[Editor's Note: The Northridge Chronicles illustrate how severe the issues in math education have become. Students entering college are becoming less and less able each year, reflecting a deterioration in achievement at all levels. XYZ High School and CSUN are to be commended for their willingness to struggle with these difficulties. The fact that there are very serious concerns about the state Math Framework in no way detracts from the fact that all parties want to see substantial improvement.]

Elena Marchisotto: David Klein has added the following comments to my report on the meeting with XYZ High School. I share them with you, below, and add my thanks to all of you who have responded so positively to the meeting.

(From David Klein)

I think the following information should be added to your report on the meeting with the XYZ High School teachers:

The XYZ High School teachers expressed strong dissatisfaction with the California Framework and "fuzzy math" in general. The XYZ High School Math Department chooses to re-bind their heavily used traditional math books because they don't want to use the new texts which incorporate the principles of the Framework. The teachers indicated that newer editions of their traditional math textbooks are not available.

In this context, the XYZ High School teachers initiated criticisms of the use of calculators in math classes. One of the teachers illustrated the negative consequences of the use of calculators for the CSUN audience by pointing out that some of his students cannot divide 612 by 3, without assistance from calculators.

Louanne Kennedy: I am puzzled by this addendum. What is fuzzy math? Since generations of students have had difficulty with math, what is the value of dusting off "traditional" texts. Is this a new wrapping on the argument of whether math education must move always toward calculus; that indeed real math is calculus based? Please enlighten me?

David Klein: I will be glad to try to answer your question.

"Fuzzy math" or the "new new math" are terms widely understood to refer to mathematics pedagogy based on "The Mathematics Framework for California Public Schools," adopted by the California State Board of Education in 1992. The issue is NOT whether calculus should be taught in highschool. Almost any approach allows for that possibility.

It is unfortunate that you were unable to attend Wayne Bishop's lecture-discussion MATHEMATICS EDUCATION IN THE EIGHTIES AND NINETIES (IN K-12). Dr. Bishop is a former member of the Mathematics Task Force and the Advisory Panel to the California State Commission on Teacher Credentialing, formed by [Formerly of the State Assembly, now ...] State Superintendent Delaine Easton. He is an expert on the Framework and is well-informed about research in mathematics pedagogy. He is also extremely critical of the "fuzzy math" advocated by the California Framework. You may wish to invite him to speak again since mathematics pedagogy is a central issue in the national press and an important matter for CSUN. I include a copy of his abstract at the very end of this message.

Short of re-inviting Bishop to campus, or in addtion, you can get a pretty good idea of what the Framework says and the damage it has caused in our public schools by reading some of the documents, reports, and summaries provided in the following web site address:

  Mathematically Correct: "2 + 2 = 4"
  http://ourworld.compuserve.com:80/homepages/mathman/

  HOLD (Palo Alto Group opposed to Calif. Math. Framework)
  http://www.rahul.net/dehnbase/hold/

  Report of the LONDON MATHEMATICAL SOCIETY,
  Critique of Current Math Pedagogy
  http://www.qmw.ac.uk/~lms/tackling/report.html

I will try to briefly summarize the shortcomings of the Framework. The 1992 Mathematics Framework for California Public Schools governs, to a considerable extent, the mathematics curriculum in California's public schools. It is a prescription for mediocrity. The Framework recommends that calculators be issued to kindergartners and used in all K-12 grades; it strongly discourages placing students by ability or achievement; it advocates that teachers do more "facilitating" and less "teaching;" it discourages testing, and promotes portfolios, "authentic assessment," and "holistic scoring rubrics;" it de-emphasizes basic skills and promotes "cooperative work" over individual responsibility. In short, it is the "bible" of "fuzzy math."

An alternative to the Framework was presented at the recent National Council of Mathematics Teachers in San Diego. I will forward that to you after I send this message. If anyone else on this list wants a copy, let me know.

[Editor's note: This document, actually presented on the Mathematically Correct web site, is A PROGRAM for RAISING the LEVEL of STUDENT ACHIEVEMENT in SECONDARY SCHOOL MATHEMATICS]

There is a down-side to this. The little testing data that has been released has been either badly flawed in its interpretation or quite discouraging. Our state's falling NAEP scores correlate with increased implementation of the methods while in the past decade enough states have implemented aspects of a competing "back-to-basics" philosophy to have successfully reversed the national trend downward. Many private schools here in Southern California follow curricula and teaching strategies that are in direct conflict with the constructivist philosophy and have standardized test results and college admission numbers that support their choice. My contribution has been to follow publicly released claims of objectively measured success of implementations of constructivist programs to their source. Misinterpretation or misrepresentation of the data has been the outcome of each and every pursuit in which the researchers were willing to respond to my request for supporting information. Some have been worthy of open derision; either the researchers were incompetent or they were lying. The most common response to requests for information about an educational experiment (i.e., the testing instruments used, the presence of control groups, the size of the population being studied, etc.) is no response at all. School districts that are considering curricular adoptions and colleges and universities that are training teachers of mathematics should be aware of the nature of the supporting data-based research and not simply the tons of chauvinistic literature.

Mark Schilling: "Fuzzy math" is a pejorative term used by opponents of mathematics reform to condemn any deviation from traditional methods and traditional subjects (e.g. statistics and discrete mathematics, fields that are not essential as preparation for calculus, are considered "inappropriate" areas for the secondary school curriculum).

I believe that Dr. Marchisotto's original memo accurately reported the activities and sentiments of those who attended. Many of the High School teachers did indeed express several statements of dissatisfaction with the California Framework, which should certainly be taken seriously given their firsthand knowledge of the effectiveness of these methods to date.

However, there was no call to simply go back to the "good old days", when, as you indicate, students have always had great difficulty with mathematics--particularly mathematical concepts, as opposed to drills. Most high school math teachers, for example, seem to accept the reality that calculators are now a permanently entrenched component of mathematical problem solving, approve of their use in at least the higher level courses, and are interested in learning how to use calculators to promote and enhance learning rather than to replace it.

Mathematics reform is inevitable, in my opinion, and it is equally inevitable that significant missteps will be made along the way. Most of our math faculty, I believe, realize and accept this. What is bothersome is that while the voices of the traditionalists are shrill and unyielding in condemning reform, they offer nothing in its place to improve the learning of mathematics by our young people.

Rajden Babayan: It seems that Mr. David Klein has forgotten to include the most important part of the Mathematics Framwork published by the California Department of Education, and that is:

"The framwork is a guideline provided by the State for local districts; therefore no legal requirement that a district must comply with them. The decision to generally follow this framework rests entirely with the school districts".

David Klein I am compelled to respond again to Provost Kennedy, to Rajden Babayan, and to Mark Schilling's mis-information and innuendo.

Schilling wrote,

"What is bothersome is that while the voices of the traditionalists are shrill and unyielding in condemning reform, they offer nothing in its place to improve the learning of mathematics by our young people."

This is sarcastic and false. It also follows a sexist tradition of using the term "shrill" to denigrate an opponent. It slanders women directly and attempts to "reduce" men to the status of women. This kind of language is what I would call "traditionalist." I don't know what Schilling means by "traditionalist." There are now so many traditions in mathematics pedagogy, that it is hard to keep track.

As to the issue, Schilling does not acknowledge alternatives proposed to the California Framework. In my message, I wrote,

"An alternative to the Framework was presented at the recent National Council of Mathematics Teachers in San Diego. I will forward that to you after I send this message. If anyone else on this list wants a copy, let me know."

The "shrill" signatories to this alternative include among many others:

Professor Frank B. Allen
Former President, National Council of Teachers of Mathematics

Henry L. Alder
Former President of the Mathematical Association of America

Gunnar Carlsson
Professor and Chair, Department of Mathematics
Stanford University

Leonard Gillman
Former President, Mathematical Association of America

Ze'ev Wurman
Director of Software, Dyna Logic Corporation

Also included in my message was the abstract of the talk given by Wayne Bishop. In it, Bishop refers to a "back to basics" approach which has resulted in better performance than the fuzzy math Calif. Framework approach.

I note that Schilling did not attend Bishop's talk.

I wonder if Schilling would mind if I forwarded his message to some of the aforementioned "shrill traditionalists."

