THE MATH WARS Implementing Standards: The California Mathematics Textbook Debacle By Bill Jacob The California mathematics textbook adoptions lead Mr. Jacob to predict that students there will be drilled on formal skills that are aligned with the test and that high expectations for thinking and reasoning will be gone. He hopes that other states will do better.

STANDARDS and accountability are today's education buzz words. Al Gore and George W. Bush stressed both in their October 2000 articles in the Kappan.1 But Kappan readers know that what happens in the classroom is more critical and that, as noted repeatedly in these pages, textbooks are a key determinant of classroom practice. This is particularly true in mathematics, where elementary teachers rarely have specialized backgrounds in the subject and where, even at the secondary level, a shortage of certified math teachers is already apparent in some districts.

Across the nation, schools are being advised to align instruction with standards. California's accountability system links school revenue to performance on standardized tests, and a high school exit exam will be required of all graduates in 2004. So the stakes are high, and the textbooks offered to teachers are critical. In this article, I examine California's recent "standards-aligned" mathematics textbook adoption process, which provides a lens to scrutinize the impact of high-stakes policies on classroom practice. And a disturbing picture emerges.

Background on California

In each content area, California has separate standards and framework documents. The standards describe the topics all students should study, and the frameworks articulate a vision of how to get there. Revised every seven years, the frameworks provide the criteria by which the state adopts instructional materials in grades K-8. (High school materials are not adopted statewide; the choice is left to local school systems.)

In 1996-97, California's mathematics standards were drafted by a volunteer Standards Commission, which met for almost a year, with input from teachers, researchers, mathematicians, and educators. The commission produced several versions of standards that were each subject to public review and comment. In what became a dominant style of policy making, the state board of education not only rejected the commission's draft standards but also chose to substantially revise and swiftly approve a new document with minimal public review. Four mathematics professors from Stanford University were asked to help create a "mathematically correct" document and did most of that work. The state board's new document entirely revised the section for grades 8 through 12 to conform with the traditional algebra I, geometry, algebra II sequence and eliminated all examples and clarifications that the commission had created to help teachers understand what the standards might mean in their classrooms. Many leaders in the education community protested the changes. Superintendent of Public Instruction Delaine Eastin publicly opposed the controversial document, whose elementary sections were finalized without significant input from teachers who know the reality of teaching students in these grades.

The significance of the standards cannot be overemphasized. State law requires that adopted instructional materials align with the standards.

In 1998 a mathematics framework that accompanied the standards was completed. Once again, essentially the same small group of advisors to the state board met in closed meetings and completely rewrote the work of an earlier committee. Teachers played a negligible role in a revision that was coordinated by university mathematicians and psychology professors expressly selected by the state board for their educational ideology. The two university mathematicians whom the board entrusted with the authority to revise the mathematics content discussions later appeared as featured speakers at a presentation, sponsored by the California Department of Education, for publishers who were interested in submitting textbooks for the 2001 state adoption. Essentially, the state's new direction bases elementary school mathematics on extensive practice of standard computation; then, in later grades, there is increased emphasis on more abstract mathematics. The use of problem solving as a means of developing conceptual understanding was abandoned and replaced by direct instruction in skills.

The next steps on the policy calendar were the mathematics textbook adoptions, slated for 1999 and 2001. Prior to the state board's adoption of instructional materials, two kinds of panels -- the Content Review Panel (CRP) and Instructional Materials Advisory Panels (IMAPs) -- are appointed to pore over the K-8 materials submitted by publishers, using the criteria approved by the state board. Their written reports and recommendations are revised by the Curriculum Commission and forwarded to the board, which has the final say.

