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DEBRA J. SAUNDERS — Man of Science Has a Problem With Real Math

DEBRA J. SAUNDERS — Man of Science Has a Problem With Real Math
Friday, December 19, 1997

THIS STORY demonstrates why you can’t trust Clinton’s education gurus to write national tests for America’s students. If there’s a sure thing in life, it’s that D.C. educrats will dumb down any subject, given half a chance and millions of dollars.

The tale begins this month as California’s state Board of Education was about to vote on math standards for public school students. A standards panel had written a document rich in trendy educratese. (“Show mathematical reasoning in solutions in a variety of ways.”) The board wanted — and ultimately approved — a meatier document with solid standards for computation and less fluff about writing about math. [an error occurred while processing this directive]

By injecting more math into math — actually expecting kids to memorize multiplication tables in the third grade and master long division in the fourth — the board invited the ire of state schools chief Delaine Eastin and the federal government. On December 11, the day before the final vote, Luther S. Williams, assistant director of the federally funded National Science Foundation, fired off a letter to board president Yvonne Larson. Basics wags call it “the blackmail letter.”

Williams, who didn’t call me back, criticized the new standards for not “elevating problem-solving and critical thinking.” His letter chided the board for preferring the “wistful or nostalgic `back-to-basics’ approach,” which he wrote, “has chronically and dismally failed.”

He then reminded Larsen that his bureaucracy gives grants totaling more than $50 million of taxpayer money to six California school districts, including Oakland. “You must surely understand,” he wrote, that his group “cannot support individual school systems that embark on a course that substitutes computational proficiencies for a commitment to deep, balanced, mathematical learning.”

On what planet does this man of science live?

First, Williams has a little jurisdictional problem. President Clinton says he doesn’t want the federal government to butt into local school business. Also, the guy works for a science — not math — agency. But he is so arrogant and power drunk that he feels free to sic his Science Foundation on California math dissidents.

Second, the state’s commitment to “deep, balanced mathematical learning” — aka new-new math — has resulted in computational deficiencies, as well as general arithmetical idiocy. For some years, trendy California educators have focused on students writing about math, repeatedly explaining how equations work and exploring their feelings about math. They’ve also taken to giving students credit for wrong answers. Thus, “critical thinking” has come to mean not being critical of students.

The result: In the last National Assessment of Educational Progress math test, California fourth-graders scored behind students from every state but Mississippi and Louisiana. Only 13 percent were rated proficient. Eastin has suggested that the state board should “get out of the dark ages.” She ought to get the schools out of the dark ages.

No wonder some parents are “nostalgic,” as Williams put it, for the days when basics were emphasized, and cash registers all had numbers on them instead of pictures of hamburgers. Back in the days of what Williams classified as failure, students scored an average of 22 points higher on math SATs.

Here’s a novel thought. Let the National Science Foundation give a grant to solve the great mystery of modern education: How is it that swells like Williams can look at the 1950s as years of math failure, but see no problem with high- school kids needing a calculator to compute 10 percent? How can you say you stand for problem solving without being able to recognize a problem?


Los Angeles Times
Friday, September 17, 1999



Education: We’re starting with basics for reading; why not give students the basics of arithmetic, algebra and geometry, too?


The new Los Angeles Unified School District Board of Education deserves praise and encouragement for its efforts to improve student academic achievement. Unfortunately, in the case of mathematics education, the board is getting bad advice from district staff.

Phonics and other basic language skills have received well-deserved national attention in recent years. As a result, “whole language” is disappearing from the curriculum. By contrast, “whole math,” the philosophical sibling of whole language, is still entrenched in district schools.

The Los Angeles Systemic Initiative, or LASI, is a multiyear, federally funded district program with the worthy goal of improving mathematics and science education. The problem is that LASI has done more harm than good. The initiative’s recommendations have caused many district schools to abandon credible arithmetic, algebra and geometry instruction. LASI has implemented the worst mathematics curricula that we are aware of, and we are aware of many due in part to our service on the California Content Review Panel for K-8 mathematics books. In that capacity, we made recommendations to the state Board of Education for statewide adoption on a huge number of math textbooks submitted by publishers–finding only a small fraction of these worthy of use by California students.

LASI has promoted an experimental K-6 math curriculum, Mathland, which has no textbooks for students. Its manual for teachers tells them not to explain the standard algorithms of arithmetic to children. In other words, children are not taught the traditional procedures for addition, subtraction, multiplication and division. Nowhere in any of these K-6 materials is the usual way to multiply two numbers, like 35 times 76, ever explained.

For high school, LASI recommends so-called integrated math curricula such as Interactive Mathematics Program. Like other integrated math programs, IMP suppresses basic algebra at all grade levels. For example, it delays an important eighth-grade algebra topic, called the quadratic formula, until the 12th grade. This defect alone puts Los Angeles students at a serious disadvantage on the California standardized testing and reporting, or STAR, exam that tests this topic in the eighth grade.

Mathland and IMP are not the only questionable programs implemented by LASI in Los Angeles schools. All of LASI’s recommendations are problematic. The heavy emphasis on calculators is particularly damaging. This often results in students needing their calculators for even the most rudimentary figuring. It is our view that calculators should be used sparingly in grades 6-12 and not at all in grades K-5. The base 10 structure of our number system together with the standard arithmetic algorithms carry the seeds of algebra. Depriving children of mastery of arithmetic closes doors to more advanced mathematics courses in ways that district staff members do not seem to understand.

