In [1], Jerry Becker and Bill Jacob [B&J] reported on the "Math War Development in the United States (California)" from their particular perspective. This they did by including facts that supported their opinions and omitting those that did not. It is the purpose of this article to supply some - but by no means all - of the essential facts missing from their article in order to enable the reader to form a more balanced view of what is widely referred to as the "math war in California."
My perspective derives from having served, as did Bill Jacob, on the 1997 mathematics framework committee ( see paragraph 1 of page 18 of B&J), being a professor of mathematics at the university of California, Davis, having served as president of the Mathematical Association of America (MAA), a member of the California State Board of Education (SBE) from 1982 to 1985, and a member of numerous other committeess concerned with mathematical education at the state, national, and international levels.
As stated by B&J (see last paragraph of page 17), "by the summer of 1995 the verdict was clear, the 1992 Mathematics Framework (MF) had failed." This verdict was arrived at among others by the numerous parent groups that had organized themselves in many California cities in opposition to what they perceived as the damaging results of the 1992 MF on the mathematical education of their children. The most active of those parent groups were those of San Diego and Palo Alto. They called themselves "Mathematically Correct" and H.O.L.D., respectively. Others, such as Q.E.D. in Santa Barbara, were equally strong in opposition to some of the reforms advocated in the 1992 MF. Most of these groups include primarily scientists with some - but relatively few - mathematicians. Their leaders include biologists and political scientists, the latter primarily because they know how to get organized effectively and to deal with the media.
The verdict was, however, also shared by many prominent mathematicians in California. Some of these had strongly advised the SBE not to approve the 1992 MF at the time it came before that board for action.
As a result of this widespread dissatisfaction with the 1992 MF, California Superintendent of the Public Instruction Delaine Eastin appointed in April 1995 a "California Mathematics Task Force" (CMTF) to address the need to improve the mathematics achievement of California students. Her message was clear and emphatic. She called for action:
"Let's do what needs to be done to turn education in mathematics around - to prepare all of California's children for success in the future by providing them with the knowledge and skills they will need. And let's do it now."
Two co-chairs were appointed to lead the CMTF. Surprisingly, one of them was them same person who is identified in the 1992 MF as having directed the development of its final stages. In September 1995 the CMTF issued its recommendation in a document "A Call to Action: Improving Mathematics Achievement for All California Students" [2] containing five major recommendations, the first one of which is the following:
"The State Superintendent of Public Instruction must act immediately to establish clear and specific content and performance standards for mathematics and to work with districts and schools to make the standards achievable by all students."
This recommendation clearly called for a revision of the 1992 MF whose lack of "clear and specific content and performance standards" and of an appropriate balance between basic skills, conceptual understanding, and problem solving had been the cause of so much of its criticism. Indeed, the SBE was deeply concerned about this when it sent, jointly with the State Superintendent of Public Instruction and the California Commission of Teacher Credentialing, a "Mathematics Program Advisory" in October 1996 to all school superintendents and principals advising them that "the Mathematics Framework will be revised during 1997 with adoption by the State Board of Education scheduled during 1998."
In August, the California Curriculum Commission (CC) recommended to SBE the appoinment of 15 members for a new Mathematics Framework Committee (MFC), to revise the 1992 MF in accordance with the recommendations of the CMTF and the Mathematics Program Advisory. The CC was, of course, required to choose these members from those who had submitted formal applications to serve on the MFC. 94 such applications had been received. The CC unfortunately selected for its nominations - with only one exception - only persons who had been involved in preparing the 1992 MF or were well known to be strong supporters of it.
The SBE, therefore, had no choice but to reject many of these nominations. The Board felt that such a Committee needs to contain a proper balance of members known to be supportive of the 1992 MF, those known to have substantial reservations about that Framework, and those who had not expressed any opinion on the matter. Accordingly the SBE appointed 8 of those recommended by the CC and chose 14 others by carefully reviewing the qualifications of those who had submitted formal applications for the position. By regulations, more than half of the MFC must consist of K-12 teachers of mathematics. Many of them had received awards for the excellence of their teaching. Among the other members of the Committee were representatives from all involved and interested constituencies (most of whom were not represented on the CC-recommended Committee), such as mathematics departments of the California State University System (which prepares the vast majority of teachers in California and had not a single representative among the CC-recommendations), the University of California, Stanford University (in fact the Committee included the current or immediately preceding chair of the mathematics departments of Berkeley, Stanford, and Davis), schools boards, parent organizations, scientists using mathematics, etc. The decision of who should chair the Committee was left for the Committee itself to make by secret ballot. The Committee selected Deborah Tepper Haimo, who has held many positions of leadership including the presidency of the MAA. In addition, she had only recently moved to California and was, therefore, not identified with any of the views on mathematical education in California.
