COMET • Vol. 1, No. 36 – 11 December 2000


(1) “State Eases Up on School Exit Exam” by Deb Kollars

Source: Sacramento Bee – 8 December 2000

Life for California students got a little easier Thursday when the state Board of Education decided to shorten the upcoming high school exit exam and eliminate some of its toughest algebra questions.

In addition, the board decided to turn this year’s round of testing into a massive “practice” exam for ninth-graders, rather than an official test used to determine graduation eligibility.

The test must be passed by any student who wants a diploma from a public high school in California, starting with the class of 2004. The exam has been a central feature of Gov. Gray Davis’ push to make sure schools are fully educating all children.

In recent months, as the exam was being developed and tested, many educators raised concerns that it was too long and difficult.

The concerns have run especially deep on the algebra portion of the test. The subject only recently became a graduation requirement, and many schools are using non-math majors to teach it because of a shortage of qualified instructors. The result is that many students are not getting the instruction they need to be able to survive a test in the subject, said State Superintendent of Public Instruction Delaine Eastin.

State leaders feared that such a situation might lead to legal challenges to the test’s fairness, which has happened in other states. As a result, the state Board of Education, with Davis’ blessing, took steps Thursday to soften the exam’s impact on students and fortify it against future lawsuits.

In a notable shift, the board agreed to make the test a practice exam for this year’s freshmen. The change, which will require new state legislation to be introduced in January, was proposed by John Mockler, Davis’s interim secretary of education.

Under existing law, ninth-graders who pass the exam this year would not be required to take it again to graduate. However, educators realize that slice of the law would cause technical problems in the test’s statistical development.

Here’s why: The state plans to give the exam to 10th-graders the following year. It will be a critical moment in the test’s development because results will be used to determine base line data and cutoff points for passage. If some ninth-graders are not in that important “cohort” group, it will affect the exam results’ statistical validity.

So Davis and his staff proposed making this year’s round of ninth-grade testing a practice exam that will be consequence-free. Then, when students face the exam again in 10th grade, it will be used to determine whether they graduate.

The change will bring benefits to schools and students, Mockler said. Because the ninth-grade test will not carry consequences, the results can be made public. People will be able to analyze how students did on a question-by-question basis and use the information to diagnose weaknesses and better prepare for the real test…

Another change, removing about 20 of the toughest algebra questions from the 100-question math test, was more controversial. An advisory panel pushed hard for the algebra questions to remain. The questions addressed important aspects of algebra outlined in the state’s mathematics standards, said James Brown, co-chair of the panel and Glendale Unified School District superintendent.

“Those algebra standards were important for students to learn to receive a diploma,” Brown said. However, Eastin said, too many schools are not yet teaching those standards to students.

“Some of the schools in California are far away from being ready,” she said. She and her staff stressed that within a few years, they hoped to restore the algebra items and add geometry to the exam.

Board members also agreed to shorten the exam by removing about 20 of the 100 questions in English/Language arts. The English questions to be cut will come from throughout the test so that all standards will still be covered…


Related information provided by Lori Hamada, Fresno County Office of Education’s Mathematics Coordinator, following a presentation by Lily Roberts, California Department of Education:

The HSEE blueprint has also been changed. For mathematics, there will now be 80 live items and 12 imbedded field test items. The recommendation will be to administer the test in 2 sessions – 40 items per session – of 2 hours each… The SBE intends to “ramp up” the number of standards in the future, but the approved blueprint is adjusted in the following way, reducing the number of algebra questions to 29 out of the 80 problems:

* Grade 6: Statistics/Probability – no change

* Grade 7: Number Sense – no change; Algebra/Functions – no change; Mathematical Reasoning – no change; Measurement/Geometry – reduced to 17 items: Standard 1.1 (3 to 2), 1.3 (3 to 2), 3.3 (3 to 2); Probability/Statistics – reduced to 6 items: Standard 1.2 (3 to 2), 1.3 (4 to 3).

* Algebra I: reduced to 12 items (all Algebra II-type items removed): Standard 2.0 (2 to 1), 5.0 (2 to 1), 7.0 (2 to 1), 15.0 (2 to 1), Standards 16.0 and above were all removed.

