Wow, Professor Rosa! It looks like "argument by inundation" (re your list of
31 references) according to my colleague, Dr. Lindsey Bramlett-Smith.
I share your distaste for most of these texts on your list. But you haven't
listed any "reform" texts at the two-year college level (incorporating all
of the following: guided discovery, emphasis on problem solving strategies
and testing of results, some collaborative learning, use of technology, an
attempt at integrating and connecting various topics in math, de-emphasis on
topics no longer as significant in a technological world); namely texts
which attempt to encourage thinking and discourage the cookbook -template
-memorization approach which the recent Third International Math and Science
Study(TIMSS) found to be so characteristic of US math (guess what teaching
methodologies were used by most of the countries who ranked higher than the US?)
I notice your reference to Saxon: the king of "Drill and Kill". Since I
still cannot discern your specific objections to reform math, I gather that
his is the approach you favor. You imply that you prefer books which are
"less verbose with more content" than recent texts.Unfortunately we have
crammed so much forgettable rote "content" into our courses that teachers,
in their race to "cover" the syllabus have little time to teach
problem-solving strategies. Much of the traditional content involves
memorization of algorithmic procedures (which certainly has its place), but
is this really learning mathematics? Isn't the major goal to produce
students who can solve problems, not simply imitattextbook templates?
The reform texts I have seen are still in preliminary or class-testing
formats. That is to say, this reform has not had a chance to really get
started yet (another conlusion of the TIMMS study-most US teachers mouth
but don't implement the NCTM STANDARDS), particularly at the two year
college level. Some of the texts you list merely "tack on" a motivating
question at the beginning of a section and/or some caculator exercises at
the end or in the margins.
You say you are not familiar with the UC Davis texts yet you list an article
critical of CPM. The CPM texts are the "UC Davis Texts"! This, along with
your list, makes me to think that you are not familiar with the reform
(embodied in the NCTM and AMATYC STANDARDS) directly - that you have
rejected it a` priori .
The attitude of the students in Toom's article(#26) - fear of any non-text
problems, resentment of "extra but interesting" problems posed by the
teacher- is the very attitude the reform is attempting to change. It is also
the common attitude of at least a generation of students subjected to a
curriculum which has hardly addressed the skills of problem solving (in
spite of the efforts of teachers like Polya`) but has emphasized Saxon- like
memorization of algorithms, many of which are obsolete. "Drill and kill"
produced Andrei Toom's pathetic students.Toom dismissed them, refusing to
accomodate their level.. He mentions no attempt to help them out of their
intellectual backwater. He simply rages about the US "system" as compared to
the Soviet students he taught in an elite school.
I still wish you would tell us SPECIFICALLY what you mean by "rubbish" and
"inappropriate" content. What is it that YOU don't care about? Forget the
quotes from the anti-reform extremists. Tell us what has been introduced
into the curriculum recently that you find so abominable and why.For
example, it seems clear that you object to the use of graphing calculators,
judging by your quote concerning a British study. Specifically, why do you
object? Ar there no situations in which graphing calculators are
appropriate at the two-year college level?
If it is not the emphasis on problem-solving you object to, is it the
attempt to make math less divided into specific courses like algebra,
geometry, trig, etc and instead connect these topics, integrate more data
analysis into them as well as probability?
What is it that you object to in the NCTM STANDARDS AMATYC STANDARDS
(Crossroads in Mathematics?. The elements of the reform are listed in these
documents. I have trouble with some of these elements (e.g "portfolios"- I
cannot see how listing one's favorite problems contributes much to
understanding). Which ones do you object to? I thought that they were
general enough to accomodate most of the mathematical community.
There is plenty to critique about the reform and the attempts to implement
it. Let us hear about your direct experiences and lets make sure we have the
right target.
I won't counter with a list of supporting literature. I will note that the
August 1995 issue of FOCUS (MAA Newsletter) contained an official statement
by the Conference Board of Mathematical Sciences, consisting of the 14
presidents of all of the Math organizations in the US, supporting the reform
efforts.
**************
>Prof. Mallen,
>I am not in a position to comment on the UC Davis and UICSM series. An
>exhaustive review of the Berkeley project has been done by Hung-Hsi Wu in
>[31]. Additional critiques appear in [1], [2], [3], [29], and [30]--articles
>that should be read by all mathematics teachers.
>The comments that I made at the end of January were about the traditional
>college preparatory curriculum that I studied in 1962-66 and the way it has
>been demolished during the last 30 years. An accurate term for the rubbish
>of the past 30 years is "post-Sputnik curriculum" (I hope that this term
>catches on).
>
>Here are some brief comments about the traditional and post-Sputnik curricula.
>
>Traditional: Algebra I books were similar to [28], but less verbose and with
>ore content. My Geometry book [24] had a ten-page introduction to the basic
>notions and postulates of plane geometry. The next 15 pages involved
>elementary constructions. Congruent triangles and proofs started on page 29.
>I have been unable to trace my Algebra II book (about 400 pages), but it
>covered matrices, vectors, introduction to trigonometry, etc. My Advanced
>Mathematics book [14] is absolutely priceless. The first 59 pages cover Solid
>Geometry (in 10th grade we had covered only plane geometry). Trigonometry
>starts on page 60, with all sorts of interesting proplems involving the
>solution of right triangles, before graphs, identities, and inverse
>functions are discussed. [27] is similar to [14] but excludes Solid
>Geometry.