Statistics from the U.S. Department of Education show that success in secondary school algebra is the single greatest predictor of success in college–not just for engineering and science majors, but for majors in all fields.

Particularly troubling to us is the justification for LASI’s watered-down mathematics programs as reported in The Times in August. An LASI supporter is quoted as saying, “There’s a move to eliminate anything but old-style math. But it’s only striking against inner-city schools where kids need a different approach–they need to see, touch and feel what they are learning.”

We vigorously disagree. Independent of skin color and wealth, students need the same rigorous foundations, including the all important “old-style math” subjects of arithmetic, algebra and geometry. The legendary Jaime Escalante, depicted in the movie “Stand and Deliver,” catapulted his disadvantaged students to national prominence using “old-style math.” The high-achieving African American and Latino students at Bennett-Kew Elementary School in Inglewood provide another example. Sacramento Unified School District abandoned the faddish LASI-style curricula for its multiethnic students and increased its first and second grade SAT-9 test scores by more than 16 percentile points this year.

Data from the recent STAR exam show that students taking integrated math courses in California–such as those promoted by LASI–scored lower than their counterparts enrolled in traditional math courses.

All of the mathematicians who served on the Content Review Panel for the State Board agree about what constitutes a good mathematics curriculum. We urge the new Los Angeles school board to set aside the recommendations of LASI, and seek advice from the broader mathematics community instead.


David Klein, a CSUN Mathematics Professor, was appointed by the State Board of Education to evaluate mathematics teacher professional development programs.

R. James Milgram is a Stanford University mathematics professor who regularly advises the state Board of Education on math issues.


Integrated Mathematics in LAUSD


Integrated Mathematics in LAUSD




In California, the integrated mathematics option refers specifically to an alternative to the algebra 1, geometry, algebra 2 secondary sequence wherein districts are allowed to provide the same content but in a different sequence over three years. All mathematics programs for K-7 are integrated in that topics from each strand of mathematics are included each year. Because the secondary integrated programs make heavy use of pedagogical approaches often called reform mathematics, these terms have unfortunately been used interchangeably. This confuses the issues.

With respect to the secondary integrated mathematics programs in use in LAUSD:

The content of these courses is not equivalent to the content required by the state standards.


No integrated 1 books were approved by the state under AB2519 – indeed most were not even submitted – as they are unsatisfactory relative to the state learning standards.

The integrated programs cannot be legitimately certified as aligned with the state standards.

Students in these programs learn less mathematics than those in traditional programs.

LAUSD students in integrated mathematics score lower than those in traditional mathematics in grades 8, 9, and 10 on the state standards-based tests according to state records.

This deficit is true for economically disadvantaged students as well as others.

This deficit is true for LEP students as well as others.

This deficit is true for male and female students.

These programs produce students who are less well prepared.

Integrated mathematics has been promoted through LA-SI (the Los Angeles Systemic Initiative, a federally funded project to implement integrated math programs) in schools around the district. Of the eleven schools associated with LA-SI the longest, all but one have experienced decline in SAT participation over the past two years. The average decline is 12% as reported by the IAU (the “Independent Analysis Unit” of LAUSD) to the Board in a report of May 12, 1999.

SAT administration across all LA-SI focal schools is down about 5% while it is up roughly 5% in non-focal schools. The SAT math average in focal schools is 445 while at the non-focal schools have an average of 462.

With respect to reform mathematics, the programs approved by the state for K-8 include a range of reform approaches and frequently note their alignment with NCTM. These approaches will still be available even when programs that fail to align with the standards are avoided.



Integrated Mathematics in LAUSD


by Paul Clopton
Member, LAUSD Mathematics Curriculum Committee



Historically, secondary mathematics in California has been taught using the courses algebra 1, geometry, and algebra 2. More recently, some schools have switched to courses that mix these topics across three courses. This is called integrated mathematics and is an optional sequence in the state Mathematics Framework. However, the integrated programs in use differ in many respects beyond the sequence of topic presentation, and thus integrated has taken on other meanings that have to do with pedagogy, presentation style, and other factors.

The new California Mathematics Standards and the Mathematics Framework require a mixture of topics from the strands of mathematics for all students in grades K-7. Districts may use either the traditional or the integrated sequence starting in grade 8. The standards stipulate exactly the same objectives for either sequence – that students learn the required mathematics.

To go along with this option, the standards-based portion of the state testing program (STAR) in mathematics has two choices for grades 8 to 10 – algebra 1, geometry, and algebra 2 or integrated 1, integrated 2, and integrated 3. The two sequences contain exactly the same items overall, but they are assigned in a different sequence across the three years.

Also, in grades 8 to 10, only students enrolled in the corresponding traditional or integrated sequence take the standards-based part of the exam. In grade 11, all students take a cumulative form of the standards-based exam covering all of these topics, regardless of what mathematics courses they have taken.

In general, the performance on these standards-based examinations has been poor. This is expected since students have not previously been expected to meet the new standards throughout their academic careers. Achievement in LA has been poor as well. However, certain comparisons are already possible given the baseline test results from the spring 1999 test administration.
Results for LAUSD

The California data file for these test results gives means for the standards-based mathematics tests in grades 8 to 10 only for those students who are “on-track” for meeting the standards, meaning that they are taking the first year in grade 8, or the second year in grade 9, or the third year in grade 10. Here are the average number of correct answers for all of LAUSD













On average, the traditional sequence scores are about 10% higher than the integrated sequence scores. We cannot be certain that the curriculum accounts for this difference, since we don’t know the characteristics of the students or teachers in each case. However, these results suggest that the integrated programs are less effective than the traditional ones in LAUSD.
Results for Economically Disadvantaged Students

The integrated programs also show weaker results for disadvantaged students. The STAR data file does not contain information on ethnic minorities, but it does summarize scores for economically disadvantaged students vs other students. Both groups achieved lower scores with integrated programs. This is not consistent with the idea that the integrated mathematics programs are better for the disadvantaged students. These results are consistent with the idea that the integrated programs lack equivalent mathematical content.