According to AIR, the test order will be (in an instructionally sound order):Number Sense; Probability/Statistics 6, 7; Algebra/Functions; Measurement/Geometry; Algebra I (Mathematical Reasoning integrated throughout).

(2) “Fear, Loathing And Algebra – Schools Must Open This Math Gateway For All”

SourceSacramento Bee – 10 December 2000

For too many of us, this was the spinach, the peas and the broccoli of secondary school. So many California middle and high school students have despised and rejected the subject of algebra. So many have graduated from high school bereft of its skills, without even a good grasp of how much they’ve missed.

Today, The Bee begins a five-part series on algebra by staff writer Deb Kollars that attempts to unravel some of the discipline’s mystery. The series makes a powerful case for California’s new insistence that all students master the subject before graduation.

This is true because algebra skills are about much more than just solving for X and Y. Algebra teaches abstract thinking and cultivates the patience needed to pick through a complex problem. It is the basic language of science and computers, and the backbone for the study of higher mathematics. Its principles pervade the fields of engineering, architecture, medicine, marketing, finance, economics and agriculture.

Students who have mastered it are far more likely to attend college than those who don’t. In short, algebra is a gateway to opportunity, and too many California students — disproportionately poor and minority — haven’t been given the keys.

To its credit, the state is trying to change that. New academic standards call on schools to begin exposing students to fundamental algebraic principles in the primary grades, and to begin algebra instruction in earnest in eighth grade, as many other countries with stronger student math achievement have long done. Last year, the Legislature passed and the governor signed a law requiring all public school students to pass Algebra 1 before graduation. And the high school exit exam, passage of which will be required for a diploma by 2004, may ask students to prove their algebra skills.

But before any of these important advances can be made, California must take care of a fundamental — and, until recently, neglected — piece of business: making sure teachers know the subject well enough to teach it. Statewide, an astonishing 40 percent of math teachers in grades seven through 12 have neither a major nor a minor in math. In poor and urban neighborhoods the percentage runs even higher. Math classes are more likely than any other subject except science to be taught by a teacher without a proper credential.

Thousands of teachers from lower-performing California secondary schools have begun cycling through new state-sponsored “professional development institutes,” summer boot camps run by the University of California designed to build teams of capable math teachers at schools statewide. The program is in its second year and needs sustained attention and funding to continue its promising work. Districts and local teachers unions should consider pay differentials to attract math experts who have so many other lucrative options in this economy…

To scale that challenge, students will need decent textbooks, which the state is on the way to giving them. But more important, they’ll need gifted teachers to lead them by the hand.


Elsewhere on the Web

Check out these algebra-related Web sites

Algebra Online, found at is a free service designed to allow students, parents, and educators throughout the world to communicate. This includes free private tutoring, live chat, and a message board, among many other features.

Get help with algebra and other math homework at

On the Web site of The National Council of Teachers of Mathematics, you can find this prestigious group’s recommended math standards for children. The site,, has many other offerings, including a “Family Corner” page with numerous links and resources for helping children to learn and like math.

The state of California’s new standards for mathematics are a gold mine for parents who want to know more about what students should be learning as they progress through the grades. The standards are public, and are a great resource for checking whether your child’s school is offering a top-notch math program to students. The standards can be found on line at

Read about the development, scoring and design of the Educational Testing Service’s product at

(3) “A Sore Subject” by Deb Kollars

Source: Sacramento Bee – 10 December 2000


…A noble yet nettlesome old subject, algebra has been around longer than there have been schools. But its treasures and tribulations have been largely limited to an exclusive band of students: those at least in ninth grade and on their way to college.

In California, those days are over.

Algebra is being ordered up as a standard course of study for eighth-graders. Its basic themes are being taught to children as young as kindergarten. And starting with this year’s freshman class, the subject is being required of every student who intends to graduate from high school.

