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Shapes: The Natural Connection Between Mathematics and Art
By Sandra Fisher

Circles, squares, rectangles, and triangles are everywhere. By using the children’s immediate world to discover shapes in things that are familiar to them, they will have the opportunity for a hands-on approach to learning both two- and three-dimensional shapes. With a close look at nature, school environments, and even common items found at home, many shapes can be observed and explored.           

Throughout the years, artists have used environments in their paintings, sculptures, and photographs. Since shapes are consistently found in our environments and since artists have used these environments as influences on their work, there is a natural connection between mathematics and art. Exposing children to the works of famous artists can show them how these artists used shapes in their paintings, sculptures, and photographs.


Andy Goldsworthy: Shapes in Nature

Andy Goldsworthy, an environmental sculptor, uses common objects found in nature and arranges them outdoors into various shapes and forms. Upon completing such an environmental sculpture, Goldsworthy captures his creation by photographing it before it evolves back into its natural environment. Leaves, wood, stones, and flowers are frequently used in Goldsworthy’s work. One of his sculptures, Dandelion Hole, features a field of dandelion where the flowers were picked and arranged to form a circle with a hole. In another work, he arranged stones in sand in a spiral form.           

On a sunny day, take the children outside to identify all the different shapes that they can see. Talk about the abstract shapes of the clouds and trees, the circular shape of the flowers and stones, the rectangular shape of bricks and windows, and the triangular shape of leaves and tree branches. Have the children collect items that may be picked up and removed, such as leaves, stones, flowers, and twigs, to create a special environmental art sculpture simulating the work of Goldsworthy. To facilitate collecting, have the children work cooperatively in groups gathering their “special shape” materials. When the collection is complete, each group will need to decide where to construct their environmental sculpture. When these shape sculptures are finished, photograph the creations. Recall that Goldsworthy created his sculptures outside so they would continue to be part of the environment. Have the children describe their “shape sculptures” and devise titles for these beautiful works of art.


Paul Cezanne’s Three-Dimensional Still-Life Shapes

Cezanne is famous for his still-life paintings of flowers and fruit. Through the use of the fruit depicted in Cezanne’s work, the teaching of three-dimensional shapes can take place. Show the children an example of one of the artist’s still-lifes (e.g., Still Life With Fruit). Discuss with the children all the shapes they see in the painting, such as the semi-circle handle, the triangles and diamonds formed in the basket weave, the rectangular table, and the circles of the oranges and apples. Give the children apples and oranges to see and feel. When they are holding a piece of fruit, discuss if what they are holding is a flat surface, like a circle, or if it has another dimension to it. Discuss how a three-dimensional shape has a different name than a two-dimensional shape (e.g. circles – spheres, squares – cubes, rectangles – rectangular solids, triangles – pyramids). Have the children locate and name the three-dimensional items in the painting. Talk about how Cezanne used shading in his objects to create the appearance of a third dimension in them.           

Give the children a table, basket, jar, vase, oranges, and apples so they can create their own still-life artwork. As the children are preparing this still-life, have them describe the three-dimensional shapes they are using. When the children finish arranging this still-life scene, give them colored pencils and white paper to draw this special “Cezanne” arrangement. Encourage the children to shade their objects to show dimension. Mount these still-life drawings and discuss with the children the three-dimensional shapes that they used and depicted.


Winslow Homer’s Play Yard Shapes

Shape exploration can also be seen in the work of Winslow Homer, an American realist painter. By looking out his studio’s window, Homer got inspiration from his environment and used it as a focus for his work. Two of the themes that Homer depicted in his paintings are schools and play yards.           

Using Homer’s famous work, Snap the Whip, have the children observe and discuss all the various shapes that they see (e.g., hoop, buttons on clothing, school building, flowers, etc.) in this schoolyard setting. Focus the children’s observation on the school and have the children describe the appearance of the school, the materials used to build this school, and the shapes that Homer used when painting the school (e.g., shutters – rectangles, door – rectangles, roof line – triangle, window panes – squares). Compare how Homer’s play area and school differ from the children’s own playground and school.           

Take the children to the playground and have them describe what they see – the play equipment, school building, play environment, etc. Discuss the different shapes that were visible in the play equipment, such as circles – tire swing, rectangle and triangle – swing frame, square – sliding board platform.  

For the children to experience a simulation of Homer’s watercolor paintings, take an easel, paper and watercolors outside (weather permitting) for the children to paint their “Shape Playground.”


Norman Rockwell’s Everyday Shapes

When the children look at the art of Norman Rockwell, they can see many familiar settings, objects, and activities and may recall similar experiences that they have had. Rockwell’s art reflects his observations of American life and traditions. As an illustrator, his work is found in advertisements, story illustrations, and magazine covers, particularly the Saturday Evening Post 

To relate Rockwell’s art to shapes, select works where scenes and incidents may be familiar to the children. As an example, Freedom From Want depicts a family being served a turkey for what may be a holiday dinner. In this painting, both two- and three-dimensional shapes can be noted (e.g. glasses – cylinders, plates – circles, grapes – spheres, serving plate – oval). To emphasize those shapes, have examples of those specific items to show the children. Ask the children to think of any other shapes that they have seen at their dinner table.           

Another activity that the children could relate to is painting. In Rockwell’s Painting the Little House, a boy is painting a birdhouse as his dog watches him. Many two- and three-dimensional shapes can be seen in this work. Using chart paper labeled with the basic shapes, have the children name what circular, triangular, rectangular, and square items they see. Write the object’s name under its appropriate column. These columns can then be counted and tallied to see what shapes Rockwell used most frequently.          

Children love to play games and Rockwell’s Saturday Evening Post cover titled Marble Champion can be an example for incorporating shapes into children’s play. Have the children look at the painting to determine what game is being played and what shape a marble has. Teach the children how to play a game of marbles using yarn for the game’s circular boundary. As the children are playing with the marbles, they will discover the properties of a sphere. Have the children think of other games they play that involve shapes, such as hopscotch.           

Rockwell’s work, April Fool: Girl With a Shopkeeper, can be used as the basis for a “Spy Shape” game. Many shapes can be recognized within this work. Have a child select and name a shape. Ask the other children to find and point out that specific shape (e.g., find a red rectangle). As the children are observing Rockwell’s painting, they will also discover that Rockwell mixed up many of the items as is suggested by the title, April Fool.



In expanding the children’s knowledge base by teaching basic shape concepts through the works of famous artists, sculptors, and photographers, the children are able to develop an appreciation for art in addition to developing an understanding of the elemental concepts of shapes.


Sandra Fisher is an Assistant Professor of Elementary Education and the Coordinator of the Early Learning Center at Kutztown University, Kutztown, PA. With over 25 years of early childhood teaching experience, she frequently presents at national, state, and local conferences. Her book, Early Childhood Themes Using Art Masterpieces, is published by Teacher Created Materials.