Economically Disadvanted

All Others






















Results for LEP Students

From the state data file, it is also possible to inspect the LAUSD results for limited English proficiency students (LEP) compared to other students. Again, both groups achieved lower scores with integrated programs than with traditional programs across the three grade levels.

LEP Students

All Others






















Results for Male and Female Students

The state data file breaks down scores by student gender. Again, both groups achieved lower scores with integrated programs than with traditional programs across the three grade levels.

Female Students

Male Students






















Integrated and Traditional High Schools

It is possible to characterize high schools as traditional or integrated based on the tests taken by the students (counts of tests taken are given even when the scores are not reported). In this example, schools were identified as traditional if at least 75% of these augmented tests were in the traditional sequence, and they were called integrated if at least 75% of the tests were in the integrated sequence. These high schools were then compared on the basis of their average scores for the 11th grade where all students take the same standards-based mathematics exam. The results were:



Number of Schools



Average Number Correct



Again, we cannot be certain about the actual cause of this difference, but the result favors the traditional approach. What about the “middle” group, those with somewhere between 25% and 75% traditional score reports? There were 15 high schools in this group with an average of 15.1 correct.
The Stanford 9 scores for these same high schools give an indication of achievement on a less rigorous assessment. The results using the NPR for the average student at each school are:

Economically Disadvantaged

All Others





















The results for the percentage of students above the 50th percentile are:

Economically Disadvantaged

All Others





















In all cases, economically disadvantaged or not, the means for the traditional program schools are higher than the means for the integrated program schools.
LA-SI Schools

The influx of integrated mathematics programs in LAUSD high schools is related to involvement with LA-SI (the Los Angeles Systemic Initiative, a federally funded project to implement integrated math programs). Schools with the longest involvement are Phase I schools. Of the eleven Phase I schools, all but one have experienced decline in SAT participation over the past two years, some rather substantially; 12% is the average reported by the IAU (the “Independent Analysis Unit” of LAUSD) to the Board in a report of May 12, 1999.

According to the IAU numbers, SAT performance across all of the LA-SI Focal schools is down about 5% in the number of takers and has a math average of 445 while the number of takers is up roughly that same 5% at the non-Focal schools with an average of 462. Neither of these numbers is terribly impressive but they suggest a reason why several high schools have abandoned integrated mathematics and are returning to more traditional programs.

The IAU only looked at the two years 1996-1998 but a longer perspective on these LA-SI Phase I schools is informative. Palisades is not on the state’s data base because of its conversion to magnet status but data from the other ten is available on the Internet. That data starts with 1992, the year in which two of them, Roosevelt and Marshall, became pilots for an integrated program called IMP. From 1992 to 1998, the data year of the IAU report, these ten schools dropped an average of 13 points in their SAT math scores while experiencing a 30% overall drop in SAT participation. These numbers compare with the overall statewide math SAT average holding steady at 516 while participation increased by 24%.

Another useful measure of success is the Entry Level Mathematics Exam (ELM) required of students admitted to any CSU campus. The most recent data at that website is for those students admitted sometime during the 1997-8 year. A successful mathematics assessment is an SAT math score of 550 or a passing score on the ELM. For the LA-SI Phase I schools, the collectively failure rate was 78%. This compares with a statewide failure rate of 55%.
Alignment with Standards

The integrated secondary programs in use in LAUSD not only mix up the order of topic presentation, they also reduce the level of mathematics covered. The state has recently approved 5 algebra 1 programs under AB2519, while no integrated 1 programs were approved. In general, the integrated secondary programs were not even submitted because of their lack of alignment with the state standards. The district cannot legitimately certify these integrated programs as being aligned to the state standards.
Reform Methods without Integrated Secondary Programs

Even without these integrated secondary programs, LAUSD students will still have integrated content in grades K-7. Even without these integrated secondary programs, schools will be able to select books with varying degrees of reform mathematics methods at all grade levels. Indeed, the state-approved texts often note their inclusion of these new methods and make reference to the NCTM which is recognized for promoting these methods. Many include leading NCTM members as authors.

LAUSD can comply with state requirements and still encourage classroom teachers to use their own professional judgment in selecting the best methods for meeting the needs of their students. Indeed, this is exactly what is recommended in the state mathematics framework.

If math were a color . . . By Marcia Tsicouris

If math were a color . . .
By Marcia Tsicouris

In 1993/94 District 205 adopted the University of Chicago Everyday Math project as its K-5 curriculum and currently utilizes it to some degree in the middle schools and at the high school level. Since then, it has come up for review and the committee elected to re-instate it for another term. Why? I can only deduce the decision was based on economics and not the program’s effectiveness. Everyday Math does not require the purchase of textbooks or workbooks. Copies are made from masters or other copies. We purchased the program only a few years after it went on the market. Is it possible to include Everyday Math among those of best practices after such a short time? The U of C acknowledged some of its shortcoming and published an optional Skills Link supplement in July 1998.