It is a huge shift for kids and for schools but one that offers lofty rewards. It will open the doors of higher mathematics and college to more students. It will give young people more options in their lives. And beyond all that, the new blanket of algebra will endow students with something invaluable: the ability to ponder, to solve problems and to sort things out no matter how tough…

Until now, the state only required two years of mathematics to graduate and did not specify the content. As a result, many students left school with classes such as “General Math” or “Basic Math” on their transcripts, never moving beyond a fifth- or sixth-grade math level. They also tended to leave with something else: the sense that math is boring and of little relevance to their lives.

It is a great loss, said Alec Ostrom, assistant superintendent in the Roseville Joint Union High School District…”It’s not just about math. Algebra teaches you how to think and how to get unstuck. Adult life will bring complex problems, and the people who can’t get unstuck get lost”…

In the Sacramento region and up and down the state, middle and high school principals are struggling to find enough teachers, books and classrooms to get the job done. Many are privately grumbling, questioning whether it is possible to teach algebra to every student, especially at the eighth-grade level.

Until now, most local districts have been putting only their highest-achieving middle school students through algebra. At the high school level, many freshmen come with math skills too low to handle the rigors of the subject. Statewide estimates indicate that about a third of high school graduates do not complete the course…

John Mockler, California’s interim secretary for education, has worked in education for years and has seen a lot of changes arrive at schools. This new drive for algebra, he said, will go down as one of the more difficult and far-reaching movements…

The algebraic summons in California mirrors a nationwide trend. It was born, in large part, of a basic question about fairness. Over the years, as people have tried to address the poor achievement of low-income and minority students, they have studied many sides of the problem: Which boys and girls take honors classes? Who goes on to college? Who ends up with the better jobs?

Increasingly, people noticed a link to an unsplashy fundamental of high school. Kids who take algebra wind up going to college at rates exceeding those who don’t. And the kids who don’t get algebra tend to be disproportionately from poor and minority backgrounds.

“For generations, algebra has been used to eliminate possibilities for people,” said Uri Treisman, a math professor at the University of Texas, Austin.

During the late 1980s and 1990s, “algebra for all” grew as a mantra across the nation. Universities, tired of having to teach remedial math to freshmen, joined the call. So did employers, whose need for better-educated workers surged with the rise of high technology.

U.S. Secretary of Education Richard W. Riley was among many prominent leaders urging that all students complete algebra, ideally by the end of eighth grade. In a 1997 policy paper, Riley said national statistics showed that 83 percent of students who took Algebra 1 and Geometry went on to college within two years of graduating from high school, compared with 36 percent of those who did not.

“Algebra is known as the gatekeeper course,” said Kati Haycock, director of the Education Trust, a nonprofit organization based in Washington, D.C., dedicated to improving the achievement of minorities and the poor. The Education Trust, like many other groups focused on schools, has been tracking algebra enrollments as a measure of equity. “It’s very clear that algebra holds the keys to the kingdom,” she said…

In this quest for more rigor in schools, algebra occupies an exalted position. But mention the word in public, and you may get an earful…

“Algebra is a most curious course,” said Sue Stickel, an assistant superintendent in the Elk Grove Unified School District. “There is this general phobia about it. Yet parents look at it as an enormous measure of success.”

Texas math expert Treisman agreed. “Parents remember it as being really difficult. And it’s the point where they are no longer able to help their kids with math homework. Yet for many adults, algebra is a cultural reference point. They see it as an important ritual.”

When explaining why all students should study algebra, math types let the metaphors roll. They speak reverently of algebra as the “backbone,” the “key,” the “foundation” for all of higher mathematics.

“It is the language of mathematics. You can’t do anything else without it,” said Tami Cooper, an algebra teacher at Laguna Creek High School in the Elk Grove district.

Not only that, algebra is the language of computers and of the sciences. It is used in medicine, business, finance, insurance, marketing and economics…

Treisman, a lifelong lover of math who not only dreams about algebra but dreams in it, said that as schools embrace algebra and teach it better and as more children are exposed to its concepts when they are young and fearless about math, the moaning and groaning associated with algebra may one day fade away…


[Accompanying article]

Lesson 1: Encounters with X

Today, in our first lesson, we will look at an algebra basic: solving for the unknown. It’s a handy thing to be able to do, and not just for those who want to study engineering or computers or higher math. Daily life has many unknowns. How much interest will this savings account earn? How much fabric will it take for new draperies? Which refrigerator is the better deal, the cheaper one with higher energy costs or the pricier one that uses less energy?

