A Critique of the

1992 MATHEMATICS FRAMEWORK FOR CALIFORNIA SCHOOLS

The Mathematics Framework is the primary guideline for all aspects of mathematics education in the state of California. There are three major areas in which the state is involved in this process. They are To summarize this critique, the 1992 Framework is adversely influencing all three areas of state involvement. The 1992 document is more than four times as long as its 1985 predecessor but with less useful information. More importantly, the philosophy that it supports, well established long before the 1985 Framework appeared, has been expanded upon to great and redundant lengths while any indication of minimal competencies on the part of either teachers or students has been removed. It is, however, being used by the state to deny approval of effective curricular programs and to deny approval of mathematics teacher preparation programs at good universities around the state.

The Framework is intentionally consistent with another long and influential philosophy statement, the National Council of Teachers of Mathematics 1989 publication, the Curriculum and Evaluation Standards for School Mathematics. That document is disingenuous from its title forward; there is no "standard" in it in the sense that most people use the term. The 1992 Framework follows the NCTM philosophy but with even less indication of the necessity of mandating deepening levels of mathematical competence and sophistication as students progress through the curriculum. Instead, there is an underlying assumption that any mathematics classroom ought to be able to offer challenge and opportunity to any student who happens to have been placed there. There are to be no assumptions of, let alone mandates of, minimal computational and conceptual competence at progressively higher grade levels. Since there is no data to support the contention that this current practice is aiding students at either end of the performance spectrum, and massive evidence that it is hindering progress of students overall (for example, compare California's numbers with those of Minnesota, let alone Taiwan), this philosophy must be critically challenged instead of embraced.

Another document used to justify the philosophy of the 1992 Framework (page ix of its preface) was the 1989 publication from the National Research Council, Everybody Counts. This persuasive little book has a picture of Jaime Escalante of Stand and Deliver fame, as the epitome of effective teaching to an audience that historically has done poorly. Conveniently omitted is the fact that Escalante was highly performance goal oriented and deliberately chose the AP Calculus exam as the measure of success of his students and of his program. Not surprisingly, his students excelled in their subsequent university work as well. No excuses are necessary if the performance numbers are strong. Many pages of excuses, essentially the content of the Framework, will not be persuasive if the numbers are weak. According to the National Assessment of Educational Progress as reported by the US Department of Education in September of 1993, California's numbers trail the nation.

Curricular Guidance

Prior to summer of 1994, the influence that the Framework would have on curricular guidance was speculative. Now it is history. The mathematics curriculum used by my own daughter's private school is highly effective in the hands of good teachers in a program that respects grade-level competence but it was rated at 20 our of 100 by the state, with 70 minimal for inclusion on the state's approved list. This same curriculum is used by the Ukiah public schools which consistently score some 60 points above the national average on the mathematics portion of the SAT. On December 14, I served on a committee with Karen Morelli, a member of the state Department of Education mathematics group involved in the evaluation and approval process. When I asked her how such a successful curriculum could merit such a low rating, her answer was quick and definitive, "It isn't consistent with the Mathematics Framework". Another curriculum that didn't make the state's approved list was that used by Chelsea Clinton at her private school in Washington, D.C. It is reasonable to surmise that it has the same deficiencies. The fact that both programs have been adopted by schools were student performance matters, whose very existence depends upon it, does not even get factored into the evaluation. The Framework is the definition and consistency with it is the criterion.

Assessment of Student Performance

Quoting verbatim from the Framework, "The type of assessment recommended in this Framework is often called authentic assessment ... Sometimes the phrase performance assessment is used ...". This recommendation parallels the movement that the state has taken to eliminate traditional evaluation of student performance. This movement to eliminate well-understood statewide assessment was the motivation for the development of the California Assessment Program (CAP) and its replacement, the California Learning Assessment System (CLAS). Although the reformers have usurped the words "authentic" and "assessment" in the same way that the NCTM has usurped the word "standards", these words still do have meaning to the general public. Ironically, there is nothing authentic about the kinds of assessment they espouse. Quite the opposite, credit is given to students who express themselves fluently even if their ideas are mathematically wrong and credit is detracted from mathematically good work if not verbal in ways that can be arbitrary. Moreover, it is impossible to tell from the results if students have learned what they were supposed to have learned, if they are prepared to move on to deeper levels of mathematical work in the areas examined, or if they can apply what they are supposed to have learned in areas that need the mathematical support. Convincing documentation of this fact is given in the Department of Education's own 1994 Mathematics Sampler that became available in December of 1994. Attached is a brief summary of that document with sample pages that show how the Framework recommendation is actually being carried out in our state.