Everyday Math. On which days exactly is this program effective? If you’re a 5th grader, maybe it works on the days you have art. Or, possibly, on the days you study nutrition, or on the days you discuss weather conditions. In lieu of practicing long division or mastering multiplication facts our 5th graders spend math time on exercises such as this:

A. If math were a color, it would be –, because –.
B. If it were a food, it would be –, because –.
C. If it were weather, it would be –, because –.

If this type of, so called, math activity takes you by surprise, I’ll allow time here for primal screams as did the author of the Wall Street Journal article where I first learned of this particular atrocity. (I verified its occurrence with my 5th grader!)

In 4th grade, my son’s fraction assignment was marked wrong when he identified 1/5 of the dogs pictured on his Home Link as being spotted. After checking it myself and talking with the teacher I found the copy quality was so poor it was nearly impossible to detect that a 2nd dog out of 5 was spotted.

1st through 3rd graders are encouraged to become dependent on calculators, peers, and parents to accomplish their goals. Calculators are introduced early and often. Internationally, U.S. students’ math scores ranked among the lowest in the world. Countries with the highest scores, Japan, China, and East Asian countries don’t permit the use of calculators until high school. They feel students must first master the concepts and operations necessary for mathematical problem solving.

Everyday Math lessons are based on a spiraling curriculum providing no room for mastery in any one area. New concepts are introduced one after another assuming children will pick up on the material as it is sporadically revisited throughout the year. It’s difficult to find two of the same type of math problem on any one Home Link. (If you do, its likely your child’s teacher has opted to supplement with worksheets from other programs such as Addison Wesley.)

In an attempt to promote problem solving skills, many exercises are done in groups. Unfortunately, it is not possible to develop mathematical problem solving skills without the basic tools necessary to arrive at a correct answer. However, Everyday Math is not concerned with correct answers. This program prefers to emphasize the creative processes used to arrive at any answer. I hope my financial advisor, banker, pharmacist, etc. don’t share the U of C’s position on this. A math problem isn’t solved until you’ve reached the correct answer. Like a carpenter, a students’ problem solving skills are useless with out proper tools!

Everyday Math places no importance on math facts, and no benchmarks are established in the program for mastering them. In place of math facts, students are required to learn a multitude of algorithms. Defenders of the program insist this clumsy process provides each student the opportunity to select the algorithm that works best for him/her. Yet, in 5th grade, instructions continue to specify which algorithm to use for the assignment.

Virtually every Home Link is prefaced with the words: Show someone at home; Have someone at home; With someone at home; Tell someone at home. The message sent to my 3rd grader is that she’s incapable of doing math independently. Thanks to this program, essentially, she is incapable. I have to re-teach each concept as it arises (in addition to teaching basic math facts) because the U of C sees no merit in mastery.

Some may argue they like the program. As with Whole Language, there is a small population of students that possess a natural aptitude for the subject. These students will excel regardless how effective or ineffective the program. Whole Language is a testament to that. For the majority, Everyday Math will create generations of math disabled students as Whole Language created generations of reading disabled students.

Back to the ridiculous 5th grade exercise: If math were a color, it would be black and white, for math is an exact science with concrete, absolute, correct solutions. If it were a food, it would be something high in nutrition like fruits and vegetables, as these would nourish and develop the brain. If it were weather, it would be clear, bright and crisp to keep skills sharp and the mind alert.

Given our students are burdened with Everyday Math; the color of math is gray and fuzzy with little importance placed on correctness and none placed on mastery. The food choice is junk food with little nutritional value serving only to clog arteries and provide immediate gratification. And, weather, no doubt, it’s a tornado whose spiraling winds leave our students strewn at the bottom of the scale.

By my calculations, Everyday Math equates to educational malpractice!

Check it out yourself. There are some great websites on the Internet. One of my favorites is Mathematically Correct at

Marcia Tsicouris
Elmhurst, Illinois

Reform Mathematics Education How to “Succeed” Without Really Trying

Reform Mathematics Education
How to “Succeed” Without Really Trying

by Paul Clopton
Cofounder, Mathematically Correct

Since the 1980’s, there have been substantial efforts nation wide to weaken mathematics education in America, and these efforts have largely been successful. This is not a communist conspiracy [Note 1]. It flows from an honest desire to help the less fortunate. This effort is based on the misguided notion that weaker mathematics will be helpful to the traditionally disadvantaged groups in our society. It is this effort, curiously known as reform, that is the root cause of what has come to be known as the math wars.

You won’t find many reformers who will openly admit that they favor “dumbed-down” mathematics. In fact, the reform movement is characterized by a plethora of rhetoric to the contrary. The diatribes are extensive and frequent and are laden with phrases like “higher order thinking” and “conceptual understanding” and “real-world problems” while shy on terms like “arithmetic” and “algebra.” Reformers have learned their scripts well, and the rhetoric comes gushing forth with little provocation.

The conditions that prompted this movement are obvious. Poor people, minorities, and women are under-represented among those who reach high levels of mathematical achievement. Those who cannot master arithmetic and algebra are unlikely to achieve a decent college education. There is no question that the educational system in this country is not successful for a great many students.

One way to deal with this problem is to make the mathematics easier. This means less rigor, less emphasis on arithmetic and algebra, more reading and art and creative projects, less emphasis on correct answers, more calculators, and a host of other reform-minded solutions. Stylish pedagogical methods combined with rhetoric about higher order thinking while downplaying or condemning outright both computation skills and mathematical proof complete the package. This is reform mathematics education.

