Reinventing math is an old tradition in this country. It has been around at least since the 1960s, when the inimitable Tom Lehrer mocked the New Math in Berkeley cafes. Even Beatniks understood that a method that highlights concepts at the expense of plain old calculation would add up to trouble. And, as it happened, the New Math's introduction in schools across the country coincided with the onset of a multi-year decline in math scores.

Today the original New Math is old hat, but many folks in the education world are hawking yet another reform. It is known by names like "Connected Math," or "Everyday Math." Not surprisingly, the New New Math has a lot in common with the Old New Math. Like its forerunner, it focuses on concepts and theory, scorning textbooks and pencil-and-paper computation as "rote drill." And like its forerunner, today's New Math has powerful allies. Education Secretary Richard Riley and other Clintonites smile on it. Eight of the 10 curriculums recently recommended for nationwide use by an influential Education Department panel teach the New New Math.

Not that all members of the Academy are joining the movement. Within weeks of the Education Department findings, 200 mathematicians and scientists, including four Nobel Prize recipients and two winners of a prestigious math prize, the Fields Medal, published a letter in the Washington Post deploring the reforms. More are now rallying on an opposition Website, "mathematicallycorrect.com".

Consider MathLand, which won a "promising" rating from the panel. Its literature says it focuses on "attention to conceptual understanding, communication, reasoning and problem solving." This sounds harmless, but consider: MathLand does not teach standard arithmetic operations. No carrying and borrowing at the blackboard here. Instead, children are supposed to meet in small groups and invent their own ways to add, subtract, multiply and divide. This detour is necessary, the handbook informs, to spare youngsters the awful subjugation of "teacher-imposed rules." MathLand also does away with textbooks--too hierarchical, we suppose. No chance therefore for anything as sane as systematic review.

Next comes Connected Math, another panel favorite. It too skips or glosses over crucial skills. Example: The division of fractions, an immutable prerequisite for algebra, is absent from its middle-school curriculum. In shutting the door to algebra, David Klein of Cal State Northridge points out, "Connected Math also closes doors to careers in engineering and science for its graduates."

Finally there is Everyday Math. No textbooks here, either. Everyday Math ensures juvenile dependency to calculators by endorsing their use from kindergarten. Rather than teach long division, the program devotes substantial time to that important area of math study, self-esteem. A Grade 5 worksheet asks students to fill in the blanks on the questions below:

And then move on to the main question: Why? The reason for the New New Math, as for many other curriculum reforms, is that teachers, school administrators and their unions are tired of being blamed for statistical declines and poor student performances. So with math, as in their campaign to dumb down the SAT, such educators work to destroy or reject the standards that brought them trouble in the first place. Children are different nowadays, goes the line, and cannot be measured by old benchmarks.

New Mathie and federal panel member Steven Leinwand explains: "It's time to recognize that, for many students, real mathematical power, on the one hand, and facility with multidigit, pencil-and-paper computational algorithms, on the other, are mutually exclusive." Or, as Professor Klein translates: "Underlying their programs is an assumption that minorities and women are too dumb to learn real mathematics."

Fortunately, America is not France, where a central government controls every aspect of schooling down to the color of the paper clips. Localities and states write their own curriculums, and can and do fight back against the New Math. California for example, reversed a calculator-friendly policy in grammar schools after scores dropped precipitously. Resource-rich families, too, one suspects, will find ways to compensate for what trendy schools omit. Still, New Math will take its casualties, especially among the poor, adding to the already mounting costs of the decline in national educational standards.

About two weeks ago, a teacher and friend in the Santa Barbara schools telephoned me to ask if I would be interested in talking to the Board of Education at their 26 September meeting. The meeting was on the MathLand curriculum, and she hoped I would speak in its defense. I explained that I had very mixed feelings about this curriculum, but would be very interested in going just as an observer, to learn what I could. I had looked through some of the material earlier in UCSB's curriculum library and found parts of it disturbing. As Chair of the UCSB Mathematics Department and the father of a high school student, I have a strong professional and personal interest in our schools making sound curricular decisions.