The Content Review Panel was added to the process in 1999, and its primary responsibility is to check to see if content aligns with the standards. In a move disenfranchising educators, the state board decreed that CRP members must have Ph.D.s and decided that K-12 teachers and those with doctorates in education would be excluded.2 Although K-12 teachers are included as members of the IMAPs, it became clear in 1999 that the CRP -- the mathematicians' panel -- was the locus of power. That year, the state board had CRP members negotiate directly with publishers and, in one case, had a CRP panelist write a new report a few days before a vote in order to ensure that it aligned with the preferences of the state board. A primary adoption in 1994 and a smaller supplemental adoption in 1997 had followed criteria set in 1992. In January 2001 the state board approved a completely different set of texts based on criteria from the 1998 framework and aligned with the 1997 standards.3

A Prelude: The 1997 Mathematics Adoption

In both the 1994 and 1997 mathematics adoptions, the state board chose a final list of programs different from those recommended by the panels and the Curriculum Commission. In 1994 the board added three "more traditional programs" to a list of nine reform-style programs. The board understood that the panels and the Curriculum Commission determined that the added programs fell short of the framework's criteria. But publishers of the additional programs had made efforts to revise their materials, and the board felt that these efforts should be recognized. Moreover, the state board believed that, during the transition, districts needed options that included materials bearing greater similarity to the traditional programs they had been using.

But in 1997 a new dimension was added to the state board's decision-making process. Instead of interpreting adoption criteria more broadly, as it did in 1994, the board decided to ignore established criteria and base its decisions on ideology. A few days before the final vote, the board liaisons to the Curriculum Commission recommended the adoption of all submitted programs. At the board meeting where the final vote was taken, board member Janet Nicholas introduced two memos outlining reasons why two programs published by Dale Seymour should be rejected. In spite of the high evaluation ratings earned by these programs, the board made a preemptive strike by rejecting them.4 Established procedure was for publishers to be given notice prior to formal consideration so that all interested parties could respond. Closed-door politics had become a central force in California' s mathematics policy.

The statements in the Nicholas memos illustrate how ideology rather than scholarship influenced the board's decision.5 Nicholas claimed that these programs 1) failed to align with Sec. 60200.5 (the textbook morality code), 2) failed to include research-based instructional strategies, and 3) contained mathematical errors.6 For example, a problem involving a "pizza pirate" was cited for failing to meet the morality code,7 and an activity that had first-graders "invent their own ways of representing their data" supposedly failed to meet research criteria. Perhaps the most egregious statement was a discussion of a supposed factual error: "The text indicates that 36 x 45 can be rewritten as an expression with three factors, such as 9 x 5 x 36 or 9 x 30 x 6. The number 30 is not, however, a factor of either 36 or 45." This program expected students to understand important number relationships, but the state board wanted texts to emphasize rules for students to follow.

As ridiculous as these statements seemed to those who knew the instructional materials (and these examples are representative), the underlying intent was clear. The priority of the state board had become choosing programs that provided direct instruction in computation over materials that emphasized student thinking and reasoning. These views were subsequently formalized in the 1998 California framework.

Research-Based Instruction Materials

The state board initiated an approach that is rapidly gaining currency across the nation: the use of the code phrase research-based instruction as a way of promoting instruction aligned with ideology. In order to accomplish this objective, the state board advocated a narrow vision of research. As we will see, their "research-based criteria" apply to a very limited body of instructional materials.

In January 1997 a board-appointed committee convened to revise the 1992 mathematics framework and was asked to include "research-based instructional strategies."8 Although the Framework Committee never discussed education research, the board persisted. The board contracted Douglas Carnine of the University of Oregon to write a report summarizing mathematics education research.9 The report, known as the Dixon report, which Carnine presented to the board, was limited to experimental research (those studies that compare the performance of experimental and control groups on skill-based exams), an unacceptable bias from the point of view of most educators. Starting from an original database of 8,727 articles, the report identified 956 as meeting the criterion of being an experimental study; of these, only 110 were judged to be of sufficiently "high quality" to be included. The report's narrow band is evident if one compares its choices to the references in the National Council of Teachers of Mathematics Standards 2000 draft: of 88 research entries cited by NCTM, only four appeared on the list of 956, and none made the final cut.

