Don't forget the parents!

Don't forget the parents!Author(s): JOHN W. DANIELSSource: The Arithmetic Teacher, Vol. 13, No. 6 (OCTOBER 1966), pp. 474-475Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41185426 .

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Don't forget the parents! JOHN W. DANIELS East Carolina College, Greenville, North Carolina

John W. Daniels is an assistant professor of mathematics at East Carolina College in Greenville, North Carolina. His article grew out of a workshop on modern mathematics that he directed.

An order to move forward in education, we must not overlook the parents of children who are involved in the study of modern mathematics. We must keep in mind that the concern of these parents, who have not been exposed to any modern mathematics, is genuine. Therefore, we should strive to help parents to achieve a better understanding of modern mathematics.

Such understanding can be reached through the cooperation of the school and the local Parent-Teachers' Association (PTA) in setting up a workshop in modern mathematics for parents. This was the case when the PTA of Elmhurst Elementary School, Greenville, North Carolina, asked to have a workshop for this purpose.

Arrangements were made to hold the workshop for four consecutive Thursday evenings in order to cover the topics of "Sets," "The System of Whole Numbers," "The Addition and Multiplication Al- gorithm," and "Number Bases." Each lecture and discussion period, lasting for one hour, was followed by a half-hour film pertaining to the topic discussed.

To create interest in such a workshop, a preliminary PTA program dealt with the topic "What Is Modern Mathematics and Why?" At this meeting parents were also told in which grades modern mathematics would be introduced for the current year. Newspaper articles concerning the workshop were published and letters were sent

to the parents to encourage them to attend. To maintain interest among the parents,

the school secured a professional mathe- matician to show some aspects of modern mathematics and how the children are taught at the elementary level. It was felt that the use of a formal textbook for the workshop would be unnecessary, consider- ing the parents' lack of time and prepara- tion for outside study. Therefore, for each of the four topics a general outline was prepared, accompanied by examples, nota- tion, and problems. The instructor made no attempt to deliver formal lectures, but rather tried to present the material in a manner comprehensible to an intuitive mind.

The first topic, "Sets," was introduced realistically by the giving of concrete examples in defining a set and the elements of a set. Examples of the empty set and the universal set were given. Also considered were relations between sets such as equality of sets, subsets, equivalent sets, and dis- joint sets. Finite and infinite sets were introduced, along with the meaning of a cardinal number. The binary operations, union and intersection, were presented with some of their properties, mainly the commutative and associative laws. Examples were used, for the most part, in introduc- ing these concepts.

The second topic, "The System of Whole Numbers," was introduced by means of the use of the cardinal numbers that represent

474 The Arithmetic Teacher



the families of equivalent sets. Thus we were able to define the counting numbers. Then the cardinal number for the empty set was used to define zero, which, with the counting numbers, forms the set of whole numbers. Addition and multiplication were explained by means of sets; it was also shown why these are called binary operations. The closure laws, as well as the commutative, associative, identity, and distributive laws, were explained in detail; and examples were given. The fact that the subtraction and division operations did not always produce elements of the set of whole numbers was brought out, thus showing that the four laws mentioned above did not, in general, hold true in these operations.

Before studying the third topic, namely, "The Addition and Multiplication Al- gorithms," the parents had first to learn the properties of zero, the definitions of an exponent and of place value, the basic addition and multiplication facts, and the laws governing the operations of whole numbers. The instructor presented the algorithms, using these concepts to show a justifiable method for addition and multi-

plication. Later a shorter method was presented by the use of the same examples.

The last topic, "Number Bases," was presented by using the whole numbers as a background. After a number base was defined, a systematic makeup of base ten was presented, and its different character- istics were pointed out. Numbers for other bases were constructed using these char- acteristics. The grouping of sets of objects by different numbers was used to develop the change from one base to another. Ad- dition, multiplication, and subtraction operations were developed using base ten and then presented, by the same methods, using other number bases. Finally, there was a discussion of the uses of different number bases.

It was felt that this modern mathematics workshop for parents was one of the most important projects carried on by the school and the PTA. It introduced to the parents an intuitive knowledge of what their children were learning and experiencing in the study of modern mathematics and instilled in them a greater appreciation for the efforts of their children in mastering this study.

Cincinnati Meeting November 11-12, 1966

Are you looking for new ideas, new ways to help pupils learn, new ways to stimulate thought? The sixty-five section speakers on the Cincinnati NCTM program for November 11-12, 1966, are prepared to help you in your search. President Donovan A. Johnson, Glenadine Gibb, Julius Hlavaty, James A. Cooley, and Murray S. Klamkin will lead off at the General Sessions. A Hos- pitality Room where participants may chat informally over coffee will be sub- sidized by the Mathematics Club of Greater Cincinnati.

The banquet speaker, Friday evening, will be Professor Phillip Jones of the University of Michigan, a past president of NCTM and a feifted speaker. His topic will be "Mathematical Models: Plato to Pluto."

Your friends in Cincinnati promise you a warm welcome and a stimulating and invigorating experience on November 11-12, 1966.

October 1966 475



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Don't forget the parents!