Tangrams and Children’s Learning Geometry

In the Chinese Language, “tangram” literally means “seven boards of skill”. It is a dissection puzzle which consists of seven pieces, called tans. The objective of the tangram game is to form a specific shape with all seven pieces without any overlapping (Wikipedia, 2008). Playing with tangrams actively involve children as they manipulate the pieces into various shapes. This makes it exciting to children and it fosters sharing among them. Having such high interest in the activity will also help promote positive attitudes towards mathematics. Playing with Tangrams can help children to develop their skills of a geometry vocabulary, shape identification, shape orientation, and discover relationships between and among the seven pieces. Such experiences are especially important for young children to recognize and appreciate geometry in their natural world (Bohning & Althouse, 1997). Nevertheless, we researchers have noticed a lack of proper usage of tangrams in our classrooms and recognize that there is a need for teachers to learn the proper way to use tangrams in the classroom to enhance children’s mathematical skills .

In review of the current practices in preschools, little is known about the implementation of tangrams in early childhood classrooms. Tangrams are simply left at learning centers, or provided as a transitional activity to keep children occupied. It is also used to keep some children busy while the others struggle to finish up their work. Often, children use the pieces for pretend play instead of forming specific shapes with them. Without adequate instructions, many children fail to use the tangrams in the intended manner and lose experiences that could sharpen their thinking skills, develop positive attitudes toward geometry, shape identification and orientation skills, and foster an understanding of basic geometric concepts and relationships (Bohning & Althouse, 1997). The children are missing out on the benefits that Tangrams can offer. This study aims to inform how we as teachers can maximize the use of tangrams, and determine how the seven geometric shapes can be an appropriate manipulative for children to gain mathematical understanding.

According to Corry (1996), Piaget’s theory is based on the idea that children actively acquire knowledge through their own actions. Knowledge is invented and re-invented as the child develops and interacts with their surrounding world. Piaget believes there are three types of knowledge, namely physical, logical-mathematical and social-arbitrary, that children will acquire. Physical knowledge involves information about objects which is gained through its observable properties. Logical-mathematical knowledge is abstract knowledge that must be invented and social-arbitrary knowledge is culture specific knowledge learned from within one’s culture group. Logical-mathematical knowledge cannot be developed until physical knowledge is attained (Corry, 1996). The colour, shape, size and texture of an object are used to construct the abstract knowledge that is important for the early foundations of mathematical thinking (Copeland as cited in Smith, 2001).

Using Tangrams is ideal for teaching mathematical skills as it provides a concrete way to learn physical knowledge of math in order to understand geometric concepts. Study suggests that tangrams are suitable manipulatives for children to use to acquire geometric knowledge. Furthermore, problem-solving strategies are explored and it enhances their spatial sense. Only with much exposure to many shape examples and discussion of their attributes will children be able to combine, subdivide and change shapes to develop their spatial sense (Bohning & Althouse, 1997). During the activity, children have fun thus developing a positive attitude towards mathematics. It is also ideal for testing children’s spatial abilities (Butler, 1994).

Tangramming activities require one to assemble figures from tans. Children are challenged to arrange and rearrange the seven tans into pictures of birds, animals, fish, people and designs. This simple act of manipulating the seven tans encourages communication between the children as they talk about the “what and the how” (Bohning & Althouse, 1997).

Some reactions from children during tangramming are: “There is nothing to show us where it goes, except experimenting with where it don’t go”; “…. Shapes can make other shapes!.....I try to cut out the picture with my mind, so that I can see which shape goes where”; “It seemed impossible when I was doing it but now, it seems clear” . It is also possible for children to use tangrams to illustrate their thoughts, giving children an alternative expressive skill in language (Bohning & Althouse, 1997). However, we recognize that locally, tangrams are not used to their full potential and that there is paucity in research involving preschoolers using tangrams as a manipulative.