
– Pete Wilson, Bill Evers
Tuesday, September 28, 1999

GOV. GRAY DAVIS and the state Legislature have adopted the popular idea of having a high school exit exam. This could help to ensure that a diploma in California means something. But if done wrong, it could set back the task of school improvement. Deciding how high to set the hurdle requires care. If the test is too hard, many students won’t graduate. Making the test too easy discourages high achievement and works against the educational improvement we desperately need. In mathematics, it looks as if California is going to take a counterproductive approach. The current plan emphasizes the least difficult math standards from grades 7 and 8.

We all want our high school graduates to know their seventh-grade math, but we simply must set higher goals. It is well known that algebra is the gateway to further achievement in math and science education, yet California has never required our students to learn it. New math standards were put in place in 1997. These standards encourage taking algebra by eighth grade so our students would catch up to those in high-performing foreign countries. With this as a long-range plan, a logical starting point is to require knowledge of algebra for high school graduation.

Unfortunately, the math test planning committee, appointed by State Superintendent of Public Instruction Delaine Eastin, has chosen to continue to avoid algebra. Do the committee members believe California’s students can’t learn it? Are they afraid that California’s teachers can’t teach it? Or do they simply believe that an easy test will make educators look good?

Setting the bar too low can have serious consequences. It says that mediocre is good enough. It encourages our teachers to emphasize low-level content. It works against any chance we have of improving California students’ currently abysmal performance in mathematics.

Worst of all, it will perpetuate existing gaps in achievement. Effectively, it says that the low achievement that is common now among poor and minority students is good enough. Yet low expectations are not what these students need or deserve.

If students are going to be prepared for the job market of the Information Age, they need to know algebra. After we climb the ladder to this point, we can require further knowledge of mathematics to bring us still closer to the achievement of students in other countries. California is just beginning to test students against its new standards, and we must continue in that direction if we are to see improvement.

Our high school exit exam has to mesh with our long-term goals.

It is time to stop rewriting the rules to avoid the truth about how poorly we are doing in mathematics education. It is time to insist that our schools teach algebra to all students. Only this can honestly be called solid education for all.

Pete Wilson was governor of California from 1991 to 1999. Bill Evers is a former commissioner of the California State Academic Standards Commission. Both are fellows of Stanford University’s Hoover Institution.

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©2005 San Francisco Chronicle

High School Students And Lab Rats
– Debra J. Saunders
Friday, March 12, 1999

MELISSA LYNN was shocked when she discovered that she placed in the bottom 1 percent of the University of Michigan math placement test. She had graduated from the affluent high-achieving Andover High School in Bloomfield Hills, Mich., with a 3.97 grade point average and A’s in math.

Lynn blames Core Plus, an experimental math program — with an emphasis on writing about math and working in groups — funded by the National Science Foundation. “It had very good intentions and wanted you to apply real principles to real life scenarios, but it was missing the crucial element of algebra,” Lynn said yesterday.

Gregory Bachelis, a math professor at Wayne State University and parent of a student in Lynn’s school district, wanted to know if Lynn’s experience was typical. He decided to do his own survey. He sent questionnaires to all 1997 graduates of Andover and the other Bloomfield Hills high school, Lahser, which has similar demographics but a traditional math program.

Bachelis heard from 112 out of 228 Andover grads, 67 of whom were Core Plus alumni; 30 percent of Lahser students responded.

R. James Milgram, a mathematics professor at Stanford University, has written a paper on Bachelis’ findings. Milgram found the following.

— Only two Core Plus grads (out of 67) reported taking calculus in their first year of college, 11 out of a similar group of 41 Lahser grads took calculus; 46 Core Plussers ended up in remedial math, compared to 18 Lahser grads.

— The average math GPA for the Core Plus grads was 1.9, 2.6 for Lahser students.

— The average SAT Math score for Lahser grads was 59 points higher than Core Plus.

As one Core Plus survivor who was placed in remedial math wrote, “I am the epitome of mathematical ignorance in a Top 10 high school in the country with a 4.0 in math.” Student comments paint a picture of students who worked hard but foundered in college math. Andover Principal John Toma takes great exception with the study. He attacked Bachelis’ bias. Bachelis was a critic of trendy math before the survey. Asked about Melissa Lynn, Toma responded, that the University of Michigan “admits that they’re going to change the placement exam because it’s flat out outdated.”

Andover allows students to opt out of Core Plus. Only 55 out of 840 do so, which shows that someone must like Core Plus. Although Lynn says she didn’t opt out because she would have had to take a bus to Lahser for math and that conflicted with her schedule.

Toma noted that studies should not rely on students to give their SAT scores and grades, that the more reliable studies get that data directly. He sent me a University of Michigan memo that reportedly checked grades and found that “reform” math students scored “nearly half a grade higher“ than traditional math grads. But the survey failed to differentiate between reform students and non-reform students, lumped them by school, provided no specific GPAs, no school names and no number of students tested — it lacks credibility.