The discussion began with an historical account by two of my colleagues from the Mathematics Department. They explained the process by which MathLand was adopted. I listened closely for their strong endorsement of the materials, but didn't hear it - the closest they came was an assertion that, when the state focussed on particular choices, MathLand's material most closely fit the legal mandate of the California Framework.

This was followed by someone with the title of Director, Elementary Curriculum. I was appalled. Her presentation consisted of a description of a complicated and murky algorithm (the "Russian peasants' algorithm") for calculating 13 x 18 = 234. By cutting and pasting various strips of paper in various places she hoped to make clear why this algorithm (involving 3 divisions, 3 multiplications, a cancellation and then an addition of three numbers) worked. I eventually figured out what the point was, but I have a Ph. D. in mathematics. Most of the audience only regarded it with a sort of amused bafflement. Exactly the attitude which, in parents, is one the deepest problems in mathematics education.

This was not some sort of "enrichment exercise". Astonishing but true --MathLand does not even mention to its students the standard method of doing multiplication. This vastly superior algorithm (the one we were taught as children) requires, for the above problem, just two multiplications and an addition of two numbers. It is an algorithm whose underlying mathematical content is crystal clear, far more so than that of the "Russian peasant". Yet it seems to appear only once in the MathLand curriculum: a fictional sixth grade student uses it incorrectly and says it was something she learned "last year". Before MathLand, apparently, since it's not in their fifth grade material either. Skipping something so beautiful and basic will handicap MathLand victims for the rest of their lives.

Following the curriculum czar's weird presentation a few pleasant and well-intentioned teachers presented some testimonials. One showed a pretty rainbow picture, apparently created by MathLand's publishers, about how the curriculum is organized. She mentioned that, to try to make up for the defects of the curriculum, the District had bought even more material ("TuneUps II") from its publisher. Another pair of teachers showed a few cute projects students had done and added that there were some students who really have taken to this curriculum. From this we can conclude only that there are a few teachers who have a few students who have thrived in MathLand.

At this point public comment was welcomed, and at the top of the list was Prof. Noel, chair of QED. I'd never met nor communicated with Prof. Noel, but admired him instantly. Though he had not been invited, and was restricted to roughly 10% of the time spent by MathLand's meandering defenders, he presented the only hard data I saw all night. It was disturbing in the extreme, and confirms his and QED's predictions precisely.

Finally, as an educator, I offer the following advice: UCSB has been invigorated by the regular review of every department by outsiders. What is needed in the school district is a curriculum review by a panel not tied to the California 1992 Framework. Ray Franco has suggested something like this. Let's do it.

MathLand was adopted for Department of Defense Dependent Schools (DoDDS) overseas last year. (Korea, Japan, Germany etc) Parents are very upset about their children's growing ignorance in math skills despite A+ grades. As one parent said bluntly, "Last year in MathLand my son learned nothing. It was a complete waste. I want to send the bill to the DoD for his tutoring when we go back to the states." Another has hired a local tutor when her son dropped from the 94th percentile in math to the 40th in one year. There is little quality homework associated with MathLAnds so the kids not only don't learn here but loose what knowledge they came with. Kids in the upper elementary grades are bored. The curriculum moves slow and is about a year behind from where many student were before they came here. Teachers were given very little training and many are frankly worried about what the kids are missing. Last year the teachers were not allowed to supplement and this year they are restricted to suppplementing twenty percent of the time. This twenty percent came in response to outcries from the parents.

Parents have been advised by the curriculum czars in Washington DC that we must wait three years to see results. We all feel our children are guinea pigs in a bad experiment. I don't know if DOD would launch a weapon system so untested!!! Additionally, we have been told to rest assured the rest of the country is headed this way and everyone fully supports the NCTM pedagogy. Those of us who have found your site are lucky indeed.

I do feel Mathland has some engaging activites that could supplement a more rigorous traditonal approach. Additionally, it will fufill the NCTM's goal of "appreciating math" because so few will actually be able to do it in the future. Salaries of those with mathematical ability ought to rise as the laws of supply and demand take over.

Who will be running DOD's research, engineering and testing facilites in the future? Who will they send to the Naval Postgraduate School or the Air Force Institute of Technology? Will the service academies have to be "dumbed down" in the future to accomodate the new new math?

