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NCTM Ignores Recent History of School Math (part 7 of Open Letter)
Posted:
Dec 11, 1995 1:03 PM


7. The NCTM ignores the 20th century history of school mathematics. Now in my 86th year, I remember most of this historyand 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 illdefined 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?}
FRANK B. ALLEN 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. Thirtyfive years as teacher of high school mathematics in the State of Illinois 5. Four years in the Army of the United States, 19421946. (PrivateCaptain) 6. President of Men's Mathematics Club of Chicago, 195253. Now called "The Metropolitan Mathematics Club of Chicago." 7. President of Illinois Council of Teachers of Mathematics, 195455. 8. Chairman of the Department of Mathematics, Lyons Township High School and Junior College, La Grange, Illinois 195668. 9. Chairman of the Secondary School Curriculum Committe of the National Council of Teachers of Mathematics, 195659. 10. Member of Board of Directors of the National Council of Teachers of Mathematics, 195861. 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, 195863, 196568. 13. Member of Textbook Panel, SMSG, 195860. 14. Chairman of the Eleventh Grade Writing Team, SMSG, 195860. 15. Member of the Council of the Conference Board of the Mathematical Sciences, 196062. 16. President of the National Council of Teachers of Mathematics, 196264. 17. President of Mu Alpha Theta, 196568. 18. Distinguished Life Member Award from Illinois Council of Teachers of Mathematics, 1969. 19. Member of the NCTM Headquarters Facility Committee, 196870. 20. Elmhurst College, Department of Mathematics, Associate Professor 1968, Professor 1972, Chairman, 19711975. 21. Elmhurst College, Division of Natural Sciences and Mathematics, Chairman 197275. 22. Member District 205 Board of Education, 197783.Chairman Curriculum Committee 23. Elmhurst Evening Lions Club, 1977 President 198081. 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, DirectoratLarge 198588 (fund raisingallocations) 27. Zoning and Planning Commission for City of Elmhurst, 198590. 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.
Quantum 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 IBMcompatable 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, rereading old classics like "Barchester Towers" and watching the four seasons march through our beautiful backyard. But I am informedand 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 cannever mind the odds. I always admired Don Quixote.