In a subsequent message, Rajden Babayan quoted,

The framework is a guideline provided by the State for local districts; therefore no legal requirement that a district must comply with them. The decision to generally follow this framework rests entirely with the school districts.

This is indeed the case. It is nevertheless true that the Framework exerts enormous influence on the way mathematics is taught in California. By way of analogy, the use of "Whole Language Learning" is also up to the school districts. But political and careerists pressures have resulted in its widespread use, at the expense of California's children (including my own).

I remind Kennedy, Schilling, and Babayan that the XYZ High School teachers animatedly criticized fuzzy math. It was they, and not me, who criticized the use of calculators in the classroom. It was the XYZ High School teachers who pointed out that they are unable to buy new copies of the traditional math textbooks because of the influence of the Framework. It is the XYZ High School teachers who re-bind these traditional textbooks. Perhaps Schilling should direct his sharp criticisms to the XYZ High School teachers themselves.

Perhaps, also, Schilling and Provost Kennedy should explain to XYZ High School, in the aftermath of their spectacular national performance, that they are too focused on "calculus based" mathematics.

Dan Hart: On the issue of Mr. Schilling's attack:

Schilling wrote:

"What is bothersome is that while the voices of the traditionalists are shrill and unyielding in condemning reform, they offer nothing in its place to improve the learning of mathematics by our young people."

That's an awesomely false statement. In no way, do I, or any teacher I respect hope to maintain the status quo. As the only high school in LAUSD using the Saxon series, we do believe in using some of the new materials given the students have mastered the requisite basics.

For example, using a graphics calculator to investigate the behavior of linear equations is fine, given the student has totally mastered graphing lines by hand. Enrichment means nothing without the basics.

As with the whole language debate, most would recommend the use of good literature AFTER the child has mastered basic decoding skills using phonics.

And, perhaps, dwarfing the curricular issue is the issue of student motivation. No one can learn who doesn't STUDY!! No matter how enjoyable or wonderful ones lesson on linear equations might be, there will be no learning unless the child studies.

Therefore, it's imperative we implement real standards with both positive and negative consequences. And the most devastating philosophy of groups like the NCTM is the overt politicization of pedagogy issues. They emphatically denounce the use of any standardized testing to help motivate our children to take responsibility for their own education.

We are faced with a situation in LAUSD where a student can fail 80% of their middle school classes and still be promoted to high school. Then these unfortunate victims of our standardless system (thanks to the PC cognoscenti), drop out of school, innumerate and illiterate, once they reach high school. It's a pitiful daily tragedy that must end.

But, of course, the NCTM tells us it can all be cured with improved math pedagogy. And to be sure, the Titanic would have refloated if they'd poured a better brand of cognac!!

Michael Neubauer: Dan Hart's glib attempt at equating mathematics pedagogy with the Titanic's refloating by pouring better cognac does absolutely nothing to further the debate. As mathematics teachers we have in general earned advanced degrees in mathematics, at CSUN most of us have Ph.D.'s, and we are more than qualified to teach the subject material of all courses we are asked to teach. This DOES NOT make us experts at the pedagogy of teaching mathematics or teaching in general. Most have sat through pretty awful lectures by some of our colleagues that lacked almost everything you'd expect from a presentation. Even the most outstanding mathematician are not always good at teaching mathematics. This is a fact that is readily established. What is lacking then? I think that as mathematicians we should pay MORE not less attention to what educators, cognitive scientists and others have to say about learning and, in return, teaching. It all starts with the student! If we don't understand what is going on how students learn we have little hope of doing the best possible job at teaching them. My training in no way prepared me for this challenge and it is something I have tried to learn about on my own and from my colleagues. Let's listen to educators and cognitive scientists and mesh it with our own experiences in the classroom. We also have to avoid the obvious fallacy of generalizing from our own experience in high school and college to that of the experience of the general population of students attending college in any generation. We, as holders of advanced degrees in mathematics, are the exception! What worked for us CANNOT and SHOULD NOT be made a model for teaching mathematics. We can ill afford to teach our beautiful, important and relevant subject to just the top, say 5%, of our students. I would bet that all of us would have succeeded in almost any teaching environment. So let's find a better way of teaching mathematics for 100% of the students. I am 100% behind such an effort. Some mistakes will be made along the way and we should monitor what is happening. Not going forward is not an option though.

Not letting students use the calculator is also a suggestion that just doesn't work. Students already have calculators! If we don't let them use it we loose credibility. A calculator is a tool and we all know this and we all know that a calculator can't replace mathematical knowledge. If the calculator is perceived as such a threat to mathematics instruction then we have been teaching what I wouldn't call mathematics. In my experience I do not have to make a big deal out of calculators. They are allowed in all classes without restriction. In return I make sure that students cannot earn credit by knowing only how to push buttons. This requires some effort on my part and is not as hard as it seems at first. Magnhild Lien has presented her experiences on this issue at the last "MATH MORSEL" seminar. It seems to work for her as well. The mathematics department has recently opened a wonderful computer lab. I want students to use it, not prohibit them from using it. I have taught a computer assisted linear algebra course and have been able to save much time in class usually spent on computations which I was able to spend on presenting more material in class. In addition, it put the fun of exploration and discovery back into the classroom that is lost so often in traditional instruction. On a smaller scale, the calculator can provide the same experience.

It is clear that neither an improved teaching pedagogy and the use of technology will solve all the problems facing education. The issues are myriad and tie in very strongly with societal forces at work. As a CSUN teacher I have to work on those changes within my realm of influence and I think that some form of reform is needed, in a lot of places already happening and ultimately inevitable everywhere.

Dan Hart: On the issue of poor pedagogy, I hardly think professors of mathematics hold any notable distinction. In fact, the worst teaching I've ever experienced was in education classes at the "graduate" level! (Not all to be sure.) By comparison, you guys with Phd's in math have nothing to feel bad about.

On the issue of calculators, I've said they have a place given the students know what the heck they're to do with them.

Last Thursday, we gave the Calculus AP exam to forty SFHS students. As you might know, graphics calculators are now mandatory for about 2/3 of the test. I don't have a big problem with that. If one is diligent, one can interwine the traditional curriculum with the use of these powerful tools. Fortunately, The College Board hasn't gone soft and the test is actually harder than it was pre-calculators days (to coin a phrase).

My main point was one of real standards with real consequences which you ignored. The point about the AP exam is what Escalante understood. External standards put the teacher and students on the same side of the fence. With the AP, I work with my students to help them achieve a standard that is understood by all in a very specific course syllabus.

I propose this to make a significant improvement in all subject areas:

• 1) Set very specific content area standards to be achieved by certain grades.
• 2) Devise standardized tests and other assessments which are accessible to different teaching techniques. (The AP exam is certainly accessible to different teaching and learning styles).
• 3) Institute the largest PR campaign in the history of our state to implore parents to turn off the TV's, sit down with their kids, and do what everyone knows is necessary to produce a successful student.
• 4) Tie consequences to a student's performance. Give meaningful alternatives to those not willing or able to master a college prep curriculum. Every kid by high school should have a specific concrete goal with exams to take and pass before receiving their certificates. Even the poorest student can have an achievable career goal that will help keep this kid off the streets and on the books. Kids with goals have hope.
• 5) Make teachers more accountable for their students' performance. You don't want teachers spending too much time teaching to an exam (although there are worse things if the kids are learning.) But the AP test is fairly resistant to this type of thing. Give us similar exams for all the subjects.
• 6) Institute mandatory summer and off-track remedial sessions for those students not passing minimal competency exams. (BTW, they're doing this in NYC.)
• 7) Correlate student performance to pedagogy and curricula. If the NCTM thinks they have a better way, this will be their opportunity to demonstrate it. Then we'll finally know what works.

Professor, you may or may not have taught K-12. I've never taught college so I won't presume to know as much as you. But you might not have an idea of how profoundly wrong things are for many of our kids (we also have a decent percentage doing fine.)

Until you've had the misfortune of trying to teach a kid algebra, any algebra, who doesn't know his multiplication tables, can't tell you what one half of one half is to save his life, shows up three to four days per week even if he likes your class, and hasn't the slightest idea of what his future economic competitors are doing overseas, then you haven't lived.