That is not to say that the Bachelis/Milgram study is without problems. It could be that only the angrier kids responded. Some may have misstated their scores.

Still, the anguish that one reads in the student comments should not be ignored. “I cannot even do basic math calculations,” wrote one grad. Wrote another: “Although I did well in high school math, I feel I don’t understand basic math concepts well enough to keep up in college.” Some had to take math courses for which they could not even receive college credit.

Milgram is most appalled at the ethics behind Andover’s math experiment. He believes that parents should have been warned and students given more opportunity to get out. Instead, public schools too frequently give students about as much choice as lab rats have. None.

Hands On, Dumb Down
– DEBRA J. SAUNDERS
Tuesday, March 9, 1999

HEY, I KNOW what California public schools need: another program.

Is that what Assemblyman Jack Scott, D-Pasadena, thought when he wrote a bill to create a new California Teacher Cadet Program? The purpose of Assembly Bill 192 is to introduce “public high school pupils to the teaching profession” and to “develop a grant program to assist school districts in offering year-long course work designed to expose pupils to teaching careers through the development of a hands-on education curriculum.”

Great idea: Add another non-academic subject to the high school curriculum. Call it: Anything but math and science. After all, today’s students are so educated that they should be spending their time tutoring other students instead of studying.

I don’t even want to know what the “hands-on education curriculum” entails. Suffice it to say that Scott’s Cadet Program is based on a South Carolina program which is considered “the most successful part of the state’s reform” because 38 percent of students who participate say they want to be teachers. That’s how educrats rate success: kids say they like it.

Of course, since the teacher cadet program is supposed to be for high-achieving students who think they might want to be teachers, that 38 percent doesn’t bode well. Figure either cadet schools have pushed kids who don’t want to be teachers into the program, or the program is driving 62 percent of students away from teaching faster than you can say “hands-on education curriculum.” The latter is my guess.

A program backgrounder boasts: “The class would focus on a basic curriculum and would get students out into schools and interacting with teachers at various levels, counselors, library-media teachers, etc.” Those are my italics, meant to highlight the idiocy of this edu-think. Apparently no one told the cadet mongers that the kids already are in schools interacting with educators, wow, even without a state program.

The bill states that it wants to promote “interaction with successful administrators and teachers.” (I guess the non-cadets can interact with unsuccessful administrators and teachers. They must save the best for state programs.)

“All day long students observe teaching, or they should if they pay attention. If they’re inclined to teaching, they will pick up on it,” Assemblyman Steve Baldwin, R-La Mesa, said yesterday. “I don’t think we need a new state program. It just sounds like a stupid program that sounds good but probably will do nothing but spend more state dollars.”

And easily take away time and energy from more academic pursuits.

Studies show that teachers haven’t had enough math or science. So what does AB 192 do? Start educrat courses into high school so that future teachers will have taken education courses, instead of science, both when they were in high school and in college.

But it sounds good, so who cares what it might do? Not the Assembly Education Committee, which passed it by a 17-2 vote last week. Only Baldwin and Assemblyman Roy Ashburn, R-Bakersfield, voted no. Despite a withering GOP analysis of the bill, five Republicans — including Jim Cuneen of Campbell and Lynne Leach of Walnut Creek — actually voted for this scheme. The committee earmarked $175,000 to start up the program, but didn’t budget for the $2,500 which AB 192 would award to each school for enrolling.

State schools chief Delaine Eastin and California State University supported the bill. No surprise: Eastin’s department gets $25,000 to implement it. CSU gets $150,000.

There was no official opposition to the bill, natch. It’s no one’s job in Sacramento to ask whether a bill is a waste of time and money. It’s in no one’s political interest to demand that legislators consider what academics might be shunted to make time for the many “hands-on” activities.

Here’s an idea for a state program. Create a scold program that reminds lawsmakers to consider how their pet programs might shortchange academics and question whether bills spend money most wisely for California students. State solons ought to do that all by their lonesomes. But apparently they’re not.

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©2005 San Francisco Chronicle

Graphic-Calculators

The Detroit News
Metro Section

June 17, 1998

Math debate heats up Professor won’t give up controversial data on Core-Plus
program in Bloomfield Hills By Rusty Hoover / The Detroit News

BLOOMFIELD HILLS — A math program at Andover High School that students say has
cheated them out of a solid math education is now causing a second round of
controversy.

This time, a university math professor, trying to find out if students in Core-Plus
math are learning anything, is battling the Bloomfield Hills School District to keep
his data confidential. Wayne State University math professor Gregory Bachelis vows
not to turn over his surveys about the math program without a court order. At issue
is whether teaching Core-Plus math at Andover is seriously handicapping
college-bound students, as indicated by some survey comments collected by Bachelis.

