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Topic: NCTM Ignores Recent History of School Math (part 7 of Open

Replies: 4   Last Post: Dec 12, 1995 11:36 PM

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Frank Allen

Posts: 17
Registered: 12/6/04
NCTM Ignores Recent History of School Math (part 7 of Open

Posted: Dec 11, 1995 1:03 PM
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7. The NCTM ignores the 20th century history of school mathematics.
Now in my 86th year, I remember most of this history--and I made some
of it at both State and National levels (See Enclosure 7 My Vita with
Addendum) The NCTM Board should study this history. If they did they
would be less likely to classify as "innovative" ideas that have been
hardy perennials throughout this century. Example: Integrated Math.

I first heard of this idea from Professor E.R. Breslich of the University of
Chicago in the late 30s at a meeting of the Men's Mathematics Club of
Chicago*. Since then it has surfaced repeatedly. The names Swenson, Howard
Fehr, Phil Jones, Philip Peak and Vernon Price come to mind. The last three
wrote a series of texts based on this principle. Moreover, this list
includes the names of three former Presidents of the Council.

*Now called "Metropolitan Mathematics Club of Chicago".

Did the Standards writers give credit to their distinguished predecessors in
the field as ethical practice requires? Did they say, "We agree with
these proponents of integration in the field of school mathematics and we
think it should be tried again?" No. To do so would have been an admission
that something worthwhile happened in school mathematics before1987. An
idea which is anathema to them. Instead they presented it as another
innovation; another one of the "visions" with which they have been
blessed, thus taking advantage of the public's ignorance on the subject.
This is shoddy and reprehensible.

Another instance where old ideas are hailed as new is provided by the
subject areacalled "Discrete Mathematics". Set language, counting theory
involving permutations and combinations, Pascals triangle, proof of the
binomial theorem for positive integer index, mathematical induction and
probability have been taught in our secondary schools for many years in
courses such as College Algebra. Texts such as Rosenbach and Whitman, Fine,
Reitz & Crawthone come to mind. It is quite misleading therefore to suggest
that the introduction of topics in discrete mathematics is a major change.
I am reminded of Molier's seventeenth century play in which one of the
characters reacts to the information that any language which is not poetry
is called prose with the exclamation "Good heavens, for more than 40 years I
have been speaking prose without knowing it."**
Yes, and the ill-defined term "discrete mathematics" denotes a very wide
range of traditional topics that we have been teaching in high schools for
well over forty years without paying much attention to the label.
{By the way, what do we call mathematics which is not discrete?}

Retired Professor of Mathematics
Elmhurst College, Elmhurst, Illinois

1. B.Ed. - Southern Illinois State Teachers College, 1929.
2. M.S. (Mathematics) - University of Iowa, 1934.
3. Graduate Study - University of Illinois. Summers 1936, 1937, 1938.
4. Thirty-five years as teacher of high school mathematics in the State
of Illinois
5. Four years in the Army of the United States, 1942-1946.
6. President of Men's Mathematics Club of Chicago, 1952-53. Now
called "The Metropolitan Mathematics Club of Chicago."
7. President of Illinois Council of Teachers of Mathematics, 1954-55.
8. Chairman of the Department of Mathematics, Lyons Township High
School and Junior College, La Grange, Illinois 1956-68.
9. Chairman of the Secondary School Curriculum Committe of the
National Council of Teachers of Mathematics, 1956-59.
10. Member of Board of Directors of the National Council of Teachers
of Mathematics, 1958-61.
11. Director of the Regional Orientation Conferences on Mathematics,
1960. (National Science Foundation Support)
12. Member of Advisory Committee for the School Mathematics Study
Group, 1958-63, 1965-68.
13. Member of Textbook Panel, SMSG, 1958-60.
14. Chairman of the Eleventh Grade Writing Team, SMSG, 1958-60.
15. Member of the Council of the Conference Board of the
Mathematical Sciences, 1960-62.
16. President of the National Council of Teachers of Mathematics,
17. President of Mu Alpha Theta, 1965-68.
18. Distinguished Life Member Award from Illinois Council of
Teachers of Mathematics, 1969.
19. Member of the NCTM Headquarters Facility Committee, 1968-70.
20. Elmhurst College, Department of Mathematics, Associate Professor
1968, Professor 1972, Chairman, 1971-1975.
21. Elmhurst College, Division of Natural Sciences and Mathematics,
Chairman 1972-75.
22. Member District 205 Board of Education, 1977-83.Chairman Curriculum
23. Elmhurst Evening Lions Club, 1977- President 1980-81.
24. Max Beberman Award for "Leadership and excellence in teaching
mathematics education" from the Illinois Council of Teachers of
Mathematics, October 1987.
25. Distinguished Service Award from the Metropolitan Mathematics
Club of Chicago for "outstanding contributions to the advancement
of education in mathematics", 1988.
26. Elmhurst United Way/Crusade of Mercy, Director-at-Large 1985-88
(fund raising-allocations)
27. Zoning and Planning Commission for City of Elmhurst, 1985-90.
28. Teacher Training Program - Northern Illinois University, 1989.
29. Elmhurst Jaycee Distinguished Service Award, 1990.
30. Grand Marshall for City of Elmhurst Fourth of July Parade
(sponsored by Elmhurst Jaycees) 1990.
31. Melvin Jones Fellow Award by the Lions Clubs International
Foundation 1990.
32. Elmhurst College establishes Frank B. Allen scholarship for senior
math major who is planning to teach, 1991. (Award is made at end of
junior year)
33. Books: Modern Algebra - A Logical Approach (Book One) (with
Pearson), Ginn & Company, 1964.
Modern Algebra - A Logical Approach (Book Two) (with
Pearson), Ginn & Company, 1966.
Basic Concepts of Geometry (with Guyer)
Dickenson Publishing Company, 1973 (college level)

Addendum to vita, slightly revised 11/9/95:

I wish to convey the idea that, since my retirement in 1979, I have
maintained my interest in both school and undergraduate mathematics and
have kept myself informed about recent developments in these fields.

I read seven magazines each month.

Mathematics Magazine
The College Mathematics Journal
Journal for Mathematics Educators
NCTM Research Journal
The Mathematics Teacher (mainly now for the "Calendar"
and "Reader Reflections" where I occasionally contribute)
UME Trends
National Forum, the Journal of Phi Kappa Phi, one of five
math/science organizations of which I am an Honorary Life Member.

I attend meetings of local math organizations with reasonable
frequency and speak occasionally. I visit local math departments where
I have seen the TI82 and "Geometer's Sketchpad" used in the classroom.

I recently purchased an IBM-compatable computer with modem and laser
printer. It also has the EXL language for mathematical symbols and the
latest version of Geometer's Sketchpad. I will evetually gain acess to the
Internet with the material that President Price ignored.

I am informed. If I were not I could go on serenely playing mediocre
bridge and mediocre tennis, working for my Lions Club, re-reading old
classics like "Barchester Towers" and watching the four seasons march
through our beautiful backyard. But I am informed--and as a result I am
appalled at the state of secondary school mathematics today and at the
bizarre role of the NCTM. I feel that I must do what I can--never mind the
odds. I always admired Don Quixote.

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