Parents who are transferring overseas should bring appropriate materials to supplement their children. People who came over unaware of the current problems are contacting family and friends for texts and other materials. There are a few tutors available but it depends on your location.

Thanks so much for the information on Mathland. I know I haven't really voiced my opinion but I am very appreciative of all the efforts on the behalf of anti-reform. I have never been so convinced of the dangers of some reform efforts since living through the experiences of my daughter XXXXX in Kindergarden and first grade.

Aside from the issue of calling this a test and assigning it a grade (this was in Kindergarden) it raised a concern which has since been further substantiated. That is, regardless of the possible merits of MATHLAND assignments such as this, it is unlikely that teachers at this level have the conceptual maturity to implement it.

I discussed this problem with the teacher and explained to her at length why XXXXX's response was correct and why many other responses are possible. The teacher, while friendly, refused to acknowledge any significance in this matter and ended the discussion by saying, "The only pattern we've discussed so far is ABAB, so she couldn't have known of any others".

The teacher places two piles of blocks in front of her. One pile contains five small green triangles and the other pile contains five larger yellow hexagons. The teacher reads the following sentence without deviation or clarification: "A student claims that there are more yellow blocks than green blocks. What would you say to that student?" The teacher then writes down verbatim what the student says. XXXXX said: "There are 1-2-3-4-5 green and there are 1-2-3-4-5 yellow, but the yellow are more". The teacher then tries to match the students response to a list of possible responses provided in the MATHLAND package.

Here again I was impressed by the inadequacy of the teacher to do anything more than follow a recipe she had been given. When I questioned XXXXX it was clear she understood the difference between number and size. The problem was one of language. She didn't understand that "more" in this context was a reference to number. This brings up another concern. That is, a child may not have the sophistication in language to accurately express concepts that they have internalized (especially, if noone helps them to clarify).

What worries me most of all is the attitude XXXXX is already developing toward math. That is that math is a very nebulous subject (fuzzy, I think is the right word) where she usually does not guess correctly what the teacher is thinking and is therefore marked down. At home we play math games involving addition and subtraction facts and identification of shapes. She loves these games and it is easy to see how mastery of these provide a natural basis for confidence and self-esteem (She's learning something too).

In trying to decide what to do I am reminded of the Jehovah's Witnesses that I went to school with who were excused from saying the pledge of allegiance based on their religion. I have thought of asking that XXXXX be excused from MATHLAND on the grounds that we don't believe in it. I suppose, however, I'll take a calmer approach for the moment and do a little research. So thanks again for the information. I'm sure it will be very helpful.

I appreciate all that you have done to provide us parents with valuable information. Here in (Northern California) we're using Mathland so I especially appreciate seeing all the information on Mathland. I could go on and on forever about my concerns over this program. To this date (two months in to school), the teacher, principal, Director of Curriculum, District Math Mentor and Superintendant have not been willing to answer my questions regarding the math curriculum. A sample of questions sent in writing to my daughter's teacher are as follows. I asked that he be VERY specific in answering my questions. These were his written responses:

Question: What will you base my child's math report card grades on? How much of her grade will be based on homework, group work, Mathland materials, tests (if any), subjective assessment, supplemental materials (if any), math journals, Arithmetwist books, etc?

Answer: Performance on a variety of experiences, both in class and at home. A rubric is used for many of the in class tasks. Basic facts quizzes are graded on % correct. Some of the tasks are to be brought home, others go into the students portfolio to be shared at parent conferences (Note: as of the date of this letter, there was nothing in my child's portfolio to show me what she was doing in class). Ongoing student observation, journal responses and teacher anecdotal notes are also considered in the grading process.

Question: What are you doing to supplement the Mathland curriculum? (Note: Our district has agreed that this program needs to be supplemented, but no program is in place to ensure that it is. It's up to each teacher to decide whether or not they will supplement the program)

Answer: Reviewing, testing previously learned skills using teacher made worksheets. This involves whole group instruction followed by independent work. With respect for the "newness" of the Mathland material, I will be providing ongoing opportunities for all students to pursue mathematic skills in a manner that is more familiar to them.

Question: What percentage of the time has been spent and will be spent in the future teaching Mathland curriculum vs. supplemental materials? What percentage of the time will be devoted to direct teacher instruction (non-group work) with an emphasis on teaching the basic skills vs. you in the role of a "facilitator?"