We are losing one-third to one-half of our kids. Is this because of bad pedagogy entirely? Believe me when I tell you this. I was a participant and mentor teacher in the California Math Project. I still use probably 20 different resources besides our Saxon texts (which work better than anything we've used) from the use of TI-82's, to programming with LOGO, to cooperative learning projects from EQUALS in Berkeley. All of this is quite fine.

However, until we connect students' academic work to their future as it's done all over the world, we will see no significant improvement in the mess we find ourselves in.

Dan Hart:

We can ill afford to teach our beautiful, important and relevant subject to just the top, say 5%, of our students. I would bet that all of us would have succeeded in almost any teaching environment.

Respectfully, professor, don't be so sure. I have heard often that students with high math ability are totally frustrated by the new new math. I spoke with students using the IMP (Interactive Math Program, a crown jewel of the high school reform movement) and there seemed to be a high disdain of the program, because they felt they weren't getting the good stuff.

In addition, I've heard teacher after teacher admit that much of the new stuff is too easy for top students. There is an overemphasis on cooperative learning and for the top student this can become a very draining, frustrating process. Cooperative learning as a means of improving individual student achievement is fine in moderation. Overusing it, to diminish individual accomplishment and to social engineer is immoral in my opinion.

So let's find a better way of teaching mathematics for 100% of the students.

I'd say John Saxon has gone some way in this regard. His process of incremental development with continuous review allows students to learn horizontally over time rather than vertically all at once. Obviously, I have no problem with supplementing the books when the time is right.

But, more importantly, the motivation issue is key. Countries with higher standards don't have this self defeating math phobia most Americans seem to revel in.

Some mistakes will be made along the way and we should monitor what is happening.

Did you happen to read the piece on whole language in the "LA Weekly"? I can send you a copy. It is an appalling story of a whole generation of kids whose reading skills have been held at risk on the educational whim of a few "reformers". I heard Bill Honig, the ringmaster of whole language, in the '80's last week on KFI. He admitted the error made with whole language and now he's doing his best to turn things around. We should listen to him and look for proof of the claims of the radical reformers. I'm only asking for a fair competition in the marketplace of ideas. Let's follow my simple program outlined in the previous post, give everyone an opportunity to compete, then see what works in a system where our kids are working somewhere near full effort.

Yes, mistakes will be made "along the way". And they can be as profound as a tornado hitting town. Let's be very careful. Last week at the NCTM conference, I looked at some of the elementary materials, in particular something called "Mathland". It's really bad stuff, in my opinion. Not so much that there's anything mathematically bad about it, but because there is no course of systematic practice. And I don't care what it is, if you don't practice it, you won't retain a thing.

Add to that the mathematical ability of most elementary teachers and we are looking at an impending disaster. We're already seeing it at the high school level since our feeder middle schools are very reform minded. Entering students know less than they ever have (and since I do a lot of the new stuff as a supplement, I can recognize any profound learning hiding in the recesses). I believe the teachers at XYZ High School stated the same thing in your meeting.

And that's about what I know. Thank you.

Jerry Rosen: I resented the tone of Provost Kennedy's initial message and Mark's response is a classic example of how math educators and their supporters stack the deck in their favor.

The Provost states (and Mark seems to agree)

"Is this a new wrapping on the argument of whether math education must move always toward calculus; that indeed real math is calculus based? Please enlighten me?"

A huge amount of real math is Calculus based unless you believe the following subjects are not important:

Engineering, Physics, Computer Animation, Micro Economics, Physical Chemistry, Theoretical Computer Science, Medical research, the myriad of industrial applications of calculus , not to mention Mathematics.

Great care should be taken before entire fields of mathematics are denigrated. I would hope the Provost's opinions are not based on her previous exposure to mathematics.

I find it unusual that the Provost would concern herself with local struggles, but I guess she (correctly) believes these are important issues. However, I believe it would be in the best interests of our students if she sided with the group advocating higher standards, not lower them as she seems to be doing.

Before I answer Mark's comments I want to establish my credentials in this debate.

Unlike Mark or one of our leading math educators (who claimed math 210 and 310 "are not my specialty") I have taught math 210 (math for prospective K-8 teachers) many times during the past three years. My wife and colleague Mary Rosen also teaches these classes regularly. We started teaching in this program for two reasons

• (1) we deeply care about the math education of prospective teachers and
• (2) getting mainstream people to teach the course has been quite difficult. The course had been staffed mainly by part time faculty - who have done an exceptional and thankless job. However, it is vital that regular faculty teach some sections of this course

I am also a member of a national mathed email group. This is a diverse group which includes world leading researchers, college teachers, high school teachers, people in the non academic sector and math educators who work in academia as well as for NSF and NCTM. The group has participants who are supporters of the Standards as well as many who are critical of the Standards. Two members of the email group, who are the most outspoken opponents of the Standards, the Framework and most Reform efforts are Richard Askey the John Bascom Professor of Mathematics at the University of Wisconsin, Madison and George Andrews the Evan Pugh Professor of Mathematics at Penn State University and the Chairman of the Mathematics Department. Askey and Andrews have spoken and written about the terrible consequences of the current math education fads.

I will now discuss Mark's message

Mark states

However, there was no call to simply go back to the "good old days", when, as you indicate, students have always had great difficulty with mathematics--particularly mathematical concepts, as opposed to drills.

Mark is constructing a straw man. This is a common technique used by math educators. They put the blame where they want it - on the "good old days" - he really means the "bad old days" - (and not where it truly is) and attack this hypothetical construct.

I will now provide a comprehensive analysis of some educational issues which indicates some of the root causes of the problems K-12 students have learning mathematics.

Mark states that teaching by drill alone is bad, this is true, but none of the responsible critics of the mathematics program proposed by the California Framework or the NCTM Standards proposes that mathematics should be taught just as drill work. There were problems, but the most likely cause was mentioned by G. Leinhardt of the Research and Development Center at the Univ. of Pittsburgh when she wrote that the average elementary school teacher is comfortable with mathematics through about fourth grade mathematics.

It is vital that prospective K-8 teachers learn algebra before starting to teach in elementary school. Part of algebra is just generalized arithmetic, and teachers need to know what their students will study next so they can be sure that their method of teaching something will help pave the way to future courses the students will take. Also, there have been recommendations that some algebra be taught in elementary school as it is in most developed countries.

Since fourth grade mathematics comes before the real introduction of fractions, it is not surprising that teachers who teach the preliminary material on fractions do it too formally, for they often do not understand why things work as they do, and so can only teach rules. You can not teach the understanding of something which you do not yourself understand.

The solution is not to throw out the development of fractions, and division, and other technical skills that are needed for further development later in school, but to make sure the text books do a good job of developing this mathematics, and to do all we can to make sure the teachers understand what they are trying to teach. This was not done in the past, and is not being done now. In the April issue of "Mathematics Teacher", the magazine published by NCTM for high school teachers, there was an article on using a graphing calculator to teach how to divide two rational functions. In the course of this article, the teacher said the students did not know how to divide two fractions, but that after working with their calculators the students knew why the rule works. That is clear nonsense. The rules work not because of what shows up on a computer screen, but because of mathematical reasons which should have been explained and learned in elementary school. In Japanese text books, this is explained very well, and problems to illustrate it are given. Some are calculations, other come from story problems. Both are necessary.

Most of our high school teachers would not make the error made in the article in Mathematics Teacher, but this article was written by a high school teacher and published in a magazine which has a high rejection rate, so the editor of Mathematics Teacher must have felt that this was important for teachers to read. The article started with the statement that it was important to see how to introduce technology into the mathematics classroom. I thought the point of mathematics classes was to teach mathematics, and that technology was to be used at times to further this goal, not as a goal in and of itself.

According to Richard Askey

The current Japanese National Curriculum recommends occasional use of calculators starting in fifth grade, but that the current series of books I have does not have an illustration of a calculator until the seventh grade, and through eighth grade there is essentially no use of them in the text books. Geoffrey Howson remarked on this absence in his new book, "Mathematics Textbooks: A Comparative Study of Grade 8 Texts", written to describe some eighth grade texts from different countries in connection with the Third International Mathematics and Science Study. The results on the national mathematics exams for 11 year olds in England last year were so poor that calculators will not be allowed on one of the two mathematics exams this year.

