Quilts and tangrams: linking literature and geometry.

"A quilt won't forget. It can tell your life story," said Grandma. "There was the red from Ted's shirt. There was Tanya's Halloween costume. And there was Grandma. Even though her patch was old, it fit right in." (The Patchwork Quilt, Flournoy, 1985)

Flournoy's story brings an appreciation of quilts to contemporary times. Some quilts tell a family's story, while others display designs and "colors bright as a rainbow after a thunderstorm" (Stevens, 1994). Making quilts of paper, felt or cloth is an exciting way for elementary students to link literature and geometry. A unique tool for forging that link is the tangram, a geometric puzzle of seven pieces that can be arranged to make animals, birds, sea creatures, people and other figures.

Quilts

Historians are not certain where or when quilting began. Quilted garments appeared in the Middle East by the time of the Crusades (11th-13th centuries) (Martin, 1992). In 18th- and 19th-century America, patchwork quilts were particularly popular. Cloth was expensive and hard to get. Consequently, women saved every scrap, sewing patches of fabric together to create a quilt. The featured quilt in My Grandmother's Patchwork Quilt (Bolton, 1993/1994) ". . . was made from little scraps of material like her father's old shirts and her mother's worn out aprons and tablecloths." Early American quilters artistically expressed themselves with needle, thread and cloth instead of pen, ink and paper (Cooper & Allen, 1989; Lyons, 1993). Women would often gather in one home for a quilting bee, where they would sew and socialize. The resulting quilts were "the prettiest patterns I ever did see. And stitches small as the wings of a firefly" (Stevens, Aunt Skilly and the Stranger, 1994).

Some quilts recorded family and regional history. In Patchwork Tales, Grandma tells how each patch reminds her of something from long ago, ". . . planting the pine tree, her wedding to Grandpa" (Roth & Phang, 1984). Sweet Clara and the Freedom Quilt incorporates a quilt into the history of the Underground Railroad (Hopkinson, 1993). Sweet Clara sews a quilt that shows the way to Canada, "a map that wouldn't be washed away by the rain - a map that would show the way to freedom."

Classroom quilts made of paper, felt or cloth can illustrate sequences from favorite stories, record an original composition or display other language arts activities. Tangram figures and designs are ideal quilting pieces for classroom use, as they fulfill both the geometric and storytelling requirements of quilt making.

The Tangram

Tangrams have been challenging children and adults for centuries (Fair, 1987), including a number of famous people. Lewis Carroll had a book of tangrams in his library, as did Napoleon Bonaparte, Edgar Allan Poe and John Quincy Adams. The tangram is an ancient Chinese puzzle, a square composed of seven geometric pieces: five triangles (two large, one medium-size, two small), one square and one rhomboid [ILLUSTRATION FOR FIGURE 1 OMITTED].

The tangram is more, however, than a seven-piece square. The challenge is to arrange the pieces to form additional shapes. The seven pieces can be arranged to make a graceful swan, a prowling lion, a quiet rabbit or a hungry fish [ILLUSTRATION FOR FIGURE 2 OMITTED].

The tangram is the opposite of a jigsaw puzzle. Instead of fitting the pieces together in only one way, the seven tangram pieces can be arranged to make a great number of different figures. The following guide can help teachers link quilting and tangrams.

A GUIDE FOR THE TEACHER: QUILTING WITH TANGRAMS

* Before you begin, try reading The Master Revealed: A Journey with Tangrams (Ford, 1990) and Tangrams: 330 Puzzles (Read, 1965). Both books are helpful references and contain many tangram figures and solutions for assembling them.

* Introduce the tangram before using literature on quilts. Draw squares [ILLUSTRATION FOR FIGURE 1 OMITTED] on construction paper or tagboard. Make them large enough so that the children can cut the pieces apart. Dickoff (1991) gives detailed illustrations for creating a tangram puzzle. After the children cut apart the seven pieces (called tans), give ample time for them to "mess around" with the pieces. Children find tangramming to be so interesting they will want to talk about the pieces, explore the shapes' similarities and differences, discover the shapes' attributes and relationships, and manipulate the pieces in a variety of arrangements. Children will soon find multiple solutions for assembling a figure.

* Introduce the rules for creating tangram figures - all seven pieces must be used, all pieces must touch and no piece can overlap. Use an overhead projector to demonstrate how to construct a few animal figures, using examples from the Ford (1990) or Read (1965) book.

* Teach children the following helpful steps to use when they assemble a figure. The strategy is based on suggestions from Hill and Redden (1984) and Phillips (1992) and is grounded in classroom practice (see Notes). The "think, try, share" strategy is most effective when used with partners. Each child should have his or her own tangram pieces.

