We are pleased that Prof. Alder has read our article and provided some additional details about the "debate" in California. In our view, however, he chose to merely describe a few events. We do not believe his discussion sheds significantly more light on the dynamics surrounding the controversy. Prof. Alder listed areas of agreement, but seems to avoid discussing the core and problematic issues identified in our article - these include the issues of: (1) what balanced standards actually are, (2) the exclusive reliance on behaviorist research and the direct linkage of state policy to this one-sided view of education, (3) the State Board's practice of circumventing public review of documents prior to major decisions as required by state law. For example, the SBE's use of gross misinformation in an important instructional materials adoption in September, 1997.
Alder mentions two important state documents - the CMTF's "A Call to Action" and the SBE's "Mathematics Program Advisory". Two key recommendations in these documents are calls for "clear and specific content and performance standards" and a "balance of basic skills, conceptual understanding, and problem solving" in California mathematics education. Both of these recommendations have wide support in California; for example, the public discussions of the Mathematics Framework Committee during 8 months of 1997 give ample evidence, in our judgement, that striving for balance and clearly articulated standards is a goal shared by all. The controversy, however, arose when the parties began the real work of trying to bring some specificity to the ideals of "high standards" and "balance". In our article, we illustrated the nature of the discussions by citing specific examples provided by those with different views (see pp. 20-21). In response, Alder does not seem to offer anything specific. Instead he presents general discussion and some history about the need for clear and high standards - it is our hope that the reader will not erroneously infer that one camp supports high standards, while the other does not. On p. 19 we note that "The press seemingly never examines why both sides claim their views represent 'high standards'." We note that Alder has seemingly also chosen to avoid this issue.
We noted (p. 18) how the processes used by the SBE of making substantial last minute policy reversals using documents withheld from public inspection has inflamed the controversy. On p. 18 we cite two examples (there are more, in our opinion) from a memo presented by Janet Nicholas to the SBE on September 9, 1997, where in a few minutes the Board reversed a recommendation to approve two Dale Seymour programs for adoption (also see [J, 1998]. Nothing is more important than providing high-quality instructional materials for teachers, yet the SBE acted hastily using blatant misinformation. Yet Prof. Alder does not comment on this central issue - perhaps because members of the parent H.O.L.D. group, mentioned by Alder, presented Mrs. Nicholas' documents to the Palo Alto School Board in April 1998 (which included her number theory "error" that "30 does not divide 36x45") in a campaign to dissuade them from choosing the Dale Seymour materials. After careful consideration of the actual documents, the Palo Alto School board adopted the Dale Seymour materials (by a 4 to 1 vote), even though state monies for their use were not available.
The Standards revision was produced by four Stanford University mathematics professors, and the SBE accepted their work in December without significant public input or consultation with K-12 teachers or mathematics education faculty. As we noted (p. 18), the Commission's draft of the Standards was hastily assembled and "both sides of the debate criticized and worked to correct" it. However, we wonder if Alder wants the reader to believe that the flaws in the Commission's document necessitated the one-sided consultation, only by research mathematicians, and that those critical of the SBE action somehow were in favor of the problems with the Standards. There were many critics of the SBE action and they felt that the revisions had lost balance in favor of automatic skills (and therefore lowered standards by short changing conceptual understanding), and that the revision's wording doesn't communicate well with teachers and parents. The only way to develop an informed opinion is for readers to compare these two documents side-by-side. In our paper, we discussed specific examples, while Alder seems to offer vague references to letters by research mathematicians aligned with one side, and a report by the Fordham Foundation whose criteria are not given; moreover, we wonder about the status of the Fordham Foundation regarding educational matters in mathematics education in the United States.
The Mathematics Framework is another instance where the SBE is now substituting documents prepared outside the public process to impose substantial policy changes. Alder notes the agreement of the 1997 FW committee to "soft pedal pedagogy". However, the proposed Framework (latest version released Nov. 23, 1998, see www.cde.ca.gov ) shows that the SBE is preparing for quite the opposite - they will demand highly prescriptive drill-and-practice teaching based upon the narrow "research" described in our article (pp. 19-20), and materials adoptions and professional development for California teachers will be tied to this (the latter specified in AB 1331 signed by Gov. Wilson in August, 1998). Much of the new Framework material was prepared by Prof. David Geary at the request of the SBE. The draft by Geary prominently cites the report by Douglass Carnine's group described in our article in his revision of the "Instructional Strategies" chapter of the new Framework. Given that the Chair of the 1997 Framework Committee adamantly refused to allow its members to present (let alone discuss) research in mathematics education as part of its deliberations, the fact that the one-sided approach of the Carnine group will now play a substantial role in California's instructional and materials adoptions will serve only to heighten tensions. California law requires that research be considered in its Frameworks and in instructional adoptions, yet Prof. Alder does not seem to comment on what we consider to be a "back door approach" to addressing this central and important issue.
Significant is the "Grade-level emphasis and instructional profiles" section in Geary's draft of the Framework, which details K-6 research-based instructional approaches. For example, the entire page and a half 3rd grade "Elaboration" does not contain any information going beyond rote mastery of symbolic procedures for number calculation. There is also a 22-page supplement for 7th grade teachers that details exactly how to teach compound interest, now a major area of skill emphasis in California. It's first sentence reads "Real applications of mathematics at the seventh grade are hard to find." In September, the Curriculum Commission added to Geary's original grade level commentary bulleted items under the title "Some of the key concepts that underlie the Standards at this grade are:", but all of these were deleted by the SBE in its Nov. 23 version. An entirely new Framework section "Special Considerations for Mathematics Assessment" has been added since the Oct. 13 version was released. Its emphasis is on "timed tests" to measure speedy recall of facts and procedures. One of its paragraphs reads:
"The level of knowledge of basic topics required for students to advance further requires that they be mastered to the level of automaticity. Consequently the best method for assessing the emphasis topics is the timed test."
This illustrates how willing this (unknown) Framework author is to ignore the importance of thoughtful problem-solving and conceptual questions as integral to balanced assessment. Anybody who studies this publicly-presented draft of the Framework will see that in spite of the claims to the contrary in its Introduction, California has now mandated an extreme back-to-basics approach that we believe will not enhance students' conceptual growth. The SBE vote on the Framework is scheduled for December 10, 1998. (We note that several key sections have not been made public by the November 23 posting of the draft.)
Contrary to the general statements such as those Prof. Alder presents, we believe that the details must be considered. The lack of balance in the California Standards and Framework will likely precipitate more bickering and tension among California mathematics teachers in the years to come - and we are already witnessing this at the present. We referred (p. 23) to the deep divisiveness of the debate over mathematics education reform in California and the nation. What is needed is constructive discourse and mutual respect for the ideas of people on all the sides of the issues. Beyond this, it seems important that the sides in the debate be willing to listen to each other and to work towards a consensus on policy documents that will play a crucial role in determining what educational materials and what teaching practices will characterize mathematics education in the future.
Jacob, B. (1998), 'Instructional materials for K-8 mathematics classrooms, the California adoption', 1997, Issues in Contemporary Mathematics, edited by E. Gavosto, S. Krantz, and W. McCallum, Cambridge, England: Cambridge University Press (to appear).
Jerry P. Becker is Professor of Mathematics Education, Department of Curriculum and Instruction, Southern Illinois University, Carbondale, IL 62901-4610, USA [jbecker@siu.edu]
Bill Jacob is Professor of Mathematics, Department of Mathematics, University of California, Santa Barbara, CA 93106-0001 USA [jacob@math.uscb.edu]