COMET • Vol. 1, No. 10 – 5 April 2000

* Note: I will be in Chicago from April 9-16 for the NCSM and NCTM conferences and the (SIG/RME) Research Presession. I hope to see many of you there. *


(1) “Before Scrapping Math Reforms, Add Up the Costs” by K.C. Cole

Source: The Los Angeles Times – 30 March 2000

Los Angeles high school teacher Guillermo Mendieta is going on a hunger strike.

Not over salary, or benefits, or working hours. He’s putting his passions where his mouth is over–of all things–mathematics, and the way it’s taught in L.A. schools.

Specifically, Mendieta is trying to stop the Los Angeles Unified School District from giving up on a decade of reforms in math teaching. He and others feel these reforms have brought the power and pleasures of math to students formerly written off as hopelessly math-inept. Many of these students are black or Latino. The rest are almost everyone else who didn’t breeze through math in high school: Allergic to algebra. Terrified of trig. Catatonic over calculus.

These widespread aversions are side effects, many believe, of the drill method of math teaching, which is about as likable as the drill method of dentistry. As antidotes, reformers brought in everything from hands-on activities to art and games.

They added alternatives to the single-minded math track that forces students to march inexorably from algebra to geometry to pre-calculus, built bridges between various branches of math and even blazed trails from math to science, humanities, literature.

Back-to-basics advocates argue that while reforms might have made math more appetizing, they don’t provide the kind of substance that leads to real competence. Appealing, perhaps, but junk food. This lack of competence, they say, shows up in the ever-dismal test scores of U.S. math students–particularly those in L.A.

To be sure, tests are invaluable as a tool to measure what students know and where they stand. But tests can’t tell you everything.

* * *

Consider that famous turn-of-the-century math student, the horse Clever Hans. When Hans’ owner asked the horse to add, say, 3 plus 5, Hans pawed out the right answer. Hans couldn’t do sums, of course, but he could read his owner’s silent cues (perhaps no less of a feat).

Lest you think Clever Hans is a quaint historical oddity, the same phenomenon turns up today, even in the most amazing places–Harvard, for example. A documentary produced some years ago by Harvard and the Smithsonian Institution, called “A Private Universe,” filmed newly minted Harvard graduates as they struggled to answer the question: Why is it warmer in summer than in winter? Most got it wrong.

All these students, one presumes, were above-average test-takers. Some had even studied astronomy. But like Hans, they had answers without understanding.

Math tests, in particular, tend to be timed–which rewards students who can solve problems quickly. This is a good, useful and sometimes important skill. But not always. “To most professional mathematicians, the focus on speed is crazy,” says mathematician Keith Devlin, author of the forthcoming “The Math Gene” and dozens of other popular math books. “Most of the good mathematicians I know are very slow. All the tests really discover is whether you can do something fast.”

Devlin and others worry that judging the success or failure of math teaching by test scores–especially timed tests–discourages students more than it helps teachers evaluate what they need.

His own daughter was left back in high school math for poor performance on tests. Given the time she needed in college, she went on to make straight A’s. When Devlin wrote about his daughter in Focus, a publication of the Mathematical Assn. of America, he received hundreds of passionate letters recalling similar experiences.

Passion, of course, is something no test measures. And it’s passion that is propelling Guillermo Mendieta to go without food for as long as it takes to make his singular appeal. He knows how it feels to be starved for the confidence that comes from being at home in the world of numbers, the pain of exclusion that dooms most children to a life of feeling inadequate–OK, let’s just say it: stupid–in math.

To go through life feeling muddled by math, Mendieta understands, can be as impoverishing as going through life hungry for food.

So before the school district junks math reform, it needs to think hard about the way it measures success. The paths to mathematical literacy are many and varied. Depriving kids of the good feeling that comes from knowing a thing or two about numbers would be far worse than letting them eat a little cake.