Apart from typographical errors, the Dixon report contained misrepresentations that reflected its ideological bias. The "spin" of the very first citation is, at best, a mistake; at worst, a deliberate lie. The report claims the research study found "no benefit in terms of academic performance to using manipulatives rather than conventional instruction for teaching oddity, seriation, and number conservation at kindergarten" (p. 13). The text of the primary source states that "scores on all measures favored the experimental group," later adding, "The instruction that the control students received was designed to foster academic achievement; hence, it would not be surprising if their verbal and mathematics scores were higher than those of the experimental children. That they are not probably reflects the increased cognitive competence of the experimental children."10 Although the experimental group in the study scored significantly better on a test of reasoning, the differences in the skill of ordering numerals were not statistically significant, which is all the Dixon report recorded. In alignment with state board ideology, the Dixon report valued rote skills and dismissed children's conceptual development in mathematics.

The report also promoted the belief that programs effective with learning-disabled students are somehow better for nondisabled learners as well. It discussed a paper on "self-instructional strategies," stating that it "showed positive effects in mathematics achievement." The paper dealt only with educable mentally handicapped students, and, in explaining the significance of their research, the authors stated that these strategies have proved effective in "reducing irrelevant verbalizations during interviews of hospitalized schizophrenics."11 How could the report have presented such irrelevant information as "high-quality mathematics education research"? The Dixon report never considered hundreds of informative papers that could have advised California policy. Instead, it selected only those that supported the board's view that school mathematics is synonymous with rote computation.

In spite of their inability to produce a credible research summary that would bolster their ideological views on pedagogy, the state board continued to require that its evaluations of professional development initiatives and instructional materials be based on "research." The 1999 instructional materials evaluation template asked reviewers to determine whether the submission "incorporates principles of instruction of current and confirmed experimental research," explicitly altering the wording of state law to reflect the Dixon report by adding the word experimental. But several CRP members had read rebuttals to the Dixon report, and during the 2001 mathematics adoption, in their written response to the state board's research criteria, they uniformly skirted the issue: "The CRP members generally agreed they would not comment on this criterion."12

What was the net effect of the state board's substantial effort to base changes on research? It had almost no impact whatsoever. Then, readers might well wonder, why repeat the tale? There are a number of reasons. First, the shenanigans of the California board can serve as an object lesson to educators and parents across the country. Second, proponents of skills-only research continue to promote their narrow views across the country as a basis for policies that dictate methods and materials for teaching all children. In the Journal for Research in Mathematics Education, Carnine recently argued in favor of the exclusive use of the experimental paradigm.13 The National Reading Panel used a similar approach in its 1999 report. But the conclusions drawn from its research have been questioned.14 Educators across the U.S. need to be aware of this game.

The 1999 Mathematics Adoption

During 1999 California had a special mathematics adoption to provide teachers with transitional materials aligned to the standards.15 The state approved two types of mathematics programs: full programs that were deemed to cover all standards and partial programs that could supplement existing materials.16 Although some districts did adopt full programs, in the two counties where I work (Santa Barbara and Ventura), the districts enrolling a majority of the K-8 students chose partial programs. This pattern was repeated across the state. Conversations with district personnel and teachers reveal the reason: partial programs are chosen to help teachers prepare students for the state's standardized tests. These programs -- essentially workbooks -- provide a page or two each day of computational procedures that students must then practice. Conceptual development is not included in these skill workbooks. This is not an oversight; it is deliberate. In a climate of hysterical emphasis on skill-based tests, there is no time for such niceties as conceptual development. In most classrooms these partial programs provide the core curriculum, even though they are not supposed to be used in that way.

By comparing how programs introduce a particular topic, one can get a sense of what this means for students. An analysis of California's 1994 and 1999 programs is revealing.17 Typical introductions to two-digit multiplication in the 1994 programs review geometric representations of multiplication, which typically use arrays or rectangular sections of graph paper in which length and width represent factors. Strategies for computing larger products can then be represented by rectangle subdivision, and students can develop their understandings of computational methods based on the geometry. But the typical 1999 program limits instruction to the traditional written procedure, with the rules of computation explicitly spelled out for memorization. Some 1999 programs instruct students to rotate lined paper sideways or to use artificial placeholders to ensure they record their procedures correctly.18 Computational accuracy thus becomes more important than understanding what multiplication means.