Think

1. Manipulate the tangram pieces by flipping, turning and sliding them.

2. Begin with the obvious pieces; the figure outline provides clues to the placement of some pieces.

Try

3. Look for the shape of a figure's missing piece; visualize the piece in different orientations - flip, turn, slide.

4. Examine the remaining spaces and remaining pieces; try some pieces by flipping, turning and sliding them.

5. Return to a problem area when there are fewer pieces to try.

Share

6. Discuss, exchange and share ideas about arrangements.

* Introduce the quilt literature. Select books from the Quilt Booklist at the end of this article. Many of these books have historical settings, and so can serve to expand lessons on early American and pioneer family life. Eight Hands Round: A Patchwork Alphabet (Paul, 1991) offers new vocabulary for understanding patchwork patterns. Roth and Phang (1984) give ten steps for making a doll's quilt, and Peterson (1994) offers specific quilting tips.

* Help students make the classroom quilt patches. Use a reference such as Bolton's My Grandmother's Patchwork Quilt (1993/1994), which shows how a quilt can be a record of the animals on a farm. Children can make animal quilt patches from tangram sets of several different sizes. Geese, horses, cats, goats, roosters and dogs are all farm animals that can be made from using tangram pieces [ILLUSTRATION FOR FIGURE 3 OMITTED].

Glue or sew the patches together and display them on the bulletin board or in other prominent areas (Barnes, 1990; Peterson, 1994). Tangram quilts are well suited for use with thematic units. Zoo, circus and farm themes lend themselves to quilt patches. Story patches depicting old favorites such as "Three Little Pigs" or "Three Billy Goats Gruff" can enhance a folk tale theme. Students could create tangram patches of cars, trains and boats for a transportation theme. Although they are more expensive, felt tangram patches make truly beautiful quilts.

* Show children how to make quilt designs from tangrams. Tangrams have both geometric and artistic features. The tangramming rules change for designs. One or more pieces can be traced many times for a pleasing design. Children like to invent their own designs and often enjoy making an entire quilt of many different patterns and colors (see Note 2). Some children like to work with two sets of tangrams.

Assess the children's work as a response to literature. Quilts can be a tool to assess achievement. They are a colorful portfolio of individual and group accomplishments. Lacampagne (1994) and Sweet (1993) note that such assessment tools allow students to interact with literature in creative ways.

Literature and Geometry

Quilting with tangrams is a positive learning experience for young children as it helps develop communication and mathematical thinking. Through a quilt, the children can communicate a story. Quilting activities encourage children to talk together, plan and share. Equally important, quilting with tangrams can be used to effectively communicate with parents. Children can introduce tangrams to their parents, and each family can be asked to assemble quilt patches showing the family's occupations, travels, important events or favorite activities, adding appropriate labeling. These family tangram patches can be glued together as panels on large mural paper and displayed in the school cafeteria, front office or media center. Such a quilting activity helps each family communicate something special about itself to the school and the community.

The National Council of Teachers of Mathematics calls for the inclusion of lessons on geometry and spatial sense in the elementary curriculum at all levels (Reys, Suydam & Lindquist, 1992). Children gain geometric insights as they discover and discuss the relationships among the tangram pieces. Quilting with tangrams helps all students feel more confident with geometric shapes and increases their ability to think about mathematics (Burton, 1986).

Quilting with tangrams holds a practical value for teachers by providing them opportunities to observe children's analytical performance in a nonverbal context (Hill & Redden, 1984). These observations give teachers the necessary information to direct their instructional decision-making (Lacampagne, 1994).

Quilts and Tangrams

"I know Papa loved that quilt because he said it had all the nice, bright colors of the day in it" (Mills, 1991, The Rag Coat). Quilts and tangrams allow children to respond to literature in bright, colorful and creative ways. Stories such as The Rag Coat and The Keeping Quilt (Polacco, 1988) are treasures to be passed along from parent to child. The tangram quilts that children make will also become family treasures.

Notes: The authors extend their appreciation to Allison Marks, Lake Stevens Elementary School, and Soraya Truillo, Holy Cross Lutheran School, for their classroom work with quilts and tangrams. The sample quilt designs in this article are from the Fun with Tangrams Kit (Johnson, 1977).

References

Barnes, D. (1990, October). Quilt crazy. Instructor, 100, 80.

Bolton, J. (1993/94). My grandmother's patchwork quilt. New York: Doubleday.

Burton, L. (1986). Girls into maths can go. New York: Holt, Rinehart and Winston.

Cooper, P., & Allen, N. B. (1989). The quilters: Women and domestic art. An oral history. New York: Doubleday.

Dickoff, S. S. (1991). Paperfolding and cutting a set of tangram pieces. Arithmetic Teacher, 18, 250-252.

Flournoy, V. (1985). The patchwork quilt. New York: Dial.

Ford, B. (1990). The master revealed: A journey with tangrams. Vallejo, CA: Tandora's Box.

Hill, D. M., & Redden, M. G. (1984). Spatial puzzles and the assessment of children's problem solving performance. School Science and Mathematics, 84, 475-483.