I have encountered unbelievable things in teaching 210. A number of these students do not know basic arithmetic. I have seen students who didn't know that 1/2 and 50% were the same. On many occasions some of these students have told me they learned arithmetic on the calculator. The course makes a good attempt to bring these students up to sixth grade level . Although a number of them do excel and will be good math teachers, there are many, who I believe, are not qualified to teach math to elementary school children. This is not the fault of our teachers or the program, it is the fault of the nationally mandated NCTM Standards and their local corollaries, such as the Framework. It is difficult for the 210/310 classes to make up for the deficits the students have when they start

Mark continues with

Most high school math teachers, for example, seem to accept the reality that calculators are now a permanently entrenched component of mathematical problem solving, approve of their use in at least the higher level courses, and are interested in learning how to use calculators to promote and enhance learning rather than to replace it.

What high school math teachers "seem to accept" is irrelevant (by the way, why does he say "seem"? If he doesn't know then he should say "one possibility is ..." That would be more honest and true. Again, we see how the fact that math (dis)educators and their supporters are forced to qualify things because they base policy on how they feel). History has shown time and time again (unless you want to reform history and just talk about politically correct issues) that huge groups of people can be convinced of anything. If in fact HS math teachers are "accepting" calculators it is due to pressure from college teachers like Mark, their own school administrators (who have been seduced by the electronics industry) and their own fear of real math, at the expense of their students.

If an 11th or 12th grader was solid on arithmetic, algebra and trigonometry then the Calculator may be of some use. But to use the calculator to teach trigonometry and graphing has been a failure. I have 90 students this semester and most used calculators in high school and/or pre calculus. I don't have one student who has gotten a grade higher than a C this semester. Dave Protas told me his averages in 103 have been around 40% (and he is an acknowledged excellent teacher). When I first started teaching here my mean grade in Calculus was 20 points higher and those students were not educated with calculators.

The fact is that the Framework advocates that very young children should learn arithmetic with Calculators. Is Mark aware of that? Has he read the Framework? Has he looked at any of the Web sites David listed? Here are a few specific facts concerning the Framework.

There was an article in the Santa Cruz Sentinel written by Harvey Soloman who is a math teacher in a HS. The article is entitled "Don't toss out the 'old' math yet.

The article condemns the California math Framework. Soloman states

The state college system is beginning to receive the fallout from the Framework implementation. From 1989 to 1993 the percentage of new students failing the math assessment test rose from 28 percent to 47 percent. At San Jose State, 17 percent failed the test in 1991 while 41 percent failed in 1995.

No wonder many math educators are against standardized tests!!

Solomon states

Districts and politicians are beginning to respond to the Framework's shortcomings. For example, Orange Glen High school in Escondido just announced it is dropping a Framework program and reinstating the traditional sequence. Chairman Steve Baldwin, Assembly Education Committee, said recently, "there is a serious question whether or not California should proceed with the . . . Framework. Preliminary research indicates that there are serious problems with the 'constructivist' approach which we believe is contributing to declining math SAT scores in districts that utilize this approach."

Richard Askey mentioned talking to the head of a state grant agency which gives out Federal support for mathematics and science education projects. He was told that the year before every proposal was sent back to be rewritten, since they all focused on technology as technology without mathematical reasons why the technology was being proposed. The mathematical ideas needed to be the main focus, and they were missing. She also told him that she was sending her daughter to after-school mathematics classes, Japanese mathematics. He replied that this was probably "Kumon" mathematics, and she said yes. He said that this was not the secret of good mathematics education which exists in Japan, but was focused on rapid and accurate calculation. She said she knew this, but her daughter needed to learn how to compute somewhere, and she was not being taught in school.

Askey has recently been told by a colleague of his, who came from Japan, that there is an after-school Kumon Mathematics class in Madison, where he lives, and it exists for the same reason. There has been far too much emphasis on the use of calculators in elementary schools, and it comes from the text books as well as the California Framework. For example, in the Addison-Wesley series, which has John Dossey as one of its advisors, the first two years when repeating decimals are discussed, they are only done with a calculator. Never do these books mention why repeating decimals come from fractions, since there are only finitely many possible remainders, so they must repeat. John Dossey was president of NCTM when the committees which wrote the Standards were appointed. The texts in question regularly state how they correspond to the NCTM Standards.

The London Mathematical Society was asked to do a comprehensive study of current educational problems and the use of calculators and computers for teaching. They condemned the over use of machines and did studies showing how the use of machines by students caused lowering of mathematics ability of school children The British were at least five years ahead of us in their changes, and the results that mathematicians had predicted occurred.

I would be glad to send a copy of this report to the President and the Provost.

In Australia there was a huge mobilization against math education practices very similar to those our math educators have proposed and instituted. I am in contact with an Australian Mathematician, Garth Gaurdy, who was one of the leaders in the fight. They got 750 mathematicians to sign a petition condemning what has been called "fuzzy" math here. Recently the Prime Minister said on National TV that he agreed and mandated that Australian schools stop watering down the curricula and return to teaching fundamental skills needed by all children. Here are some quotes from Gaurdy which you may find interesting:

We have been having problems in Australia very similar to he ones which you outline . . It seems that a disease is sweeping the Western World, particularly the English-speaking part. I conducted an outspoken campaign in the press and TV in Sydney about the proposed new Years 9-10 Advanced Mathematics course for NSW. I am pleased to say that the Sydney Morning Herald, and, to a lesser extent, the XYZ and SBS TV channels, supported me strongly. The proposed syllabus did away with what I understand to be mathematics, and replaced it by button pressing on calculators, cutting up paper etc. No concepts. Lots of misconceptions masquerading as relevance, etc. Fortunately, my campaign succeeded, even to the extent of it becoming a front-line election issue in the recent State election. There has been a change of government from Liberal(conservative) to Labor. The new Premier has been outspokenly critical of developments in curricula. He is an intellectual (historian by original training), and approached me for advice some time ago. He and I share the view that good quality education is an essential ingredient of social progress and personal advancement.

The US context is quite different, I realize. We have an advantage of sorts in that the State Government mandates curriculum. Nevertheless, I am utterly convinced that professional mathematicians can regain some of the ground which we have lost over the years to the education gurus, in each of our countries. Is there any such initiative in the US? Here, the professional mathematicians have been very united.

Mark ends with

Mathematics reform is inevitable, in my opinion, and it is equally inevitable that significant missteps will be made along the way. Most of our math faculty, I believe, realize and accept this. What is bothersome is that while the voices of the traditionalists are shrill and unyielding in condemning reform, they offer nothing in its place to improve the learning of mathematics by our young people.

Have the would be reformers and (dis)educators made any "significant missteps" yet? Reformers like Mark, defend every misstep and resent anyone with the integrity to improve mathematics education beyond the low standards advocated by the Framework.

The first thing which must be reformed (and this isn't a joke) is all the garbage which has been passed off as reform.

In Mark's reform program statistics would play a leading role.

Is it a coincidence that Mark is a statistician? Is there a conflict of interest?

When I was in HS we did learn a little discrete math and this was good. Permutations and combinations used to play an important role in HS algebra along with the binomial theorem. There is little of this now and should be more.

But why in God's name would we want to teach statistics to students who can barely add and know very little algebra and no trigonometry? One of our math education colleagues provided an answer to this at one of the teas when they said one good thing about statistics is that "it can be taught without algebra". Perhaps some people would be happy if most of our math majors were in the Statistics Option.

Well I have some very bad news for you, courtesy of Mark.

Mark invited a speaker last semester who is a statistician who works for the government. Unfortunately most of the department didn't show up (there were quite a few students there). Klein and I were there. The speaker at one point put a graph on the screen which showed that the use of statistics has increased exponentially since 1960. On another graph the speaker showed that the use of statisticians in the nonacademic sector has increased linearly with a slope barely greater than zero.