But the school district, which includes Andover and another high school that doesn’t
use the math program, has filed a Freedom of Information Act request to obtain
Bachelis’ documents.

Some Andover parents are angry that their children were forced into the Core-Plus
pilot program, which relies on the use of graphing calculators, which allow students
to enter an equation and get a visual representation of it. Parents have demanded a
choice of math courses.

That is too late for Melissa Lynn, 18, who graduated summa cum laude with a 3.97
grade point average from Andover last year. She failed the math placement test at the
University of Michigan, scoring in the first percentile, the lowest possible.

Worse, she didn’t recognize what was being asked on the test. She called 14 other
U-M students who had taken Andover’s Core-Plus math and found they placed
anywhere from the first to the sixth percentile, she said. “Everything I didn’t know
was algebra,” Lynn said.

But proponents of Core-Plus say the program does a better job of preparing students
to handle math and higher order thinking in a complex world. But critics say the
program doesn’t focus heavily enough on basic algebra. Core-Plus was implemented
as a pilot program at Andover five years ago, with the first class of Core-Plus
students graduating in 1997.

The battle has widened. John Toma, Andover principal, has written to Wayne State
University President Irvin Reid, calling Bachelis’ character into question and saying
that Andover will caution students about attending Wayne State.

“Our community and our educators have been maligned and I think we have the right
to see the complete information,” said Gary Doyle, superintendent of the Bloomfield
Hills School District. Bachelis said a parents’ group is funding the survey, which he
is doing on his own time. Bachelis sent surveys to all the 1997 graduates of the
Bloomfield Hills School District — students who took traditional math and those who
took four years of Core-Plus, a controversial new math program. Bachelis wants to
see how Core-Plus students did their first year in college, compared to students who
took traditional math — algebra, geometry, trigonometry, calculus. Wayne State
officials said Bachelis’ survey is not a Wayne State project and they don’t have the
documents to give to Bloomfield Hills.

Bachelis said he wants to make sure that students’ names won’t be revealed because
he promised them confidentiality. Doyle said he doesn’t care about the names, he just
wants the data. It would be of interest to Andover graduate Loren Thal, 19. He is
taking a beginning math course this summer to make up for what he didn’t learn in
four years of Core-Plus, earning A’s and B’s. He took a math placement test at
Michigan State, and wound up in Math 103, the lowest level math course a student
can take for credit. He had to drop the class. “I was having tremendous difficulty with
it. It stems back to Core-Plus.

The basic and fundamental ideas weren’t covered in class,” he said. “I got (stuck) in
this program. I did not have a choice,” he said. Although he had tested in the superior
range in math capability, he said he is not successful in math right now. “I have to
relearn all my math.” Bachelis said that the problem with Core-Plus is that students
do not drill in algebra — practice solving a number of similar problems. If a
student can’t do algebra, the student can’t move on to calculus, Bachelis said.

But Christian Hirsch, a Western Michigan University math and math education
professor who developed Core-Plus, said that algebra is integrated into the program.
Since the first four-year Core-Plus class graduated from Andover in 1997, the
course has been revised with more emphasis on things like algebraic factoring.

He said that many students from traditional math programs go to college and fail the
placement tests. “People then tend to say the student didn’t have a good day and the
failure isn’t ascribed to the math program.” Andover will add a traditional algebra
class to the curriculum this fall, along with a survey class of algebra and geometry.
Students can also opt to take a traditional math curriculum by going to nearby
Lahser High School, Toma said.

Behind the debate

Core-Plus math Students work in groups to investigate, experiment with and apply
math concepts. Students use graphing calculators to solve problems, but don’t spend
as much time on drills — doing repetitive problems to learn a concept.

Critics say Program is light on algebra. Proponents say Algebra is woven into many
lessons. Origin Developed at Western Michigan University and financed by the
National Science Foundation. Goal To apply new standards developed by the National
Council of Teachers of Mathematics.

Where offered Bloomfield Hills, West Bloomfield, Southfield-Lathrup, Ypsilanti and
Southwestern High School in Detroit.

Sources Western Michigan University, Bloomfield Hills Schools and Detroit

News research.

Copyright 1998, The Detroit News

Giving Thanks For Turkey And Nuts
– DEBRA J. SAUNDERS
Tuesday, November 25, 1997

THIS THANKSGIVING, I raise my glass to the nuts. I toast Americans who care enough to fight and push and demand quality in the world around them. I give thanks to parent activists who have worked to restore phonics to reading instruction, sanity to math curricula and rigor to dumbed-down schools.

I can’t name them all, there are many. Suffice it to say that when I think of the great nuts, I think of people like the godlike — watch her thunder — Marion Joseph, the Phonics Queen recently appointed by Governor Wilson to the state board of ed. Molecular biologist Mike McKeown and statistician Paul Clopton and all the other nuts at Mathematically Correct in San Diego, who are pushing for strong math programs. Stanford’s Hoover Institution prof. Bill Evers and the dissident parents of Palo Alto. Wisconsin mother Leah Vukmir who founded Parents Raising Educational Standards in Schools. Bay Area math teacher Monica Brown and colleagues who have begged for challenging books and programs.