Answer: Basic skills span the eight strands of Mathematics. Regardless of what mathematics program is considered, basic skills are found in all of the strands. The curriculum guide of the xxxxxxxxxx School District reflects the areas of emphasis for the fourth grade.

Question: Is the work that is being sent home for homework being taught in class? (Note: This teacher's idea of supplementing the program is to send home basic skills worksheets for homework, but not teach the same in class) Why is the work that is being done in class not coming home?

Answer: Homework is sent home on Fridays. Much of the classroom work is kept in a portfolio to be reviewed at anytime (with parents and students) and shared at parent conferences. (Note: In the same letter asking these questions, I mentioned that we were concerned that after 8 weeks of school the only piece of paper in my daughter's portfolio was an assessment of a group activity. NOTHING to show us what she had learned in class!)

We asked in our letter for very specific reponses to our questions and feel that we got very evasive (at best!) responses. The only thing that appeared very clear was that my child was spending 70-80% of the time working in a group during math!

The watering-down of the curriculum (at our school, children learned to master their multiplication facts in third grade and were introduced to long division at the end of the third grade. Under Mathland, children don't start learning their multiplication facts until fourth grade and aren't introduced to division until 5th grade!)

Most of all, I object to my daughter being experimented on. Nobody can provide me with any evidence what-so-ever to show that Mathland actually has been successful. No one can provide me with any evidence to prove that this is a better way to teach my child math. I have asked over and over again. The fact that the district has refused to answer my questions in writing has me very concerned. It appears that no one wants to be held accountable should this program fail.

A parent in our district provided the school board and the Superintendant with an overwhelming amount of controversial information about Mathland and the Framework. The district choose to ignore it and went ahead and spent $xxxxxx to purchase Mathland materials. The saddest thing of all is that the Director of Curriculum for our district stated that they expect to see math scores drop the first one to two years under the Mathland program. As a parent, I feel this is unacceptable... to set my child up for failure.

A final note: I have worked in my daughter's class one day a week, every week for the past four years. I was working in my daughter's class this year one day a week, during math time. Since I have expressed my concerns about the math curriculum, I have been asked by my daughter's teacher to no longer work in the class until "a workable solution to my concerns" can be reached. The teacher feels that my concerns about the math program are making him feel like he's "under the microscope" and that it's effecting his teaching. (The principal at the school supported his feelings.) If Mathland is such a wonderful program (the district obviously thought it must have been to justify spending money on it), then I would think that the teacher, principal and the district would encourage parents to be in the class (regardless of their feelings about the program) during math time.

My hope is that parents will take the time to evaluate Mathland for themselves. Thanks to your web site, there's plenty of information to help them evaluate whether or not they feel Mathland or any other Framework approved program is what they want for their child.

The supporters of these programs defend their selection using three arguments.The first is that these programs work better for minorities and girls than other programs. To justify this assertion they quote statistics supplied by MathLand for six unidentified elementary schools in southern California that used MathLand. They assert a dramatic rise in scores on nationally normed exams in these schools after the introduction of this program.

Unfortunately, repeated attempts to obtain the names of these schools from the publisher have been unsuccessful. However, by accident, one of them was identified. What was found was that these gains came in the third year of the program, following a dramatic drop in scores after the first year and the introduction of supplementary material. Moreover, the gains did not bring the scores for this school up to the level they had been at BEFORE MathLand had been introduced. But even more is true - Mathematics Professor Wayne Bishop, who discovered the identity of this school, reports in more detail on the students at the school who were not counted in the MathLand statistics:

"This school was heavily Hispanic, some 80% of its students were taught and tested in Spanish using the Spanish language edition of MathLand. These students continued to decline in their third year to the 15th percentile nationally, so low that the overall performance was not recovery but continued decline. This information was not included in the MathLand information on student performance nor in the information that they supplied to the U.S.Department of Education as evidence for their rating of "Promising" that was made public in October of 1999."

The second argument is that these programs are modeled after one of the best and most successful programs in the world. The Japanese mathematics program is held up as a model for programs of the MathLand, Connected Mathematics type. It is asserted that these programs work in the same way and at the same level as the Japanese program. It is also pointed out that the Japanese mathematics program propelled them to their remarkable success in all international comparisons of mathematics achievement - second only to Singapore - for the last 20 years.