This is all very simple. The people who Mark are talking about when he refers to traditionalists believe that like most academic disciplines mathematics is hierarchical. Most useful math topics depend on preceding ones. This isn't reactionary, this is every day life. Almost everything we ever learned is predicated on this principle. The would be reformers are the true reactionaries. They seek to deny knowledge and their solution is to "dumb down". One of our colleagues stated, while discussing the Harvard text in the mailroom:

We have inferior students and we must teach them in an inferior manner.

I would rather not say who said this for it pains me to think that one of my colleagues would feel this way. I know that many of the reform supporters don't believe this, but that is what is happening in too many cases.

Mark is dead wrong when he said we have nothing to offer.

Did Mark read David's message? Klein wrote

An alternative to the Framework was presented at the recent National Council of Mathematics Teachers in San Diego. I will forward that to you after I send this message. If anyone else on this list wants a copy, let me know.

Did Mark bother to read the Frank Allen memo concerning the Standards? Is he aware of the fact that there have been a number of alternatives proposed to the Framework? For example he and the Provost should visit the HOLD web site. It is clear that Mark, the Provost and Michael Neubauer have not taken the time to familiarize themselves with most of the issues and information available concerning this enormously important debate. I guess they feel comfortable making statements based on a "gut" feeling.

I am certainly willing to "put my money where my mouth is". I would be glad to head up a committee to make concrete recommendations to the President and Provost for improving math education at CSUN. I know of others who would be glad to serve. I have learned interesting and useful information concerning math education issues and have a number of valuable contacts around the country.

I urge the President and the Provost to consider this recommendation. I believe that, as in the case of Whole Language Learning (which I discuss below), the Framework will soon be exposed as highly detrimental to math education in the state. If CSUN makes this assessment before others, we can take the lead in suggesting true innovations and reforms. This would certainly have several benefits for our institution.

Before ending I want to mention the Whole Language Learning (WLL) fiasco. The reason being that the analogy with the Framework is quite good. Also, all the education experts who participate in the math education debate have been unusually silent on this issue.

WLL was an attempt to do away with traditional methods of teaching reading in an attempt to raise reading levels. There was no scientific basis for the proposal. The educators who proposed WLL had a feeling they knew what was wrong with the traditional method and created WLL. The end results have been devastating. When the story first broke, the LA Times reported that as a result of WLL 60% of the 4th graders in the state could not read at basic levels.

This past Saturday an article in the LA Times appeared which was a follow up to the original articles on WLL.

The article claims that Whole Language Learning was responding to the perception ....

... that many kids were bored with drills, hated reading and could not discuss the meaning of stories. To fix things, the state's reading experts declared that repetitive exercises would be discouraged in favor of the best children's literature. They urged teachers to engage their students in thoughtful discussions of values and to downplay "mechanical" skills ...

But in emphasizing those elements, the state failed to tell teachers that it was also essential to explicitly teach children about letters, sounds, syllables and other building blocks of language. . .

Stung by reading test scores that have made them the butt of jokes on late night television shows, California educators have been working for the past year to update their approach, trying to respond to widely accepted research showing that it also is essential to explicitly teach children about the building blocks of language.

Reid Lyon, who directs clinical trials in reading at 12 sites across the country for the National Institute of Child Health and Human Development, said that 13 years of research prove that unless readers can use sounds and letters to automatically identify words, they will not be able to read fluently.

"If you are a slow, labored reader, about 98% of the time, you're not going to get a thing out what you have read," Lyon said. . .

Other states, including Ohio and Texas, are mounting efforts to restore skills instruction to classrooms. Other states are sure to follow."

The article goes on to say that California will spend

... as much as $175 million to buy text books, train teachers and certify that new teachers are familiar with the latest in beginning research. Several witnesses, however, said that many new teachers are still being trained to ignore that research and that schools rarely use it to shape programs.

According to Deputy Supt. Ruth McKenna "the next step . . must be the adoption of statewide standards to measure how school districts are doing." Standards are "absolutely necessary if we are going to do the job of teaching children to read."

AMEN!!!

Current math reform (on all levels, including the Framework) are based, just like WLL, on false, unsubstantiated perceptions. All these reforms are failing just as WLL has failed. The failure of the Framework has been rapid and quite spectacular.

As in the case of WLL the math (dis)educators and their supporters will never admit they are wrong. Instead, as in the case of WLL, they will choose to sink on the a ship full of holes of their own making. Let them sink, but let's get California's children out of the ship fist.

Jerry Rosen: It was a pleasure to read your messages. It is encouraging to see there are educators on the "front line" who do not sell their student's short. It was HS math teachers such as yourself who provided me (a student not in the top 5%) with the mathematical foundation as well as the motivation to major in mathematics at another institution (Brooklyn College) which maintained high standards. The solid training that I received in HS and college were far more important to my education than anything I learned in graduate school.

In 8th grade I was truant and in danger of being leftback. I was doing poorly in all my classes (including math). My parents hired an out of work (and down on his luck) HS math teacher - Mr. Lloyd Wisoff - to tutor me in math.

The first day he came to my house he brought a copy of (I still have it with his name in it) Birkhoff and MaClane's Modern Algebra book. He said to me something like "kid, I'll have you getting A's within a month. Then you can start reading this book. You won't understand it, but you must always strive to surpass the limits which are set for you."

His method was not radical. He just got me to study on a regular basis. Once I started doing well (just like Escalante's students) the success kept me at it.

In 9th grade through 12th I never got less than an A on any math exam and I got 100% on the algebra, geometry and trig. regents.

Unfortunately I wasn't smart enough to understang Birkhoff and MaClane's book until I was a junior in college.

I will never forget what this man did for me.

I am sure many of your students have felt the same way about you.

It is really gratifying to see some integrity and common sense injected into these discussions. As you probably read from my previous long message, I belong to a national mathed email group with a large number of participants. I have read over 1000 messages since joining this group and not one of them was as insightful and memorable as your two messages.

I would like to shake your hand one day.

In my message to the President et al I left out a quote at the end of the message from the article in the Times om WLL. It should have been part of the last quote. I am sending it because I consider it to be the most important part of the entire quote.

Foorman's study used the newest version of an instructional program called Open Court. An older version of the program is used with substantial success at the Kelso and Bennett-Kew schools in the LA Unified School District and in about 25 to 35 other districts in Southern California. But because Open Court is seen as a phonics-based program, many school districts have rejected it and even prevented schools that wanted to use it from doing so.... Teachers at Kelso, which ... serves a largely poor African American and Latino population, credit the Open Court program for first- and second-grade test scores that are frequently in the 70th and 80th percentile. The school is the highest-ranking school in the district and is on par with schools serving far more affluent students in Manhattan Beach and Torrance.

My colleague Michael Neubauer states

So let's find a better way of teaching mathematics for 100% of the students. I am 100% behind such an effort.

It looks like these teacher's "found" a better way. They would be glad to know Michael is behind them 100% even though their methods violate his teaching philosophy.

It is amazing what can be accomplished when students are not sold short.

I am glad HS's are learning about topics on the ELM exam and I am tickeled pink that by the year 2007 (or whatever) the number of remedial math courses in the CSU system will be below some very small percent. I have just one tiny question

HOW IN GODS NAME IS THIS GOING TO BE ACCOMPLISHED???

Answer: With the Standards and Framework in place much fewer middle and working class students will be admitted into college.

Those of us who have 20 or more years left until retirement better think about this real carefully.

Fortunately I don't believe the President or the Provost (or almost anyone else at CSUN) wants to exclude students from getting a college education at CSUN. We all have pride in our institution and want to see it thrive.

Lets get behind well thought out policies which will give our prospective teachers the necessary skills to send us students who won't need as much (and eventually no) remediation.

Louanne Kennedy: I am responding to the tone of the exchange that followed my question and comment of last week.

I believe it is critical to the ideal of collegiality that we be able to ask questions and to disagree on topics of importance to the campus community and to our society. The issue of mathematics education has reached a critical point for our students, for the university and for our state. Students are coming to us poorly prepared for college level mathematics despite the intellectual work and pegagogy of their high school and elementary school teachers. We prepare many of these teachers. Those involved in mathematics education have different views about how we may improve math knowledge and skills.