(2) “Math That’s Worth a Hunger Strike” by Guillermo Mendieta (editorial letter)

Source: Los Angeles Times – 31 March 2000

Consider a teacher in a traditional classroom who tells students what a ratio is, expecting them to remember the definition. Now imagine a teacher in an integrated mathematics classroom who has her students figure out how many dimes placed on one side of a scale are equivalent to one quarter on the other side. Then, after discovering that the same number of dimes must be added again to balance an additional quarter, the children come to make sense of the concept of ratio for themselves.

Or consider a traditional mathematics class where students are told to solve yet another contrived word problem (“A train leaves Washington, D.C, heading west at 65 mph . . . .”) Now imagine an integrated mathematics classroom where students are asked to compare the weight of two pieces of bubble gum–one chewed and one not, one with sugar and one without–making predictions, recording results, explaining the differences, all the while adding, subtracting, multiplying, dividing, using decimals, percentages, learning to estimate and extrapolate. In which classrooms are they more likely to see math as relevant, appealing and something at which they can be successful?

Integrated mathematics was developed about 10 years ago because more than 80% of U.S. students were graduating with poor mathematical understanding or hating mathematics. In traditional mathematics programs, students are required to put fragmented and forgettable facts and formulas into short-term memory so they can pass the next test. But integrated mathematics programs actively engage students in applying mathematical ideas to real-life problems. Integrated mathematics seeks to help students make connections between mathematics and other disciplines and their own lives. Integrated mathematics engages students in making sense of and applying their mathematical understanding.

Integrated mathematics has reversed the national trend of students dropping out of mathematics as soon as they can, and this is why students taking integrated mathematics have been found to be better problem-solvers than students studying under the old approach.

Civil rights activist Bob Moses has said that algebra “is to the students of this new century what reading and writing were to the children of the sharecroppers. Algebra has become a civil rights issue.” A student without access to a college preparatory mathematics sequence has a higher than 70% chance of not entering college, of dropping out, of ending up at a low-end wage job or on welfare. A Latino or an African American student in California is more likely to be put in jail than to graduate from college. For each child not completing college, our communities lose more than $150,000 in gross income over the subsequent 10 years. Integrated mathematics is substantially increasing the number of minority students completing the mathematics college requirements.

So why are some state and Los Angeles Unified School District board members considering switching out of integrated mathematics? Why ignore the recommendations made by the National Science Foundation, which, after conducting an evaluation of mathematics programs, gave integrated programs the highest rating, exemplary? It turns out that some policymakers have instead chosen to listen to a small group of professors with no K-12 mathematics education background, a group that does not have the endorsement of any university department of education or any professional organization of mathematicians in the country.

On Saturday, I will go on a hunger strike because it is a crime to eliminate a program that is substantially improving the mathematics preparation of our students. I will go on a hunger strike because schools are in the midst of planning next year’s course offerings, and it is urgent that the school board keep integrated programs a viable option in Los Angeles. I will go on a hunger strike because the biggest problem in education is not “traditional or reform” approaches, but rather disengagement.

I hope that every person who thinks of himself or herself as an advocate of children will heed the words of the great American freedom fighter, W.E.B. DuBois: “The freedom to learn has been bought by bitter sacrifice. And whatever we may think of the curtailment of other civil rights, we should fight to the last ditch to keep open the right to learn.”

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Guillermo Mendieta Is Director of Mathematics Education for the Nonprofit Achievement Council. in 1987, he Was Named Los Angeles County Teacher of the Year by the NAACP.

(3) “Math Teaching Plan Combines Methods” by Richard Lee Colvin

Source: Los Angeles Times – 1 April 2000

A tense battle over a proposed overhaul of math instruction in the Los Angeles Unified School District would be defused, at least for now, under recommendations that have been prepared for the school board.

A committee of teachers, administrators and outside consultants has been wrestling with the math issue since last fall. That process thrust the district into a nationwide debate over traditional teaching methods that focus on drills and “reform” methods that emphasize “hands-on” experience. And it led one of the participants in the process, Guillermo Mendieta, a consultant who helps teachers with nontraditional math lessons, to threaten to go on a hunger strike, beginning today.

On Friday, Mendieta said that he was confident his terms would be met and that he had canceled the hunger strike. “I’m very, very, very, very pleased and relieved,” he said.