By contrast, the strongest school in my geographical area, Pasadena Polytechnic, uses a battery of exams from the Educational Records Bureau, the ERB Comprehensive Testing Program, to measure the performance of its students and thereby its programs. The tests consist only of multiple choice items because of speed, cost, and consistency of scoring. Nobody in Pasadena argues that Polytechnic is failing to teach the deeper levels of mathematical understanding that the "authentic" types of evaluation are supposed to engender. Polytechnic and all other good schools do plenty of regular work with applied situations in which an underlying mathematical base is present. Of course, the students are expected to see it, to use it, and to present their conclusions appropriately and convincingly. Having the state pretend to find out whether or not that is happening in our public schools by having students write a letter to the principal as a measure of mathematical communication is simply absurd.

Teacher Credentialing and Licensing

Having served since 1988 as a member of the mathematics advisory panel to the Commission for Teacher Credentialing (CTC), I am very familiar with the influences that drive implementation of the portions of the education code which govern certification of prospective mathematics teachers. Strictly speaking, the 1992 Framework could not have influenced work that was already underway in 1990. In fact, however, the people of influence on our committee were also people of influence in the preparation of the Framework. Their mathematics education philosophy is seen throughout the document that we prepared, Standards of Program Quality for the Subject Matter Preparation of Candidates for the Single Subject Teaching Credential in Mathematics. As with its NCTM predecessor, the word "standard" in the title is disingenuous; there is no real standard in the document. Instead it reflects a philosophy that has allowed nearly all of the CSU applications for program approval to be rejected because that philosophy is not adequately reflected in the programs under review. Instead of subject matter preparedness in mathematics, i.e., mathematical competence, the document is being used, and was intended to be used, to confirm that new teachers share the same educational philosophy as the state.

As an example, programs are being rejected because the courses have not been taught "using the multiple teaching strategies that the candidates will be using in their own classrooms". This is not mathematical competence; it is educational philosophy taking precedence over mathematical competence. Among the few pages of substance in the 1985 Framework were the portions of pages 6 and 7 that specified specific course requirements for teaching at Levels I, II, and III of precollegiate education. The most cynical, but also the most probable, reason that this was eliminated in the 1992 version was because it made too many of our state's poorly prepared mathematics teachers feel bad. Current CTC practice not only fails to require appropriate mathematical content, it is attempting to reject giving credit for appropriate mathematical content if it wasn't taught according to the Framework guidelines. Universities are attempting to resist the mandate to compromise quality as dictated by mathematically less knowledgeable people but the pressure is definitely present and some will feel compelled to acquiesce. Inducing mathematics students from the strongest universities into teaching, already a difficult task, will be even more difficult since the state will not be recognizing their educational background as appropriate subject matter preparation.

Another area for which programs are being rejected is failure to use appropriate technology and credit for this is also due to the Framework mandates. Since there is almost no data-based research that supports that requirement, the position again mandates that mathematical competence is less important than mathematics education philosophy.

A third criterion for rejection of programs, and once again with Framework support, is failure to appropriately address issues of diversity and multiculturalism in the curriculum. This position mandates that mathematical competence is less important than the evaluators' own form of racism. Perhaps the greatest gift of Jaime Escalante was the dramatic confirmation that Hispanics, and by extension Blacks or any other racial or ethnic subgroup, learn mathematics just like Whites and Asians. Until the educational community actually hears that message, however, such glimpses of true egalitarianism will remain isolated and underrepresented communities will remain in that status.

The most serious problem with teacher certification in California, however, is not at all due to the Framework, the NCTM Standards, or any other document. It is directly due to the legislative mandate that created and maintains a gaping hole through the credentialing maze that allows the majority of prospective teachers of mathematics to study little of the discipline beyond high school mathematics and to avoid these university mathematics programs entirely. For more than two decades, the CTC has authorized an exam of minimal competence that is described as measuring mathematical competence at the level of calculus and beyond. The reality is that bright high school students who have never studied anything beyond algebra have taken the test and scored well above the level that the CTC deems passing. The availability of such an exam has vastly disguised the problem of having teachers who are not properly credentialed in the discipline they teach; they are credentialed but they understand mathematics only at a low level of sophistication. Until this option is removed, the majority of prospective mathematics teachers will continue to obtain certification by the alternate route: Meet the qualifications for a credential in some other discipline, brush up or take a monkey-see monkey-do course to pass the waiver exam, and add mathematics to the credential. The whole operation can be done with the initial application for a teaching credential and permanent mathematics certification magically appears.

Since university mathematics can be challenging, it is easy to see why so many choose this route. The CBC refuses to release the number or the percent of teachers who have received their mathematics credential by this means but it is at least 50% and perhaps higher than 80% of the state's mathematics teaching force. This may well be the primary reason that underlies the Framework philosophy downplaying the necessity of verifiable mathematical competence at deepening levels of sophistication as students pass through the curriculum. It may also be the reason that public schools have been so reluctant to recruit displaced aerospace engineers into the teaching force. That level of mathematical competence is just too threatening to both administrative and teaching personnel.

Respectfully submitted,
Wayne Bishop
Mathematics and Computer Science
California State University, LA
January 1, 1995