For their trouble, they’ve been called every name in the book — evil, mean, rigid, anti-education, anti-public school, pinheads who don’t want children to think for themselves, rote nazis, tools of the Religious Right, extremists. Nuts.

It’s true. They are nut cases. Many could afford to send their kids to private schools that cleave more closely to their idea of a solid education; instead they work to change the public schools. A thankless task. They don’t just think of helping their own children, they also want to help other people’s children — and that makes them nuts.

They make waves. They think their own thoughts. They rely on their common sense instead of common dogma. They believe in knowledge, not process- mongering. They must be crazy.

When they could be dining out, they are pouring through research on various curricula. They don’t blindly trust in the experts. Unlike many of the reporters who write about proposed standards and many board members who vote on them, these loons actually read drafts in their entirety. Folly. Worse: work!

Then they go to board meetings where they are told that their informed opinions don’t count and aren’t welcome. Good parents aren’t supposed to question educational orthodoxy. Good parents should sit up straight with their hands folded. Good parents should behave like battered wives — love the system, even when it hurts the kids.

Sometimes, these parents tell me I am brave. Sorry, I get paid to write a column. I know that what I produce will be taken seriously by someone. These parents put in months on commissions, or attending groups for parents who aren’t welcome on commissions, often only to be shunned. They pour their hearts into projects — all the while knowing that they are battling an establishment more interested in proving itself not to have been wrong than in exploring how it could improve. They labor, then they’re laughed at.

They question school authority, then fear their children may be punished for it. They stick to their principles.

This week, the PBS series “Liberty! The American Revolution” has shone the spotlight on America’s unlikely patriots — dreamers who risked all for the hope of a better world.

Modern Americans have elevated achieving personal comfort to an art form. Life is so easy that standing up for an ideal is something only quacks do. In an age when eating in all week is considered a hardship, I sometimes think such giants could not be found today. But then I think of Marion Joseph, Mike McKeown, Bill Evers, Leah Vukmir and Monica Brown.

You can read Debra J. Saunders on The Gate at www.sfgate.com.

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©2005 San Francisco Chronicle

The Fuzziest of Disciplines

by Alexander Nazaryan and Alexander Wilson

In the early 1990s, a group of public school districts clustered in the American West — California, Arizona, Texas, Iowa — selected a set of Math curricula, for children from kindergarten through their last year in high school, that promised new approaches to learning and a more enticing mathematical climate. It was hoped these changes would increase students’ interest in and capability with Math and ultimately help close the lauded mathematical gap between lagging American students and those in the rest of the industrialized world.

These school districts received about $50 million in Federal aid from the National Science Foundation to implement these curricula, collectively (and colloquially) known as `The New New Math.’

Five years on, these programs are a universal educational disaster. In one California school district, the average standardized test score moved from the 86th percentile to the 55th in only the first two years after the New New Math curricula was implemented. The test scores quickly rose back to the 77th percentile after the school’s old, traditional Math curricula were reinstated.

This is consistent with other results, and though the National Science Foundation has announced it will withdraw funding from any school district which abandons the New New Math curricula, many of those school districts who initially adopted these curricula are reverting to more traditional (proofs and rote) methods of learning mathematics.

The academic tail, however, may well still be wagging the educational dog. Whatever the level of its popular rejection, the New New Math is still extensively taught in American graduate schools. Though New New Math was only developed in 1989, it is estimated that fully half of American Math teachers are trained in Fuzzy Math, the central component of the New New Math.

The impetus for the New New Math curricula is political and, as its name suggests, it is a political antecedent to the `New Math’ movement of the 1960s.

In the 1960s, Math teachers, overwhelmed by notions of cultural subjectivism and inclined, as was the contemporary zeitgeist, to question rigid theories of learning as potentially autocratic, decided that the Arabic number system’s (the number system we use) reliance on the number `10′ as a base for arithmetic, geometric, and algebraic learning was arbitrary and probably Euro-centric. Instead, the New Math devoted extensive time to learning alternate number bases, such as 7. (In a base seven system, the number `6′ would still be written `6′, but `12′ would be written as `15′ and `16′ would be written as ’22’).

The idea was not to develop a better basis for understanding higher math (since base 7 is pretty useless in, for example, calculus) but to convince students of the fallacy of the objective reality of numbers. `12′, in the New Math, is not necessarily ’12,’ since in a base 7 system it would be ’15.’ Numbers, for New Mathematicians, are nothing other than `numerals,’ signifiers. Though the concept of ’15 elephants’ is real, it would be insufficient to abstract that to ’15,’ since `15′ is unnecessarily filial to the base ten number system. Instead, to answer the question, “How many elephants are there?” a student would have to answer something along the lines of “The amount of elephants that, in a base ten number system, we would usually express using the numeral `15′.” The New Math also focused extensively on things like set theory and `congruence arithmetic’ rather than multiplication tables and long division.