While everything that is asserted about the Japanese program is true, the assertion that programs of the MathLand, CMP type are modeled after the Japanese programs is so far from true as to be a sort of sour joke to those of us who actually know something about these issues. In the following three paragraphs we explain how these programs actually measure up against the Japanese curriculum.

The current California Mathematics Standards are aligned with those of Japan, Singapore, and Hungary, three of the highest achieving countries in mathematics in the world. Indeed, in the writing process, it was these three standards that were used as references for both the topics in the California Mathematics Standards and when they would appear in the curriculum.

In 1999, Connected Mathematics was submitted by its publisher to be evaluated for approval as a PARTIAL PROGRAM - a program which, while perhaps not quite at the level of the California Standards, met a significant number of the grade level standards and could be used as a supplemental program. The mathematicians and teachers who reviewed it rejected it, asserting that it was at least two years below grade level and that it contained numerous and significant mathematical errors.

After the 2000-2001 academic year, state monies can no longer be used to buy Connected Mathematics for local school districts, as CMP was not even submitted for evaluation this year for the full program evaluation. Nor will state funds be available to buy MathLand.The publishers of MathLand did not submit their program for evaluation either as a partial program or as a full program. Perhaps they understood that MathLand was so far below the level of the California Mathematics Standards that the fact that the reviews would be publicly available could seriously cut into their sales in other states.

While an attempt is made to introduce mathematical reasoning as part of the curriculum, it fails badly in programs like MathLand and Connected Mathematics. The main reason for this is that the authors really do not understand the process themselves.

The ideas about problem solving that were used in developing these programs rest primarily on a serious misunderstanding of the work on mathematical problem solving by the mathematician, G. Polya. Polya was at Stanford during the 1960's when mathematics educators were starting to quote his work and use it to shape their attempts to introduce mathematical reasoning as a component of the K - 12 mathematics curriculum. He repeatedly tried to get them to stop, explaining that his work had been done with juniors and seniors at Stanford majoring in mathematics, and was not appropriate for use until students had a deep grounding in the subject.

Interestingly, the author and creator of the Japanese mathematics curriculum - the great mathematician Kunihiko Kodiara - was also at Stanford during the 1960's. Problem solving is very strongly a part of the Japanese text books, but it is introduced in a very measured and controlled way. The Japanese method is completely at variance with the process used in programs of the MathLand, Connected Mathematics type, where the underlying assumption is that students will learn everything they need to know by working in groups and devising their own solutions to partially posed problems.

A typical problem at third grade level in texts like MathLand is the following: "Marta and Akoshi are in different third grade classes in the same school. They want to know which classroom is larger. How do they decide?"

As stated, this problem is not well posed, hence is not a problem in mathematics. It is necessary to assign a precise meaning to the word larger in order to make a mathematics problem out of it. However, since the meaning of this term is not specified, the only correct answer would consist of the entire collection of all answers associated to all possible meanings of larger - an infinite set. Such an understanding is unlikely to be achievable at the third grade level. Indeed, it is unlikely to be achievable by most elementary school teachers. Thus one has to proceed in a much more careful and structured way in order to inculcate the desired skills and understandings in our students. These are among the reasons for the differences between the approach to problem solving in the Mountain View school system and that in Japan.

It is, perhaps, interesting to get some idea of the true success of the Japanese program. Here is a quote from the introduction to the UCSMP translations of the Japanese books for grades 7 - 11. These books were published in Japan in 1984, and the translations were published in 1992.