Now in this space, we can’t teach all the algebra needed to solve all the mathematical unknowns in your life. After all, there is a reason it requires a thick textbook, a great teacher and a good year or so to master algebra: The subject is hard and covers a lot of unfamiliar territory for most people.

What we will do today is go over a couple of equation basics. Consider it a little refresher session for those of you who have studied algebra in the past, and an introduction for those of you who have never seen it before…

(4) “The X Factor: For Some, Audits and Root Canals Hurt Less Than Algebra” by Deb Kollars

Source: Sacramento Bee – 11 December 2000

…With algebra, there are many truisms to ponder and learn: a plus b equals b plus a; if you subtract a quantity from one side of an equation, you must do the same to the other side; to multiply numbers with exponents, you add the exponents when the bases are the same. Then there is the most dependable maxim of all: Algebra equals pain.

It is happening now for Heather Holder, a freshman at Hiram Johnson High School in Sacramento. Heather is among the first crop of high school students in California who must complete Algebra 1 to graduate. The new statewide graduation requirement, approved by the governor this fall, takes effect with the graduating class of 2004.

Heather has reached the point in school that arrives for many students: Her parents can no longer help her with math homework. “It looks like Chinese to me,” her mother said…

Heather Holder is one of those kids who has never liked math or done well in it. To help such students meet the new algebra mandate, Hiram Johnson, like many other schools, has set up first-year algebra classes that span two years. The pace is slower, with lots of review; the goal is to make sure all the students not only pass but really learn it well…

Out of all the math branches, algebra in particular has a reputation as an academic heartbreaker. For generations, it sorted the college-bound from the rest of the crowd.

“If you failed algebra, it meant there were a lot of things you couldn’t do. So it’s not surprising people have had a bad feeling about it,” said Uri Treisman, a math professor at the University of Texas, Austin…

Crossing this continental divide of mathematics has long been a rough rite of passage. Students must move from the familiar and repetitive arithmetic they have studied since kindergarten and navigate a new world of letters and symbols.

Suddenly, math looks like a foreign language. For many, it is a leap large and terrifying.

“The whole idea that x is going to stand for something is really abstract and hard to grasp,” said Kathy Zungri, a teacher at Spring View Middle School in Rocklin who works with students behind in their studies…

People like Nilson shouldn’t feel bad about their struggles, educators say. It often hasn’t been their fault. Algebra is a subject notorious for being poorly taught.

Difficulties actually start in the elementary grades, where the majority of teachers have neither a strong background nor an affinity for math. The message that too often goes out to students: Math is a drag.

“A lot of elementary teachers just do not like teaching math,” said Pat Haddeman, an algebra teacher at Hiram Johnson High. “I’ve had some of my parents and students tell me that their teachers gave them math worksheets as punishment. It’s no wonder there is all this math phobia out there”…

Those lacking a math background can draw on the math they know, follow a teacher’s manual and get the basics across. But when teachers don’t have a deep understanding of the subject, algebra can get passed on as a bunch of isolated rules and formulas that to kids are not only difficult, but pointless…

The quality of teaching is not the only problem, Calandri and others said. The algebra deficit is exacerbated by students who arrive unprepared at its doorstep. If they don’t know their multiplication tables or understand the concept of common denominators in fractions, they are guaranteed a rougher time in algebra…

The push is reaching all the way down into the elementary grades, with children as young as kindergarten now being introduced to early algebra concepts. It is a kinder, gentler approach designed to subtract the fear, the foreignness and the lack of preparation from the algebra experience…



“No Gain by U.S. Students on International Exam” by Nanette Asimov

Source: San Francisco Chronicle – 6 December 2000

American 13-year-olds performed better than average on a major international test of math and science skills — but showed no improvement in the four years since they last took the exam.

Black eighth-graders were the nation’s only large ethnic group to significantly raise their math scores on the exam, known as the Third International Math and Science Study-Repeat (TIMSS-R). As a group, however, their scores remained below the international average.

