# Measuring up: teaching geometry through art.

Do your students know how to use a ruler? Can they create margins, rules and simple geometric forms by measuring and connecting dots? In elementary grades, students often do not gain sufficient basic skills to give them a foundation for understanding geometry. Many art activities provide a variety of hands-on opportunities to give students the experience they need. Learning in both art and geometry can be enhanced by introducing processes of visualization, measuring and recognition of characteristics in pattern and symmetry.

Norman Shapiro, an art teacher with broad experience on all levels of instruction, developed his own program called Teaching Geometry through Art. He based this program on his observations of the students he was working with at Medford Avenue Elementary School in the Patchogue-Medford School District. Mr. Shapiro discovered that his students seemed unable to use a ruler either as a measuring tool or as a straight line maker. He discovered when he assigned simple drawing tasks with the ruler, students did not know they should begin a measurement by aligning the zero end of the ruler with the edge of the paper. Children were having difficulty in placing a mark corresponding to any given subdivision. Mr. Shapiro began to realize that no program of instruction was being carried out on a developmental level in this area. His response was to create his own program in the artroom.

Drawing Full-Circle

Mr. Shapiro began by finding ways to integrate the use of a ruler into each art project he assigned on all grade levels. He discovered that it is no simple matter for a young child to hold a straightedge steady on the desk with one hand while drawing a line with the other. Nor is it any simpler for a child to connect two dots in this way. Connecting dots infers a whole universe of concepts. Dots become coordinates --the very concept of coordinates is basic to a variety of literacies: geometric, geographic and mathematical to mention a few. He decided to provide a simple tool for constructing arcs and circles. Plastic covers used for coffee cans and other plastic covers provide excellent tools for making designs. They make it possible to align the "circle-center" with the drawn line of the perimeter. Compass use requires higher level manual skills which are only possible with upper elementary grade levels.

Students were taught that the circle could be the foundation for constructing other pure geometric shapes. They could construct equilateral triangles, squares, hexagons and six pointed stars by subdividing the circle into equal parts. They could superimpose these shapes in a variety of ways: by connecting subdivisions of the circle in either random or symmetrical ways, the students found they could create sparkling geometric designs.

A sampling of the design problems used in this program are featured below. The design of basic lessons for teaching the use of the straightedge and the compass were based on logic and deductive reasoning.

A Design Problem Sampling

Given a circle grid with 100 divisions numbered in units of 5, solve the following geometric art problems. Connect coordinate points on the circumference to discover geometric relationships.

A. Find the Center of the Circle. * Rotate a square on an axis.

* Find the rectangles within the circle.

* Find triangles within the circle.

B. Compass Designs

* Create a concentric design of assorted size arcs and circles.

* Create a symmetrical design

of arcs and circles.

* Create hexagonal designs using only a compass.

One technique for providing children with a non-verbal analysis of their designs is to use one to four colors in the following ways. Photocopy one of the student's designs. The student should color each copy of the work with different combinations, focusing on dominance, contrast, distribution of color, light and dark, etc.

Through the use of varied colors within one linear design, the student will discover the dramatic and graphic role that color plays in a work of art.

The Pay-Off

These are but a few beginning exercises which teach both geometry and high-quality design. They provide a frame of reference for initiating a full-scale program. The students enjoy the challenges presented by these problems. The high quality of the finished work will delight both art and classroom teachers.

Mr. Shapiro sums up his discoveries from offering his Teaching Geometry through Art program. "I believe I am filling a real gap in the instruction as it presently exists in my school. Art, because it involves motor skills and a variety of hands-on media, is really a very appropriate place for the incorporation of geometry and measurement in art projects. To learn about rulers and what to do with them, requires that children be given real tasks, not suppositional ones. Providing a blend of media-based activities of a freely expressive kind along with essentially structured alternatives involving rulers, grids, compasses and geometric concepts, builds a foundation of basic experiences necessary for our present generation of children to creatively address the spatial world of our existence."

The pay-off on these activities is always the art project itself. These projects flow with the special look one finds when an assigned project is on target. Teaching Geometry through Art is one of those on tar get programs that will add luster to the art program in any elementary school.

John Bouleris is Director of Art Education For Patchogue-Medford Schools, Patchogue, New York.