I had hoped that our department of mathematics along with math educators in our school of education, community college teachers and K-12 teachers would be able to advance the conversation toward the best possible outcomes that would result in improved student success in mathematics. Instead, I seem to have entered a world that does not value collegiality nor the free exchange of ideas. What I find most difficult to accept and understand are the attacks on those faculty who either agreed with my concerns or at least found some merit in them. They have been treated in a manner that I find to be outside the usual standards for discourse whether in the academy or in any other social or work conversation. This is especially troublesome given the great need for working together to find solutions that can benefit students.

Whether we support traditional teaching of math or the newer California frameworks, the use of calculators, or any of the myriad other disagreements that permeate the e-mails of the past weekend, I hope we do not lose sight of the goal - the development of math competency in the young people of California and the opportunity to explore math based disciplines in their future careers. At present, what is clear is that we have not so far been able to assure this success for many students. In some cases we are successful with traditional models, in other cases with non-traditional programs; what will assuredly be unsuccessful are hostile responses between and among our math department faculty.

I will ask Bill Watkins and Interim Dean Klinedinst to try to be helpful in reducing the anger now present in the discussion. I am willing to be helpful as well. In the meantime, I would encourage more face to face interaction on this topic and an agreement that academic collegiality will be an important ingredient for finding solutions to this complex topic.

Dan Hart: Thanks for the kind words. I wish I was that kind of teacher. I think we've all had that kind of teacher and I think perhaps we've all been that kind of teacher for a few kids for perhaps a few moments. In fact, there is an article in the Daily News today about an LAUSD physics teacher at Grant HS who's been nominated for National Teacher of the Year.

At my school, we have a fellow named Richard Gigger, our band director, who's in the mold of a great teachers who really make a difference. Jaime Escalante is certainly the archetype and the unfortunate thing is when he left Garfield, his program just didn't keep going like he and Ben Jimenez had built. Garfield's AP program is still better than most and I'm sure the people who are continuing on are quite dedicated and excellent. And I'm afraid when Gigger retires, our band probably will decline (and the band is only a means to producing involved, educated kids).

Teachers will always have a profound impact on their students. Humanity will never be an unimportant part of our profession. However, this points up a problem with American education. We rely too heavily on teachers to be great at what they do. As paid employees, we owe our employers a decent day's work for a decent day's pay. And frankly, there are too many who don't fulfill that simple contract.

But for the majority of us who do; it's not enough. I don't know of any other profession which depends on excellence to produce mediocrity. We're not all Jaime Escalantes. Most of us are pluggers who need some help from the system. And we get ZERO help. It's frustrating beyond belief if you care about our future and our young people.

I was really cheered when the CSU voted to eliminate remedial classes. I thought for once help was on the way. Perhaps, it would've signaled the beginning of real standards. But, of course, the Board of Trustees capitulated. That didn't send a good message.

BTW. Get ahold of Frank Allen's proposal to improve secondary math education. It's all in there.

David Klein: Leadership requires balance and a sense of objectivity. I respectfully suggest that your last message shows neither. Moreover, you seem to show little tolerance for intellectual discourse and the competition of ideas normally associated with a university.

Your original message below was posted to most people on the email list.

I am puzzled by this addendum. What is fuzzy math? Since generations of students have had difficulty with math, what is the value of dusting off "traditional" texts. Is this a new wrapping on the argument of whether math education must move always toward calculus; that indeed real math is calculus based? Please enlighten me?

This challenged the practice of the XYZ high school teachers. Perhaps your original question should have been to them. Since you directed it instead to this group and I was the author of the referent passage [appearing in the first message from Elena Marchisotto], I responded via email to the same list. If you had wanted "face to face interaction" on this topic as you indicate in your letter, why did you not choose that method yourself?

I responded to your inquiry with what I believe to be a collegial and informative message (Thu, 9 May 1996 21:58:01 -0700 (PDT)). I include it for your easy reference at the end of this message. What if anything do you find uncollegial in that message? I would appreciate a specific response from you.

Subsequently, Mark Schilling, who you apparently agree with for unstated reasons, wrote a message which, as I indicated before, was hostile and sexist. Specifically, he wrote,

Most of our math faculty, I believe, realize and accept this. What is bothersome is that while the voices of the traditionalists are shrill and unyielding in condemning reform, they offer nothing in its place to improve the learning of mathematics by our young people.

Do you find this paragraph collegial, Provost Kennedy? Do you endorse this tone of writing? In your recent letter, you state,

I had hoped that our department of mathematics along with math educators in our school of education, community college teachers and K-12 teachers would be able to advance the conversation toward the best possible outcomes that would result in improved student success in mathematics. Instead, I SEEM TO HAVE ENTERED A WORLD THAT DOES NOT VALUE COLLEGIALITY NOR THE FREE EXCHANGE OF IDEAS. WHAT I FIND MOST DIFFICULT TO ACCEPT AND UNDERSTAND ARE THE ATTACKS ON THOSE FACULTY WHO EITHER AGREED WITH MY CONCERNS OR AT LEAST FOUND SOME MERIT IN THEM. THEY HAVE BEEN TREATED IN A MANNER THAT I FIND TO BE OUTSIDE THE USUAL STANDARDS FOR DISCOURSE WHETHER IN THE ACADEMY OR IN ANY OTHER SOCIAL OR WORK CONVERSATION. [my capitalization]

This to me indicates that you agree with Schilling and disagree with me, Hart, and Rosen. Your condemnation in the above paragraph is solely directed toward the latter three and yet Schilling was the first to initiate insults. Can you explain this? Do you approve of Schilling's tone, even though he agrees with you?

After Dan Hart wrote his insightful response to Schilling's message, Neubauer sent in a note which began,

Dan Hart's glib attempt at equating mathematics pedagogy with the Titanic's refloating by pouring better cognac does absolutely nothing to further the debate. As mathematics teachers we have in general earned advanced degrees in mathematics, at CSUN most of us have Ph.D.'s, and we are more than qualified to teach the subject material of all courses we are asked to teach.

Do you find this acceptably collegial? Would you like one of your statements referred to as a "glib attempt." If I were less gentle, I could easily and credibly describe your original question in such terms.

Perhaps most disconcerting is your Orwellian statement, "I SEEM TO HAVE ENTERED A WORLD THAT DOES NOT VALUE COLLEGIALITY NOR THE FREE EXCHANGE OF IDEAS" [my capitalization]" The exchange was free enough, but the data, the force of argument, and the logic did not support your opinions. Thus, it is not a "free exchange."

I suggest you call upon all parties to honor each other with collegial communications, not just those who disagree with your views.

Barnabas Hughes: Let me suggest that we maintain a clear distinction between "the teaching of mathematics" and "the mathematics that is taught." This distinction is not the same as that between "those who teach mathematics" and "mathematicians." While the former distinction accepts two disjoint sets, the latter distinction recognizes two sets that clearly intersect.

Wayne Bishop: David has been passing along some of the messages of the CSUN edition of the national math ed controversy that is belatedly following the Whole Language controversy both in its imposition and in its eventual demise. The reports of its death are, following tradition of course, premature but it is only a matter of time. In exactly the same way that Whole Language (in the absence of actually teaching kids to read, not decent age-appropriate reading) is now being proved to be the industry lie that it has always been, people will start to demand that a performance (and I do not mean "performance" as redefined by the education industry) component be involved in the evaluation and recommendation of mathematics curricula and instructional methodology. The necessity to "kill all the messengers" (eliminate standardized tests of quantitative reasoning) in order to avoid the message is only now coming to light. We can thank the reading folk for breaking the ice but math is right behind. That message is that kids have not been learning better under the reform movement that has been underway for the last decade or two; in fact, (hard as it is to believe) they have been learning less, sometimes much less, than in well run traditional programs that were described as the ideal before and occasionally still exist (My daughter is in one that is better now than it was a decade ago when her brother was there. He is working on his PhD in chemistry at Princeton).

One oft-quoted idea in your message caused me to jump out off the sidelines and into the fray:

We can ill afford to teach our beautiful, important and relevant subject to just the top, say 5%, of our students. I would bet that all of us would have succeeded in almost any teaching environment.