"Let us take a brief look at the schooling behind much of Japan's economic success. The Japanese school system consists of a six-year primary school, a three-year lower secondary school, and a three year upper secondary school. The first nine grades are compulsory, and enrollment is now 99.9%. According to 1990 statistics, 95.1% of age-group children are enrolled in upper secondary school, and the dropout rate is 2.2%. In terms of achievement, a typical Japanese student graduates from secondary school with roughly four more years of education than an average American high school graduate. The level of mathematics training achieved by Japanese students can be inferred from the following data:

"Japanese Grade 7 Mathematics (New Mathematics 1) explores integers, positive and negative numbers, letters and expressions, equations, functions and proportions, plane figures and figures in space. Chapter headings in Japanese Grade 8 Mathematics include calculating expressions, inequalities, systems of equations, linear functions, parallel lines, and congruent figures, parallelograms, similar figures and organizing data. Japanese Grade 9 Mathematics covers square roots, polynomials, quadratic equations, functions, circles, figures and measurement, and probability and statistics. The material in all three grades (lower secondary school) is compulsory for all students."

It is also worth noting that when Japanese students continue on to upper secondary school, 40% of them elect a lower track, and 60% elect an upper track which culminates with a serious course in Calculus in 12th grade. The number of Japanese high school graduates who have had calculus is more than 50%. In the United States, the best estimate is less than 6%, and this number appears to have been dropping nationally with the introduction and growing adoption of programs of the MathLand, CMP types.

(The author is one of the four Stanford mathematicians who rewrote and revised the California Mathematics Standards for the California Board of Education. He and H.-H. Wu were the mathematicians who largely wrote and put together the new California Mathematics Framework for the California Board of Education. He has consulted on state standards for numerous other states, and is currently part of the Achieve Panel creating national standards for this country. He was also one of the members of the Content Review Panel for the California 1999 Partial Adoption and is currently a member of the Content Review Panel for California's Full Adoption. He is one of the authors of the letter to Secretary of Education Riley that pointed out the problems with programs of the MathLand, CMP type, and he has testified before congress on these issues.)

LAST OCTOBER, the U.S. Department of Education released a list of 10 math programs which department educrats considered ``exemplary'' or ``promising.'' It would have been more accurate to rate the 10 programs as ``trendy'' or ``math-lite.'' Some 200 appalled mathematicians and scientists -- including three Nobel laureates -- ran an ad in the Washington Post calling on Secretary Richard Riley to rescind the seal of approval.

Susan Sarhady, a parent from Plano, Texas, knows what the middle-school Connected Mathematics program -- rated ``exemplary'' -- did for her community. Some high-achieving students didn't test well in math. Parents were baffled by assignments, like the tossing of marshmallows to see how many landed on their ends or their sides. Her friend Kathy bought a traditional math textbook and started spending a half hour every night with her son to make sure he didn't miss math he would later need. Kathy found it galling that if her son scores well, Connected Math will get the credit.

Rachel Tronstein, a University of Michigan freshman, was enrolled in an accelerated Core Plus program -- also ``exemplary'' -- at Andover High School in Michigan. When she attended Stanford University's summer session in 1998, she took the pre- calculus course after taking pre-calculus in Core Plus. She said, ``the vast majority of material in that course was material to which I had never been exposed.''

Stanford mathematics professor R. James Milgram explained that he became interested in K-12 math curricula when he noticed that highly motivated math students couldn't do well in their college math classes because they had received a ``third-rate education.''

In 1989, the National Council of Teachers of Mathematics released the trendy math standards -- which eschewed traditional math in favor of group work and discovery learning -- which were the basis for the Department of Educrats' Top Ten. By 1989, California schools had started using at least three trendy programs that were written to in conjunction with the new pedagogy. Milgram noted that since 1989, the percentage of California State University students -- who are restricted to the top 30 percent of state high school graduates -- who were required to take remedial math has more than doubled from 23 percent in 1989, to 55 percent.

Linda Rosen of the Department of Education argues that 23 percent is not exactly a number to brag about. And: ``These new materials have only been out'' for two to three years. She has a point. In 1989, participation in new-new math was uncommon. Since then, not every school has gone fuzzy, although many have.

California led the nation in the rush to dumb down math. The state's 1985 math framework began the slide and the 1992 framework mastered it. Teachers who followed the framework adopted the math- lite approach years ago. Five years ago, the dissident math group Mathematically Correct was born when parents angry about the ``exemplary'' College Preparatory Mathematics realized the problem wasn't just in their three school districts, but had become widespread.

Michigan parent Mark Schwartz testified, ``If medical doctors experimented with our kids in the same fashion school districts do, they would be in jail.'' In edu- land, they get named to a on a panel that chooses pet math programs.