A Report on "New Math" Workshops Conducted Duringthe Summer of 1962 for Teachers in the

Elementary SchoolsConducted by the Sisters of St. Francis,Mount Saint Francis, Dubuque, Iowa*

Sister Mary Paschal, O.S.F.’Wahlert High School, Dubuque, Iowa

At the close of our workshop, one of the participating teacherscommented: "As I see it, the whole approach to the teaching of math-ematics has changed. Algebra and geometry are no longer tabootopics prior to high school; algebraic terms and geometric figures areused from kindergarten through grade eight. Being able to choose aprecise one of many interchangeable symbols and realizing that it isjust that�a symbol for an abstract idea, simplifies the whole pictureand makes for a gradation of integrated learning rather than a twelve-year ^piecequilt5 where the pieces do not always fit."One very strong argument in favor of the so-called "new math" is

the conviction that here are the tools and the techniques for unifyingall arithmetic, algebra, geometry, trigonometry, and everything elseemployed in "quantitative thinking." The various branches of mathe-matics in the generation just passing have been taught, quite gener-ally, as separate topics, planted one upon the other. They would growtogether, it was naively hoped, layer by layer, as the pupil worked hisway from counting on his fingers and memorizing the addition combi-nations, through agonizing hours spent in learning the multiplicationtables by rote, on through somewhat reluctant acceptance of histeacher’s justification for the Pythagorean Theorem, blindly on andon. The trend to-day is to view the entire realm of mathematics as a

mightly network whose threads intertwine, whose partial usefulnessand total understanding are dependent upon the coordination ofmany threads. Hence, there are certain basic concepts which must beclearly understood by all who would propose to develop the mathe-matics curriculum. Teachers in the elementary grades as well as thoseengaged in secondary and college education must be well acquaintedwith such topics as: Thought Processes Rather than MechanicalOperations; Numeral as Something Distinct from Number; Systemsof Numeration; Basic Patterns of Structure in Mathematical Sys-tems; The Idea and Notation of Function; Equations and Inequali-ties; Properties of Numbers; Development of the Real Number Sys-tem; Ratio and Proportion in Problem Solving; Measurement withAllowable Inaccuracy; The Notion and Language and Theory of Set

� Paper presented at the CASMT Convention, St. Louis, Missouri, November 22-24, 1962.

583

584 School Science and Mathematics

as a Major Unifying Factor; Statistical Inference and Probability;Logical Deduction and Valid Generalization.When asked to arrange a program in the form of a two-weeks^

workshop for orientating a heterogeneous group of primary, middle-grade, and junior-high arithmetic teachers in the concepts of"modern math," I was overjoyed with the opportunity. For sometime, we had realized that here was an urgent need to be filled. Butthe organization of such a program presented quite a problem. Cer-tainly there exist copious notes on the subject�current mathematicaljournals are filled with pertinent articles; there is much useful litera-ture available in the several serious studies recently published. Todecide just which of these to use, how much to attempt to master intwo weeks, how to proceed with teachers having such varied, and inmost cases, definitely limited mathematical background was not easy.Almost as if in answer to prayer, just at the time we were setting up

our course of action, there fell into our hands a copy of the Addison-Wesley publication: "Fundamental Concepts of Elementary Mathe-matics" by Brumfiel, Eicholz, and Shanks. Even the first hasty sur-vey told us that here we had, hot off the press, a comprehensive text,authored by recognized experts in the field. And, best of all, it was ausable text, not the forbidding type of highly theoretic math, whichcan be frightening to the point of hasty departure for any but theseasoned student of mathematics. We adopted it and followed it. Andthe teachers liked it. In fact, most of them made the voluntary deci-sion to purchase it, with the prospect of using it in professional meet-ings and follow-up work with their fellow teachers. We also found thematerials so generously supplied by the various textbook publishingcompanies most helpful.

Ours was a rather handy physical situation. St. Mary^s Convent,Waterloo, Iowa, has faculty housing for thirty Sisters. Because manyof the regular teachers of the local parish school were on other assign-ment during the summer, it was possible for all the members of theworkshop to reside "at home." The adjoining school building wasused for meetings. Classes met twice daily, six days a week, for ninety-minute periods. Though it would have been relatively easy to secureaffiliation with Briar Cliff College, Sioux City, Iowa, conducted bythe Sisters of our Community, and obtain college credit for the course,the "off-campus" status was too convenient to sacrifice. Besides,nearly all these teachers hold bachelors degrees in education as wellas state-accredited teaching certificates. There was a psychologicalfactor, too, in the freedom from overhanging examinations and re-quisite course fulfillments. Certainly, the attention and enthusiasm ofthe teacher-members of the workshop were not lacking, and the study

