ONE POINT OF VIEW: Flight to realityAuthor(s): MARGUERITE BRYDEGAARDSource: The Arithmetic Teacher, Vol. 19, No. 2 (FEBRUARY 1972), pp. 83-84Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41187929 .

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ONE POINT OF VIEW

Flight to reality

By MARGUERITE BRYDEGAARD

X f we are to teach geometry to young children, we must take flight to reality. We no longer live in an age in which we can be satisfied with merely requir- ing teachers to take university credits and then implementing their inadequacy with in-service workshops. The new age demands a new revolution - a revolution in which action is taken that produces knowledgeable, enlightened, liberated teachers. Such liberation calls for teachers who (1) understand the concepts and language of the informal geometry that is basic to the ele-

mentary school program, and (2) see and master excellent procedures for

teaching the subject. Teachers have a tendency to teach in a way similar to that in which they were taught. Teachers should create classroom environ- ments that are innovative, creative, and designed to challenge the scholarly thinking of pupils. The flight to reality must be fashioned in a search for wisdom that extends beyond the acquisition of knowledge.

Informal geometry is a recognized, significant part of mathematics edu- cation for pupils of grades K-8. Geometry is the study of spatial relation-

ships, and the term spaceometry more aptly identifies the study than the term geometry. The study of simple relationships of three-dimensional space should probably be initial experiences for children. The child's experiences in a three-dimensional world lead him to intuitively sense, explore, wonder about, and "measure" his world of space. He thinks about such things as location ("whereness"), shape, direction, size, and distance. The informal geometry developed should provide the intuitive basis for the formal geometry to be developed later.

As guidelines for making strides to meet the goal of helping teachers achieve excellence, let us consider the following questions:

1. Are teachers receiving the necessary mathematics education that lib- erates them to teach informal geometry? What is the place of the identifica- tion and development of basic concepts that open the field to deeper under- standing of the geometry that they will teach?

2. In what ways can we develop a high level of communication among university professors of mathematics education, in-service mathematics edu- cators, and classroom teachers?

February 1972 83

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3. What is the role of authors of textbooks for teachers and children in developing the concepts and materials that meet the challenge of informal geometry? How are teachers' guides for pupils organized to enhance the study of geometry without recourse to the formal lists of defined and un- defined terms such as point, line, line segment, ray, and curve? How can symbolism become an outgrowth of study rather than a beginning?

4. What is the place of abstraction in geometry? Does informal geometry become formal almost before it gets off the ground? And, if so, how can this be prevented?

5. Do teachers see bits and pieces of woefully incomplete patterns? Do they seek help through trying to find small units and ideas to enliven a pro- gram rather than seeing a live program?

Serious consideration of the questions raised here lead one to the realiza- tion that now is the time for the search for wisdom. This search for wisdom is the flight to reality.

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84 The Arithmetic Teacher

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