The exam originally was given in 1995 to fourth- and eighth-graders around the world. But its accompanying education study focused international attention on the different ways countries teach math and science — and what the United States may be doing wrong.

It was the TIMSS that made infamous the notion that American math and science classes are “a mile wide and an inch deep,” meaning that teachers in the United States are encouraged to cover many topics each semester, but none thoroughly enough for students to fully comprehend. By contrast, instruction in higher-scoring nations such as Singapore, China and Russia, covers fewer topics far more in depth.

The current exam, given in 1999, was taken by eighth-graders in 38 countries.

“(The results) reaffirm our belief that the U.S. needs to focus on stronger math and science preparation in middle school,” said Judith Sunley of the National Science Foundation, which funded the U.S. portion of the TIMSS.

“The curricula at that level are not strong, and teachers are not as well- prepared as they are in the countries that perform better, where the teachers are more likely to hold degrees in the disciplines they are teaching,” Sunley said.

Fourteen nations performed significantly better than the United States in each subject, with Singapore at the top in math, and Taiwan at the top in science. Six nations performed about as well as the United States in math, and six in science. These included New Zealand, Latvia and Bulgaria in both subjects. Seventeen nations performed significantly worse than the United States in math, and 17 were worse in science. South African students scored the lowest in both subjects.

U.S. experts in math and science instruction say they are disappointed but not surprised by the results of the latest TIMSS.

The original exam spawned studies and videos comparing teaching in different countries — often showing yawning American children buried in workbooks, while in Japan students worked in small groups with attentive teachers.

But the American education system is not only slow to change, its architects are perhaps reluctant to change it.

“We’ve declared that we’ll do better, but there’s been very little movement in supporting students and teachers to actually do better,” said Ruth Cossey, president of the California Mathematics Council and a math education professor at Mills College. “We’re still teaching inch-deep, mile-wide curriculum.”

She pointed to California’s recently adopted math standards, which the state Board of Education hopes will help improve instruction. Cossey thinks that is unlikely. “The standards, unfortunately, turned into a laundry list, which means that California is still heading towards lots and lots of math items — but not much depth.”

Besides, she said, instruction is driven by the state’s annual achievement test, which contains few questions that even reflect the new standards.

Christopher Cross, president of the Council for Basic Education in Washington, D.C., said TIMSS has shown that teachers in top-scoring nations have time to collaborate, discuss the best teaching methods, and plan, plan, plan.

“Teachers in the U.S. simply do not have enough time,” he said. And as evidence that American instructors spend more time racing through the required curriculum rather than “teaching for understanding,” Cross suggested picking up a math textbook. “They weigh a ton,” he said.

The same is true for science, said paleontologist Kevin Padian, president of the National Center for Science Education in Berkeley. Worse yet, he said, teaching methods, textbooks and official standards combine in failing to help students understand the world around them.

“We’re teaching factoids, not science literacy,” said Padian. “There’s got to be something wrong when the majority of biology undergrads at UC Berkeley don’t recognize that plate tectonics is the central organizing principal of earth science”…


Eighth-graders in 38 countries were tested last year in the world’s largest cooperative study of math and science skills. Known as TIMSS, the study includes math and science exams and a survey of classroom instruction. Both tests are scored on a scale of 1-to-1,000.

The chart below shows how students in each nation fared on the exams. The nations are listed in order of highest to lowest achievers. [See web site for more information.]


[Editor’s note]

Additional news reports on TIMSS-R results

“US Eighth-Graders Beat Global Average in Math”

“U.S. Math, Science Students Still Trail Top Ranks”

“Pursuing Excellence: Comparisons of International Eighth-Grade Mathematics and Science Achievement from a U.S. Perspective, 1995 and 1999”

Abstract: This report provides initial findings from the Third International Mathematics and Science Study-Repeat (TIMSS-R), a successor to TIMSS 1995. The report details findings on the performance of eighth-grade students in mathematics and science in 1999, as well as changes in mathematics and science achievement in participating nations between 1995 and 1999. In addition, initial findings on education-related contextual factors related to teaching and curriculum in 1999 are discussed.