>
>The post-Sputnik curriculum: I cannot understand why the Houghton Mifflin
>series--[7], [13] (congruent triangles appear on p. 190), the original
>edition of [5], and [8]--was ever written, published, and adopted. These
>books would have been highly inappropriate for most of the students, like
>me, who were enrolled in the college prep courses. I now understand why my
>teachers retired as soon as they could, why so many young math teachers
>left for the private sector in the 1970s, and why so many students have
>been destroyed by these books. The current versions of these books--[6],
>[16], [17], [18], [21], [22]--are even worse than the originals. If
>anyone can find any redeeming value in [9], [11], and [19], let me know.
>
>If the traditional curriculum had been used as a foundation for the present
>reforms, as I have done in overhauling all my courses, significant
>improvements could have been achieved. Unfortunately, most current reformers
>are as misguided as those who promoted the post-Sputnik curriculum--see
>[4], [10], [12], [15], [20], [23], and [26].
>Great Britain implemented a national curriculum based on intensive use of
>calculators and the "guided discovery method." The results of the 1995
>national tests were an abject failure, especially among 11-year-olds,all
>of whom had been educated under the new curriculum [25].
>
>Dom Rosa
>
> REFERENCES
>
> 1. George E. Andrews, Mathematical education: a case for balance,
> Coll. Math. J., 27(1996) 341-348.
>
> 2. Richard Askey, Reviews, Amer. Math. Monthly, 102(1995), 78-81
>
> 3. Richard Askey, Reviews, Coll. Math. J., 23(1992) 445-448
>
> 4. Michael J. Bosse, The NCTM standards in light of the New Math
> movement: a warning!, J. Math. Behavior, 14(1995) 171-201.
>
> 5. Richard G. Brown et al., Algebra and Trigonometry: Structure and Method,
> Book 2, Houghton Mifflin, 1992, 880p.
>
> 6. Franklin Demana et al., Intermediate Algebra: A Graphing Approach,
> Addison-Wesley, 1994, 900+p.
>
> 7. Mary P. Dolciani et al., Algebra 1, Houghton Mifflin, 1967, 650p.
>
> 8. Mary P. Dolciani et al., Modern Introductory Analysis, Houghton Mifflin,
> 1964, 651p.
>
> 9. Robert E. Eicholz et al., Addison-Wesley Mathematics (Grades 4-5),
> Addison-Wesley, 1991, 541p. and 545p.
>
>10. Efim A. Galperin, Compumatics versus Mathematics?, Notices Amer. Math.
> Soc., 43(1996), p. 741-742.
>
>11. Mary Ann Haubner et al., The Mathematics Experience (Grade 5),
> Houghton Mifflin, 1992, 503p.
>
>12. Enoch Haga, Before the Apple Drops, 1994. (15 Essays written by a 35-
> year veteran math teacher of the California public scools)
>
>13. Ray C. Jurgensen et al., Geometry, Houghton Mifflin, 1969, 650p.
>
>14. William E. Kline et al., Foundations of Advanced Mathematics,
> American Book Co., 1959, 519p.
>
>15. Neal Koblitz, The case against computers [and graphics calculators] in
> K-13 math education, Math. Intelligencer, Vol 18, No 1 (1996) p. 9-16.
>
>16. Edwin E. Moise et al., Geometry, Addison-Wesley, 1982, 680p.
>
>17. Motohico Mulase, A book review, available at the Web site:
> http://ourworld.compuserve.com:80/homepages/mathman/
>
>18. Eugene D. Nichols et al., Holt Algebra with Trigonometry,
> Holt, Rinehart and Winston, 1992, 862p.
>
>19. Jack Price et al., Mathematics: Applications ad Connections,
> Course 1 and 2, Glencoe, 1995, 620p and 652p.
>
>20. Jerry Rosen, Mathematics Education and Policy, Notices Amer. Math. Soc.,
> 43(1996), p. 534-535
>
>21. Rheta N. Rubinstein et al., Functions, Statistics, and Trigonometry,
> Scott, Foresman, 1992, 937p.
>
>22. Merilyn Ryan et al., Advanced Mathematics: A Precalculus Approach,
> Prentice Hall, 1993, 946p.
>
>23. John Saxon, The coming disaster in science education in America,
> Notices Amer. Math. Society, 41(1994), p.103-105.
>
>24. William G. Shute et al., Plane and Solid Geometry,
> American Book Company, 1960, 448p.
>
>25. Tackling the Mathematical Problem, A Report to the London Mathematical
> Society, Institute of Mathematics and its Applications, and the Royal
> Statistical Society, October 1995.
>
>26. Andrei Toom, A Russian Teacher in America, J. of Math. Behavior 12
> (1993), 117-139.
>
>27. Glen D. Vannatta, Advanced High School Mathematics, Merrill, 1961, 420p.
>
>28. Alden T. Willis et al., Elementary Algebra, Wadsworth, 1987, 388p.
>
>29. Hung-Hsi Wu, The Mathematics Education Reform: What is it and why should
> you care, (preprint) June 10, 1996.
>
>30. Hung-Hsi Wu, Reviews, Mathematical Intelligencer, 17, No.1(1995), 68-75.
>
>31. Hung-Hsi Wu, Review of College Preparatory Mathematics (CPM) at Berkeley
> High School (1992).
>
>
***********************************
Mike Mallen
Professor, Mathematics
Mathematics Department
Santa Barbara City College
721 Cliff Drive
Santa Barbara, CA 93109
805-965-0581- ext 2267
mallen@dospueblos.sbceo.k12.CA.us (home)
or mallen@gate1.sbcc.cc.ca.us (school)