Honest Open Logical Debate (HOLD)
                   on math reform
           510 Center Drive, Palo Alto, CA 94301
              329-9276 (day); 858-1688 (eve.)

May 16, 1995

James R. Brown
Mathematics Task Force
721 Capitol Mall, Rm 610
Sacramento, CA 95814

Dear Jim,

As you requested, the steering committee of HOLD, a parents' math-oriented
group in Palo Alto, has summarized what we feel are the main problems with
the California Mathematics Framework.

Please forward this document to the Mathematics Task Force members, so that
we can convey to them what we feel are the concerns of a great many
California parents.

We thank you for soliciting our input, and wish the Task Force success with
this crucial endeavor.


Barbara Chu
Bill Evers
Hanna Hoffman
Marina Polyak

HOLD Steering Committee

CC: Delaine Eastin, Superintendent of Public Instruction

Page 1 The Problems with the California Mathematics Framework HOLD - Honest Open Logical Debate Palo Alto, May 1995 Probably the biggest problem with the California Mathematics Framework of 1992 ("Framework") is what it is not - it is not a Framework. Educational frameworks are about standards: - Content standards: what is to be taught - and learned - at various grade levels - Performance standards: what students are expected to know and master at various grade levels In lieu of content standards, the Framework defers to the NCTM 1989 standards. In lieu of performance standards, it cannot defer to the NCTM, as that document doesn't have them either, so it just punts and says nothing. Instead, the Framework uses all of its 218 pages (1) to exhort and sermonize about the wisdom of a new way of teaching mathematics, without providing a single research reference that clearly demonstrates that this method works, and without 'bothering' to define how the success of the Framework will be assessed. The following are what we see as the major weaknesses of the Framework. 1. ==> It focuses totally on the 'constructivist' model. As a part of that, it insists on the teacher's role as facilitator only. (2) - The constructivist model is unproved, and there is no (i.e., zero) experience with its broad and exclusive application to instruction. - The Framework totally ignores the proven fact (3) that direct teaching is the most efficient method of transferring knowledge. 2. ==> It focuses only on mathematics applications, assuming that facts and procedures will somehow permeate the learner, without any direct or extensive instruction during such applications.(4) - Students will never get a clear and solid understanding of any branch of any subject area, as they never spend enough time to understand it. They just sample it as it pops up in the problems. - Students get bits and pieces of various topics, often spending enormous amount of time on esoteric and mostly useless but 'cute' ones, like tessellation.
Page 2 - There is no cohesion introduced by a clear scope and sequence, and no building on existing foundations. Instead the curriculum revolves around a collection of mostly disjoint 'problems'. - There are no textbooks, and those that are starting to come out are more activity books than textbooks. Students have nowhere to turn if they need individual study to catch up (e.g., during illness), while parents are helpless without any clear document describing the course content and its expectations. 3. ==> It blindly pushes for total de-laning and heterogeneous grouping based on equity arguments, while pretending that this will not harm achievement.(1) Empty promises like "In an empowering program no student will have to do 'simplified' material; neither will they be held back from challenging ideas because the content is slotted for a later grade."(2) have no substantiation in the text, and they give rise to ludicrous logical contortions such as: "Unusually talented young mathematicians need even more experience working with a cross section of their age group. When enrolled in classes for the gifted or pull-out programs, they are deprived [sic] of important perspectives and learning opportunities for working on complex tasks that they would enjoy [sic] if enrolled with a more representative cross-section of their peers."(3) Such extremism caused even the relatively cautious California State Board of Education to warn: "Regrettably, interest in the benefits of heterogeneous grouping as a tool to facilitate the learning of students in some situations has been interpreted to mean that advanced learners should never be grouped together or that they should be held back to assist less proficient learners. This is not our intent! Appropriate and adequate educational services for all children cannot be obtained by identical services for all. The particular educational and developmental needs of each student, including the gifted and talented student, are ignored when efforts provide only for uniform educational experiences for all."(4) - Laning is beneficial to academic achievement, as has been proven over and over again by research,(5) disinformation to the contrary by dogmatic egalitarians notwithstanding.