This system, the `New Math’ of the 1960s, was, predictably, a resounding failure which did little more than confuse students. Test scores plummeted, students turned away from Math, and before long the New Math was dropped.

Thirty years later, enter the New New Math.

The New New Math, originally conceived as a curricular notion in 1989 by a report of the National Council of Teachers of Mathematics, takes the same impulse, the rejection of the objective abstract reality of numbers, and combines it with a series of voguish concepts in Mathematical education — `fuzzy math’, `ethnomathematics’, and `constructivism’.

Since numbers are not really `real,’ in the conception of New New Mathematicians, focusing the study of mathematics on finding a `correct’ answer is pretty trivial. The emphasis thus belongs to the process of learning math, recognizing patterns in the numeric symbols – not numbers – and on making “shrewd guesses” from visual models. There is a lot of emphasis, in the New New Math, on using two and three-dimensional models, which can show the reality (`three blocks’) from which numbers stem, with little emphasis on numeric manipulation itself. (Blocks and tiles are in, pens and pencils are out).

This branch of the New New Math (which holds that the teachers should discourage abstract numerical manipulation in search of an absolute answer and encourage shrewd, intuitive guesses, regardless of whether they are right or not, based on recognized visual patterns in objects like tiles or blocks) is called `Fuzzy Math.’

Martin Gardner, writing in The New York Review of Books, gives a good example of what Fuzzy Math means: “Teachers traditionally introduced the Pythagorean theorem by drawing a right triangle on the blackboard, adding squares on its sides, and then explaining, perhaps even proving, that the area of the largest square exactly equals the combined areas of the two smaller squares. According to Fuzzy Math, this is a terrible way to teach the theorem… [The students] cut from graph paper squares with sides ranging from two to fifteen units. Then they play the following `game.’ Using the edges of the squares, they form triangles of various shapes. The `winner’ is the first to discover that if the area of one square exactly equals the combined area of the other two squares, the triangle must have a right angle with the largest square on the hypotenuse. For example, a triangle of sides 3,4,5.”

Students who never discover the theorem are said to have `lost’ the game. Thus, with no help from teacher, the children are supposed to discover that with right triangles a(squared) + b(squared) = c (squared).” (This is `constructivism,’ perhaps best defined as the method of teaching New New Math, which stresses that students should figure out answers for themselves – elsewhere called `experiential learning’ – instead of being fed formulas and theorems by the teacher).

`Ethnomathematics,’ which stems from a whole range of multicultural impulses, is a secondary component of the New New Math curricula, though it is more sociological than mathematical in structure. It has two effective curricular influences.

The first is to encourage the study of the way primitive tribes counted and added. There is a popular text, released only in 1997 but already in full use, called Africa Counts: Pattern and Number in African Culture by a woman named Claudia Zaslavsky which gives extensive examples of different methods of dealing with Math and numbers. (As Carl Sagan and others have pointed out, the arguments for the mathematical and scientific success of ancient tribes are, in large part, fabrications).

The fact, of course, is that Math, like Physics or Chemistry, is a progressive effort. We don’t study Aristotle’s physics because we have Einstein’s. The effect of ethnomathematics is to reduce science from a way of understanding the world to a way of understanding culture.

The second effect of ethnomathematics is to suffuse the texts of the discipline with multicultural “examples” that have at best a dubious relation to mathematics. One popular textbook quotes a Maya Angelou poem in whole (there is an accompanying photograph of Ms. Angelou with President Clinton) and claims the parallelism in the poem is weighty evidence, contributing to an enhanced understanding of parallel lines and geometric structures.

The same text asks, “Is the time it takes to read an Alice Walker novel always a function of the number of pages?” John Leo, the US News & World Report columnist, examined several New New Math texts and found numerous “photos of President Clinton, and Mali wood carvings, lectures on what environmental sinners we all are and photos of students with names such as Taktuk and Esteban who … offer their thoughts on life.”

Since fuzzy math and constructivism stress the formation of subjective and personal mathematical algorithms and ethnomathematics stresses sociology and Maya Angelou, the bulk of responsibility for ensuring that students do well on traditional measures of mathematical acuity, like standardized tests, falls squarely on the shoulders of calculators. Calculators are a necessary part of the New New Math curricula, and are hence now being introduced as early as the first grade. The upshot is that students no longer need to know multiplication tables or how to do long division — they can simply press a few buttons.

Some states and standardized testing agencies have caught on to this effort to cheat the evaluation system, and so (California is notable here) have banned the use of calculators on tests.

Parents and educational policy-makers alike have been consistent in their opposition to the New New Math, and the associated dependence on the calculator.