A check of other topics yields similar conclusions: leading 1999 programs have retreated from a pedagogy of sense-making in mathematics. Concern about a need for more computational practice has led to a knee-jerk, skill-drill response, leaving many students limited to a view of mathematics as a subject dominated by rote repetition. The test scores may have won in the short run, but in the long term, student understanding and inspiration have lost.

The Publishers' Meeting for the 2001 Adoption

In order for publishers to prepare materials for the 2001 adoption, the state department of education sponsored a meeting highlighting the California standards and framework. Mathematics professors Hung-Hsi Wu of the University of California, Berkeley, and James Milgram of Stanford University, principal authors of the 1998 framework, were featured. They raised three of their pet concerns: calculators, computation, and mathematical proof.

Professor Milgram spoke forcefully against the use of calculators and in favor of stressing the standard algorithm for long division. With regard to calculators, he stated, "When calculators are used, students do not learn basic skills. They learn basic button-pressing skills." To support his claim, he offered a chart showing computational skills of adults from varying age groups in the U.S., Asia, and Eastern Europe. He pointed to one section stating, "This is exactly coinciding with the introduction of the New Math in the U.S." When pressed, he did concede that U.S. students did not use calculators in the 1960s, but he replied that it was "the first time for which the primary part of math education was no longer basic arithmetic." Milgram continued, "This is the research of David Geary, and there are numerous other studies that tend to show the same thing." But he did not supply any citations.

About the importance of long division, Milgram lamented the poor performance of engineering students at Stanford, describing a connection between long division and optimization. He said, "Optimization is done through the analysis of things -- eigenvalues, eigenvectors. . . ." Then he added, "So if you take long division out, you have to replace it with a huge amount to make up for what you took out." Milgram seems to hold elementary teachers responsible for his difficulties in teaching differential equations to students at California's most elite university, and his solution is to promote the same rote computation his students experienced in the 1980s during California's last back-to-basics swing.

Professor Wu discussed the mathematical reasoning that he believed to be critical at grade 7 and included an example. He wrote down the equation (-2/5) x (7/4) = -(2/5) x (7/4) and offered the following line of reasoning to present to students. First, (-2/5) x (7/4) + (2/5) x (7/4) = (-2/5 + 2/5) x (7/4) = 0 x (7/4) = 0. So as (-2/5) x (7/4) and (2/5) x (7/4) add to 0, we have (-2/5) x (7/4) = -(2/5) x (7/4). The audience was confused about why this proof was a priority, and Wu repeated (essentially) the same calculation three times in an attempt to answer. Responding to one member of the audience, he said, "I'm puzzled as to why this is difficult. I'm not trying to make fun of you." Members of the audience had been developing texts at these grade levels for decades.

The picture that emerged from professors Milgram and Wu was one in which the practice of traditional computation would dominate the elementary years and would be followed by formal symbolic manipulations (including an introduction to proofs) in middle school. There was no mention of the use of context or the posing of thought-provoking problems as an instructional tool. Missing was any discussion of developmentally appropriate practices to help students acquire concepts over time. But this is no surprise. The notion of "developmentally appropriate practice" is itself under attack by back-to-basics advocates. The approved California vision is direct instruction in formal mathematics as understood by mathematics professors trained to do mathematical research.

Rhetoric of Skill-Based Proponents

With the 2001 text adoption approaching, skill-based proponents stepped up their attack against earlier reform materials. State board member Nancy Ichinaga summarized the new state board views in a 2 May 2000 statement to the Los Angeles School Board:

I am here to ask for your support in requiring all the K-12 schools in Los Angeles to adopt a systematic mathematics program which meets the state content standards. . . . Integrated math, reform math, CPM, or college math, no matter what you call it, it is still watered-down math, fuzzy and substandard math, and does not meet the new state math requirements. . . . Integrated math instruction is akin to the now discredited whole language instruction in reading. . . . The district must support its teachers by giving them a systematic skill-based program which tells them what to teach and how to teach it.19