Sometimes dubbed traditional or anti-reform, the second perspective has come in abreaction to the first and is mainly supported by parents and mathematicians. This perspective holds out that the mathematics must not be “dumbed-down.” The key in this perspective is to increase achievement rather than to decrease expectations. Central to this position is that the traditionally less fortunate are not well-served by weaker mathematics and, in fact, should be insulted by it. The real key to success is real mathematics achievement, and every effort should be made to foster this achievement.

Ironically, the struggle to promote real mathematics education is left up to those outside of the field – mostly parents. The perspective is traditional in the sense that it seeks to prevent learning expectations from being further eroded away by putative reform efforts. Mathematics education in America has not been very successful. However, do not look for relief in the reform notions. We would be better off if all the energy behind the reform was redirected toward clearly defined achievement goals and we measured progress toward those goals frequently and objectively.

Obliterating Distinctions between Success and Failure

The reform designs open the door to claims of successfully teaching mathematics without really doing so. The reform writings and methods are many and varied, but a common feature is that they end up obscuring the failure to teach mathematics. In reform mathematics education, the goal of success for all is not supported by achievement but rather by redefining success and, mostly, by obscuring failure. Here are but a few examples:

Group Learning and Group Tests – The story of Apollo 13 is used to promote group learning and group assessments with the argument that our students must learn to work together like people do in the real world. Never mind that people in the real world don’t sit in groups doing algebra problems. Group learning is plagued by inequities that most parents identify quickly – some do the work while others learn that they can “succeed” without learning the material and without effort. Group assessments effectively erase the ability to monitor individual achievement or to provide useful diagnostic information. Whether or not individuals are learning is obscured by these methods. 
Calculators – Many argue that routine skills are out of date, and that technology has changed the mathematics that today’s students need to know. The position includes multiplication and division, obviously. However, today’s calculators can manipulate fractions and solve equations as well. Distancing students from these activities takes away the learning experiences that help form the foundation of mathematical understanding. By far, most American parents want their children to be able to solve problems without calculators. The reliance on calculators allows reformers to claim success even when children do not learn the fundamental operations of arithmetic. Soon they will claim success in algebra for students who have not learned how to solve equations. 

Authentic Assessment – One of the greatest evils from the reform perspective is objective testing. It would have to be because these measures can identify failure. Many arguments are advanced for this perspective, but addressing them in detail is beyond the scope of this report [Note 2]. The proposed alternative is frequently called authentic assessment. Translating this bit of jargon into English isn’t easy. Basically, it refers to a variety of procedures that involve less mathematics, more writing or talking, and very subjective evaluation. In the worst instances, students suffer if they do not support the intended politically correct perspective in their response. But, politics aside, these methods are reliably unreliable. The subjective nature leaves little opportunity for valid information to be obtained. Sometimes, one cannot even tell who actually did the work. In the long run, many invalid assessments tend to average out (false equity) and, again, real differences in achievement go undetected. 

Measuring Content

With the educational bureaucracy in this country prone to jump on the bandwagon of pedagogical fads, assuring that children receive a decent education becomes the responsibility of their parents. Effective parenting now includes keeping a watchful eye on what happens in school and what the children are and are not learning. When deficiencies are found, parents can try to change the schools, to increase learning experiences at home, or to find outside resources to provide the needed learning experiences. The entire process of monitoring and remedying this situation is very demanding.

The first stage of this process, examining the content of the school program, can be a little easier for parents who make use of existing resources that identify content by grade level. Coming on the heels of failed reform efforts in California, expectations for achievement that are roughly in line with those of the most successful countries of the world were developed. These documents identify achievement levels in terms that are sufficiently clear for parents to evaluate. Parents are encouraged to measure the school programs against these contents as a way of finding out whether or not important content is being covered.

The California Mathematics Standards
The San Diego Mathematics Standards
The NCITE-LA Achievement Test Items
Number Sense in California

With the aid of these materials, parents can more easily find what is present and what is absent in the programs used in local schools. These documents enable parents to match local content to grade levels according to high-level standards.

Projects – The reform programs are loaded with projects and activities, often called investigations. Part of the argument for these methods relates to stimulating student interest. There are also claims of richer mathematics and the importance of context. Even a casual inspection of these activities will show that they tend to be very time consuming while involving very little mathematics. Time for mathematics, both in class and at home, is seriously limited and must be used as efficiently as possible. These activities are inefficient learning methods. But, beyond that limitation, they promote the evaluation of students on the basis of non-mathematical dimensions such as how artistic the display is or the writing style of the report or the social value of the application. 
Standards – The reform movement claims to be based on standards, although most parents will be surprised by what they find – and what they don’t find – in reform standards documents. It is contrary to the goal of the reform to produce explicit statements about what students know and should be able to do – again, spotting failure would be too easy. Consequently, the reform movement produces standards that are so vague that one cannot tell whether they have been met or not. Any attempt to write tests for these standards, for example, will be unreliable because the required content is unclear. Reformers hate lists of clearly stated objectives and call them laundry lists. However, vague learning expectations are effectively the same as no learning expectations at all. Again, it becomes impossible to differentiate success from failure. 
Strands – When attempts are made to subdivide mathematics into content areas, such as algebra and geometry, the subdivisions are often called strands. The reform movement uses this technique while simultaneously avoiding explicit content. Thus, all of the elementary school work with arithmetic falls into one strand which becomes just one of many topic areas students are supposed to address. The consequence is that students can still succeed while failing in arithmetic. The same thinking reduces algebra to just one component of mathematics in later grades with similar consequences. 
Pedagogical Fads – The reform movement places great emphasis on classroom methods, such as those that involve groups, calculators, activities and projects, manipulatives, explorations, art work, and non-mathematical themes. Irrespective of any relationship between these methods and learning (or lack thereof), there are consequences of the fact that the emphasis on these styles is pervasive in reform documents. Even reformers bemoan the fact their followers often carry out reform by adding a few new gimmicks to their bag of classroom tricks. The heavy emphasis on style quite naturally takes attention away from mathematical content. As teachers attend to implementing these processes, their evaluations of students become biased toward process and away from content. Mathematical learning will often take a back seat to artistic ability, cooperation, or even political correctness again blurring the distinctions between success and failure when it comes to learning mathematics. 