The fact of the matter is that we are not close teaching our beautiful, important and relevant subject to the top 5% in our poorer ethnic communities. Probably not the top 1%. In the last year for which data has been released, 205 of the 220 Afro-American freshman enrollees to CSUN failed the ELM. That is, 93% were incompetent at the intermediate algebra level at the end of high school and that number has been rapidly climbing along with that of all other subgroups of incoming students. Obviously, it won't climb much more. There is outrageous unintended racism involved in assuming that bright kids learn deep concepts without an excellent educational environment. Of course, it is true for a minuscule subset; almost anything is. If it were true generally, however, the logical extension would be that Afro-American and Hispanic students simply don't have the intellectual capacity to suceed in our beautiful, important and relevant subject. That is exactly the David Duke conclusion that much of society makes. The fact of the matter is, most have never been in a learning environment where the bulk of the students were taught appropriately. The modus operandi is to pass them through the grades (as Dan Hart says, failing 80% of middle school courses but on to high school anyway with a well taught "what, me worry?" attitude), never having had to develop decent study habits, and we are ecstatic if they don't drop out. Who cares if they haven't learned anything? Our universities will find a way to admit them and to pretend that they have become students. The thought of a math based major would be laughable if it were not so tragic.

These 220 represent the TOP students, at least beyond the 600-700 in the state who qualified for regular UC admission. Most don't apply. Some can't even read the application. That number should be at least ten times as high but it will not change if we just do more of the same; worse, mandate curricula (CPM and IMP come to mind, or Mathland early in the grades) that avoid even the appearance of mathematics content mastery. That is the most important strength of the CCRI. Although, our universities will decry its racism, the insidious racism of the status quo is profoundly worse.

So let's find a better way of teaching mathematics for 100% of the students.

Provided you are not including the learning disabled, we already do have one and always have had. Of my daughter's class, 100% will have successfully completed Algebra 1 by the end of their freshman high school year and most by the end of eighth; some by seventh. All will take enough additional math and do well enough to pass the CSU Entry Level Math exam. Over 80%, and probably more than 90%, will have SAT scores that will waive it. Ames, IA, has had a full decade in which their 11th grade ITED (Iowa Tests of Educational Development) lowest math SUBscore was the 96th percentile and the last two years it has been the 98th. These are traditional programs that are not the charicature that is presented by the math ed reformers. These programs do open doors for kids, doors that by nature have mathematics locks on them, and it has been proven. Show me comparable data on ANY of the new reform movement programs and I'll subject myself to your choice of public humiliation (within limits of decency, of course).

Throwing such out, in the absence of proof of something better, should warrant someone's dismissal. Instead, it is probably good for an educational enhancement grant in the millions.

Rajden Babayan: If the pros and cons of using calculator in high schools are argued without using statistical inferences, the arguments will be worthless. After all, statistics is not combination and permutation only.

Consider two groups of students in a high school, group A and Group B, who are taking algebra. Suppose group A students are permitted to use calculator whereas group B students are not. Suppose their final exam results indicate an average of 82% for group A and 88% for group B. Can we jump on conclusion and say that group B did better because they did not use calculator?. Anyone with a little knowledge of statistics will know that we cannot draw a conclusion unless we perform statistical significance tests.

Assuming the performance of students studying under the guidelines of mathematics Framework has been evaluated and compared with that of students studying simultaneously in a traditional program, everything else being equal. Has anyone tried to find out if the observed differences are statistically significant?. If the answer is yes, I would like to see the study results. But if the answer is no, then as I said earlier, the arguments are baseless and invalid. For your information, I am teaching advanced statistics to our graduate students.

Mark Schilling: Since my message to our Provost was forwarded to you (without my permission, but apparently email is effectively in the public domain), I would like to briefly comment on your message and to clarify my own position on the teaching and learning of mathematics.

It is clear that you have great concern, as do many others including myself, about the unacceptable state of mathematical learning and performance taking place in our schools. Furthermore, I agree with the great majority of what you have to say--it is thoughtful, reasonable and relevant.

It is encouraging to hear that you and your colleagues do not "hope to maintain the status quo", use graphing calculators in appropriate situations, believe that cooperative learning can have value in moderation, etc. It is just as good to know that you still believe in emphasizing the basics. You are obviously not someone that I would call a traditionalist. In fact, your teaching philosophy sounds very much like my own.

Unfortunately, there are a number of people who have expressed opposition to ANY sort of change from the curriculum or pedagogy of the past. It is these individuals to whom I was referring in my CSUN memo.

Please notice that nowhere have I indicated that I support the California State Mathematics Framework. To construe such from the fact that I do not agree with the extreme position of the traditionalists would be wholly incorrect. I respect your first- hand opinion, and those of many other high school teachers from whom I have heard, of the Framework's flaws.

I believe, however, that we have a responsibility to find a way to teach mathematics more effectively than simply settling for the inadequacy of the old methods and curricula. My sense is that you and many of your colleagues share this goal.

Mark Shilling: Subject: "shrill"

Webster's Dictionary offers:

shrill (adj.):        (Definitions 1 & 2 refer to sound and the senses.)
                       Definition 3:  intemperate, extravagant

intemperate (adj.):    not temperate

temperate (adj.):      keeping or held within limits: not extreme or
                       excessive...
                       marked by an absence or avoidance of ... extreme
					   partisanship

David Klein: I was delighted to see the recent improvement in your attitude and your receptiveness to criticisms of the California Framework, commonly referred to as the "new new math" or "fuzzy math."

Considering the bitterness of your first memo, in response to my criticisms of the Framework, I have to say you've really taken a turn for the better. Your recognition of the value of Dan Hart's observations is surely a good sign. It was really nice when you wrote to Dan,

You are obviously not someone that I would call a traditionalist.

Many of us, like Dan, use a variety of teaching methods, including occaissional group work. I hope you will take this opportunity to add your name to the Allen Memo, which many of us consider an excellent alternative to the Framework (and as I and several others at CSUN have done).

I recall from your first memo, that you did not even choose to acknowledge the existence of any alternatives at that time. With your new attitude, I'm sure you will go to the "Mathematically Correct" web site I sent you, and read it. I, and several other people at CSUN, have added our names, as you will see. You may recall from our meeting with the XYZ High School teachers, that one of them said (approximately), "One thing you [CSUN faculty] can do for us is get rid of the Framework." Instructions are at the bottom of the list of signatories.

Isn't it nice that we agree so much now about the only real issue brought up in my original response to Provost Kennedy, namely, the serious deficiencies of the Framework?

Oh yes, I almost forgot! You still seemed a bit upset about something in your recent memo. Remember? You wrote:

Unfortunately, there are a number of people who have expressed opposition to ANY sort of change from the curriculum or pedagogy of the past. It is these individuals to whom I was referring in my CSUN memo.

I was just wondering, Mark, who are those people? You know. The ones who have expressed opposition to ANY sort of change from the curriculum or pedagogy of the past? Funny, I've never met anyone like that at CSUN. I sure hope--no, I know you wouldn't--well ...I hope even though the XYZ High School teachers referred to their books as "traditional," you won't put them down. They did use that word, "traditional," you remember, in describing the books they re-bind.

It sounds like a caricature, but I know you wouldn't describe people in such crude terms, now that you're being nice again.

By the way, Mark, what is a traditionalist anyway? Is that somebody who likes the "new math" of the 60's? Or is it someone who thinks we should put children from different grades in the same classrooms, like they did in the 1800's (and some are doing again now)? I'm a little mixed up about that term. Gee, and here I thought you meant people who disagree with the Framework were traditionalists. But no, that was from your first memo (in response to mine). Things are different now.

P.S. Darn, I almost forgot to compliment you on your dictionary work. You're right, Mark, the dictionary definition of "shrill" doesn't even use the word "woman." I even looked it up myself. And gosh darn, the dictionary definition of "boy" doesn't mention African-American men either. Isn't that a heck of a coincidence?

Dan Hart:

It is encouraging to hear that you and your colleagues do not "hope to maintain the status quo", use graphing calculators in appropriate situations, believe that cooperative learning can have value in moderation, etc. It is just as good to know that you still believe in emphasizing the basics.

If you agree with what I'm saying, then perhaps you're not aware of how truly wacky things are getting. The curricula being pushed by the LAUSD has a severe overreliance on technology and cooperative learning.