But Robert Collins, the district administrator who presided over the sometimes heated math discussion, said the suggestions that will be sent to the Board of Education next month do not represent a victory for either side in the debate but will call for using elements of both methods.

The state established standards in 1997 for what all students should know in all grades. But textbooks designed with those standards in mind will not be ready until next year. Collins said he will recommend to the board that schools not purchase math books until the new versions are available and approved by the state.

The publishers of programs oriented toward “hands-on” activities that are among the most popular in the district do not plan to try to win approval in the next round of textbook purchases. That means that math lessons will have to include traditional approaches.

Collins said the district’s current math program is disjointed and confusing for students, parents and teachers. “We have kids going from first to third to fifth grade who go from reform to traditional to reform and then go into a reform middle school and a traditional high school,” Collins said. Under the recommendation, committees would choose a single set of textbooks to be used by all schools.

Collins said this will “provide a process to develop a math program that we think will provide both reform and traditional approaches.”

(4) Update from Guillermo Mendieta (5 April 2000)

I want to let everyone know that it is official. Integrated programs will continue to be supported in LAUSD – furthermore, any school in the district can use district money to purchase additional integrated materials. Also, both versions of the augmented test (integrated and traditional) will be available to all schools. Lastly, Genethia Hayes, the board President, will join us in advocating at the State level to make sure sensible instructional policies are put in place for all districts, schools teachers and students in the state.

I hope to see many of you next week in Chicago – I will be presenting on Saturday – I still need people to let me know if they can help with the petition table for a 3-hour period: We need people to help at the petition table on Thursday from 8:30 to 11:30, Friday from 8:30 to 11:30 and from 2:30 to 5:00, and lastly, we need people Saturday from 11:30 to 2:30 and from 2:30 to 5:00 p.m. Please let me know ASAP if you can help. Please e-mail the time slot you will be able to help at the petition table – or

We have the state petition online []. I ask that everyone sign and send us the state petition and that you give this petition to everyone you know, work with, relatives, etc.

Below is the statement I have released to the press in regards to the new developments and what lies ahead —

While the thousands of teachers, administrators and other advocates for children are elated about the fact that Integrated and other effective mathematics programs will continue to be an option in LAUSD we call on all school board members from across California, all administrators, teachers, professors, parents and students to join us in dealing with the same inequities and bad instructional policies at the State Level. We ask that The Governor, Delaine Eastin and all the members of the State Education Board listen to the experts in the field of mathematics education, to the teachers and administrators who work directly with our students – we need the State Board to address 5 key issues:

1) Integrated programs are supported by the framework but were not included in the list of textbooks schools can purchase this year, this must be amended. Some of the highest performing secondary schools in the State have been using Integrated programs.

2) Integrated and other effective mathematics programs such as MathLand, Dale Seymour and others must be placed in the list of approved textbooks for the next 7-year adoption cycle. There are too many schools who are performing at high levels with those programs; it would be a crime to ask them to stop using programs they have successful with. Furthermore many of these textbooks have received the highest rating, Exemplary, by the largest and most complete evaluation of instructional materials every undertaken by our nation’s Department of Education.

3) The State must include experts in the field of mathematics education in the content review panel. It must also remove the many members of Mathematically Correct who have been assigned to be part of this panel – this group is known for its desire to eliminate all mathematics and science reform from public schools and they have no experience in K-12 education, and do not represent the consensus of expert opinion.

4) The State must include experts in the fields of mathematics assessment and curriculum and instruction in the committees in charge of designing the State standards-based assessment. Currently, many of the people in charge of this task have no background in curriculum and instruction, K-12 education or in the area of assessment. Given that the state is moving towards making various assessments high-stakes test, the State is responsible for making sure the proper expertise in the field of mathematics assessment is used in the development of these tests. Otherwise it will be opening itself to many law-suits on the grounds that improper tests were used to make high state decisions that will affect millions of students.

5) The professional development policy must also be revised – the existing policies are totally inflexible. A flexible policy will permit districts to rely on their teacher leadership to review and make recommendations on materials and curricula and to organize and lead professional development in their districts.