Page 3 - The ill effects of old-style tracking (tracking across the whole curriculum, limiting access to challenging material or good teachers, stigmatizing, low expectations, being 'stuck' in a lane) are mostly things of the past, and have little relation to currently practiced per-subject ability grouping and pull-out programs. In fact, a recent survey(1) found that almost 50% of high school students in Palo Alto changed math lanes, with over 50% of those moving to higher lanes. 4. ==> It insists on manipulatives at all levels(2) and calculators at all times.(3) - Manipulatives are heavily over-stressed. They are mostly important in the primary grades, and should be limited afterwards only to special situations. - This over-emphasis creates 5th grade students who still do 2 digit addition with their fingers. 5. ==> It focuses on what students "understand and can do rather than on what they don't know or can't do."(4) - This encourages mediocrity and feeling good, rather than achievement and excellence. - It removes teacher accountability for student performance - if the student doesn't perform, "he is not yet ready," and it becomes "nobody's fault." 6. ==> It expresses a strong disdain for any objective testing,(5) pretending that a teacher's subjective assessment ("authentic assessment" in newspeak) is much more reliable. The director of the University of Chicago Schools Mathematics Project has this to say on the subject: "Let us drop this overstated rhetoric about all the old tests being bad. Those tests were used because they were quite effective in fitting a particular mathematical model of performance - a single number that has some value to predict future performance. Until it can be shown that the alternate assessment techniques do a better job of prediction, let us not knock what is there. The mathematics education community has forgotten that it is poor performance on the old tests that rallied the public behind our desire to change. We cannot pick up the banner but then say the test are no measure of performance. We cannot have it both ways."(6) - Subjective assessment creates an absence of clear expectations of proficiency at all grade levels. As a result, it removes teacher accountability. - It obstructs student transfers between different programs and schools, a fact admitted by the Framework itself.(7)
Page 4 7. ==> It stresses communication about mathematics, rather than doing mathematics. - For some reason, what the Framework calls mathematics communication is English. It blandly ignores the mathematical symbolism that was developed over the years exactly to avoid the fuzziness and ambiguity that come with English language explanations. - The Framework has no real answers for low English proficiency students, and innocently exhorts us that they "must be given the opportunity to do mathematics ... in their primary language."(1) How will this be achieved without using mathematical symbolism? - We have seen students penalized because they didn't fill enough pages with prose, irrespective of how good their mathematics was. Teachers are urged to stress form over content, and give students false feelings of success or failure. For all of these reasons, we feel that the Framework is seriously flawed and must be subject to a total rethinking. On the other hand, we should also be clear that we do not reject all of the ideas in the Framework out of hand. This paper is a summary of what we feel is wrong with the Framework; however, there are many ideas in it with which we agree, for example devoting increased attention to probability and statistics, and to graphing and data visualization. We also feel that problem solving deserves an important place in the curriculum -- we just don't agree that an entire program should be based on it. In the end, however, we believe that it is only through honest, open, logical debate that our community can reach decisions on what we want our schools to look like.
Footnotes: Page 1 ----------------- (1) For comparison, Delaware's Mathematics Framework is 32 pages long, Maryland's 42, and Virginia's 55. They all include both performance and evaluation standards. (2) California Mathematics Framework (CMF), pp. 41 (3) See, for example, Watkins, C.L. Project Follow Through: A story of the identification and neglect of effective instruction. Youth Policy, v10 n7 (July 1988). Youth Policy Institute, Washington, D.C. (4)CMF, pp. 43 Footnotes: Page 2 ----------------- (1) CMF pp. 61-62, pp. 66 (2)CMF pp. 40-41 (3)CMF pp. 66 (4)California State Board of Education: Instructional Grouping, Gifted and Talented Education and Advanced Classes. Sept. 9, 1994, Sacramento, CA. (5)Kulik, J.A. Meta Analytic Findings on Grouping Programs, Gifted Child Quarterly v36 n2, pp 73-77. (Spring 1992). Footnotes: Page 3 ----------------- (1) PAUSD Mathematics Parents Survey, January 1995. (2) CMF pp. 41 (3) CMF pp. 181 (4) CMF pp. 42 (5) CMF pp. 183 (6) Z. Usiskin. What Changes Should Be Made for the Second Edition of NCTM Standards. UCSMP Newsletter, n12 pp. 10 (Winter 1993). (7) CMF pp. 134-135 Footnotes: Page 4 ----------------- (1) CMF pp. 45