An unwillingness to allow teachers to make instructional decisions has become a significant factor in setting state policy. The CRP report on Everyday Mathematics, prepared by the panel in October 2000, echoed Ichinaga's distrust in its evaluation, which states: "It is highly teacher-dependent (and consequently, not teacher-proof)." Milgram, a member of the CRP, subsequently made a special appeal to the Curriculum Commission to block this program on these grounds. His statement illustrates a ridiculous extreme:

As currently written Everyday Math requires in the teacher that is teaching it, and this is at grades K through 3, the mathematical maturity equivalent to the following college level courses at a serious Tier I school. At least one course in calculus, a strong course in linear algebra, a strong course in abstract algebra - I don't mean intermediate algebra, I mean groups, rings, and fields - and a junior level course in classical geometry. Less than that will not do.20

This attack on teacher professionalism, a view that teachers are not capable of instruction and must be told how to teach, is neither unique nor isolated. The teacher-bashing comment came in the face of testimonials from 14 district superintendents who documented the success of Everyday Mathematics and wrote to the state board in support of the program. Referring to nationwide efforts to promote scripted instruction as the "teacher stupidification movement," Richard Allington has collected numerous examples of distortions of research and practice by proponents of basic skills.21 Educators across the country need to unite in the face of such attacks.

Those who advocate most strongly for basic skills also use inflammatory language to attack programs. Borrowing a term popularized by Lynne Cheney in her 1997 Wall Street Journal article bashing the National Council of Teachers of Mathematics (NCTM), assorted publishers, equity, and President Clinton, Ichinaga used the word "fuzzy." Another of the favorite terms of skill advocates is "whole math." Although this terminology is never used by those developing or implementing the materials, the press, like Cheney, can spot a good inflammatory label and makes frequent use of the phrase when describing the math wars. Cal Tech math professor Barry Simon explained it this way to school board members in Los Angeles in May 2000.

First I want to mention the fact that the terms of reform and traditional, which tend to get used, are actually misleading terms and loaded terms. Reform or integrated should actually be called whole math. It is the same untested and failed philosophy as whole language. . . . On the other hand, traditional proponents aren't asking to return to anything. A much better name would be skills-based mathematics.22

Skill-based proponents have distorted program content as part of their advocacy. In his testimony, Simon referred to a unit of the Mathland program at grade 5: "And while spending only one week on basic arithmetic, it spends two weeks on how to use a calculator." The five-week unit in question begins with a week in which students focus on strategies to memorize multiplication facts they haven't mastered, and teachers are explicitly instructed to discuss with them the importance of rapid recall of facts. The next two weeks are devoted to number computation (using both written and mental strategies). Then students study number patterns and computation strategies for two more weeks. In these two weeks, they may use a calculator as a tool in some situations (such as looking at 66 x 66, 666 x 666, 6,666 x 6,666 to find a pattern). But calculators are used only for the purpose of exhibiting number relationships, and the unit is not about learning to use a calculator for basic computation, which is what Simon hoped listeners would infer. As with all materials, this program has strengths and weaknesses, but in this case Simon misrepresented its objectives in order to promote his own narrow views. Simon asked the school board to immediately adopt either Saxon Mathematics or the Sadlier-Oxford Publishers' Progress in Mathematics series, both of which are based largely on drill and practice in number computation. Six months later, the district chose neither.

The 2001 Adoption

During October 2000, advisory panels prepared reports for the 2001 mathematics adoption. The Curriculum Commission modified these recommendations in November, and the state board made its final decisions in January. Unlike the partial programs chosen by districts during 1999-2001, the materials submitted do represent an attempt to include mathematical connections for students. But the adopted programs are lacking in concept-building investigations or in problem solving and are limited to direct instruction in the kinds of computations and facts listed in California's standards. Most disturbing, however, was the ideological, politicized process used by the state board in voting on the approved list.