Nevertheless, the development and persistence of contemporary trends in American schools of education seems to indicate that the New New Math may be here to stay.

It is ultimately teachers that determine the way students are taught, and the number of teachers who are trained in and teaching fuzzy math, constructivism, ethnomathematics, and the rest of it, is rising.

My Turn: Forget the Fads—The Old Way Works Best

What will fix public education? A teacher, a chalkboard and a roomful of willing students

By Evan Keliher
NEWSWEEK

Flunking the Tests
– DEBRA J. SAUNDERS
Sunday, February 15, 1998

THE HOUSE killed funding for President Clinton’s proposed national education tests this month by a 242-to-174 vote. While Education Secretary Richard Riley denounced the vote as a “partisan attack” on “voluntary national tests,” the issue isn’t as simple as test supporters make it out to be.

The plus of the tests is clear: Give every fourth grader a reading test and every eighth grader a math test, as the administration has proposed, and parents and teachers should know which children need remedial attention. Schools then should provide remedial education. Done right, a national test could prevent the social promotion of illiterate students who otherwise might be doomed to spend their school careers in a haze of half understanding.

But can parents trust federal educrats to do the test right?

I certainly wouldn’t trust federal edu-swamis with math. Consider the saga of National Science Foundation grant-monger Luther Williams. Williams wrote a letter to state schools chief Delaine Eastin warning her that California schools might lose federal funds because the state school board, to Eastin’s dismay, voted in favor of math standards that — horrors — mandate that third-graders memorize multiplication tables and fourth-graders master long division.

Williams was appalled at this rejection of new-new math. He derided the board for buying into a “wistful or nostalgic approach” that “has chronically and dismally failed.” He apparently failed to notice that California’s commitment to trendy math — write about math, but you don’t have to be right about math — put California fourth-graders so far behind in the National Assessment of Educational Progress math test that they scored behind every NAEP-taking state but Mississippi and Louisiana.

Another reason not to trust federal educrats with a math test is the debacle California educrats created in their 1994 California Learning Assessment System (CLAS) tests. Before state lawmakers put CLAS out of its misery, the the state department of ed directed scorers to give students with wrong answers, but nice essays, higher scores than students who gave correct answers, but didn’t embellish them with happy-face prose.

This there-is-no-wrong answer philosophy comes straight from the “deep, balanced mathematical learning” playbook, dear to Williams and other basics-hostile faddists.

House Education and Workforce Committee Chairman Bill Goodling, R-Pa, fears that national tests will create national curricula. If he’s right, and federal faddists dictate what goes in the tests, national tests ineluctably would dumb-down curricula nationwide. Local districts would be faced with the choice of teaching math-lite or living with low-test scores because their students aren’t adept at writing about how happy they are about math.

Reading is different. You would hope that federal swells could figure out a way to test reading ability without mucking that up too much. But good reading tests already exist. Some schools use them. California is about to launch its own tests and shouldn’t need a federal tests.

A national reading test, therefore, may be a waste of money that otherwise could be spent on needed teacher training for those teachers who were never schooled in sound phonics instruction.

“Why would you waste $100 million to tell half the kids they don’t read well?” Goodlng asked during a recent interview.

It wouldn’t be a waste if you knew the new test, unlike others, would be a good measure of student literacy. You’d do it if you trusted this test would prompt schools to teach failing students the basics. You would do it if you trusted D.C. educrats to recognize a strong curriculum. But do you?

You can read Debra J. Saunders on The Gate at www.sfgate.com.

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©2005 San Francisco Chronicle

Experts Attack Math Teaching Programs

Education: Top mathematicians and scientists urge U.S. to withdraw endorsement of methods that leave out basic skills. Federal official says change is unlikely.

By RICHARD LEE COLVIN, Times Education Writer

Nearly 200 top mathematicians and scientists, including four Nobel laureates, are urging U.S. Secretary of Education Richard W. Riley to withdraw the government’s endorsement of math programs that experiment with nontraditional teaching methods.

The strongly worded letter expresses outrage that some of the 10 widely used programs leave out such basic skills as multiplying two-digit numbers and dividing fractions.

“These curricula are among the worst in existence,” said David Klein, a Cal State Northridge math professor who was one of the letter’s authors. “To recommend these books as exemplary and promising would be a joke if it weren’t so damaging.”

Those signing the letter fear that a government endorsement of the programs will be a powerful force pushing teachers and school districts to use “dumbed down” instructional materials and methods. Several said they see the letter, which is to be publicized widely today, as providing a countervailing argument.

Klein was joined by math professors and physicists from UC Berkeley, Stanford University, Harvard University, the University of Chicago and elsewhere. The signers also include two winners of the Field Medal, which is the top honor in the field of mathematics, and Nobel laureates in physics Steven Chu (1997), Sheldon Lee Glashow (1997), Leon M. Lederman (1988), and Steven Weinberg (1979).