"New Math" Workshops 585

and hard work which they evidenced could not have been greater hadthere been a "grade" at stake. Several meetings of the workshop weredevoted to panel discussions, each and every member participating,during which were analyzed and evaluated the latest textbooks inarithmetic. Practically all the leading publishers were represented inthe "most modern" of mathematics texts on our display table. Teach-ers at specified grade levels held informal seminars in which theydiscovered and proposed practical ways of bridging the gap and pre-paring the way for the inevitable adoption of textbooks which utilizethe new trends in the teaching of mathematics.Was the venture successful? Without exception, the teacher-

workers felt that, in many ways, it was a worthwhile experience. Well,no, we didn’t learn everything about all those topics I mentionedearlier. We took a quick look at every topic in the textbook and westudied several sections quite thoroughly. We made the acquaintanceof such friendly advisors as The Arithmetic Teacher, The MathematicsTeacher, SCHOOL SCIENCE AND MATHEMATICS. There wasn’t time todo more than touch lightly or taste quickly. There were tacit as wellas expressed resolutions to try to "keep up" with progressive meas-ures through reading during the course of the school year. Reactionsof the teachers indicated that the workshop had done much to dispeltheir fear and distrust of the impending "change" about to be thrustupon them. They were quite elated when they, themselves, discoveredthe "joy of discovery" and they spoke with eagerness of the oppor-tunities they intended to provide so that their pupils might find thesame satisfaction. I sensed a sort of apostolic spirit�they wanted togo out and make other converts to the cause of the "new math." I wasimpressed with the apparent desire on the part of teachers to learn asmuch as possible about mathematics preceding and following theparticular grade level at which they were teaching. They welcomedthe opportunity to hear and evaluate problems confronting teachersat other grade levels. This observation was to me some compensationfor the peculiar hardship of adapting to so wide a range. We shallmake some changes as we do more of this sort of thing. Many finehelps have come to our attention since last summer; another time weshall do some things quite differently, more effectively. We did find,all of us, that the workshop was enjoyable, challenging, even intrigu-ing. In this and in our over-all objectives, I believe we need no revi-sion. It was not our aim to impart a maximum of knowledge in twoshort weeks, not specifically to replace long established teachingprocedures with revolutionary notions, but, rather, we wanted topresent a challenge toward more meaningful teaching, to plant aspark of enthusiasm for accepting that challenge, to open the door to

586 School Science and Mathematics

self-education, ^on-the-job^ learning, and to cultivate an attitude ofcourageous open-mindedness in the face of even more radical changeslikely to accompany the automation revolution now in progress.

TOMATOES ATTRACTIVE EVEN TO MAGNETSA large magnet may some day become a standard kitchen device for the house-

wife who wants her vegetables ripe in time for supper.Two Utah horticulturists have shown that green tomatoes put under a mag-

net, especially near its south pole, will ripen much faster than those a few feetaway.

After six days their average magnetized tomato was at the "breaker" stage�starting to color�while the average control tomato was still green.

In eight days the average magnetized tomato was pink. It took the controlgroup three more days to reach that point. By then the magnetized tomatoeswere almost red.The idea that magnetism has an effect on organic substances is not new. A

century ago the French chemist Louis Pasteur applied magnets to tartaric acidobtained from the bottom of wine casks.He noticed that magnetized molecules of the acid deflected a plane of light in

only one direction. Normal tartaric acid molecules are optical isomers, somedeflecting light to the right and others to the left.Three years ago it was noted that a magnetic field seems to give a boost to

germinating seeds. The effect was named magnetotropism.It has been suggested that the effect on the seeds and on tomatoes is due to a

loss or gain of protons or other reactive groups in magnetized compounds.They theorize that a magnet, or even the earth’s natural magnetic field, ac-

tivates or quickens an enzyme system and thus respiration.

ILLINOIS COUNCIL OF TEACHERS OFMATHEMATICS FALL MEETINGS

OCTOBER 11-12, 1963ILLINOIS COUNCIL OF TEACHERS OF MATHEMATICS, ANNUAL CONFERENCE

UNIVERSITY OF ILLINOIS, CHAMPAIGN-URBANA, ILLINOIS

OCTOBER 18, 1963ILLINOIS COUNCIL OF TEACHERS OF MATHEMATICS, SECTIONAL CONFERENCE

ALTON SENIOR HIGH SCHOOL, ALTON, ILLINOISFor further information, write:

David PaisleyPublicity Committee ChairmanIllinois Council of Teachers of MathematicsMaine Township High School West1755 South Wolf RoadDes Plaines. Illinois