Although the members of the board considered the recommendations of the panels, the board exercised its authority and changed four recommendations. In two cases, the panels offered compelling evidence that the board ignored because of intense pressure from special interests. Saxon Mathematics was recommended for rejection by the Instructional Materials Panels in grades 4 through 6. The reports recognize the program as strong in drill and practice but severely lacking in conceptual development. Professor Hung-Hsi Wu, who played a major role in the development of the 1998 framework, offered the following remarks during the CRP's public discussion of Saxon Mathematics:

But I think that what perhaps disturbs me the most about Saxon is to read through it. I myself do not get the feeling that I am reading something that when the children use it they would even have a remotely correct impression of what mathematics is about. It is extremely good at promoting procedural accuracy. And what David says about building everything up in small increments, that's correct, but the great pedagogy is devoted, is used, to serve only one purpose, which is to make sure that the procedures get memorized, get used correctly. And you would get the feeling that - I think of it as a logical analogy - you can see the skeleton presented with quite a bit of clarity, but you never see any methods, your never see any flesh, nothing - no connective tissue, you only see the bare stuff.

A little bit of this is okay, but when you read through a whole volume of it, really I am very, very, uneasy. . . . When I do this, I want to emphasize that I do not single out one or two examples. I am trying to describe through one or two examples the overall, the overriding, impression that I have. And when that happens, you get the feeling that, if my students use this, how could they not get the idea that mathematics is just a collection of techniques? If that is the case, what happens to them when they go on to middle school, and then to high school, and after that, God forbid, you might be facing them in your freshman calculus classes. And that is a frightening thought.23

The state board ignored Wu's advice, proving that, where ideology is concerned, experts come and go.
The primary reason for the board's support of Saxon Mathematics may be intense pressure from basic-skill advocates who have published enthusiastic endorsements. Saxon also lined up numerous testimonials for the November meeting of the Curriculum Commission. A statement by a high school principal who flew to Sacramento for his two-minute commentary illustrates these views.

My basic philosophy is a back-to-basics, fundamental approach. . . . I believe in fundamentals and repetition. I know this has nothing to do with football, but I think it is a good analogy. In the lower levels of football, in the high schools, in the colleges and in the pros, if you go to their practices, guess what? They practice the same fundamentals year in and year out. Why do they do those things? So they become automatic. So you don't have to think about them when you are in a game situation. . . . And Saxon math is yes, repetitious, boring, but guess what? It works, it prepares [for] students automatic tools so they don't have to think about it -- they know their math. And that is the goal.24

Now, California school districts may select a state-approved program about which both supporters and opponents agree. Saxon Mathematics will train students so that they don't have to think. Reasoning and understanding are not priorities. In a spirit of promoting excellence for all, California's 1992 instructional materials criteria stated, "Students should think and reason in all mathematical work." But by 2001, this criterion has vanished from the landscape.

Bias against materials designed to encourage children's mathematical understanding is evident in the state board's rejection of Everyday Mathematics, a K-6 curriculum published by Everyday Learning since the early 1990s. The program is widely recognized for its emphasis on student reasoning and understanding, as well as mastery of basic skills. In its report, the Instructional Materials Panel endorsed the program and said, "Everyday Mathematics offers a complete K-3 mathematics program that contains the essential guiding principles and key components of an effective mathematics program." A videotape of the CRP deliberations includes conversations between the mathematicians on the committee, who are genuinely encouraged by the depth of the mathematics in the Everyday program. State superintendent Eastin also endorsed Everyday. Yet the state board rejected it. Why? Perhaps the board was influenced by Milgram's insistence that the program was insufficiently "teacher-proof." Apparently, the board had other priorities, and Everyday Math was consigned to the waiver category. The California Education Code includes a waiver process, whereby school districts can make special application to the state board to waive the adoption requirements if board-designed criteria are met, such as adequate documentation of student achievement. In a flurry of last-minute brokering before the board's adoption vote, districts in which schools were already successfully using Everyday Mathematics expressed concern to the board and the governor's office, and the board decided to consider waiver applications to use the materials. As of mid-August, seven school districts had received waivers, which will allow them to purchase the program using state funds. One district application was rejected.

Undoubtedly the most significant change in California education policy, as reflected in the 2001 adoption, came as no surprise. The only eighth-grade materials available are three traditional, first-year algebra texts.25 For the past half-century, significant numbers of ninth-graders who have enrolled in courses identical to those adopted have failed. Now, California is pushing this course on all eighth-graders. And the state has no plan for helping students succeed -- other than to move pre-algebra to seventh grade, with the hope that accountability measures coupled with algebra courses for teachers will yield the desired result. Training teachers to copy equations on the board will not accomplish the goal. With its new policies, the state has tossed out programs that provide contexts for students to develop early algebraic thinking as well as a meaningful understanding of variables.