Personally, I wouldn't give up my TI calculators, but sometimes I wonder if our pedagogy is sometimes affected by OUR appreciation of new technologies. While every AP student in our school has been issued a TI-82 for the last two years, I've had to confiscate the calculators for a month or so each year until the kids learned calculus through their fingers, like we did.

You are obviously not someone that I would call a traditionalist.

I consider myself a "modern traditionalist". Take that for what it's worth.

On the issue of cooperative learning, I think it serves a good purpose as an instructional tool to help the individual learn, not as a center of a wacky curriculum. The whole math folks have this goofy paradigm about people working constantly in groups, conjecturing upon their navels.

While the ability to work together IS important, my impression from the recent educational summit is that business and industry want people who are competent and trainable. This idea that we need to train "problem solvers" by the millions is laughable, utopian, and probably impossible.

Sunday's LA Times had an interview with the new president of Santa Monica College. (I'm sorry I can't remember her name.) When asked about vocational training, she replied that her initial idea on training graphics artists (for instance) was to train them in the latest software and technology. Then she spent time speaking with employers in this industry. You know what they said. "Give us people who can draw."

The other day I received a report on San Fernando's senior class of 1993 that entered CSU as freshman that year. Only 17% of our seniors (of about 50 entering) passed the English exam. Only 24% passed the ELM! That's a disgrace for our school and our system. I would hope with our use of the Saxon books we'll be able to pass along students to you "who can do math". I know you can take it from there. But I also know until we implement the kind of rigorous standards we've discussed here, any curricular changes will be window dressing. If you believe one thing I say, believe this.

I believe, however, that we have a responsibility to find a way to teach mathematics more effectively than simply settling for the inadequacy of the old methods and curricula. My sense is that you and many of your colleagues share this goal.

On the curricular issue, the reformers have taken some good ideas and driven them into the ground. For instance, our department chair, brought back a paper from a recent meeting of LAUSD high school math chairs. The powers that be were very interested to show an assignment done by a young man from Bell HS.

The assignment consisted of writing a story about a company whose five year sales figures were pictured in a histogram. That was it! A little bit of math as part of an English assignment. This fellow spent one hour of that year's 180 hours of mathematics doing an English paper. (And you know this is what they want the kids doing most everyday)

On the other hand I've seen supplementary lessons which have a series of small graphs relating variables requiring short answers. This is a math assignment with some English thrown in. Great!

My point here is that we teach mathematics and there are plenty of people who would like to deconstruct our subject into a hodge-podge of touchy feely exercises, subjectifying it to suit their political purposes. (That's pretty strong, but the overpoliticization of pedagogy is rampant.)

And perhaps, more importantly, nothing is learned without a systematic program of practice based on good old fashioned commitment,determination, and study. Let's fight for a system that promotes that and I think our curricular differences will actually mean something!

David Klein: TO THOSE OF YOU WHO PARTICIPATED IN THE EMAIL DEBATES CALLED THE "NORTHRIDGE CHRONICLES:"

The front page of today's [Sept. 13, 1996] Los Angeles Times reported a major breakthrough in mathematics education in the state of California. The State Board of Education released a Public Advisory which recommends against the excesses of the 1992 California Math Framework.

The following is taken from the organization "Mathematically Correct," [which can be found through "Yahoo" or at http://ourworld.compuserve.com:80/homepages/mathman/] one of whose leaders, Mike McKeown, served on Delaine Eastin's Math Advisory Panel, which drafted the Public Advisory. According to Mathematically Correct:

"The Program Advisory specifically notes that the 1992 Framework will be revised in 1997 and that districts may wish to seek waivers to allow them to achieve a balanced math program now. Waivers from the State Board of Education allow districts to purchase materials that are not approved under the current state Framework. THE ADVISORY STATEMENTS ARE ABOUT AS CLOSE AS THE BOARD CAN LEGALLY COME TO TELLING DISTRICTS THAT THE FRAMEWORK AND THE BOOKS THAT HAVE BEEN APPROVED ARE INSUFFICIENT TO MEET THE NEEDS OF CALIFORNIA'S CHILDREN. THIS SHOULD BE TAKEN AS A VERY STRONG STATEMENT TO THE PEOPLE OF CALIFORNIA. [my caps]"

Those of you who participated in the "Northridge Chronicles" debates, both in support and against the Framework may take pride in contributing to this very positive development. The "Northridge Chronicles" has been posted on the Mathematically Correct Web page for several months and has been available to many influential education leaders in California. Provost Kennedy is to be particularly commended in this regard for spurring the debate and taking a position. Congratulations to all! Jerry Rosen and I have personally read several draft versions of the Advisory already and we believe the children of California will be well-served by it. Once you see it, we think you will arrive at the same conclusion.

Jerry and I hope also that the "Northridge Chronicles" has led to greater interest of subject matter professors in the affairs of public education. In the words of educators Kurt Kreith and Abigail Thompson from University of California, Davis:

"...the demise of California's reading program (based on the Whole Language theory espoused in one such Framework) and a growing frustration among parents of children whose instruction is based on California's Mathematics Framework have focused attention on the university's role in such educational reform efforts. Shouldn't universities be scrutinizing such State Frameworks rather than just implementing them? How does one separate fact from the politically charged rhetoric that pervades these documents? And aside from their success in generating funds, what justification can universities provide for their implicit endorsement of the pedagogical principles on which these professional development programs are based?

Separating truth from dogma can be difficult in any field, but especially so in education. Given their unique and defining role as arbiters of truth, it seems incumbent upon universities to reexamine their roles in the form of teacher professional development..."

Congratulations and Thanks for your Contributions to Education in California.

Mark Schilling:

snip
  > Those of you who participated in the "Northridge
  > Chronicles" debates, both in support and against
  > the Framework
snip

David Klein: Once again I wish to commend you on your role in the creation of the Northridge Chronicles. Had you not argued against criticisms of the 1992 California Framework, the Chronicles would never have been born. But I really think it is time look to the future, rather than dwell on the past. Provost Kennedy's admonition is as sound now as it was when she wrote it in her second contribution to the Chronicles:

"Whether we support traditional teaching of math or the newer California frameworks, the use of calculators, or any of the myriad other disagreements that permeate the e-mails of the past weekend, I hope we do not lose sight of the goal - the development of math competency in the young people of California and the opportunity to explore math based disciplines in their future careers." (L. Kennedy, 13 May 1996)

CSUN now has the opportunity to assume a greater responsibility in the evaluation of Frameworks rather than just their perfunctory implementations in its credential programs. Jerry Rosen's prophetic statement from one of his contributions to the Chronicles is worthy of serious reflection by President Wilson and Provost Kennedy:

"I believe that, as in the case of Whole Language Learning ... the [1992 Math] Framework will soon be exposed as highly detrimental to math education in the state. If CSUN makes this assessment before others, we can take the lead in suggesting true innovations and reforms. This would certainly have several benefits for our institution." (J.Rosen, 12 May 1996)

Inferior curricula such as Whole Language and Whole ("fuzzy") Math, as embodied by recent Frameworks, provide a tremendous impetus for the Voucher Movement. So long as Universities like CSUN support such flawed curricula in their teacher training programs, the enemies of public education have at their disposal compelling arguments, and the public is listening. Recent polls indicate that large public support of the Voucher Movement stems from dissatisfaction with the lack of attention given to basic reading and mathematics skills by the public schools (L.A. Times, May 23). The integrity of the curricula used by the public schools will be a pivotal issue for the future of free public education in the state of California.

Steven Oppenheimer: Congratulations. There is no doubt that your work and that of your colleagues has led to a pivotal juncture in K-12 mathematics education in the State of California. What is especially outstanding about the new guidelines is that they provide a return to key basics, yet also allow for the use of new teaching methods that individual teachers feel are appropriate for particular groups of students. I truly feel that this is a landmark policy that will catch on around the nation. I appreciate your keeping me informed about these developments. They will help me immensely in my work on the Policy Committee for the State's Science Stardards. As a direct result of the new math policy, I am already thinking about a preamble to the Science Standards document that stresses the same sort of BALANCE presented in the math policy. I think the past polarization of traditional versus reform is giving way to balance. And balance makes so much sense, I feel, to everyone. It is really good to see what can be accomplished when dedicated people work hard for the good of the country.