“I’m hoping to provide ammunition for teachers who are under pressure to adopt some of these programs,” said Richard Askey, who holds an endowed chair in math at the University of Wisconsin.

More broadly, those signing the highly unusual letter want the federal government to refrain from taking sides in the continuing national education debate that some have dubbed the “math wars.”

Linda P. Rosen, Riley’s top math advisor, said the endorsements are not likely to be withdrawn. She said Congress directed the department to create the panel of experts that made the recommendations and that the intent was to help school districts make informed choices when purchasing math programs.

But, she said, such decisions remain “absolutely locally based” and that school districts must take local opinions into account.

Steven Leinwand, a member of the federal panel that judged the books, defended the selection process.

“Every one of the programs designated as exemplary had real, clean data that showed test scores going up,” said Leinwand, a consultant to the Connecticut Department of Education.

But he acknowledged a difference of opinion among mathematicians as to what constitutes good mathematics. “These programs do not teach kids to do five-digit by three-digit long division problems,” he said. “Instead, they teach all kids, not just a few kids, when and why people need to divide.”

Rosen and others said the letter represents an escalation in the back-and-forth rhetorical struggle over how to promote mathematical understanding without sacrificing the ability to compute accurately.

As a result of the controversy, the nation’s leading mathematics education group and the leading proponent of nontraditional methods, the National Council of Teachers of Mathematics, has sought input from professional mathematicians. Some fear that this letter will hamper those efforts.

“I have an uncomfortable sense that everyone is talking past one another,” Rosen said. “What’s missing in the whole darn thing are the students . . . and that’s very unfortunate and just devastating to all of us who care deeply about young people.”

Hung-Hsi Wu, a UC Berkeley math professor and a co-author of the letter, acknowledged that not all mathematicians agree with it. But, he said, he wrote it out of a sense of “social obligation” to improve math instruction.

The use of nontraditional instructional materials by schools has sparked protests in communities across the nation. Usually, those who complain are parents who are concerned that their children are failing to learn fundamental skills, that solving algebraic equations is being de-emphasized and that math class has been downgraded to math appreciation class, leaving high school graduates unprepared for college-level courses.

In California, at least, the traditionalists have gained the upper hand. The state adopted standards for math classes that stress memorization of multiplication tables and only limited use of calculators, as well as an understanding of concepts such as place value.

As a result, the state rejected, or did not consider, all of the math programs recommended by the federal government except for a part of one, so school districts are prevented from using state textbook funds to buy them.

Still, the materials on the federal recommended list remain in widespread use across the state and have been the focus of protests by parents in Palo Alto, Escondido, Torrance, Simi Valley, Los Angeles and many other cities around the state.

As a result of the parents’ protest, the school district began paying more attention to basic skills and added an after-school math tutoring program for high school students.

“The children haven’t learned the basic facts. They move on to advanced math before they’ve laid a strong foundation and they’re in a muddle,” said Amy Riley, a leader of the parent protest there.

Rick Blake, a spokesman for the Everyday Learning Co., defended the program, saying the company has overwhelming evidence that students do well on computation as well as on more advanced topics.

“We’ve got kids doing algebra by the fifth grade,” he said. “This is not fuzzy math. It’s hard.”

In Plano, Texas, the parents of more than 600 middle-school students demanded alternatives to Connected Math, a program that the expert panel called “exemplary.” The school district has refused and the parents have filed a federal lawsuit.

The text of the letter sent to the U.S. Department of Education can be found at http://www.mathematicallycorrect.com/

The text of the U.S. Department of Education report on math programs can be found at

Education Panel Lays Out Truce In Math Wars

Effort to Fix ‘Broken’ System Sets Targets for Each Grade, Avoids Taking Sides on Method

Wall Street Journal  By JOHN HECHINGER  March 5, 2008; Page D1

A presidential panel, warning that a “broken” system of mathematics education threatens U.S. pre-eminence, says it has found the fix: A laserlike focus on the essentials.

The National Mathematics Advisory Panel, appointed by President Bush in 2006, is expected to urge the nation’s teachers to promote “quick and effortless” recall of arithmetic facts in early grades, mastery of fractions in middle school, and rigorous algebra courses in high school or even earlier. Targeting such key elements of math would mark a sharp departure from the diverse priorities that now govern teaching of the subject in U.S. public schools.

The panel took up its work amid widespread alarm at the sorry state of math achievement in America. In the most recent testing by the Program for International Student Assessment, released late last year, U.S. 15-year-olds achieved sub-par results among developed nations in math literacy and problem-solving, behind such countries as Finland, South Korea and the Netherlands.

“Without substantial and sustained changes to the educational system, the United States will relinquish its leadership in the twenty-first century,” reads a draft of the final report, due to be released next week by the Department of Education.