Traveling the same politically expedient trails as so many of his brethren on both sides of the aisle, the governor originally advised the state board that the High School Exit Exam (HSEE) should be "a test of proficiency in algebra." Although approximately 36% of the test focuses on algebra items, student success will be tightly linked to the eighth-grade experiment. Fearing that "opportunity to learn" lawsuits might derail the HSEE, the governor supported legislation to postpone the effective date by a year just a few weeks before the class of 2004 took the exam in March 2001. But he was short on votes in the senate, and most students did not know until the day of the exam that it did count.

The day after the test was given, John Mockler, executive secretary of the state board, was quoted in the press as saying that about 40% of California's high school students were graduating without passing algebra. Referring to this chaotic situation, a middle school administrator from a large district wrote: "And, once again, I am stuck trying to put someone else's harebrained idea into a workable perspective so that I can help my school site develop a plan and take care of its students."26

The passing score on the HSEE mathematics section was eventually set in May at 55%. The HSEE Panel (an advisory body) was dismissed in January, several months ahead of schedule, which means that this most critical decision was made by the board without input from K-12 educators and without a public forum for anyone to voice concerns. Members of the HSEE Panel publicly expressed their frustrations over working with the state board and the governor's office. One member had already resigned for these very reasons. As with the development of standards and frameworks and with textbook adoptions, students' futures in California are ruled by closed-door politics. Students may be denied diplomas and dropout rates may increase, all because the state board believes students can learn to manipulate equations through more of the very drill and practice that haven't worked in previous decades.

What Have We Lost?

Ask any California teacher who has been active in improving quality and leadership in mathematics instruction if he or she will be volunteering to serve on future committees and task forces convened by the state board. "Never again" will probably be the response. Venture to speculate on a possible reason for withdrawing from public service or allude to the "kangaroo court" of past proceedings intended to garner so-called professional input, and you will no doubt hear a resounding "Yes." The voices of teachers have been lost in California education policy.

The idea of balance is frequently part of the rhetoric of state mathematics policy. Board spokespersons advocate balance -- in theory. However, the actual text of key documents, standards, frameworks, and textbook adoption criteria exhibit an unbalanced, rigid emphasis on procedure, skill, and method. So add balance to the casualty list, and make room for flexibility as well. Districts need flexibility to define their own vision of balance in instruction and, above all, to guard against extreme policies.

Focusing on the board-approved list of mathematics textbooks for adoption, a number of programs were approved that go beyond the "drill and practice" definition.27 One would hope that the materials represent an acceptable middle ground, allowing for students to develop conceptual understanding, problem solving, and basic skills. But this is hardly the case. While they do not take the form of tightly scripted lessons that allow for no variation by a teacher, the materials satisfy the bare necessities of matching content to standards. Topics such as two-digit multiplication and concepts such as the meaning of division by fractions are reduced to what is known in the publishing trade as the "two-page spread." The materials are literal translations of each standard, providing a tidy capsule lesson in which teachers are encouraged to do what they have been doing for decades: 1) explain a topic, 2) show an example from the book on the chalkboard, and 3) have the students practice similar examples. This conventional model of teaching has not provided students adequate access to algebra and more advanced topics, and it has been repeatedly cited in research studies as a major weakness of mathematics instruction in the U.S.28

With the exception of one series for which current users may obtain a waiver, the 2001 adoption list excludes many successful mathematics curricula, including those identified by the U.S. Department of Education as exemplary and promising. Evidence of the effectiveness of these programs has appeared in the research literature.29 The studies indicate that the students in these programs make progress in skill acquisition that is comparable to that of students in other programs and that they excel in some problem-solving and conceptual areas. Unfortunately, many publishers of innovative mathematics materials declined to submit their books for the 2001 textbook adoption, after having been summarily dismissed in the 1999 emergency adoption. The bias in favor of direct instruction in the textbook criteria and on the part of the reviewers was cause for concern.30

California also requires that programs align with standards on a grade-by-grade basis, and several topics were required to be introduced one year earlier than many consider to be acceptable practice. As a result, the approved list of mathematics textbooks that California districts can purchase is a limited one. The programs are designed to rush students through a long list of computational skills and procedural acrobatics, with little room for them to understand what they are doing.

