Statements from the pastAuthor(s): MARILYN N. SUYDAMSource: The Arithmetic Teacher, Vol. 17, No. 5 (MAY 1970), pp. 417-418Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41186226 .

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Statements from the past MARILYN N. SUYDAM The Pennsylvania State University, University Park, Pennsylvania

Marilyn Suydam is associate director of the Center for Cooperative Research with Schools and teaches courses in mathematics education. She is a member of the Editorial Panel of The Arithmetic Teacher. Currently, she is directing an interpretive study of research in mathematics education, for which bulletins and films are being developed.

J' study of textbooks written about the teaching of elementary school mathemat- ics during the past hundred years is an enlightening process - and an enjoyable one! Some of the statements made by these educators indicate a degree of romanticism, others stress then-current psychological be- liefs, while still others are universal gen- eralizations. Perhaps teachers will find the following samples provocative.

1. ... names beyond billion are of no par- ticular importance. Large numbers should always represent genuine American con- ditions.

2. As in all cases, the work is first presented several times by the teacher, then the class works at the blackboard under her direct supervision until the process is mas- tered and before any home or seat work is given.

3. Educators today have come to realize that it is the business of the schools not to teach the science of arithmetic as such to the pupils, but rather through the teaching of arithmetic to prepare the pupils for life.

4. (It is important) not to group all geo- metric work into one grade, but to intro- duce it gradually and make it coextensive with the course of arithmetic.

5. The present chaotic state of our methods in mathematics seems due to a number of causes: (1) the various views of what number is; (2) difference of opinion as

to what shall be selected from the whole field to be taught in grades 1-6 of the elementary schools; (3) the bondage we owe to past ideals; (4) the inertia of the school itself, or the slowness with which a great institution like the school changes; (5) recent marked progress in the indus- trial world, demanding different life prep- aration of graduates; (6) social progress; and (7) the great demand for teachers.

6. Number was primarily a thought in the mind of Deity. He put forth His creative hand, and number became a fact of the universe. . . . Man was created to ap- prehend the numerical idea.

7. Principles are determined by philosophy, devices by rational experience. The teacher must be loyal to principles, but the slave of no man's devices.

8. In our teaching how frequently do we find

that when our enthusiasm betrays us into introducing something beyond the experi- ence of the children, they suddenly come to life and share our enthusiasm.

9. A question draws the pupil's attention and prepares his mind for the reception of new information. . . . Anything may be unan- swerably propounded, by means of figures, to those who cannot think upon numbers.

10. A textbook, in its problems, as well as in its explanations, should be a guide, not a slave driver.

11. Proportion, it is reported, is seldom used; therefore, proportion shall not be taught. Then it will continue not to be used. Its

Excellence in Mathematics Education - For All 417

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true value may be anything from zero to infinity, but it cannot be taught because it is not used and it cannot be used be- cause it is not taught.

12. One of the chief reasons for the failure of pupils in arithmetic is that general ideas are not explicitly taught. Teachers expect pupils to think abstractly and to general- ize when they have had no adequate in- struction in these difficult intellectual proc- esses.

13. Just as he calls the words in a reading lesson without consciously recalling the letters of each word, so he must be able to call sums, products, etc., without being conscious of the numbers represented by the figures.

14. The equation lies at the base of mathe- matical reasoning; it is the key with which we unlock its most hidden prin- ciples; the instrument with which we develop its profoundest truths.

15. ... instead of stating to a class that 4 + 5 = 9, and drilling on this and other rela- tions, the schools have generally tended to have the pupils discover the fact and then memorize it. ... A child likes to be a dis- coverer, to find out for himself how to add and multiply, always under the skill- ful guidance of the teacher.

16. Present society is changing in its tech- nicalities, but the fundamentals of com- petent and useful living are not changing so rapidly that reasonable predictions or demands a generation or two in the fu- ture are either impossible or undesirable.

17. Today educational practices, curriculum materials, and teaching methods are being subjected to minute scrutiny, and must be demonstrably good if they are to be per- mitted to remain.

18. The possibility of completely revamping the present program is quite remote.

19. The vast majority of our elementary school pupils are not destined to enjoy the ad- vantages of a high school education.

20. The newer pedagogy of arithmetic, then, scrutinizes every element of knowledge, every connection made in the mind of the learner, so as to choose those which provide the most instructive experiences, those which will grow together into an orderly rational system of thinking about numbers and quantitative facts.

Sources

1. Smith, 1909 11. Buckingham, 1930 2. Stone, 1918 12. Judd, 1927 3. Overman, 1920 13. Stone, 1918 4. Klapper, 1916 14. Brooks, 1876 5. Smith, 1909 15. Smith, 1909 6. Brooks, 1876 16. Knight, 1930 7. McLellan and 17. Morton, 1927

Dewey, 1895 18. Thiele, 1935 8. Buckingham, 1930 19. Klapper, 1916 9. Cajori, 1896 20. Thorndike, 1922

10. Smith, 1909

References

Brooks, Edward. The Philosophy of Arithmetic. Lancaster, Pa.: Normal Publishing Co., 1876.

Buckingham, B. R. "The Social Value of Arith- metic." In Report of the Society's Committee on Arithmetic. Twenty-ninth Yearbook of the National Society for the Study of Education. Bloomington, 111.: Public School Publishing Co., 1930.

Cajori, Florian. A History of Elementary Mathe- matics. New York: Macmillan Co., 1896.

Judd, Charles Hubbard. "Psychological Analysis of the Fundamentals of Arithmetic." Supple- mentary Educational Monographs, no. 32, Feb- ruary 1927.

Klapper, Paul. The Teaching of Arithmetic. New York: D. Appleton & Co., 1916.

Knight, F. B. "Introduction." In Report of the Society's Committee on Arithmetic. Twenty- ninth Yearbook of the National Society for the Study of Education. Bloomington, 111.: Public School Publishing Co., 1930.

McLellan, James A., and John Dewey. The Psychology of Number. New York: D. Apple- ton & Co., 1895.

Morton, Robert Lee. Teaching Arithmetic in the Primary Grades. New York: Silver, Burdett & Co., 1927.

Overman, James Robert. Principles and Meth- ods of Teaching Arithmetic. Chicago: Lyons & Carnahan, 1920.

Smith, David Eugene. The Teaching of Arith- metic. Boston: Ginn & Co., 1909.

Stone, John C. The Teaching of Arithmetic. New York: Benjamin H. Sanborn & Co., 1918.

Thiele, С. L. "The Mathematical Viewpoint Ap- plied to the Teaching of Elementary School Arithmetic." In The Teaching of Arithmetic. Tenth Yearbook of the National Council of Teachers of Mathematics. Washington, D.C.: The Council, 1935.

Thorndike, Edward L. The Psychology of Arith- metic. New York: Macmillan Co., 1922.

418 The Arithmetic Teacher/ May 1970

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