With the demise of our ability to differentiate success from failure, the reform movement will claim broad successes. School systems in America have the uncanny ability to claim improvements and reforms year after year while the content is gradually leeched out of the system. Meanwhile, fewer students will suffer wounds to their self-esteem because their failures will go undetected. Such a system will identify fewer failures among poor and minority group students, so reformers will claim a victory for equity.

Unfortunately, success in this approach will have lost its value. The claims of success operate like social promotion as applied to education bureaucrats. We may gain some “equity” at the cost of achievement, but the more advantaged parents will continue to find ways to make sure that their children learn in spite the best efforts of the reform-minded. Meanwhile, the net effect of the reform will be further deterioration in the mathematical abilities of America’s youth. The majority of these students will not find alternative forms of education to make up this deficit. It is from this majority that we will draw our next generation of teachers.


Note 1: Although not a communist conspiracy, there is some justification for the belief that some sort of conspiracy is at work. The reform designs are heavily promoted by the National Council of Teachers of Mathematics (NCTM). In turn, the educational branch of the National Science Foundation (NSF) then funds the development of curriculum materials that align with the NCTM dictates. The products of these efforts are then advertised by the U. S. Department of Education, while the NSF pushes for their adoption by states and districts.

Note 2: The interested reader should see Chapter 6, “Test Evasion,” in The Schools We Need and Why We Don’t Have Them by E. D. Hirsch, Jr., Doubleday, New York, 1996.

How a new math program rose to the top

TUESDAY, MAY 23, 2000

How a new math program rose to the top

Critics say the process of giving ‘Core-Plus’ a top rating lacked rigor and evidence of long-term positive impact

Mark Clayton (
Staff writer of The Christian Science Monitor


A plaque in Andover High School’s main office announces that this Bloomfield Hills, Mich., school is no ordinary place – it is ranked one of America’s “100 best” high schools.

Mathematics is a serious matter here. Andover students are drawn from a community of auto-industry engineers and business elites who expect their children to use high-level math skills in a variety of high-tech careers. More than 95 percent of students go on to college.

Andover’s math test scores soar above those of most other schools in the state. Despite that, the prestigious school stopped offering its traditional math curriculum to new students in 1994 and began an experimental program known as Core-Plus Mathematics, based on National Council of Teachers of Mathematics 1989 (NCTM) standards.

Several such programs have come online at all grade levels during the past decade. All have had an important goal: to boost US students’ performance and interest in math. But their method, which some say favors a broad conceptual approach that doesn’t adequately teach skills, has come under attack from mathematicians, scientists, and parents.

The story of Core-Plus is a tale of how such programs got high scores from the US Department of Education that encouraged their adoption in schools – a process that critics say is deeply flawed.

Core-Plus materials were not festooned with arcane math notation. Its texts focused on architectural design, manufacturing, and air-pollution problems. Instead of teaching algebra one year, geometry the next, then advanced algebra, trigonometry, and precalculus, Core-Plus wove together strands of each.

Guided by teachers, Andover students began working in small groups using powerful calculators, writing paragraphs to justify the mathematical rationale for their answers. It sounded promising.


High rating


Developing Core-Plus was a team effort, but it was Christopher Hirsch’s baby. So it was a happy moment for the professor of mathematics and math education at Western Michigan University at Kalamazoo, when he got the good news last fall: Education Secretary Richard Riley had named Core-Plus an “exemplary” program. Riley’s 16-member expert panel had sifted through a crop of 61 new programs. Core-Plus had popped to the top with nine others.

“We wanted to teach math as a whole – not this layer-cake approach,” says Professor Hirsch, a leading name in math education who helped write the 1989 NCTM standards the program followed. “Students advance along these strands so they develop a sense that mathematics is very connected.”

Andover became a Core-Plus pilot school in 1993, and the next year it became one of 36 “field test” high schools. The Education Department “exemplary” rating was vindication for that choice.

“Of course we were pleased,” says John Toma, Andover’s principal. “We really believed in what we were doing and had a strong belief in making the study of math applicable to daily life.”


A student’s view


But Melissa Lynn felt differently. A freshman at Andover in 1993, she became worried her Core-Plus class wasn’t very hard. She asked to switch into a traditional class. But she would have had to travel by bus to another school.

So she threw herself into the Core-Plus program and received straight A’s. She graduated in 1997 at the top of her class, with a 3.97 grade-point average.

Then she took the math placement test at the University of Michigan at Ann Arbor and bombed it. She found herself in “remedial math.” She’s still upset.

“I wasted precious time and money,” she wrote in a 1998 letter to a university professor. “I did receive an ‘A’ in my [university] precalculus class, but I did so in spite of Core-Plus.”

“Core-Plus has strong points,” she acknowledges now. She liked the real-life problem solving. Yet the emphasis on expanding math into other aspects of life was done “at the cost of teaching the basic algebraic manipulations,” she says.

