# Stairways to Integrated Learning

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Enter the world of endless stairways and you enter the mystical world of Escher. The artwork of Escher is fascinating to study. Students are drawn into his fantasy world where math and science play key roles.

The work of one artist became the impetus for an integrated curriculum across three grade levels. Students in my eighth grade drawing classes read biographies about the Dutch-born artist. They discovered he made his first linoleum cut prints in high school. They also learned it was a trip that Escher took in 1936 to the Alhambra in Spain that influenced his art until his death in 1972.

Islamic Art Influences

At the Alhambra, Escher discovered the way Islamic artists repeated geometric shapes in colorful mathematical variations. Islamic art shows no representations of humans, birds or animals. Instead, the artistic modes of expression are repeating geometric shapes, flora, images of vegetables, flowers, trees and calligraphy--the most revered art form in Islam because it conveys the word of God.

I showed my students slides of Islamic art--objects and buildings covered with complex patterns, all created with a compass and ruler. The students learned that the circle is the foundation of the complex patterns. I told the students that Islamic geometric patterns are created from the center outward and not designed to fit within a frame, as is typical of Western art.

Next, the students examined Escher's tessellations which were inspired by the Alhambra. For many years after his visit to Spain, Escher did not use recognizable imagery in tessellated designs out of respect for the Islamic religion. Eventually, Escher's creative urges found expression in his woodcuts, lithographs and wood engravings.

Developing a Tessellation

What is a tessellation? A tessellation is a pattern of shapes that completely covers a flat surface with no gaps and no overlapping. The word tessellation comes from the Latin word tesselae meaning "tile." A tessellation using only one shape (a regular polygon) in a pattern is called a regular tessellation. A regular polygon is a shape Wit]l all sides of equal length and all angles of equal measure. Semiregular tessellations are formed by combinations of two or three polygons. Irregular tessellations may have equal line segments but different angles.

I provided the students with a variety of grid-pattern worksheets for assistance in developing designs. The most favored worksheet was the dotted grid. By drawing a line shape between point A and point B, and by drawing another line shape between point B and point C, a student can begin drawing a shape. Next, the student puts a piece of typing paper on top of the dot-grid paper and marks the dots. Then, the student traces the previously drawn lines. The dot-grid paper is then shifted to the right, and the dots are aligned with the top typing paper. The student traces the original lines to create a shape that tessellates.

Art medium options included water-based marker, colored pencils or cut-paper designs. The students were excited about their tessellations and many continued to create designs outside of class. Since we were the first classes in the school to study Escher, my students volunteered in pairs to help math classes learn about and create tessellations. …