Lastly, given the overwhelming consensus among the experts in the field of mathematics education, the State must move to revise the Standards, to improve them with the input from the teachers, administrators and experts in field.



“By Rhyme or Reason? The Debate over Memorization” by Marjorie Coeyman

Source: Christian Science Monitor – 4 April 2000

To some, it’s a dreary task carried over from archaic 19th-century concepts about education. To others, it’s a useful tool being overlooked by today’s teachers.

Memorization is an issue that’s acquiring some urgency as advocates and detractors of the practice battle for the hearts and minds of America’s teachers.

“For generations, memorizing the addition, subtraction, multiplication, and division tables has been a rite of passage for elementary school students,” writes former US Secretary of Education William Bennett in his new book, “The Educated Child” (Free Press).

“Today, however, you may encounter schools where such work is no longer emphasized.” The book, co-written with John Cribb Jr. and Chester Finn Jr., concludes: “Neglecting this responsibility can be a big mistake.”

But many progressive educators worry that heavy reliance on standardized tests in public schools is shifting attention from a focus on skill-based learning to a concern with fact-based learning.

“All of us can remember studying for a test, putting everything on the test, and then going away from it and forgetting everything,” says Peggy McNamara, co-director of the reading and literacy program at New York’s Bank Street College of Education. That’s an experience, she points out, that has nothing to do with “deep learning.”

Educator Alfie Kohn backs that viewpoint in his new book, “The Schools Our Children Deserve” (Houghton Mifflin). “Committing things to memory may train you to be a better memorizer, but there is absolutely no reason to think it provides any real cognitive benefits,” he writes. “Stuffing facts into your head doesn’t help you to think better; indeed, the time spent stuffing is time not spent analyzing or inventing or communicating, making distinctions or drawing connections.”

Some educators say the debate over the value of memorization has been going on for almost 100 years. In the 19th century, rote memorization was accepted as a mainstay of education. That approach, however, was rejected by the 1920s.

“And four or five times since then, we’ve shifted back and forth,” says Frederick Hess, assistant professor of education and government at the University of Virginia in Charlottesville. “In the late 1950s and early 1960s, we moved away from it, and in the late 1980s we began to move back.”

But Professor Hess says a number of the charter schools springing up today in urban areas tend to be returning to a particularly heavy reliance on memorization.

“In some schools, with some kids that may be a good thing,” he adds. When students don’t have a solid grounding in a certain amount of factual information, he says, it’s hard to engage in other methods such as teaching through discussion.

“Memorization got a bad rap” for some years, says Ray Beck, project director of the Basic Skill Builders curriculum produced by Sopris West in Longmont, Colo. Basic Skill Builders is a series of one-minute skill sheets that help drill students in the basic facts of core academic areas. The program relies heavily on memorization.

Rather than inhibiting more creative learning, Mr. Beck argues, memorization frees students to do different kinds of work with more speed and enjoyment. “A student of creative writing shouldn’t have to sit there and struggle over the spelling of the word ‘beautiful’ until he loses his train of thought,” says Beck. Memorization, he insists, leads to greater “fluency” in academic tasks.

But some caution that a dramatic shift back toward memorization will not serve students well.

Sally Kilgore, president of the Modern Red Schoolhouse Institute based in Nashville, Tenn., participated in a study in the early 1980s that compared the achievements of students in parochial and public schools. “Kids in [Roman] Catholic schools memorized a lot more, but also forgot more,” she says. That’s her concern about encouraging memorization without also focusing on understanding.

“Improving long-term memory is an important part of education reform,” she says. “But short-term [memorization] can be nothing more than a form of mental gymnastics”.


COMET is an online newsletter that seeks to provide timely information in a digest format about state (California) and national news, articles, events, opportunities, and web resources related to mathematics education. Information from a variety of print and online sources is compiled and distributed via COMET approximately once a week. The target audience includes California PreK-12 teachers of mathematics and school/district administrators, as well as university faculty throughout the nation who are interested in issues related to mathematics education (with a focus on California news).