MATH ESSENTIALS

The National Mathematics Advisory Panel is expected to call for the following “critical foundations” or benchmarks for U.S. school children.

Fluency with whole numbers:

1. By the end of grade three, students should be proficient with the addition and subtraction of whole numbers.
2. By the end of grade five, students should be proficient with multiplication and division of whole numbers.

Fluency with fractions:

1. By the end of grade four, students should be able to identify and represent fractions and decimals, and compare them on a number line or with other common representations of fractions and decimals.
2. By the end of grade five, students should be proficient with comparing fractions and decimals and common percents, and with the addition and subtraction of fractions and decimals.
3. By the end of grade six, students should be proficient with multiplication and division of fractions and decimals.
4. By the end of grade six, students should be proficient with all operations involving positive and negative integers.
5. By the end of grade seven, students should be proficient with all operations involving positive and negative fractions.
6. By the end of grade seven, students should be able to solve problems involving percent, ratio and rate and extend this work to proportionality.

Geometry and measurement:

1. By the end of grade five, students should be able to solve problems involving perimeter and area of triangles and all quadrilaterals having at least one pair of parallel sides (i.e. trapezoids).
2. By the end of grade six, students should be able to analyze the properties of two dimensional shapes and solve problems involving perimeter and area, and analyze the properties of three-dimensional shapes and solve problems involving surface area and volume.
3. By the end of grade seven, students should be familiar with the relationship between similar triangles and the concept of the slope of a line.

Source: Draft of National Mathematics Advisory Panel final report

Unlike most countries that outperform the U.S., America leaves education decisions largely to state and local governments and has no national curriculum. School boards and state education departments across the country are likely to pore over the math panel’s findings and adjust their teaching to make sure it aligns with the nation’s best thinking on math instruction. The federal government could also use the report to launch a national program in math instruction, as the government did for literacy after findings from a similar advisory panel on reading in 2000.

The math panel’s draft report comes amid the so-called math wars raging in the nation’s public classrooms. For two decades, advocates of what has come to be known as “reform math” have promoted conceptual understanding over drilling in, say, multiplication and division. For example, to solve a basic division problem, 150 divided by 50, students might cross off groups of circles to “discover” that the answer was three. Some parents and mathematicians have complained about “fuzzy math,” and public school systems have encountered a growing backlash.

The advisory panel’s 19 members include eminent mathematicians and educators representing both sides of the math wars. The draft of the final report declines to take sides, saying the group agreed only on the content that students must master, not the best way to teach it.

The group said it could find no “high-quality” research backing either traditional or reform math instruction. The draft report calls a rigid adherence to either method “misguided” and says understanding, which is the priority of reform teachers, and computation skills, emphasized by traditionalists, are “mutually supported.”

Larry Faulkner, the panel’s chairman and president of the Houston Endowment, a philanthropic foundation, said in an interview that the group had “internal battles” but decided “it’s time to cool the passions along that divide.” The panel held 12 meetings around the country, reviewed 16,000 research publications and public-policy reports and heard testimony from 110 individuals.

The advisory group also doesn’t take a position on calculator use in early grades, a contentious issue among educators and parents. The draft says the panel reviewed 11 studies that found “limited to no impact of calculators on calculation skills, problem-solving or conceptual development.” But the panel, noting that almost all the studies were more than 20 years old and otherwise limited, recommended more research on whether calculators undermine “fluency in computation.”

Still, the draft report says calculators shouldn’t be used on tests used to assess computation skills. Some states allow disabled children to use calculators on tests of arithmetic.

The draft report urges educators to focus on “critical” topics, as is common in higher-performing countries. The panel’s draft report says students should be proficient with the addition and subtraction of whole numbers by the end of third grade and with multiplication and division by the end of fifth. In terms of geometry, children by the end of sixth grade should be able to solve problems involving perimeter, area and volume.

Students should begin working with fractions in fourth grade and, by the end of seventh, be able to solve problems involving percent, ratio and rate. “Difficulty with fractions [including decimals and percents] is pervasive and is a major obstacle to further progress in mathematics, including algebra,” the draft report says.

These benchmarks mirror closely a September 2006 report by the National Council of Teachers of Mathematics, which many viewed as a turning point in the math wars because it recognized the importance of teaching the basics after the group for years had placed more emphasis on conceptual understanding.

Francis Fennell, president of the math teachers group and a panel member, said the group’s specific recommendations could help parents determine whether their kids are on the right track.

The draft report recommends a revamp of the National Assessment of Educational Progress, a widely followed test administered by the Education Department, to emphasize material needed for the mastery of algebra, especially fractions. The draft calls for similar changes to the state tests children must take under the federal No Child Left Behind Law.

The document urges publishers to shorten elementary and middle-school math textbooks that currently can run on for 700 to 1,000 pages and cover a dizzying array of topics. Publishers say textbooks often must cover a patchwork of state standards.