Bloomfield Hills officials point out that Ms. Lynn did well in precalculus and later college math – showing that Core-Plus worked. She disagrees. “My eighth-grade math helped me out more in college than Core-Plus did,” she says.


A panel’s mandate


In summer 1996, a mathematician at University of Texas at San Antonio, Manuel Berriozabal, got a surprise phone call.

A Department of Education official wanted him to join a panel of experts whose congressional mandate was to identify top math programs.

“I was quite flattered,” he recalls. “I thought this was a first step that would help straighten out the math and science education system at the precollege, elementary and middle-school levels.”

Today, he is disappointed.

“The panel was a good idea,” Dr. Berriozabal says, “but we made some bad judgments. From the best I could tell, none of the programs we selected as ‘promising’ or ‘exemplary’ had any kind of long-term track record of achievement.”

After Berriozabal arrived in Washington, the panel began debating the criteria to determine a successful program. Berriozabal thought that long-term proof of achievement should top the list.

Most others on the panel wanted to require programs to conform to NCTM standards – then gauge achievement.

“These programs were just too new to require long-term impact studies,” says Steven Leinwand, co-chair of the expert panel on math. “To require that would have postponed any designation for years…. If we had built that criterion in, it would have been an uneven playing field, since many programs just haven’t been around long enough to have that kind of impact data.”

In 1997, after nearly a year of debate, the Education Department’s expert panel had decided on eight criteria – one of which required evidence of “a measurable difference in student learning” in order for a program to be “exemplary” or “promising.” But long-term evidence was not a factor.

Berriozabal abstained or voted against all 10 programs designated “exemplary” or “promising.”


On a mission for better math


Efforts to develop better ways to teach math emerged from concern about American students’ math performance. Especially after the results in 1997 of the Third International Math and Science Study, which showed US seniors lagging well behind their international counterparts, fears grew that America could one day lose its technological and economic lead. To help reverse the nation’s dwindling ranks of technical majors, the White House and Congress ramped up spending on K-12 math education in the early 1990s. Even the National Security Agency today sends speakers to schools to talk about the importance of math achievement, the basis for code breaking.

But one of the most influential powers in math education today is the National Science Foundation. And even before the report of the Education Department’s panel, the NSF had decided Core-Plus and others were winners.

Between 1990 and 1997, the Education and Human Resources (EHR) Division of the NSF put out calls for research proposals to explore new ways of teaching math. The division spent about $86 million in the past decade to fund 13 multiple-grade level math-curriculum projects and build four “implementation centers,” says John Bradley, EHR’s mathematics program officer.

At the elementary school level, approximately 2.5 million students are using NSF-funded math programs today, Bradley says. Another 5,000 middle schools use NSF-funded math programs. No numbers were available for the number of high schools involved in NSF math programs. But at least 500 high schools use Core-Plus, for example.

Still, the process troubled critics: Where was the independent evidence that they worked? For Connected Math, a middle school program, the NSF “outside evaluation” was done by a team that included Mark Hoover, now at the University of Michigan. For Core-Plus it was a team led by Harold Schoen, a University of Iowa professor.


Opening the floodgates of criticism


Those were questions on Norman Lynn’s mind. In fall 1997, four years after Core-Plus started at Andover, Dr. Lynn told his daughter’s story at a school board meeting, calling her and other Andover students “academic guinea pigs.” Many parents were shocked.

One of those was Gregory Bachelis, a mathematician at Wayne State University in Detroit. He decided to find out if Melissa’s math experience was unique. So he and a colleague put together a questionnaire to survey Melissa Lynn’s graduating class. Nearly half responded. Dr. Bachelis also surveyed graduates of nearby Lahser High School, the Andover rival that stuck with traditional math.

The results: 96 percent of Andover graduates who took Core-Plus and responded to the survey had taken remedial math in college, they said. Among Lahser High graduates who responded, 62 percent took remedial math.

What surprised Bachelis most, he says, were bitter comments from dozens of Andover graduates, including: “I have very few math skills, and none of them helped me with [math] in college.” Also, “I am … not the least bit confident with my math ability. I am upset that I was ever placed in a Core class.”

Not everyone was up in arms, though. Lisa Robinson, a freshmen at the University of Michigan, liked the new math program at Andover.

“I liked Core-Plus,” she says. “The math I’m doing here at U of M is the same kind of program. There’s a lot of calculator stuff. It’s the same thing.”

Several mathematicians reviewed Bechelis’s work and found it solid. Still, Bachelis and his survey were castigated by Bloomfield Hills and Core-Plus officials. A lawsuit was threatened.

“The Bachelis study is flawed,” wrote Bloomfield Hills superintendent Gary Doyle in a letter earlier this year to the American School Board Journal. “He repeatedly contacted students … especially if he believed that they were negative about the program.” Bachelis agrees he persisted to get a complete sample, but denies selecting negative views.

A study that rebutted Bachelis was soon unveiled. It said Andover graduates’ grades at the University of Michigan, Ann Arbor were “stronger” than years before the program was adopted, it said. But that study, too, is debated.

“What’s passing for educational studies these days is really embarrassing,” says David Symington, principal at Lahser High. “We tried Core-Plus. And I’ve been watching it for four years. I would not go to it and my math department wouldn’t either.”

Of the rebuttal study, he says, “They didn’t even have the correct year. They didn’t account for 100 students from Andover taking regular math classes here at Lahser, that made Core-Plus look better.”

Core-Plus director Hirsch dismisses the Bachelis survey as a manifestation of national “math wars.” Some of our critics will go to almost any length to marginalize the good that’s coming from these projects,” he says.

