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.
Sincerely,
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