These lost opportunities come at a time when teachers, mathematics educators, and mathematicians are setting a far better example elsewhere. The NCTM recently completed its Principles and Standards for School Mathematics. This volume replaces three earlier NCTM documents and was developed over a three-year period through an open and inclusive process. The team of authors represented all stakeholders, a substantial public review was included, and 15 different professional mathematics organizations provided formal input.31

The value of the document is its balance, along with its delineation of the important role of skills that readers of earlier documents may have misinterpreted. It contains examples showing how problem solving can be used to develop conceptual understanding and how those understandings, in turn, can lead to acquisition and retention of basic skills. A broad base of research accompanies and supports the document. The NCTM has shown how to move forward, building upon what works. But this document has, in effect, been blacklisted in the chambers of California policy makers, adversely affecting professional development initiatives and materials adoptions. More than just a loss, what has been created is a vacuum of useful scholarship in mathematics education.

Concluding Remarks

In California, an era of devising standards and choosing curriculum came to a close in 2001 with a mathematics adoption. A new high-stakes testing system had begun in 1998, and policy makers claim that teachers have standards-aligned instructional materials with which to prepare students for the tests. Will the new era bring balanced mathematics instruction that incorporates basic skills, concepts, and problem solving, as the state board called for in 1996? Or will mathematics classes be reduced to computational drill in preparation for standardized tests?

These are not rhetorical questions. Many of the writers who contributed to the standards and framework believe that the "rigor" in the documents will lead to better reasoning and understanding in K-12 mathematics. However well intentioned, they are wrong. They failed to take into account the public's view that "mathematics is computation," and they failed to realize that most publishers would respond to a renewed emphasis on skills with programs that focus on drill and practice. Understanding is an afterthought.

During 1999-2001 my professional work gave me the opportunity to meet with numerous K-8 teachers, visit classes, and discuss the impact of the recent policies. The pressures to prepare students for the STAR exam consumed most of our conversations. Teachers shared with me the test-prep materials their students work through prior to the exam. Valuable time needed for conceptual development (in some cases months) is lost entirely to drill, and while some students can complete the practice pages, others are fed procedures too quickly for them to make sense. Further increasing stress levels, parents can now buy STAR prep booklets in local stores. After the spring testing season is over, many teachers report that they and their students are too emotionally exhausted for meaningful work during the rest of the year.

And the situation doesn't promise to get much better after 2001. The state board approved the program that one of its key advisors described as not giving students "a remotely correct impression of what mathematics is about." And the board rejected a program about which the review endorsing it said, "It contains extremely interesting and thought-provoking material." Why? In addition to the reasons I've cited here, observers say that, on the day of the vote, the state board responded to pressure from the governor's office. In other words, politics superseded quality in the choice of California mathematics programs.

Kappan readers know that the Bush Administration has launched its own education agenda calling for yearly testing of students and has proposed a new federal layer of accountability. Proponents argue that the plan will lead to higher achievement, while opponents claim it will promote a dumbed-down curriculum and encourage teaching to the tests. How is the public to decide? The California mathematics textbook adoptions provide an answer. We can expect that students will be drilled on formal skills that are aligned with the test and that high expectations for thinking and reasoning will be gone. In California, this may not have been the intent of policy designers, but it is a consequence of pushing high-stakes accountability on a system that relies on a publishing industry to produce materials that will allay the fear of failure and its consequences. What we see in California is not in the best interest of that state's students. They need to think and reason in their mathematics classes. We can only hope that other states -- and the nation -- will do better.

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Kappan Professional Journal
Last updated 8 November 2001
URL: http://www.pdkintl.org/kappan/k0111jac.htm
Copyright 2001 Phi Delta Kappa International