Yet from 1994 to 1998, the years when Core-Plus was Andover students’ only choice, math ACT scores at the school remained flat. Meanwhile, math ACT scores of rival Lahser High, and those of schools across Michigan and the US, rose about 6 percent, according to a study by R. James Milgram, professor of mathematics at Stanford University and a critic of some new NCTM programs.

Exactly what held Andover students back is not known. But the ACT scores, which Andover and Lahser provided to Milgram, are not in dispute, he says.

Colleen Zematis, mother of a student at Andover who went through three years of Core-Plus, decided action was needed. She and others rallied and circulated petitions until, last fall, Andover returned to offering a traditional math option.

Andover Principal Toma says the school likes Core-Plus and was never dissatisfied with it. “Parents’ wishes must be respected,” he says. Half of students now take traditional math, he says.


Opposition to Top 10 math programs


Meanwhile, pressure has been growing elsewhere. Last fall, the Education Department released its Top 10 list of math programs. Reaction was swift.

Within weeks, a full-page open letter to Secretary Riley protesting the department’s choices appeared in The Washington Post, signed by more than 200 mathematicians, physicists, and four Nobel laureates. Few math researchers were involved in the federal review, and there were many mistakes in the new textbooks, they charged.

Some also wondered whether the Education Department criteria were unduly biased toward NCTM standards. Others, whether the panel had relied on unbiased studies of student achievement.

There were other concerns as well. In congressional testimony last month, David Klein, a mathematician at California State University at Northridge, said conflicting interests on the expert panel were a key problem.

“This [expert panel’s] list includes some of the worst math programs you can find anywhere,” said Klein, who signed the open letter to Riley. “The minutes of the [Education Department’s] expert panel show that the panel was aware of the problem of conflicts of interest,” he continued. “They raised the issue – and then dismissed it.”

Education officials and panel members say conflict-of-interest guidelines were followed scrupulously. But they concede the appearance of vested interests.

Luther Williams, for instance, was appointed to the panel in 1996. By most accounts, Dr. Williams, director of the Education and Human Resources division of the NSF that funded math-curriculum development, played a minor role on the panel. He did not attend meetings and left the panel entirely in 1998 before it voted.

But some panel members were mystified and wondered whether having NSF officials on the expert panel opened the door to charges of vested interests.

“Not enough thought had gone into the makeup of the panel,” says James Rutherford, an adviser to the American Association for the Advancement of Science, who was on the panel, too. “I really wondered if Luther should have been there at all. After all, at the NSF he was directly involved in funding the very programs we were evaluating.”

Even after Williams left the panel, there was another NSF official on board. In the end, six of the 10 programs selected by the panel were NSF funded – a striking success rate since only 13 were NSF funded in the 1990s.

“We were just trying to get people with experience,” an Education Department official says. “The NSF had experience.” Both that official and Janice Earle, a program director in the EHR division of NSF, also on the expert panel, deny NSF programs were favored. “They weren’t my programs,” Ms. Earle says.

But critics say other issues raise questions about whether the process was as objective and thorough as it should have been:


  • Programs did not have to show long-term evidence of achievement. But Leinwand says the programs are “too new” for that – and congressional pressure was building for action.
  • Studies showing evidence of higher achievement did not have to be independently reviewed by being published in peer-reviewed journals before being submitted. Rutherford says the panel did a good job but relied on “very soft evidence.”


The dearth of solid research tended to show up most with programs tagged as “promising.” Take, for instance, Middle-school Mathematics through Applications. One of two impact reviews says: “Because the outside evaluation was not complete … the program did not submit sufficient data to substantiate its effect on student achievement…”

A second reviewer rated it “marginal for promising.” The panel rated it “promising.”

Another reviewer wrote of Everyday Math, a K-6 curriculum: “In reviewing all the evidence provided … it does not provide meaningful evidence for program effects….”


  • Only three of the 96 reviewers had published a mathematical paper, says Richard Askey, a math professor at the University of Wisconsin at Madison and a reviewer. Most reviewers were not professional mathematicians, though many were math educators, he concludes. 


  • Several panel members were affiliated with programs being judged. Most notable was the co-chairman of the panel, Mr. Leinwand, who also sat on advisory boards of three programs being judged, two of which were later selected as “exemplary” programs – Connected Mathematics Project and Interactive Mathematics Program. Mr. Leinwand and others say that he reported his affiliations and left the room for all discussions and voting on them. 


  • Critics say the panel favored NCTM standards, which the panel mandated as “a filter,” according to meeting minutes. All 10 programs were based on the standards. But Leinwand denies his position on the NCTM board influenced that. Too, “those were the only national standards out there,” says panel member Jack Price, a math professor from California State Polytechnic University at Pomona, and former NCTM president. Forty-three states had NCTM-based standards.


Linda Rosen, adviser to Secretary Riley on math, says the recommendations are “just one tool.” “What [school districts] do with this tool … is up to them.”

But that’s small consolation for Robert Daitch, now a junior at the University of Michigan. He took four years of Core-Plus before graduating from Andover in 1998.

“Since I was a kid, I loved auto engineering,” he says. “So I attended a session for those who wanted go into engineering. When they asked how many of us took calculus, all the others raised their hands. I began to realize my dream was not going to happen.” So Mr. Daitch took remedial math at the university – and became a communications major.

Higher Goals for Exit Exams California cheats its students by expecting too little        Return to regular view

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

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

Hands On, Dumb Down
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.

Page A – 21

©2005 San Francisco Chronicle



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

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