Since B&J report "an elimination of all discussion of pedagogy" from the MF draft, it should be noted that the MFC agreed to soft-pedal pedagogy and emphasize content as one of the frequently voiced objections to the 1992 MF had been its strong advocacy of one particular teaching strategy without any clear evidence that it is the most effective one in all situations. This decision also resulted from the desire on almost everybody's part to give teachers as much freedom as possible to use the teaching strategies they deem most effective for their individual circumstances. The MFC, however, urged a balance in the use of several possible instructional strategies in its draft which also included a description of properties of a good lesson.
As reported by B&J, "in 1997 the framework committee met, developed and sent a draft to the CC with all eight CC-recommended framework members voting against it." Not reported there is the fact that, of the 14 additional members appointed by SBE, 13 voted for it and 1 against so that the draft was approved by a vote of 13 to 9.
The draft was then sent out for field review with 2,000 copies sent to country offices of education, school districts, universities, and mathematics experts and 300 individuals who requested a copy. Reviewers generally supported most parts of the framework "as they marked very good/good over 50% of the time for chapters I, II, III, IV, V, VII, VIII, X, XI, XII, Appendices B and C" (a quotation from the Field Review Results, prepared by the CC). That chapter VI (Curriculum Content) did not enjoy full support is not surprising. The MFC knew that it would have to be rewritten after the school mathematics (K-12) standards would become available (which they were not at the time the draft was completed by the MFC) and, therefore, did not develop that chapter with the same care as it did the others.
As reported by B&J (see page 17, paragraph 2), "Standards are new to California." They were developed by a "Standards Commission" (SC) that completed its work in September 1997 and sent its draft for action to the SBE. The SC included only one member with any expertise on mathematics, a middle school mathematics teacher.
Public hearings on these draft Mathematics Standards were held. All mathematicians present at the public hearing I attended on October 20, 1997, in Sacramento, without exception, gave testimony why these Standards in their present form were completely unacceptable. Accordingly, the SBE asked a group of mathematicians, mostly from Stanford University, to revise the Mathematics Standards to address the concerns made known at the public hearings. This revised draft was approved unanimously by the SBE in December 1997. As a former member of the board, I note that it is rather unusual for any action by the SBE to be approved unanimously.
When a few teacher educators in California raised strong objections to the Mathematics Standards approved by the SBE, an open letter to them was prepared from which the following is a brief quotation:
"We urge you to recognize the important and positive role California's recently adopted mathematics standards can play in the education of future teachers of mathematics in the State of California."
This letter was signed by more than 100 mathematicians from California's institutions of higher education including the chairs of the mathematics departments at Stanford, California Institute of Technology, the Irvine and Riverside campuses of the Univeristy of California, The California State University at Los Angeles, The Vice President of the American Mathematical Society, etc. Many mathematics teachers at the elementary and secondary level, including Jaime Escalante, added their personal endorsement of this Open Letter.
Perhaps more important than these favorable statements about the new California Mathematics Standards is the document " State Mathematics Standards: An Appraisal of Math Standards in 46 States, the District of Columbia, and Japan," by Ralph. A. Raimi and Lawrence S. Braden, commissioned by the Thomas B. Fordham Foundation. While this booklet appears in the list of references of the article by B&J, no mention of it is made in the body of that article. The following is a brief description of its contents: The report represents a detailed analysis of all mathematics standards that were available, 47 in all. Grades of A, B, C, D, or F were given to each state, based on an analysis of the contents according to criteria and grade levels described early in the report. The highest score possible was 16.0, which only California received, Japan was next with 15.0, followed by North Carolina with 14.2 Only threes states received a grade of A, and just nine others a grade of B, seven a grade of C, twelve a grade of D, and sixteen a grade of F.
B&J conclude: " Perhaps we can see that the California 'math wars' have in their final analysis, served a useful purpose." I certainly agree. Just think for a moment where California mathematics education would be now without this war. The National Assessment of Educational Progress in which California ranked 41st out of 43 states, would likely rank it at its next administration at the bottom of all states. More importantly, the math wars in California have forged a very strong coalition among the many constituencies with a vital interest in a significant improvement in mathematics education in California, most notably mathematicians, teachers, parents, and members of the SBE. If this strong coalition can be preserved once the war has ended, the future of mathematics education in California looks bright indeed, and developments in California can serve as a model for other states and even nations who wish to advance their mathematics education significantly.
This article has benefited greatly from valuable suggestions made on an earlier draft by Ruth Asmundson, Deborah Tepper Haimo, Martha Swartz, and Voula Steinberg.
[1] Jerry P. Becker and Bill Jacob,
Math War Developments in the
United States (California), The International Commission on Mathematics
Instruction, Bulletin No. 44, 1998.
[2]
California
Department of Education, A Call to Action: Improving
Mathematics Achievement for All California Students, Sacramento,
California, September 1995 [3]
Ralph A. Raimi and Lawrence S. Braden,
State
Mathematics Standards, Thomas B. Fordham Foundation
Henry Alder is Professor of Mathematics, Department of Mathematics, University of California, Davis, CA 95616-8633, USA [hlalder@ucdavis.edu]