Hopkinson, D. (1993). Sweet Clara and the freedom quilt. New York: Knopf.

Lacampagne, C. B. (1994). State of the art: Transforming ideas for teaching and learning mathematics. Washington, DC: U.S. Department of Education.

Lyons, M. E. (1993). Stitching stars: The story quilts of Harriet Powers. New York: Scribner.

Martin, J. (1992). Reading quilts. New York: Learning Links.

Mills, L. (1991). The rag coat. Boston: Little, Brown.

Paul, A. W. (1991). Eight hands round: A patchwork alphabet. New York: HarperCollins.

Peterson, S. (1994). The friendship quilt. Teaching PreK-8, 24(4), 76-78.

Phillips, C. (1992). Tangrams in action K-4. Lincolnshire, IL: Learning Resources.

Read, R. (1965). Tangrams: 330 puzzles. New York: Dover.

Reys, R. E., Suydam, M., & Lindquist, M. (1992). Helping children learn mathematics (3rd ed.). Boston, MA: Allyn and Bacon.

Roth, S. L., & Phang, R. (1984). Patchwork tales. New York: Atheneum.

Stevens, K. (1994). Aunt Skilly and the stranger. New York: Ticknor & Field's.

Sweet, A. P. (1993). State of the art: Transforming ideas for teaching and learning to read. Washington, DC: U.S. Department of Education.

ANNOTATED QUILT BOOKLIST

Bolton, J. (1993/1994). My grandmother's patchwork quilt. New York: Doubleday. Grandmother's doll quilt was a record of the animals on the farm.

Brown, C. (1989). The patchwork farmer. New York: Greenwillow. A farmer repairs his blue jeans with colorful patches.

Coerr, E. (1986). The Josefina story quilt. New York: HarperCollins. Josefina, the pet hen, saves the family from being robbed.

Dorros, A. (1991). Tonight is carnaval. New York: Dutton. The illustrations are hand sewn arpilleros for the carnaval in Peru.

Fair, S. (1982). The bedspread. New York: Morrow. Two elderly sisters decorate their plain white bedspread with memory patches.

Flournoy, V. (1985). The patchwork quilt. New York: Dial. Tanya's grandmother, with the family's help, makes a patchwork quilt of special events.

Hopkinson, D. (1993). Sweet Clara and the freedom quilt. New York: Knopf. Sweet Clara uses scraps to sew a quilt map showing slaves the way to Canada and freedom.

Jonas, A. (1984). The quilt. New York: Greenwillow. Quilt pieces from favorite pants, curtains and a crib sheet give memories to the quilt.

Johnston, T., & dePaola, T. (1985). The quilt story. New York: Putnam. Abigail's quilt helps her feel at home when her family moves from place to place.

Mills, L. (1991). The rag coat. Boston: Little, Brown. The Quilting Mothers made a child's coat.

Parton, D. (1994). Coat of many colors. New York: HarperCollins. Brightly colored rags are sewn into a warm coat; the story follows the song by the same name.

Paul, A. W. (1991). Eight hands round: A patchwork alphabet. New York: HarperCollins. Early American patchwork patterns are used to represent the alphabet.

Polacco, P. (1988). The keeping quilt. New York: Simon and Schuster. Immigrants from Russia pass the quilt from mother to daughter.

Ringgold, F. (1991). Tar beach. New York: Scholastic. Fictional narrative, painting and quilt making are combined into one art form.

Roth, S. L., & Phang, R. (1984). Patchwork tales. New York: Atheneum. Ten steps for making a doll's quilt.

Stevens, K. (1994). Aunt Skilly and the stranger. New York: Ticknor & Field's. A goose chases away a quilt thief.

Turner, A. (1994). Sewing quilts. New York: Macmillan. A child watches her mother sew a log-cabin quilt.

Whittington, M. (1991). The Patchwork Lady. San Diego, CA: Harcourt Brace Jovanovich. The Patchwork Lady lives in a house that looks like a colorful quilt.

TANGRAM RESOURCES

Cuisenaire. (1991). Learning with tangrams. New York: Author.

Ernest, L., & Ernst, L. (1990). The tangram magician. New York: Abrams.

Fair, J. (1987). Tangram treasury. Books A, B, C. White Plains, NY: Cuisenaire.

Ford, B. (1990). The master revealed: A journey with tangrams. Vallejo, CA: Tandora's Box.

Johnson, S. (1977). Fun with tangrams kit. New York: Dover.

Phillips, C. (1992). Tangrams in action K-4. Lincolnshire, IL: Learning Resources.

Read, R. (1965). Tangrams: 330 puzzles. New York: Dover.

Tompert, A. (1990). Grandfather Tang's story: A tale told with tangrams. New York: Crown.

Gerry Bohning is Instructor, Mathematics Methods and Rebecca Williams is Instructor, Children's Literature, Adrian Dominican School of Education, Barry University, Miami Shores, Florida.